Add files using upload-large-folder tool

preprint/preprint__000437fb18cd2e9611d4b5cc606b31bfecf3f2621083c764bd7bfd945510ca7c/images_list.json

@@ -0,0 +1,117 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "C",
+    "footnote": [],
+    "bbox": [
+      [
+        57,
+        67,
+        900,
+        270
+      ]
+    ],
+    "page_idx": 31
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "d",
+    "footnote": [],
+    "bbox": [
+      [
+        57,
+        308,
+        930,
+        440
+      ]
+    ],
+    "page_idx": 31
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 31
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 32
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "C",
+    "footnote": [],
+    "bbox": [
+      [
+        50,
+        228,
+        470,
+        419
+      ]
+    ],
+    "page_idx": 33
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 33
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "C",
+    "footnote": [],
+    "bbox": [
+      [
+        50,
+        240,
+        483,
+        425
+      ]
+    ],
+    "page_idx": 34
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "e",
+    "footnote": [],
+    "bbox": [
+      [
+        50,
+        457,
+        560,
+        641
+      ]
+    ],
+    "page_idx": 35
+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_4.jpg",
+    "caption": "Supplementary Figure 4",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 35
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "a",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 35
+  }
+]

preprint/preprint__000437fb18cd2e9611d4b5cc606b31bfecf3f2621083c764bd7bfd945510ca7c/preprint__000437fb18cd2e9611d4b5cc606b31bfecf3f2621083c764bd7bfd945510ca7c.mmd

@@ -0,0 +1,486 @@
+
+# Senolytic therapy alleviates physiological human brain aging and COVID-19 neuropathology  
+
+Julio Aguado ( j.aguadoperez@uq.edu.au ) The University of Queensland https://orcid.org/0000- 0002- 1841- 4741  
+
+Alberto Amarilla University of Queensland  
+
+Atefeh Taherian Fard Australian Institute for Bioengineering and Nanotechnology https://orcid.org/0000- 0002- 9126- 4540  
+
+Eduardo Albornoz University of Queensland  
+
+Alexander Tyshkovskiy Brigham and Women's Hospital, Harvard Medical School https://orcid.org/0000- 0002- 6215- 190X  
+
+Marius Schwabenland Institute of Neuropathology, Faculty of Medicine, University of Freiburg https://orcid.org/0000- 0003- 2205- 5427  
+
+Harman Chaggar Australian Institute for Bioengineering and Nanotechnology, The University of Queensland  
+
+Naphak Modhiran University of Queensland  
+
+Cecilia Gomez- Inclan The University of Queensland  
+
+Ibrahim Javed University of Queensland  
+
+Alireza Baradar University of Queensland  
+
+Benjamin Liang University of Queensland  
+
+Malindrie Dharmaratne  
+
+Australian Institute for Bioengineering and Nanotechnology, The University of Queensland  
+
+Giovanni Pietrogrande  
+
+Australian Institute for Bioengineering and Nanotechnology, The University of Queensland  
+
+Pranesh Padmanabhan  
+
+Queensland Brain Institute https://orcid.org/0000- 0001- 5569- 8731  
+
+Morgan Freney University of Queensland
+
+<--- Page Split --->
+
+Rhys Parry University of Queensland  
+
+Julian Sng University of Queensland  
+
+Ariel Isaacs University of Queensland  
+
+Alexander Khromykh University of Queensland  
+
+Alejandro Rojas- Fernandez Universidad Austral de Chile  
+
+Thomas Davis University of Queensland  
+
+Marco Prinz Medical Center - University of Freiburg https://orcid.org/0000- 0002- 0349- 1955  
+
+Bertram Bengsch University of Freiburg  
+
+Vadim Gladyshev Brigham and Women's Hospital and Harvard Medical School https://orcid.org/0000- 0002- 0372- 7016  
+
+Trent Woodruff University of Queensland https://orcid.org/0000- 0003- 1382- 911X  
+
+Jessica Mar University of Queensland  
+
+Daniel Watterson University of Queensland  
+
+Ernst Wolvetang The University of Queensland https://orcid.org/0000- 0002- 2146- 6614  
+
+## Article  
+
+# Keywords:  
+
+Posted Date: March 16th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 2675698/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.
+
+<--- Page Split --->
+
+Version of Record: A version of this preprint was published at Nature Aging on November 13th, 2023. See the published version at https://doi.org/10.1038/s43587-023-00519-6.
+
+<--- Page Split --->
+
+# 1 Senolytic therapy alleviates physiological human brain aging and COVID-19 neuropathology  
+
+3 Julio Aguado \(^{1,*}\) , Alberto A. Amarilla \(^{2,14}\) , Atefeh Taherian Fard \(^{1}\) , Eduardo A. Albornoz \(^{3}\) , Alexander Tyshkovskiy \(^{4,5}\) , Marius Schwabenland \(^{6}\) , Harman K. Chaggar \(^{1,7}\) , Naphak Modhiran \(^{1,2}\) , Cecilia Gomez- Inclan \(^{1}\) , Ibrahim Javed \(^{1}\) , Alireza A. Baradar \(^{1}\) , Benjamin Liang \(^{2}\) , Malindrie Dharmaratne \(^{1}\) , Giovanni Pietrogrande \(^{1}\) , Pranesh Padmanabhan \(^{8}\) , Morgan E. Freney \(^{2}\) , Rhys Parry \(^{2}\) , Julian D.J. Sng \(^{2}\) , Ariel Isaacs \(^{2}\) , Alexander A. Khromykh \(^{2,9}\) , Alejandro Rojas- Fernandez \(^{10}\) , Thomas P. Davis \(^{1}\) , Marco Prinz \(^{6,11}\) , Bertram Bengsch \(^{11,12}\) , Vadim N. Gladyshev \(^{4,13}\) , Trent M. Woodruff \(^{8}\) , Jessica C. Mar \(^{1,14}\) , Daniel Watterson \(^{2,14}\) , and Ernst J. Wolvetang \(^{1,14}\) .  
+
+13 1 Australian Institute for Biotechnology and Nanotechnology, University of Queensland, St Lucia, QLD 4072, Australia. 15 2 School of Chemistry and Molecular Biosciences, University of Queensland, St Lucia, QLD, Australia 4072. 17 3 School of Biomedical Sciences, Faculty of Medicine, University of Queensland, St Lucia, Queensland 4072, Australia. 19 4 Division of Genetics, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02115, USA. 21 5 Belozersky Institute of Physico-Chemical Biology, Moscow State University, Moscow 119234, Russia. 22 6 Institute of Neuropathology and Center for Basics in NeuroModulation (NeuroModulBasics), Faculty of Medicine, University of Freiburg, Freiburg, Germany 24 7 Cellese Ltd, Cardiff Medicentre, Heath Park, Cardiff, United Kingdom. 25 8 Clem Jones Centre for Ageing Dementia Research, Queensland Brain Institute, The University of Queensland, Brisbane, QLD, Australia 27 9 Australian Infectious Disease Research Centre, Global Virus Network Centre of Excellence, Brisbane QLD, Australia. 29 10 Institute of Medicine, Faculty of Medicine, Universidad Austral de Chile, Valdivia, Chile. 30 11 Signalling Research Centers BIOSS and CIBSS, University of Freiburg, Freiburg, Germany 31 12 Faculty of Medicine, Clinic for Internal Medicine II, Gastroenterology, Hepatology, Endocrinology, and Infectious Disease, University Medical Center Freiburg, Freiburg, Germany 33 13 Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA. 34 14 These authors contributed equally to this work as co- senior authors. 35 \*Corresponding author. Email: j.aguadoperez@uq.edu.au
+
+<--- Page Split --->
+
+## Abstract  
+
+Aging is the primary risk factor for most neurodegenerative diseases, and recently coronavirus disease 2019 (COVID- 19) has been associated with severe neurological manifestations that can eventually impact neurodegenerative conditions in the long- term. The progressive accumulation of senescent cells in vivo strongly contributes to brain aging and neurodegenerative co- morbidities but the impact of virus- induced senescence in the aetiology of neuropathologies is unknown. Here, we show that senescent cells accumulate in physiologically aged brain organoids of human origin and that senolytic treatment reduces inflammation and cellular senescence; for which we found that combined treatment with the senolytic drugs dasatinib and quercetin rejuvenates transcriptomic human brain aging clocks. We further interrogated brain frontal cortex regions in postmortem patients who succumbed to severe COVID- 19 and observed increased accumulation of senescent cells as compared to age- matched control brains from non- COVID- affected individuals. Moreover, we show that exposure of human brain organoids to SARS- CoV- 2 evoked cellular senescence, and that spatial transcriptomic sequencing of virus- induced senescent cells identified a unique SARS- CoV- 2 variant- specific inflammatory signature that is different from endogenous naturally- emerging senescent cells. Importantly, following SARS- CoV- 2 infection of human brain organoids, treatment with senolytics blocked viral retention and prevented the emergence of senescent corticothalamic and GABAergic neurons. Furthermore, we demonstrate in human ACE2 overexpressing mice that senolytic treatment ameliorates COVID- 19 brain pathology following infection with SARS- CoV- 2. In vivo treatment with senolytics improved SARS- CoV- 2 clinical phenotype and survival, alleviated brain senescence and reactive astrogliosis, promoted survival of dopaminergic neurons, and reduced viral and senescence- associated secretory phenotype gene expression in the brain. Collectively, our findings demonstrate SARS- CoV- 2 can trigger cellular senescence in the brain, and that senolytic therapy mitigates senescence- driven brain aging and multiple neuropathological sequelae caused by neurotropic viruses, including SARS- CoV- 2.
+
+<--- Page Split --->
+
+## Introduction  
+
+Although severe acute respiratory syndrome coronavirus 2 (SARS- CoV- 2) is primarily a respiratory viral pathogen and the cause of coronavirus disease 2019 (COVID- 19), persistent post- acute infection syndromes (PASC) derived from viral infections including SARS- CoV- 2 are emerging as a frequent clinical picture<sup>1,2</sup>. In fact, most COVID- 19 patients including individuals with or without comorbidities, and even asymptomatic patients, often experience a range of neurological complications<sup>3,4</sup>. ‘Long- COVID’ is a type of PASC that is gaining significant awareness, with patients reporting persistent manifestations, such as hyposmia, hypogeusia, sleep disorders and substantial cognitive impairment, the latter affecting approximately one in four COVID- 19 cases<sup>5- 7</sup>. These clinical symptoms are supported by ample evidence of SARS- CoV- 2 infectivity in multiple cell types of the nervous system<sup>8- 16</sup> and significant structural changes in the brains of COVID- 19 patients<sup>17</sup>. Furthermore, patient transcriptomic data from postmortem brain tissue indicate associations between the cognitive decline observed in patients with severe COVID- 19 and molecular signatures of brain aging<sup>18</sup>. In agreement with this observation, postmortem patient biopsies show that SARS- CoV- 2- infected lungs — compared to uninfected counterparts — accumulate markedly higher levels of senescence<sup>19</sup>; a cellular phenotype known to contribute to organismal aging<sup>20</sup> and co- morbidities such as chronic degenerative conditions<sup>21</sup>. Importantly, although recent data supports a role for senescent cells in driving neurodegeneration and cognitive decline in in vivo models of neuropathology<sup>22,23</sup> and in physiologically aged mice<sup>24</sup>, their contribution to COVID pathology in the central nervous system (CNS) and human tissue brain aging remains unknown.  
+
+In the past decade, numerous strategies have been developed to target senescent cells<sup>25</sup>. Among these, the pharmacological removal of senescent cells with senolytic drugs has become one of the most explored interventions, with many currently in human clinical trials<sup>26</sup>. A group of these senolytics — such as the cocktail of dasatinib plus quercetin (D+Q), or fisetin — exhibit blood- brain barrier permeability upon oral administration<sup>22,27</sup>, making these formulations particularly valuable to test the contribution of senescence in the brain in vivo.  
+
+In the present study, we first document the efficacy of multiple senolytic interventions in clearing senescent cells in physiologically aged human pluripotent stem cell- derived brain organoids. Transcriptomic analysis across individual senolytic treatments revealed a differential effect in modulating the senescence- associated secretory phenotype (SASP), with a distinctive impact of D+Q administration in rejuvenating the organoids transcriptomic aging clock. Importantly, we report an enrichment of senescent cells in postmortem brain tissue of COVID- 19 patients and
+
+<--- Page Split --->
+
+further show a direct role for SARS- CoV- 2 and highly neurotropic viruses such as Zika and Japanese encephalitis in evoking cellular senescence in human brain organoids. SARS- CoV- 2 variant screening identified Delta (B.1.617.2) as the variant that exerts the strongest induction of cellular senescence in human brain organoids, and spatial transcriptomic analysis of Delta- induced senescent cells unveiled a novel type of senescence that exhibits a different transcriptional signature from senescent cells that naturally emerge in in vitro aged uninfected organoids. Furthermore, senolytic treatment of SARS- CoV- 2- infected organoids selectively removed senescent cells, lessened SASP- related inflammation and reduced SARS- CoV- 2 RNA expression, indicating a putative role for senescent cells in facilitating viral retention. Finally, to gain in vivo relevance of these findings, we examined the treatment effects of senolytics in transgenic mice expressing human angiotensin- converting enzyme 2 (hACE2) previously infected with SARS- CoV- 2 and observed improved clinical performance and survival, reduced viral load in the brain, improved survival of dopaminergic neurons, decreased astrogliosis, and attenuated senescence and SASP gene expression in the brains of the infected mice. Our findings suggest a detrimental role for virus- induced senescence in accelerating brain inflammation and the aging process in the CNS, and a potential therapeutic role for senolytics in the treatment of COVID- 19 neuropathology.  
+
+## Results  
+
+## Senolytics target biological aging and senescent cells in physiologically aged human brain organoids.  
+
+To model the efficacy of senolytics in clearing senescent cells from human brain tissue models, we generated 8- month- old human brain organoids (BOs) from embryonic stem cells and exposed these to two doses of senolytics for one month at 2 weekly intervals (Supplementary Fig. 1a). We tested the Bcl- 2 inhibitors navitoclax and ABT- 737, as well as D+Q senolytic drug combination, and quantified the abundance of cells exhibiting senescence- associated \(\beta\) - galactosidase activity (SA- \(\beta\) - gal). Exposure to senolytics resulted in significantly lower SA- \(\beta\) - gal activity as compared to vehicle- treated controls (Fig. 1a, c), indicating that all treatments eliminated a large number of senescent cells in the treated BOs. In agreement with this, analysis of lamin B1 protein expression — a nuclear lamina marker often downregulated in senescence<sup>28</sup> — within organoid sections revealed a significantly higher content of lamin B1 in the senolytic- treated organoids as compared to control counterparts (Fig. 1b, d), further indicating that senolytics cleared senescent cells by enriching for lamin B1<sup>High</sup> cell populations.
+
+<--- Page Split --->
+
+We next performed whole- organoid RNA sequencing to compare the transcriptomes of fenolytic- treated and vehicle control 9- month- old BOs. Consistent with our protein expression data (Fig. 1b, d), LMNB1 (lamin B1) mRNA levels were significantly upregulated in all three fenolytic- treated organoids compared to vehicle- treated counterparts (Fig. 2a- c). We further identified 81 senescence- associated genes (including the proinflammatory genes CXCL13 and TNFAIP8) that were consistently suppressed upon all three fenolytic interventions (Fig. 2d and Supplementary Fig. 1b). We however also noticed that each fenolytic treatment exerted substantially different effects in modulating the SASP and other senescence- associated genes (Fig. 2a- c). For instance, SERPINF1 was significantly repressed upon ABT- 737 administration (Fig. 2b) while D+Q did not modulate SERPINF1 expression but greatly suppressed IL8, SERPINE1 and IL1A (Fig. 2c). Compared to navitoclax and ABT- 737 – compounds that modulate multiple shared genes that are enriched for a few pathways (e.g. K- Ras signalling) (Fig. 2e) –, D+Q had a broader spectrum effect, mitigating multiple pro- inflammatory pathways characteristic of cellular senescence, such as NF- \(\kappa\) B and IFNγ signalling (Fig. 2e and Supplementary Fig. 1c). In addition, we identified mTOR as a significantly supressed pathway upon D+Q treatment (Fig. 2e), validating the effects reported for Q as an inhibitor of mTOR kinase. We next performed aging clock predictions based on whole transcriptome sequencing to further explore the impact of fenolytic on the aging process. Remarkably, in addition to their fenolytic mechanisms of action, D+Q treatments on 9- month- old organoids reverted their gene expression age to levels comparable of 8- month- old counterparts according to transcriptomic brain aging clock analysis (Fig. 2f), a phenotype not recapitulated by the other two fenolytic tested. Besides negative association with aging, gene expression changes induced by D+Q treatment were positively correlated with mammalian signatures of established lifespan- extending interventions, such as caloric restriction and rapamycin administration (Fig. 2g), indicating a health- promoting role of D+Q in targeting cellular senescence and biological aging in human CNS tissues.  
+
+## SARS-CoV-2 infection triggers cellular senescence in the brains of COVID-19 patients and in human brain organoids.  
+
+Given the observed neuroinflammatory effects of SARS- CoV- 2 infection during acute COVID- 19 disease<sup>29</sup> and its association with molecular signatures of aging in patient brains<sup>18</sup>, we postulated that part of this pro- inflammatory aging- promoting environment is brought about by SARS- CoV- 2- induced senescence in the brain. To test this hypothesis, we quantified the prevalence of senescent cells in postmortem frontal cortex from age- matched brains of patients that either died following severe COVID- 19 or patients who died of non- infectious, and non- neurological reasons. Notably, in situ high- throughput analysis of over 2.7 million single cells
+
+<--- Page Split --->
+
+across 15 individual brain samples (7 COVID- 19 and 8 non- COVID- 19 frontal cortex sections) revealed increased p16 immunoreactivity frequencies in COVID- 19 patient brains, with a \(>7\) - fold increase in the number of p16- positive cells as compared to non- COVID- 19 age- matched controls (Fig. 3). These results suggest a potential role for SARS- CoV- 2 in triggering cellular senescence, a cellular phenotype that contributes to cognitive decline and that could pose a risk in the acceleration of neurodegenerative processes associated with long- COVID.  
+
+To study the role of neurotropic viruses in aging- driven neuropathology, we exposed human BOs to different viral pathogens, including SARS- CoV- 2. Consistent with previous reports \(^{8,9,16,30}\) , SARS- CoV- 2 BO infections were detected largely within populations of neurons and neural progenitors (Supplementary Fig. 2a, b). To test putative virus- induced senescence phenotypes, we screened seven SARS- CoV- 2 variants by infecting human BOs at identical multiplicity of infection (MOI) and ranked them based on SA- \(\beta\) - gal activity as initial readouts of cellular senescence. Notably, most variants elicited a significant increase in SA- \(\beta\) - gal, with Delta (B.1.617.2) showing the strongest induction (Fig. 4a, b). In addition, serial sectioning of Delta- infected organoids revealed a distinctive colocalization between SA- \(\beta\) - gal and viral spike protein (Fig. 4c), further supporting a role for SARS- CoV- 2 in driving virus- induced senescence in the brain. This phenotype was confirmed when organoid sections were co- immunolabelled with antibodies against p16 and SARS- CoV- 2 nucleocapsid antigens (Fig. 4d). Because of the mechanistic role of DNA damage in affecting most aging hallmarks \(^{31}\) , including the onset of cellular senescence \(^{32}\) , we next explored whether SARS- CoV- 2 infection led to DNA double- strand break accumulation. Consistent with previous evidence \(^{19,33}\) , we detected significantly heightened levels of phosphorylated histone H2AX at serine 139 (known as \(\gamma\) H2AX) in SARS- CoV- 2- infected organoid regions as compared to uninfected organoid cells (Fig. 4e, f), indicating increased DNA damage response marks upon SARS- CoV- 2 infection. Importantly, virus- induced senescence also became detectable in response to a variety of human neurotropic viruses, including Japanese Encephalitis virus (JEV), Rocio virus (ROCV) and Zika virus (ZIKV) in human BOs (Fig. 4g).  
+
+As SARS- CoV- 2 infection is coupled with cognitive decline and signatures of aging, we further assessed associations of transcriptomic changes in COVID- 19 patients and SARS- CoV- 2- infected human BOs. Specifically, we compared post- mortem frontal cortex transcriptomic data from a COVID- 19 cohort study of 44 individual patient brains \(^{18}\) with bulk RNA sequencing we performed on human cortical brain organoids 10 days post infection. Notably, among 1,588 differentially expressed genes (DEGs) between SARS- CoV- 2- infected human BOs compared and uninfected counterparts, 485 genes (30.54%) were also differentially expressed in COVID- 19 patient brain samples. Of note, this common gene set was enriched for known aging and senescence pathways,
+
+<--- Page Split --->
+
+identified in the hallmark gene set collection of the Molecular Signatures Database<sup>34</sup> (Supplementary Fig. 3a).  
+
+To better understand the differential effects of the ancestral Wuhan virus and Delta (B.1.617.2) SARS- CoV- 2 variants on senescence induction in hBOs, performed NanoString GeoMx spatial transcriptomic sequencing on p16 protein- expressing regions of interest (ROIs) within organoid sections (Fig. 4h). ROI selection was performed to enable the capture of targeted transcriptome from sufficient senescent cell tissue (>300 cells per ROI) to generate robust count data. Our bulk RNA sequencing analysis revealed 1,250 DEGs in Wuhan- infected BOs as compared to a lower 474 DEGs in Delta- infected counterparts (Supplementary Fig. 3b), a result possibly explained by the higher infectivity rate observed in the Wuhan- infected organoids (Supplementary Fig. 3c). Strikingly, spatial transcriptome analysis of p16- positive cells identified over 1,100 DEGs in Delta- infected organoids, an effect 100- fold greater than Wuhan where only 9 DEGs were detected (Supplementary Fig. 3b). This was explained by principal component analysis, where gene set space determined that the Delta- infected ROIs were separable from overlapping transcriptomes from Wuhan- infected and uninfected senescent cell regions (Supplementary Fig. 4a). Upon extensive analysis of significantly modulated gene expression in p16- positive ROIs of Delta- infected organoids, we identified 458 genes associated with cellular senescence that differentially clustered from Wuhan- infected and uninfected ROIs (Fig. 4i), with many interleukins significantly elevated in Delta- infected ROIs (Fig. 4j). Importantly, this unique Delta- specific senescence transcriptional signature was detected in the presence of heightened normalized SARS- CoV- 2 gene expression in Delta compared to p16- positive cells of Wuhan- infected organoids (Fig. 4k). Altogether, these results demonstrate a direct role for SARS- CoV- 2 and neurotropic flaviviruses in fuelling virus- induced senescence, and revealed a specific effect of Delta (B.1.617.2) in inducing the selective induction of a de novo transcriptional signature and simultaneous accumulation of SARS- CoV- 2 in senescent cells of human BOs.  
+
+## Senolytics reduce SARS-CoV-2 viral expression and virus-induced senescence in human brain organoids.  
+
+The results described so far support a functional role of SARS- CoV- 2 in inducing brain cellular senescence. To investigate whether this virus- induced phenotype could be pharmacologically targeted, we next tested the impact of the selective removal of senescent cells with the same senolytic interventions we previously showed were effective in eliminating senescent cells from physiologically aged organoids (Fig. 5a). We observed that senolytic treatments 5 days post SARS- CoV- 2 infection significantly reduced the number of brain organoid cells that display SA- \(\beta\) - gal activity (Fig. 5b). Notably, senolytic treatment in Delta- infected organoids had an overall
+
+<--- Page Split --->
+
+more prominent and statistically significant effect in reducing cellular senescence as compared to Wuhan- infected counterparts, consistent with the stronger virus- induced senescence phenotype observed upon Delta infections in our initial SARS- CoV- 2 variant screening (Fig. 5a, b). Moreover, senolytics were able to revert lamin B1 loss induced by Delta infections (Supplementary Fig. 4b). Remarkably, treatment with senolytics reduced the viral load in BOs up to 40- fold as measured by intracellular SARS- CoV- 2 RNA levels (Fig. 5c), indicating a putative role of senescent cells as reservoirs that may preferentially facilitate viral replication. To characterise cell type- specific SARS- CoV- 2- induced senescence, we performed deconvolution of spatial transcriptomic data from p16- positive cells (Fig. 5d), a type of analysis that enables cell abundance estimates from gene expression patterns \(^{35}\) . We identified layer 6 corticothalamic neurons (L6CT L6b, \(>9\) - fold induction) and GABAergic ganglionic eminence neurons (CGE, \(>4\) - fold induction) as the two neuronal populations that showed significantly increased senescence incidence upon SARS- CoV- 2 infections in brain organoids (Fig. 5e); two brain cell populations that are vital for modulating neural circuitry and processing incoming sensory information \(^{36}\) . Importantly, all the three senolytic treatments tested prevented the accumulation of cellular senescence in both L6CT L6b and CGE brain organoid cell populations (Fig. 5e).  
+
+## Senolytic treatments mitigate COVID-19 brain pathology in vivo.  
+
+To investigate the consequences of CNS SARS- CoV- 2 infection and ensuing brain virus- induced senescence in a more physiologically complete system, we utilised transgenic mice expressing human ACE2 gene under the control of the keratin 18 promoter (K18- hACE2) \(^{37}\) and performed intranasal SARS- CoV- 2 infections, where we found brain viral nucleocapsid antigen in cerebral cortex and brainstem regions (Supplementary Fig. 5a). Experimentally, 24 hours post infection we initiated oral administration of the senolytic interventions navitoclax, fisetin and D+Q – drugs known to exert blood- brain barrier permeability \(^{22,38}\) – with subsequent treatments every two days (Fig. 6a). As previously reported, SARS- CoV- 2- infected K18- hACE2 transgenic mice undergo dramatically shortened lifespans upon infection \(^{37}\) , with a median survival of 5 days. Strikingly, treatment with D+Q or fisetin significantly improved the survival of K18- hACE2 mice as compared to vehicle- treated controls, with extended median lifespans of 60% (Fig. 6b). Furthermore, while at 10 days post infection all vehicle- treated control mice were already dead, at survival experimental endpoint (12 days post infection) a percentage of senolytic- treated mice – 22% (fisetin), 38% (D+Q) and 13% (navitoclax) – remained alive (Fig. 6b). This significantly improved survival upon senolytic administration of infected mice concurrently delayed the rapid weight loss observed in the infected control group (Supplementary Fig. 5b). Throughout the first week of the in vivo experiments, mice were clinically monitored and scored daily for behavioural
+
+<--- Page Split --->
+
+and physical performance (Fig. 6c). Notably, senolytic interventions resulted in a profound reduction of COVID- related disease features, especially in the D+Q- treated group (Fig. 6c).  
+
+Given the positive survival and improved clinical performance outcomes brought about by senolytic treatment, we investigated whether the oral administration of senolytics impacted the histological architecture and pro- inflammatory makeup of brains from infected mice. To this end, we first tested the impact of senolytics on brain viral RNA levels. In accordance with our brain organoid data (Fig. 5c), senolytic treatments of infected K18- hACE2 mice showed a significantly lower viral gene expression compared to infected vehicle- treated mice (Fig. 6d), further supporting a putative role for senescent cells in preferentially sustaining SARS- CoV- 2 replication. We next tested whether senescent cell clearance directly impacted the transcription of SASP and senescence genes in the brain. mRNA expression analyses from brains of uninfected and infected mice indicated an overall increase in inflammatory SASP and p16 senescence markers in the brains of infected mice (Fig. 6e). Most importantly, all three senolytic interventions consistently normalised brain SASP and senescence gene expression of infected mice to levels comparable to those of uninfected brains (Fig. 6e).  
+
+Neuroinvasive viral infections can result in loss of dopaminergic neurons and ensuing PASC such as parkinsonism<sup>39</sup>. Given the long- term neurological impact of COVID- 19 including coordination and consciousness disorders<sup>40</sup>, we therefore tested the impact of SARS- CoV- 2 infection on altering dopaminergic neuron survival within the brainstem, an important region of the brain known to regulate these behaviours. Strikingly, Delta variant infection induced a dramatic loss of dopaminergic neurons in the brainstem, as measured by tyrosine hydroxylase immunolabelling (Fig. 6f, g), and this was accompanied by increased astrogliosis (Fig. 6f, h), a neurotoxic process common to multiple neurological disorders<sup>41</sup>. Importantly, recurrent senolytic treatments initiated 24 hours after SARS- CoV- 2 exposure partly prevented dopaminergic neuron loss and abrogated the onset of reactive astrogliosis (Fig. 6f- h).  
+
+## Discussion  
+
+Brain aging and related cognitive deficiency have been attributed to diverse molecular processes including chronic inflammation and cellular senescence<sup>42</sup>. This has been studied both in normal murine aging<sup>24</sup>, as well as in different age- related mouse models of neurodegeneration such as Parkinson's disease<sup>43</sup>, tauopathies<sup>23,44</sup>, amyloid- beta neuropathology<sup>22</sup>, and neuropsychiatric disorders<sup>45</sup>. However, whether the endogenous age- related onset of cellular senescence impacts brain aging in human tissue systems has not been investigated. Neither have the putative
+
+<--- Page Split --->
+
+consequences of neurotropic viral infections in accelerating the onset of cellular senescence in the brain been examined.  
+
+Our findings herein show that: (1) senescent cells accumulate in physiologically aged brain organoids of human origin and that long- term (4 weeks), intermittent, senolytic treatment reduces inflammation and cellular senescence; (2) interventions unique to D+Q treatments induce anti- aging and pro- longevity gene expression changes in human BOs; (3) brains from COVID- 19 patients undergo accelerated cellular senescence accumulation compared to age- matched controls; (4) SARS- CoV- 2 and neurotropic viruses including Zika and JEV can infect human BOs to directly induce cellular senescence; (5) Delta (B.1.617.2) variant induces the strongest SARS- CoV- 2- dependent induction of cellular senescence, where spatial transcriptomic sequencing of p16- positive cells identifies a Delta- specific SASP signature; (6) short- term (5 days) senolytic treatments of SARS- CoV- 2- infected organoids reduce viral gene expression and prevent the onset of senescent neurons of corticothalamic and GABAergic nature; and (7) senolytic treatment following SARS- CoV- 2 intranasal infection of K18- hACE2 mice ameliorates COVID- 19 neuropathology, including improvements in clinical score and survival, alleviation of reactive astrogliosis, increased survival of dopaminergic neurons, and reduced viral, SASP and senescence gene expression in the brain of infected mice.  
+
+To evaluate the relationship between senescent cell accumulation and brain aging, we designed studies to eliminate senescent cells through pharmacologic approaches (D+Q, navitoclax and ABT- 737) and hypothesized that senolytic interventions may have beneficial consequences in targeting brain aging. We found that physiologically aged human BOs accumulate senescent cells and that senolytic treatment can be used as a proof- of- concept strategy to revert Lamin B1 levels, and alleviate differential SASP expression and senescent cell burden in human brain BOs systems. In addition to senolytic activity, transcriptomic aging clocks identified D+Q as an intervention that achieved tissue rejuvenation, as 8- month- old human brain organoids displayed comparable aging clocks to D+Q- treated 9- month- old counterparts. Given that senescent cell clearance results in reversal of the aging process, these findings support an important role for senescent cells in driving human brain aging.  
+
+Further to normal brain aging, we tested the possibility of virus- induced senescence upon BOs neurotropic infections. We found that flavivirus JEV, ROCV and ZIKV infections, and multiple SARS- CoV- 2 variant infections lead to a significant increase in BO cellular senescence. Importantly, upon senolytic delivery BOs display a dramatic loss of SARS- CoV- 2 viral RNA expression, suggestive of a role for senescent cells in preferentially facilitating viral entry and retention, consistent with data showing increased ACE2 expression in human senescent cells<sup>46</sup>.
+
+<--- Page Split --->
+
+Furthermore, SARS- CoV- 2 induces metabolic changes in infected and neighbouring neurons<sup>8</sup>, a paracrine phenomenon reminiscent of the bystander effect characteristic of senescent cells<sup>47</sup>. Here, spatial transcriptomic sequencing cell deconvolution of p16 protein- expressing cell clusters identified two neuronal populations – corticothalamic and GABAergic – that become senescent and broadly develop a de novo SASP signature upon Delta (B.1.617.2) infection. It will therefore be of interest to determine whether neuronal virus- induced senescence contributes to neuroinflammation and the long- term neurological impact of COVID- 19.  
+
+In the brains of SARS- CoV- 2- infected K18- hACE2 mice, we found that senolytic treatment alleviates p16 and the levels of proinflammatory cytokines which may be due, in part, to removal of virus- induced senescence and ensuing SASP expression. However, secondary anti- inflammatory and/or anti- viral effects of D+Q, fisetin or navitoclax – for instance by direct inhibition of the observed astrogliosis – are also possible. Upon systematic monitoring of clinical performance in SARS- CoV- 2- infected mice, we found that intermittent senolytic treatment significantly improved animal behaviour and survival. This beneficial clinical effect of senolytics was associated with reduced inflammation and increased survival of dopaminergic neurons. Indeed, inflammatory cytokines as part of the SASP can impair brain plasticity<sup>48</sup>, suggesting that the beneficial effects of senolytic treatment on COVID- 19 neurological clinical picture may result from suppression of senescence- dependent inflammation and improved neuronal survival. This is consistent with pre- clinical studies demonstrating a beneficial effect of senescent- cell clearance in reducing inflammatory/SASP gene expression in the brains of geriatric mice infected with a SARS- CoV- 2–related mouse \(\beta\) - coronavirus<sup>49</sup>. Whether our in vivo effects of senolytics on COVID- 19 neuropathology exclusively results from clearance of cellular senescence or also involves actions on dopaminergic neurons and other brain regions remains to be determined. Nevertheless, in this study we have provided important evidence that paves the way for future clinical studies that will test the hypothesis that senolytic therapies can suppress long- COVID neuropathology and other long- term disorders caused by acute neurotropic viral infections.  
+
+## Methods  
+
+Ethics and biological safety. The use of animals was approved by the University of Queensland Animal Ethics Committee under project number 2021/AE001119. Mice were housed within the BSL- 3 facility using IsoCage N- Biocontainment System (Tecniplast, USA), where each cage was supplied with a HEPA filter, preventing viral contamination between cages. This IsoCage system also provides individual ventilation to the cages, maintaining the humidity under 65- 70% and
+
+<--- Page Split --->
+
+temperature between 20–23 °C. Mice were kept under a 12- h light/dark cycle with food and water provided ad libitum.  
+
+Pathogenic SARS- CoV- 2 variants and encephalitic flaviviruses were handled under a certified biosafety level- 3 (BSL- 3) conditions in the School of Chemistry and Molecular Biosciences (SCMB), Australian Institute for Bioengineering and Nanotechnology (AIBN) and Institute for Molecular Bioscience (IMB) at The University of Queensland, Australia. All approved researchers have used disposal Tychem 2000 coveralls (Dupont, Wilmington, NC, USA; #TC198T YL) at all times and used powered air- purifying respirators (PAPR; SR500 Fan Unit) or Versaflo- powered air- purifying respirators (3M, Saint Paul, MN, USA; #902- 03- 99) as respiratory protection. All pathogenic materials were handled in a class II biosafety cabinet within the BSL- 3 facility. For downstream analysis, all samples containing infectious viruses were appropriately inactivated in accordance with the BSL- 3 manual. Liquid and solid waste were steam- sterilised by autoclave. This study was approved by the Institutional Biosafety Committee from The University of Queensland (UQ) under the following approvals IBC/485B/SCMB/2021 and IBC/447B/SCMB/2021. The analysis of human brain sections was performed with the approval of the Ethic Committee of the University of Freiburg: 10008/09. The study was performed in agreement with the principles expressed in the Declaration of Helsinki (2013).  
+
+Generation and culture of PSC- derived human brain organoids. Organoid generation was carried out as previously described<sup>50</sup>, with some modifications. Human H9 (WA09) pluripotent stem cells (hPSCs) were obtained from WiCell with verified normal karyotype and contamination- free; and were routinely tested and confirmed negative for mycoplasma (MycoAlert, Lonza). hPSCs were maintained in mTeSR media (STEMCELL Technologies, cat. #85850) on matrigel- coated plates (Corning, No. 354234). On day 0 of organoid differentiation, PSCs were dissociated with Accutase (Life Technologies, cat. #00- 4555- 56) and seeded at a density of 15,000 cells per well on a 96- well low- attachment U- bottom plate (Sigma, cat. #CLS7007) in mTeSR plus 10 μM ROCK inhibitor (VWR, cat. #688000- 5). The 96 well- plate was then spun at 330 g for 5 minutes to aggregate the cells and make spheroids. The spheroids were fed every day for 5 days in media containing Dulbecco’s modified eagle medium (DMEM)/F12 (Invitrogen, cat. #11330- 032), Knock- out serum (Invitrogen, cat. #11320- 033), 1:100 Glutamax, 1:200 MEM- NEAA supplemented with dual SMAD inhibitors: 2 μM Dorsomorphin (StemMACS, cat. #130- 104- 466) and 2 μM A- 83- 01 (Lonza, cat. #9094360). On day 6, half of the medium was changed to induction medium containing DMEM/F12, 1:200 MEM- NEAA, 1:100 Glutamax, 1:100 N2 supplement (Invitrogen, cat. #17502048), 1 μg ml- 1 heparin (Sigma, cat. # H3149) supplemented with 1 μM CHIR 99021 (Lonza, cat. #2520691) and 1 μM SB- 431542 (Sigma, cat. # S4317). From day 7,
+
+<--- Page Split --->
+
+complete media change was done with induction media followed by everyday media changes in induction media for the next 4 days. On day 11 of the protocol, spheroids were transferred to 10 \(\mu \mathrm{l}\) - droplets of Matrigel on a sheet of Parafilm with small 2 mm dimples. These droplets were allowed to gel at \(37^{\circ}\mathrm{C}\) for 25 minutes and were subsequently removed from the Parafilm and transferred to and maintained in low- attachment 24- well plates (Sigma, cat. #CLS3473) containing induction medium for the following 5 days. From day 16, the medium was then changed to organoid medium containing a 1:1 mixture of Neurobasal medium (Invitrogen, cat. #21103049) and DMEM/F12 medium supplemented with 1:200 MEM- NEAA, 1:100 Glutamax, 1:100 N2 supplement, 1:50 B27 supplement (Invitrogen, cat. #12587010), \(1\%\) penicillin- streptomycin (Sigma, cat. #P0781), \(50~\mu \mathrm{M}\) 2- mercaptoethanol and \(0.25\%\) insulin solution (Sigma, cat. #I9278). Media was changed every other day with organoid medium. Organoids were maintained in organoid media until the end of experiments, as indicated.  
+
+Human tissue preparation: frontal cortex tissue from patients that had tested positive for SARS- CoV- 2 and died from severe COVID- 19 was obtained at the University Medical Center Freiburg, Germany. The tissue was formalin- fixed and embedded into paraffin (FFPE) using a Tissue Processing Center (Leica ASP300, Leica). Sections (3 \(\mu \mathrm{m}\) thick) were cut and mounted onto Superfrost objective slides (Langenbrinck).  
+
+Cell lines. RNA Vero E6 cells (African green monkey kidney cell clones) and TMPRSS2- expressing Vero E6 cell lines were maintained in Dulbecco's Modified Eagle Medium (DMEM, Gibco, USA) at \(37^{\circ}\mathrm{C}\) with \(5\%\) CO2. Additionally, as previously described, the TMPRSS2- expressing Vero E6 cell line was supplemented with \(30~\mu \mathrm{g / mL}\) of puromycin<sup>51</sup>. C6/36 cells, derived from the salivary gland of the mosquito A. albopictus were grown at \(28^{\circ}\mathrm{C}\) in Royal Park Memorial Institute (RPMI) medium (Gibco, USA). All cell lines media were supplemented with \(10\%\) heat- inactivated foetal calf serum (FCS) (Bovogen, USA), penicillin (100 U/mL) and streptomycin (100 \(\mu \mathrm{g / mL}\) ) (P/S). C6/36 media was also supplemented with \(1\%\) GlutaMAX (200 mM; Gibco, USA) and \(20~\mathrm{mM}\) of HEPES (Gibco, USA). All cell lines used in this study were tested mycoplasma free by first culturing the cells for 3- 5 days in antibiotic- free media and then subjected to a mycoplasma tested using MycoAlert™ PLUS Mycoplasma Detection Kit (Lonza, UK).  
+
+Viral isolates. Seven SARS- CoV- 2 variants were used in this study. \(i\) ) Ancestral or Wuhan strain: an early Australian isolate hCoV- 19/Australia/QLD02/2020 (QLD02) sampled on 30/01/2020 (GISAID Accession ID; EPI_ISL_407896); \(ii\) ) Alpha (B.1.1.7) named as hCoV- 19/Australia/QLD1517/2021 and collected on 06/01/2021 (GISAID accession ID EPI_ISL_944644); \(iii\) ) Beta (B.1.351), hCoV19/Australia/QLD1520/2020, collected on
+
+<--- Page Split --->
+
+29/12/2020 (GISAID accession ID EPI_ISL_968081); iv) Delta (B.1.617), hCoV- 19/Australia/QLD1893C/2021 collected on 05/04/2021 (GISAID accession ID EPI_ISL_2433928); v) Gamma (P.1), hCoV- 19/Australia/NSW4318/2021 sampled on 01- 03- 2021 (GISAID accession ID EPI_ISL_1121976); vi) Lambda (C.37), hCoV- 19/Australia/NSW4431/2021 collected on 03- 04- 2021 (GISAID accession ID EPI_ISL_1494722); and vii) Omicron (BA.1), hCoV- 19/Australia/NSW-RPAH- 1933/2021 collected on 27- 11- 2021 (GISAID accession ID EPI_ISL_6814922). All viral isolates obtained were passaged twice except for Gamma and Lambda variants, which were passed thrice. Viral stocks were generated on TMPRSS2- expressing Vero E6 cells to ensure no spike furin cleavage site loss. To authenticate SARS- CoV- 2 isolates used in the study viral RNA was extracted from stocks using TRIzol LS reagent (Thermo Fisher Scientific, USA) and cDNA was prepared with Protoscript II first- strand cDNA synthesis kit as per manufacturer's protocol (New England Biolabs, USA). The full- length Spike glycoprotein was subsequently amplified with Prime Star GXL DNA polymerase (Takara Bio) and the following primers CoV- SF GATAAAGGAGTTGCACCAGGTACAGCTGTTTTAAG CoV- SR GTCGTCGTCGGTTCATCATAAATTGGTTCC and conditions as per previously described51. For encephalitic flaviviruses, virulent strains of Zika virus (ZIKV, Natal [GenBank: KU527068.1]), Japanese encephalitis virus (JEV, Nakayama strain [GenBank: EF571853.1]) and Rocio virus (ROCV, [GenBank: AY632542.4]) were propagated on C6/36 to generate a viral stock for all the experiments. Viral titres were determined by an immuno- plaque assay52. RNA isolation. RNA from brain organoids and mouse tissue was extracted with RNeasy Mini Kit (Qiagen) for mRNA detection, according to the manufacturer's instructions. Mouse tissue was homogenised with a TissueLyser II (Qiagen) at 30 Hz for 60 seconds. RNA integrity of brain organoids and mouse tissue was evaluated by analysis on the 2100 Bioanalyzer RNA 6000 Pico Chip kit (Agilent) using the RNA Integrity Number (RIN). RNA samples with a RIN > 7 were considered of high enough quality for real- time quantitative PCR, and transcriptomic library construction and RNA sequencing according to the manufacturer's instructions. Real- time quantitative PCR. 1 \(\mu \mathrm{g}\) of total RNA was reverse transcribed using iScript cDNA Synthesis Kit (Bio- Rad). A volume corresponding to 5 ng of initial RNA was employed for each real- time PCR reaction using PowerUp SYBR Green Master Mix (Applied Biosystems) on a CFX Opus Real- Time PCR detection system. Ribosomal protein P0 (RPLP0) were used as control transcripts for normalization. Primers sequences (5'- 3' orientation) are listed in Supplementary Table 1.
+
+<--- Page Split --->
+
+Viral infection of organoids. Brain organoids in low- adhesion plates were infected overnight (14 hours) with the indicated flaviviruses and SARS- CoV- 2 variants at multiplicity of infection (MOI) 0.1 and 1, respectively. Then, brain organoids were thrice washed with LPS- free PBS and added maintenance media and kept for 5 days post- infection.  
+
+Senolytic treatments in vitro. For infection experiments, 5 days after viral exposure brain organoids were treated with a single dose of navitoclax (2.5 \(\mu \mathrm{M}\) ), ABT- 737 (10 \(\mu \mathrm{M}\) ) or D+Q (D: 10 \(\mu \mathrm{M}\) ; Q: 25 \(\mu \mathrm{M}\) ) and monitored for 5 days following treatment. As for senolytic interventions on physiologically aged 8- month- old organoids, brain organoids were treated with a weekly dose of navitoclax (2.5 \(\mu \mathrm{M}\) ), ABT- 737 (10 \(\mu \mathrm{M}\) ) or D+Q (D: 10 \(\mu \mathrm{M}\) ; Q: 25 \(\mu \mathrm{M}\) ) for 4 weeks and subsequently collected for downstream analysis.  
+
+SARS- CoV- 2- driven COVID- 19 animal experiments. In vivo experiments were performed using 6- week- old K18- hACE2 transgenic female mice obtained from the Animal Resources Centre (Australia). For animal infections, SARS- CoV- 2 was delivered intranasally — 20 \(\mu \mathrm{l}\) of the Delta variant at \(5 \times 10^{3}\) FFU per mouse — on anesthetized mice (100 mg \(\mathrm{kg}^{- 1}\) ketamine and 10 mg \(\mathrm{kg}^{- 1}\) xylazine). Control animals were mock- infected with the same volume of RPMI additive- free medium. One day after infection, K18- hACE2 mice were randomly distributed into three treatment groups (n = 16 each) and one solvent- only control group (n = 16). From 1 day after infection, randomly chosen animals were treated via oral gavage routes with navitoclax (100 mg \(\mathrm{kg}^{- 1}\) ), D+Q (D: 5 mg \(\mathrm{kg}^{- 1}\) ; Q: 50 mg \(\mathrm{kg}^{- 1}\) ) or fisetin (100 mg \(\mathrm{kg}^{- 1}\) ) dissolved in 5% DMSO and 95% corn oil every other day. For tissue characterization (n = 8 for each infected group), on day 6 after infection animals were euthanised and brain specimens were collected for RNA expression analysis and histopathological assessment. For clinical and survival evaluation, mice were monitored daily for up to 12 days post infection. Clinical scoring included: no detectable disease (0); hindlimb weakness, away from littermates, ruffled fur (0.5- 1); partial hindlimb paralysis, limping, hunched, reluctant to move (1.5- 2); and complete paralysis of hindlimb, severely restricted mobility, severe distress, or death (2.5- 3).  
+
+Organoid sectioning and histology. Brain organoids were fixed in 4% paraformaldehyde (PFA) for 1 hour at RT and washed with phosphate- buffered saline (PBS) three times for 10 minutes each at RT before allowing to sink in 30% sucrose at \(4^{\circ}\mathrm{C}\) overnight and then embedded in OCT (Agar Scientific, cat. #AGR1180) and cryosectioned at 14 \(\mu \mathrm{m}\) with a Thermo Scientific NX70 Cryostat. Tissue sections were used for immunofluorescence and for the SA- \(\beta\) - Gal assay. For immunofluorescence, sections were blocked and permeabilized in 0.1% Triton X- 100 and 3% Bovine Serum Albumin (BSA) in PBS. Sections were incubated with primary antibodies overnight at \(4^{\circ}\mathrm{C}\) , washed and incubated with secondary antibodies for 40 minutes at RT. 0.5 \(\mu \mathrm{g}\) ml- 1 DAPI
+
+<--- Page Split --->
+
+(Sigma, cat. #D9564) was added to secondary antibody to mark nuclei. Secondary antibodies labelled with Alexafluor 488, 568, or 647 (Invitrogen) were used for detection. SA- \(\beta\) - gal activity at pH 6.0 as a senescence marker in fresh or cryopreserved human samples was assessed as previously described \(^{53}\) .  
+
+Nanostring spatial transcriptomics. OCT- embedded organoids were freshly sectioned and prepared according to the GeoMX Human Whole Transcriptome Atlas Assay slide preparation for RNA profiling (NanoString). Fastq files were uploaded to GeoMX DSP system where raw and Q3 normalized counts of all targets were aligned with ROIs. The 0.75 quantile- scaled data was used as input. DESeq2 R package \(^{54}\) was used to identify differently expressed genes in the ROI cell subsets. DESeq2 was performed between the pairwise comparisons of interest and genes were corrected using the Benjamini & Hochberg correction and only genes that had a corrected P- value of \(< 0.05\) were retained. Cell abundances were estimated using the SpatialDecon R library, which performs mixture deconvolution using constrained log- normal regression.  
+
+Whole organoid RNA sequencing. Before mRNA sequencing, ribosomal RNA from bulk organoid RNA was depleted with the Ribo- Zero rRNA Removal Kit (Illumina). Transcripts were sequenced at Novogene Ltd (Hong Kong) using TruSeq stranded total RNA library preparation and Illumina NovaSeq 150bp paired- end lane. FastQC was used to check quality on the raw sequences before analysis to confirm data integrity. Trimmed reads were mapped to the human genome assembly hg38 using Hisat2 v2.0.5. To ensure high quality of the count table, the raw count table generated by featureCounts v1.5.0- p3 was filtered for subsequent analysis. Differential gene expression analysis was performed using Bioconductor DESeq2 R packages. The resulting P- values were adjusted using the Benjamini and Hochberg's approach for controlling the false discovery rate. Genes with an adjusted P- value \(< 0.05\) found by DESeq2 were assigned as differentially expressed.  
+
+Association with gene expression signatures of aging and longevity. To assess the effect of senolytics on transcriptomic age of BO samples, we applied brain multi- species (mouse, rat, human) transcriptomic clock based on signatures of aging identified as explained in \(^{55}\) . The missing values were omitted with the precalculated average values from the clock. Association of gene expression log- fold changes induced by senolytics in aged BO with previously established transcriptomic signatures of aging and established lifespan- extending interventions was examined as described in \(^{55}\) . Utilized signatures of aging included multi- species brain signature as well as multi- tissue aging signatures of mouse, rat and human. Signatures of lifespan- extending interventions included genes differentially expressed in mouse tissues in response to individual interventions, including caloric restriction (CR), rapamycin (Rapamycin), and mutations
+
+<--- Page Split --->
+
+associated with growth hormone deficiency (GH deficiency), along with common patterns of lifespan- extending interventions (Common) and ECs associated with the intervention effect on mouse maximum (Max lifespan) and median lifespan (Median lifespan).  
+
+For the identification of enriched functions affected by senolytics in aged BO we performed functional GSEA<sup>56</sup> on a pre- ranked list of genes based on log10(p- value) corrected by the sign of regulation, calculated as:  
+
+\[- (p v)\times s g n(f c),\]  
+
+where pv and lfc are p- value and logFC of a certain gene, respectively, obtained from edgeR output, and sgn is the signum function (equal to 1, - 1 and 0 if value is positive, negative or equal to 0, respectively). HALLMARK ontology from the Molecular Signature Database was used as gene sets for GSEA. The GSEA algorithm was performed separately for each senolytic via the fgsea package in R with 5,000 permutations. A q- value cutoff of 0.1 was used to select statistically significant functions.  
+
+Similar analysis was performed for gene expression signatures of aging and lifespan- extending interventions. Pairwise Spearman correlation was calculated for individual signatures of senolytics, aging and lifespan- extending interventions based on estimated NES (Fig. 2g). A heatmap colored by NES was built for manually chosen statistically significant functions (adjusted p- value \(< 0.1\) ) (Supplementary Fig. 1a). Complete list of functions enriched by genes perturbed by senolytics is included in the source data file.  
+
+Imaging and analysis. Immunofluorescence images were acquired using a Zeiss LSM 900 Fast Airyscan 2 super- resolution microscope or a Zeiss AxioScan Z1 Fluorescent Imager. For organoid staining, the number of positive cells per organoid for senescence, cell type and viral markers tested was analysed by the imaging software CellProfiler, using the same pipeline for each sample in the same experiment. Custom Matlab scripts were developed to streamline high throughput imaging data.  
+
+Antibodies. anti- p16 (Cell Signalling, 80772, 1:400); anti- NeuN (Millipore, ABN78, 1:1000); anti- GFAP (Agilent, Z0334, 1:2000); anti- Sox2 (Cell Signalling, 23064, 1:1000); anti- SARS- CoV- 2 Nucleocapsid C<sup>257</sup>; anti- SARS- CoV- 2 spike protein<sup>58</sup>; anti- \(\gamma\) H2AX (Millipore, 05- 636, 1:1000); anti- Tyrosine Hydroxylase (Invitrogen, PA5- 85167, 1:1000); anti- lamin B1 (Abcam, ab16048, 1:5000); anti- Chicken IgG (Jackson ImmunoResearch, 703- 545- 155, 1:500); anti- rabbit IgG (Invitrogen, A10042, 1:400); anti- rabbit IgG (Invitrogen, A21245, 1:400); anti- mouse IgG (Invitrogen, A11029, 1:400); anti- mouse IgG (Invitrogen, A21235, 1:400); anti- human IgG (Invitrogen, A21445, 1:400).
+
+<--- Page Split --->
+
+Statistical analysis. Results are shown as mean \(\pm\) standard error of the mean (s.e.m.) or standard deviation (s.d.) as indicated. No statistical methods were used to predetermine sample size. P value was calculated by the indicated statistical tests, using R or Prism software. In figure legends, n indicates the number of independent experiments or biological replicates.  
+
+## Competing Interests  
+
+The authors declare no competing interests.  
+
+## Data availability  
+
+RNA- seq raw data have been deposited in the European Nucleotide Archive with the primary accession code PRJEB58180. RNA- seq files from Mavrikaki et al. are available through the Gene Expression Omnibus accession number GSE188847. Source data are provided with this paper.  
+
+## Acknowledgements  
+
+We thank Novogene for performing bulk RNA sequencing experiments and bioinformatic analysis; Aaron McClelland from NanoString (Seattle, USA) for technical and computational assistance on GeoMx spatial transcriptomic sequencing; the scientists and pathologists of Queensland and New South Wales Department of Health, and Kirby Institute for providing the SARS- CoV- 2 variants; Maya Patrick and Barb Arnts (UQBR animal staff) at the AIBN and Crystal McGirr (BSL- 3 facility manager at the IMB) for technical assistance; Robert Sullivan from the Queensland Brain Institute for technical advice; Jasmyn Cridland (Regulatory Compliance Officer, Faculty of Science at UQ) and Amanda Jones (UQ Biosafety) for advice on Biosafety approvals and BSL- 3 manual and safety procedures; Shaun Walters, David Knight and Erica Mu from the School of Biomedical Sciences Imaging and Histology facilities (The University of Queensland) for technical support; and EW, JM and DW laboratory members for discussions. MS was supported by the Berta- Ottenstein- Programme for Clinician Scientists, Faculty of Medicine, University of Freiburg, and the IMM- PACT- Programme for Clinician Scientists, Department of Medicine II, Medical Center – University of Freiburg and Faculty of Medicine, University of Freiburg, funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 413517907. TW was supported by the NHMRC (2009957). EW was supported by the NHMRC and an ARC Discovery Project (DP210103401). JA was supported by a University of Queensland Early Career Researcher Grant (application UQECR2058457), a National Health and Medical Research Council (NHMRC) Ideas Grant (2001408), a Brisbane Children's Hospital Foundation grant (Project- 50308) and a Jérôme Lejeune Postdoctoral Fellowship.
+
+<--- Page Split --->
+
+## Contributions  
+
+ContributionsJA and HC generated human brain organoids. JA, HC, AT, ATF, MD, MS, AA, GP, EA, NM, BL, AI, DP, IJ, AB, MF, RP, JS, CG, TW, JM and EW contributed to acquisition, analysis, or interpretation of data. AAA, EA, NM and BL participated in the infections and treatments of mice and monitored their clinical performance. JA, ATF and AT analysed transcriptomic data. JA, AA, AF, EA, JM and EW contributed to experimental design. JA planned and supervised the project and wrote the paper. All authors edited and approved the final version of this article.  
+
+## References  
+
+References1 Nalbandian, A. et al. Post-acute COVID- 19 syndrome. Nat Med 27, 601- 615 (2021). https://doi.org:10.1038/s41591- 021- 01283- z2 Choutka, J., Jansari, V., Hornig, M. & Iwasaki, A. Unexplained post- acute infection syndromes. Nat Med 28, 911- 923 (2022). https://doi.org:10.1038/s41591- 022- 01810- 63 Taquet, M., Geddes, J. R., Husain, M., Luciano, S. & Harrison, P. J. 6- month neurological and psychiatric outcomes in 236 379 survivors of COVID- 19: a retrospective cohort study using electronic health records. Lancet Psychiatry 8, 416- 427 (2021). https://doi.org:10.1016/S2215- 0366(21)00084- 54 Monje, M. & Iwasaki, A. The neurobiology of long COVID. Neuron 110, 3484- 3496 (2022). https://doi.org:10.1016/j.neuron.2022.10.0065 Ceban, F. et al. Fatigue and cognitive impairment in Post- COVID- 19 Syndrome: A systematic review and meta- analysis. Brain Behav Immun 101, 93- 135 (2022). https://doi.org:10.1016/j.bbi.2021.12.0206 Hartung, T. J. et al. Fatigue and cognitive impairment after COVID- 19: A prospective multicentre study. EClinicalMedicine 53, 101651 (2022). https://doi.org:10.1016/j.eclinm.2022.1016517 Davis, H. E., McCorkell, L., Vogel, J. M. & Topol, E. J. Long COVID: major findings, mechanisms and recommendations. Nat Rev Microbiol (2023). https://doi.org:10.1038/s41579- 022- 00846- 28 Song, E. et al. Neuroinvasion of SARS- CoV- 2 in human and mouse brain. J Exp Med 218 (2021). https://doi.org:10.1084/jem.20202135 29 Zhang, B. Z. et al. SARS- CoV- 2 infects human neural progenitor cells and brain organoids. Cell Res 30, 928- 931 (2020). https://doi.org:10.1038/s41422- 020- 0390- x 30 Meinhardt, J. et al. Olfactory transmuscol SARS- CoV- 2 invasion as a port of central nervous system entry in individuals with COVID- 19. Nat Neurosci 24, 168- 175 (2021). https://doi.org:10.1038/s41593- 020- 00758- 5311 Pellegrini, L. et al. SARS- CoV- 2 Infects the Brain Choroid Plexus and Disrupts the Blood- CSF Barrier in Human Brain Organoids. Cell Stem Cell 27, 951- 961 e955 (2020). https://doi.org:10.1016/j.stem.2020.10.001 32 Samudyata et al. SARS- CoV- 2 promotes microglial synapse elimination in human brain organoids. Mol Psychiatry (2022). https://doi.org:10.1038/s41380- 022- 01786- 23335 Albornoz, E. A. et al. SARS- CoV- 2 drives NLRP3 inflammasome activation in human microglia through spike protein. Mol Psychiatry (2022). https://doi.org:10.1038/s41380- 022- 01831- 03336 Schwabenland, M. et al. Deep spatial profiling of human COVID- 19 brains reveals neuroinflammation with distinct microanatomical microglia- T- cell interactions. Immunity 54, 1594- 1610 e1511 (2021). https://doi.org:10.1016/j.immuni.2021.06.002
+
+<--- Page Split --->
+
+641 15 Cantuti- Castelvetri, L. et al. Neuropilin- 1 facilitates SARS- CoV- 2 cell entry and infectivity. Science 370, 856- 860 (2020). https://doi.org:10.1126/science.abd2985
+642 16 Stein, S. R. et al. SARS- CoV- 2 infection and persistence in the human body and brain at autopsy. Nature (2022). https://doi.org:10.1038/s41586- 022- 05542- y
+643 17 Douaud, G. et al. SARS- CoV- 2 is associated with changes in brain structure in UK Biobank. Nature 604, 697- 707 (2022). https://doi.org:10.1038/s41586- 022- 04569- 5
+644 18 Mavrikaki, M., Lee, J. D., Solomon, I. H. & Slack, F. J. Severe COVID- 19 is associated with molecular signatures of aging in the human brain. Nature Aging (2022). https://doi.org:10.1038/s43587- 022- 00321- w
+645 19 Lee, S. et al. Virus- induced senescence is a driver and therapeutic target in COVID- 19. Nature 599, 283- 289 (2021). https://doi.org:10.1038/s41586- 021- 03995- 1
+646 20 Lopez- Otin, C., Blasco, M. A., Partridge, L., Serrano, M. & Kroemer, G. Hallmarks of aging: An expanding universe. Cell (2022). https://doi.org:10.1016/j.cell.2022.11.001
+647 21 Di Micco, R., Krizhanovsky, V., Baker, D. & d'Adda di Fagagna, F. Cellular senescence in ageing: from mechanisms to therapeutic opportunities. Nat Rev Mol Cell Biol (2020). https://doi.org:10.1038/s41580- 020- 00314- w
+648 22 Zhang, P. et al. Senolytic therapy alleviates Abeta- associated oligodendrocyte progenitor cell senescence and cognitive deficits in an Alzheimer's disease model. Nat Neurosci 22, 719- 728 (2019). https://doi.org:10.1038/s41593- 019- 0372- 9
+649 23 Bussian, T. J. et al. Clearance of senescent glial cells prevents tau- dependent pathology and cognitive decline. Nature 562, 578- 582 (2018). https://doi.org:10.1038/s41586- 018- 0543- y
+650 24 Ogrodnik, M. et al. Whole- body senescent cell clearance alleviates age- related brain inflammation and cognitive impairment in mice. Aging Cell 20, e13296 (2021). https://doi.org:10.1111/acel.13296
+651 25 Gasek, N. S., Kuchel, G. A., Kirkland, J. L. & Xu, M. Strategies for Targeting Senescent Cells in Human Disease. Nat Aging 1, 870- 879 (2021). https://doi.org:10.1038/s43587- 021- 00121- 8
+652 26 Chaib, S., Tchkonia, T. & Kirkland, J. L. Cellular senescence and senolytics: the path to the clinic. Nat Med 28, 1556- 1568 (2022). https://doi.org:10.1038/s41591- 022- 01923- y
+653 27 He, W. B., Abe, K. & Akaishi, T. Oral administration of fisetin promotes the induction of hippocampal long- term potentiation in vivo. J Pharmacol Sci 136, 42- 45 (2018). https://doi.org:10.1016/j.jphs.2017.12.008
+654 28 Freund, A., Laberge, R. M., Demaria, M. & Campisi, J. Lamin B1 loss is a senescence- associated biomarker. Mol Biol Cell 23, 2066- 2075 (2012). https://doi.org:10.1091/mbc.E11- 10- 0884
+655 29 Spudich, S. & Nath, A. Nervous system consequences of COVID- 19. Science 375, 267- 269 (2022). https://doi.org:10.1126/science.abm2052
+656 30 Ramani, A. et al. SARS- CoV- 2 targets neurons of 3D human brain organoids. EMBO J 39, e106230 (2020). https://doi.org:10.15252/embj.2020106230
+657 31 Schumacher, B., Pothof, J., Vijg, J. & Hoeijmakers, J. H. J. The central role of DNA damage in the ageing process. Nature 592, 695- 703 (2021). https://doi.org:10.1038/s41586- 021- 03307- 7
+658 32 d'Adda di Fagagna, F. et al. A DNA damage checkpoint response in telomere- initiated senescence. Nature 426, 194- 198 (2003). https://doi.org:10.1038/nature02118
+659 33 Kulasinghe, A. et al. Transcriptomic profiling of cardiac tissues from SARS- CoV- 2 patients identifies DNA damage. Immunology (2022). https://doi.org:10.1111/imm.13577
+660 34 Liberzon, A. et al. The Molecular Signatures Database (MSigDB) hallmark gene set collection. Cell Syst 1, 417- 425 (2015). https://doi.org:10.1016/j.cels.2015.12.004
+
+<--- Page Split --->
+
+690 35 Danaher, P. et al. Advances in mixed cell deconvolution enable quantification of cell types 691 in spatial transcriptomic data. Nat Commun 13, 385 (2022). 692 https://doi.org:10.1038/s41467-022-28020-5 693 Kim, J., Matney, C. J., Blankenship, A., Hestrin, S. & Brown, S. P. Layer 6 corticothalamic 694 neurons activate a cortical output layer, layer 5a. J Neurosci 34, 9656-9664 (2014). 695 https://doi.org:10.1523/JNEUROSCI.1325-14.2014 696 McCray, P. B., Jr. et al. Lethal infection of K18-hACE2 mice infected with severe acute 697 respiratory syndrome coronavirus. J Virol 81, 813-821 (2007). 698 https://doi.org:10.1128/JVI.02012-06 699 Krasieva, T. B., Ehren, J., O'Sullivan, T., Tromberg, B. J. & Maher, P. Cell and brain tissue 700 imaging of the flavonoid fisetin using label-free two-photon microscopy. Neurochem Int 701 89, 243-248 (2015). https://doi.org:10.1016/j.neuint.2015.08.003 702 Rosen, B., Kurtishi, A., Vazquez-Jimenez, G. R. & Moller, S. G. The Intersection of 703 Parkinson's Disease, Viral Infections, and COVID-19. Mol Neurobiol 58, 4477-4486 704 (2021). https://doi.org:10.1007/s12035-021-02408-8 705 Xu, E., Xie, Y. & Al-Aly, Z. Long-term neurologic outcomes of COVID-19. Nat Med 28, 2406-2415 (2022). https://doi.org:10.1038/s41591-022-02001-z 706 Escartin, C. et al. Reactive astrocyte nomenclature, definitions, and future directions. Nat 707 Neurosci 24, 312-325 (2021). https://doi.org:10.1038/s41593-020-00783-4 708 Nelke, C., Schroeter, C. B., Pawlitzki, M., Meuth, S. G. & Ruck, T. Cellular senescence in 709 neuroinflammatory disease: new therapies for old cells? Trends Mol Med 28, 850-863 710 (2022). https://doi.org:10.1016/j.molmed.2022.07.003 711 Chinta, S. J. et al. Cellular Senescence Is Induced by the Environmental Neurotoxin 712 Paraquat and Contributes to Neuropathology Linked to Parkinson's Disease. Cell Rep 22, 930-940 (2018). https://doi.org:10.1016/j.celrep.2017.12.092 713 Musi, N. et al. Tau protein aggregation is associated with cellular senescence in the brain. 714 Aging Cell 17, e12840 (2018). https://doi.org:10.1111/ace1.12840 715 Ogrodnik, M. et al. Obesity-Induced Cellular Senescence Drives Anxiety and Impairs 716 Neurogenesis. Cell Metab 29, 1061-1077 e1068 (2019). 717 https://doi.org:10.1016/j.cmet.2018.12.008 718 Sepe, S. et al. DNA damage response at telomeres boosts the transcription of SARS-CoV- 719 2 receptor ACE2 during aging. EMBO Rep 23, e53658 (2022). 720 https://doi.org:10.15252/embr.202153658 721 da Silva, P. F. L. et al. The bystander effect contributes to the accumulation of senescent 722 cells in vivo. Aging Cell 18, e12848 (2019). https://doi.org:10.1111/ace1.12848 723 Golia, M. T. et al. Interplay between inflammation and neural plasticity: Both immune 724 activation and suppression impair LTP and BDNF expression. Brain Behav Immun 81, 484-494 (2019). https://doi.org:10.1016/j.bbi.2019.07.003 725 Camell, C. D. et al. Senolytics reduce coronavirus-related mortality in old mice. Science 726 373 (2021). https://doi.org:10.1126/science.abe4832 727 Aguado, J. et al. Inhibition of the cGAS-STING pathway ameliorates the premature 728 senescence hallmarks of Ataxia-Telangiectasia brain organoids. Aging Cell, e13468 729 (2021). https://doi.org:10.1111/ace1.13468 730 Amarilla, A. A. et al. A versatile reverse genetics platform for SARS-CoV-2 and other 731 positive-strand RNA viruses. Nat Commun 12, 3431 (2021). 732 https://doi.org:10.1038/s41467-021-23779-5 733 Amarilla, A. A. et al. An Optimized High-Throughput Immuno- Plaque Assay for SARS- 734 CoV-2. Front Microbiol 12, 625136 (2021). https://doi.org:10.3389/fmicb.2021.625136
+
+<--- Page Split --->
+
+738 53 Aguado, J. et al. Inhibition of DNA damage response at telomeres improves the detrimental 739 phenotypes of Hutchinson-Gilford Progeria Syndrome. Nat Commun 10, 4990 (2019). 740 https://doi.org:10.1038/s41467-019-13018-3 741 54 Love, M. I., Huber, W. & Anders, S. Moderated estimation of fold change and dispersion 742 for RNA-seq data with DESeq2. Genome Biol 15, 550 (2014). 743 https://doi.org:10.1186/s13059-014-0550-8 744 55 Tyshkovskiy, A. et al. Identification and Application of Gene Expression Signatures 745 Associated with Lifespan Extension. Cell Metab 30, 573-593 e578 (2019). 746 https://doi.org:10.1016/j.cmet.2019.06.018 747 56 Subramanian, A. et al. Gene set enrichment analysis: a knowledge-based approach for 748 interpreting genome-wide expression profiles. Proc Natl Acad Sci U S A 102, 15545-15550 749 (2005). https://doi.org:10.1073/pnas.0506580102 750 57 Isaacs, A. et al. Nucleocapsid Specific Diagnostics for the Detection of Divergent SARS- 751 CoV- 2 Variants. Front Immunol 13, 926262 (2022). 752 https://doi.org:10.3389/fimmu.2022.926262 753 58 Valenzuela Nieto, G. et al. Potent neutralization of clinical isolates of SARS-CoV- 2 D614 754 and G614 variants by a monomeric, sub-nanomolar affinity nanobody. Sci Rep 11, 3318 755 (2021). https://doi.org:10.1038/s41598-021-82833-w
+
+<--- Page Split --->
+
+## Figure legends  
+
+Figure 1 Long- term senolytic treatment prevents selective accumulation of senescent cells in physiologically aged human brain organoids. Brain organoids were generated and grown in vitro for 8 months, and subsequently exposed to two doses (each dose every two weeks) of either navitoclax (2.5 \(\mu \mathrm{M}\) ), ABT- 737 (10 \(\mu \mathrm{M}\) ) or \(\mathrm{D + Q}\) (D: \(10~\mu \mathrm{M}\) ; Q: \(25~\mu \mathrm{M}\) ) administration within the following month, after which the organoids were collected for in situ analysis. (a) SA- \(\beta\) - gal assays were performed on organoid sections. Each data point in the bar graph represents a single organoid analysed. Error bars represent s.d.; at least 8 individual organoids were analysed per condition; one- way ANOVA with Tukey's multiple- comparison post- hoc corrections. (b) Lamin B1 staining was performed on organoid sections. Each data point in the scatter plot represents the integrated intensity of each cell within organoid sections. At least 8 individual organoids were analysed per condition; one- way ANOVA with Tukey's multiple- comparison post- hoc corrections. (c,d) Representative images from quantifications shown in a and b, respectively. Scale bar, \(0.3\mathrm{mm}\) .  
+
+Figure 2 Transcriptomic characterization of distinct senolytic interventions on brain aging hallmarks. Brain organoids were generated and grown in vitro for 8 months, and subsequently exposed to two doses (each dose every two weeks) of either navitoclax (2.5 \(\mu \mathrm{M}\) ), ABT- 737 (10 \(\mu \mathrm{M}\) ) or \(\mathrm{D + Q}\) (D: \(10~\mu \mathrm{M}\) ; Q: \(25~\mu \mathrm{M}\) ) administration within the following month, after which the organoids were collected and subjected for bulk RNA sequencing analysis. (a- c) Volcano plots show vehicle- treated versus (a) navitoclax- , (b) ABT- 737- and (c) \(\mathrm{D + Q}\) - treated brain organoid differential expression of upregulated (blue) and downregulated (red) genes. (d) Venn diagram shows differentially repressed senescence- associated genes among senolytic- treated organoids defined with a significance adjusted P value \(< 0.05\) . (e) Gene Set Enrichment Analysis was carried out using aging hallmark gene sets from the Molecular Signature Database. The statistically significant signatures were selected (FDR \(< 0.25\) ) and placed in order of normalized enrichment score. Bars indicate the pathways enriched in individual senolytic treatments as compared to vehicle- treated brain organoids. (f) Transcriptomic age of organoids treated with either vehicle or senolytic compounds assessed using brain multi- species aging clock. (g) Spearman correlation between gene expression changes induced by senolytics in aged organoids and signatures of aging and established lifespan- extending interventions based on functional enrichment output. Normalized enrichment scores (NES) calculated with GSEA were used to evaluate correlations between pairs of signatures.  
+
+Figure 3 Brains of COVID- 19 patients exhibit increased accumulation of p16 senescent cells. (a) Immunofluorescence images showing DAPI (blue), and p16 (red) immunoreactivity in sections
+
+<--- Page Split --->
+
+of frontal cortex regions from patients with severe COVID- 19 and age- matched non- COVID- related controls. Scale bar, \(50 \mu \mathrm{m}\) . (b) Box plots show the percentage of p16- positive cells. Each data point in the graph represents a single patient analysed, with a total of 2,794,379 individual brain cells across 7 COVID- 19 and 8 non- COVID- 19 patients. Whiskers represent min- max values; two- tailed Student's t- test.  
+
+Figure 4 Neurotropic viral infections elicit virus- induced senescence in human brain organoids. (a) SARS- CoV- 2 variant screening was performed on brain organoids at multiplicity of infection 1 and monitored for SA- \(\beta\) - gal activity at 5 days post infection. Scale bar, \(0.3 \mathrm{mm}\) . (b) Quantification of data presented in a. Bar graphs show the percentage of SA- \(\beta\) - gal- positive cells. Each data point in the bar graph represents a single organoid analysed. Error bars represent s.d.; at least 5 individual organoids were analysed per variant- infected condition; one- way ANOVA with Dunnett's multiple- comparison post- hoc corrections. (c) Representative images of serially sectioned Delta- infected organoid regions stained for SA- \(\beta\) - gal and SARS- CoV- 2 spike protein. (d) Representative images of the region shown in c. co- immunolabelled with p16 and SARS- CoV- 2 nucleocapsid (NC) antigen. (e) Organoids infected for 5 days with the indicated SARS- CoV- 2 variants were stained for \(\gamma \mathrm{H2AX}\) and SARS- CoV- 2 Spike protein. Scale bar, \(40 \mu \mathrm{m}\) . (f) Quantification of data presented in e. Scatter plot show the number of \(\gamma \mathrm{H2AX}\) foci per cell in infected regions (red) versus uninfected counterparts (black). Each data point in the scatter plot represents a single cell analysed; at least 400 cells per variant- infected condition have been analysed; two- tailed Student's t- test. (g) Human brain organoids were infected with the neurotropic flaviviruses Japanese Encephalitis virus (JEV), Rocio virus (ROCV) and Zika virus (ZIKV) at multiplicity of infection 0.1; and monitored SA- \(\beta\) - gal activity 5 days post infection. Box plots show the percentage of SA- \(\beta\) - gal- positive cells. Each data point represents a single organoid analysed. Whiskers represent min- max values; at least 5 individual organoids were analysed per virus- infected condition; one- way ANOVA with multiple- comparison post- hoc corrections. (h- k) Uninfected, Wuhan- and Delta- infected human brain organoids where subjected to Regions of Interest (ROI) selection based on p16 protein expression for spatial profiling by the Nanostring GeoMX digital spatial profiler assay and further sequenced for the GeoMx Human Whole Transcriptome Atlas. Three organoids were used per condition for ROI selection. (h) Representative p16- positive ROIs. (i) Heat map of polarity with shown expression above (blue) and below (red) the mean for each differentially heightened SASP gene of Delta- infected p16- positive ROIs. (j) Senescence heat map gene expression signature of Delta- infected p16- positive cells. (k) Box plots show the expression enrichment of SARS- CoV- 2 genes (Spike, ORF1ab) for each SARS- CoV- 2 variant. Each data point in the box plot represents a normalized fold change
+
+<--- Page Split --->
+
+value of SARS- CoV- 2 genes on p16- positive ROIs relative to p16- negative counterparts (depicted by a grid line). Whiskers represent min- max values; at least \(\mathrm{n} = 3\) p16- positive ROIs were analysed per condition; two- tailed Student's t test.  
+
+Figure 5 Senolytics clear virus- induced senescence in specific neuronal subtypes. (a) Schematic representation of experimental design that applies to b- e. Human brain organoids were SARS- CoV- 2- infected at multiplicity of infection 1 for 5 days and subsequently exposed to the indicated senolytic treatments for 5 additional days. Analysis was performed at the end time point of the 10- day experiment. (b) SA- \(\beta\) - gal activity was evaluated at 10 days post infection. Bar graphs show the percentage of SA- \(\beta\) - gal- positive cells. Each data point in the bar graph represents a single organoid section analysed. Error bars represent s.d.; at least 5 individual organoids were analysed per variant- infected condition; one- way ANOVA with multiple- comparison post- hoc corrections. Scale bar, \(0.3\mathrm{mm}\) . (c) Total RNA from individual organoids uninfected or infected with the SARS- CoV- 2 Delta variant was used to quantify the RNA expression levels of the indicated viral genes and normalized to RPLP0 mRNA and compared to infected vehicle controls. Error bars represent s.e.m.; \(\mathrm{n} = 3\) independent organoids; one- way ANOVA with multiple- comparison post- hoc corrections; nd: not detected. (d) Stacked bars show NanoString GeoMx deconvolved p16- positive ROI cell abundance using constrained log- normal regression from organoids uninfected or infected with the SARS- CoV- 2 Delta variant. L4/5/6 IT Car3: Glutamatergic neurons; L5 ET: Cortical layer 5 pyramidal neurons; L6CT L6b: Corticothalamic (CT) pyramidal neurons in layer 6; CGE: GABAergic ganglionic eminence neurons; EC: Endothelial cells; VLMC: vascular and leptomeningeal cells. (e) Bar graphs show the percentage of deconvolved p16- positive neuronal populations significantly modulated upon SARS- CoV- 2 Delta variant infection and subsequent senolytic interventions. \(\mathrm{n} = 3\) independent ROIs per condition tested; \(* \mathrm{P} < 0.05\) ; one- way ANOVA with multiple- comparison post- hoc corrections.  
+
+Figure 6 Senolytic treatments mitigate COVID- 19 brain pathology in vivo. (a) Schematic representation of experimental design that applies to b- h. K18- hACE2 transgenic mice were exposed to Delta variant infections on day 0 and subsequently treated with the indicated senolytics every other day starting on day 1. Two mouse cohorts were randomly allocated for scheduled euthanasia on day 5 for brain tissue characterisation as well as end time point experiments to monitor clinical score and survival. (b) Kaplan–Meier curve of uninfected mice ( \(\mathrm{n} = 3\) ), and SARS- CoV- 2- infected mice treated with vehicle ( \(\mathrm{n} = 6\) ), fisetin ( \(\mathrm{n} = 9\) ), D+Q ( \(\mathrm{n} = 8\) ), or navitoclax ( \(\mathrm{n} = 8\) ). \(* \mathrm{P} = 0.032\) for vehicle vs fisetin curve comparison; # \(\mathrm{P} = 0.0087\) for vehicle vs D+Q curve comparison; Kaplan–Meier survival analysis. (c) Graph shows the average combined behavioural and physical clinical score over time of uninfected mice ( \(\mathrm{n} = 3\) ), and SARS- CoV- 2- infected mice
+
+<--- Page Split --->
+
+treated with vehicle \(\mathrm{(n = 6)}\) , fisetin \(\mathrm{(n = 8)}\) , \(\mathrm{D + Q}\) \(\mathrm{(n = 8)}\) , or navitoclax \(\mathrm{(n = 8)}\) . Error bars represent s.e.m.; color- coded \(^{*}\mathrm{P}< 0.05\) for comparisons between vehicle and each color- coded senolytic treatment; one- way ANOVA with multiple- comparison post- hoc corrections for every timepoint tested. (d) Total RNA of individual brains from mice uninfected or infected with the SARS- CoV- 2 Delta variant and treated with various senolytic interventions was used to quantify the RNA expression levels of the indicated viral genes and was normalized to \(Rplp0\) mRNA and compared to infected vehicle controls. Error bars represent s.e.m.; \(\mathrm{n} = 8\) mouse brains per condition; one- way ANOVA with multiple- comparison post- hoc corrections; nd: not detected. (e) Total RNA of individual brains from mice uninfected or infected with the SARS- CoV- 2 Delta variant and treated with various senolytic interventions was used to quantify the mRNA expression levels of the indicated senescence and SASP genes and was normalized to \(Rplp0\) mRNA. Each column in the heatmap represents an individual mouse brain analysed. (f) Representative immunofluorescent images of brainstem regions of coronal brain sections from uninfected or infected mice with the SARS- CoV- 2 Delta variant and treated with the indicated senolytics. Samples were immunolabelled with antibodies against TH (red; scale bar, \(100\mu \mathrm{m}\) ) and GFAP (green; scale bar, \(50\mu \mathrm{m}\) ). (g) Quantification of the TH data presented in f. Bar graph shows the intensity of tyrosine hydrolase (TH) staining within the brainstem. Each data point in the bar graph represents a single brain section analysed. Error bars represent s.d.; \(***\mathrm{P}< 0.0001\) ; 3 brains per condition were analysed; one- way ANOVA with multiple- comparison post- hoc corrections. (h) Quantification of the GFAP data presented in f. Dot plot shows the intensity of GFAP per cell within the brainstem. Each data point in the dot blot represents a single cell analysed. \(***\mathrm{P}< 0.0001\) ; 3 brains per condition were analysed; one- way ANOVA with multiple- comparison post- hoc corrections.
+
+<--- Page Split --->
+
+## Supplementary Figure legends  
+
+Supplementary Figure 1. (a) Schematic representation of experimental design that applies to Fig. 1,2 and to Supplementary Fig. 1b- c. 8- month- old human brain organoids were exposed to two doses of the senolytic treatments navitoclax (2.5 \(\mu \mathrm{M}\) ), ABT- 737 (10 \(\mu \mathrm{M}\) ) or D+Q (D: 10 \(\mu \mathrm{M}\) ; Q: 25 \(\mu \mathrm{M}\) ): the first one on day 1 and the second dose on day 16. Analysis was performed at the end time point of the 1- month experiment as well as at initial timepoint of 8 months organoid culture. (b) Heat map shows senescence- associated RNA transcriptomic expression of downregulated genes shared across all three senolytic interventions. (c) Functional enrichment analyses of gene expression signatures and multiple senolytic treatment of brain organoids. Heat map cells are coloured based on the normalized enrichment score (NES).  
+
+Supplementary Figure 2. (a) Representative images of neural progenitors (Sox2), neurons (NeuN), or astrocytes (GFAP) co- stained with SARS- CoV- 2 nucleocapsid protein. Human brain organoids were 3 month- old at time of infection with the indicated SARS- CoV- 2 variants at multiplicity of infection 1. (e) Stacked bar graphs shoe quantifications from d.  
+
+Supplementary Figure 3. (a) Venn diagram on the left shows 485 differentially expressed genes shared across SARS- CoV- 2- infected organoids and postmortem brains of COVID- 19 patients defined with a significance adjusted P value \(< 0.05\) . On the right panel, bar graph indicates the pathways enriched within this 485- gene cohort. Gene Set Enrichment Analysis was carried out using aging hallmark gene sets from the Molecular Signature Database. The statistically significant signatures were selected (FDR \(< 0.25\) ). (b) Volcano plots show uninfected versus either Wuhan or Delta- infected brain organoid differential expression of upregulated (blue) and downregulated (red) genes. DEG analysis was performed from whole- organoid RNA- seq data and p16- positive senescent- cell regions of interest (ROIs) from NanoString spatial transcriptomic sequencing. (c) Bar graph shows quantifications of nucleocapsid- positive cells from brain organoids infected with the indicated SARS- CoV- 2 variants and analysed at 5 days post infection. Each data point in the bar graph represents a single organoid section analysed. Error bars represent s.d.; at least 7 individual organoids were analysed per variant- infected condition; one- way ANOVA with multiple- comparison post- hoc corrections.  
+
+Supplementary Figure 4. (a) Principal component analysis from NanoString spatial transcriptomic sequencing of p16- positive cells in the subspace defined by these differential genes showing clustering of uninfected and Wuhan- infected human brain organoids away from the Delta- infected counterparts. (b) Total RNA from individual organoids uninfected or infected with the SARS- CoV- 2 Delta variant was used to quantify Lamin B1 mRNA expression levels and
+
+<--- Page Split --->
+
+normalized to RPLP0 mRNA and compared to infected vehicle controls. Error bars represent s.d.; \(\mathrm{n} = 3\) independent organoids; one- way ANOVA with multiple- comparison post- hoc corrections. Supplementary Figure 5. (a) Representative immunofluorescent images of viral nucleocapsid (NC) antigen in whole brain coronal sections of brains from SARS- CoV- 2- infected K18- hACE2 transgenic mice (5 days post infection). CTX: Cerebral cortex; BS: Brainstem. (b) Percentage weight loss up to 7 days post infection. Uninfected mice \((\mathrm{n} = 3)\) , and Delta SARS- CoV- 2- infected mice treated with vehicle \((\mathrm{n} = 6)\) , fisetin \((\mathrm{n} = 8)\) , \(\mathrm{D} + \mathrm{Q}\) \((\mathrm{n} = 8)\) , or navitoclax \((\mathrm{n} = 8)\) .
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+ 
+
+<center>C</center> 
+
+![](images/Figure_unknown_1.jpg)
+
+ 
+
+<center>d</center> 
+
+![](images/Figure_3.jpg)
+
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+
+<--- Page Split --->
+![](images/Figure_unknown_2.jpg)
+
+<center>Figure 3</center>  
+
+![](images/Figure_6.jpg)
+
+
+<--- Page Split --->
+![](images/Figure_unknown_3.jpg)
+
+
+<--- Page Split --->
+![](images/Figure_unknown_4.jpg)
+
+<center>Figure 5 </center>  
+
+![](images/Supplementary_Figure_4.jpg)
+
+<center>C </center>  
+
+![](images/Figure_unknown_5.jpg)
+  
+
+![PLACEHOLDER_35_3]
+  
+
+![PLACEHOLDER_35_4]
+
+
+<--- Page Split --->
+![PLACEHOLDER_36_0]
+
+<center>Figure 6 </center>  
+
+![PLACEHOLDER_36_1]
+
+<center>C </center>  
+
+![PLACEHOLDER_36_2]
+
+<center>e </center>  
+
+![PLACEHOLDER_36_3]
+  
+
+![PLACEHOLDER_36_4]
+  
+
+![PLACEHOLDER_36_5]
+  
+
+![PLACEHOLDER_36_6]
+
+
+<--- Page Split --->
+
+Supplementary Figure 1 
+
+a 
+
+![PLACEHOLDER_37_0]
+
+ 
+
+C 
+
+![PLACEHOLDER_37_1]
+
+ 
+
+Epithelial mesenchymal transition
+PI3K AKT mTOR signaling
+Unfolded protein response 
+
+![PLACEHOLDER_37_2]
+
+
+<--- Page Split --->
+
+# Supplementary Figure 2  
+
+![PLACEHOLDER_38_0]
+
+
+<--- Page Split --->
+
+Supplementary Figure 3  
+
+a  
+
+![PLACEHOLDER_39_0]
+  
+
+DEGs from postmortem brains of COVID- 19 patients from Mavrikaki et al.  
+
+![PLACEHOLDER_39_1]
+
+
+<--- Page Split --->
+![PLACEHOLDER_40_0]
+
+<center>Supplementary Figure 4</center>  
+
+![PLACEHOLDER_40_1]
+
+
+<--- Page Split --->
+![PLACEHOLDER_41_0]
+
+<center>a </center>  
+
+![PLACEHOLDER_41_1]
+
+
+<--- Page Split --->
+
+Supplementary Table 1  
+
+<table><tr><td>Primer</td><td>Target</td><td></td><td>Sequence (5&#x27;-3&#x27; orientation)</td></tr><tr><td rowspan="2">RPLP0</td><td rowspan="2">Human and mouse</td><td>Fw</td><td>TTCATTGTGGGAGCAGAC</td></tr><tr><td>Rv</td><td>CAGCAGTTTCTCCAGAGC</td></tr><tr><td rowspan="2">RdRP</td><td rowspan="2">SARS-CoV-2</td><td>Fw</td><td>CATGTGTGGCGGTTCACTAT</td></tr><tr><td>Rv</td><td>TGCATTAACATTGGCCGTGA</td></tr><tr><td rowspan="2">Spike</td><td rowspan="2">SARS-CoV-2</td><td>Fw</td><td>CTACATGCACCAGCAACTGT</td></tr><tr><td>Rv</td><td>CACCTGTGCCTGTTAAACCA</td></tr><tr><td rowspan="2">Envelope</td><td rowspan="2">SARS-CoV-2</td><td>Fw</td><td>TTCGGAAGAGACAGGTACGTT</td></tr><tr><td>Rv</td><td>CACACAATCGATGGCGAGTA</td></tr><tr><td rowspan="2">Nucleocapsid</td><td rowspan="2">SARS-CoV-2</td><td>Fw</td><td>CAATGCTGCAATCGTGCTAC</td></tr><tr><td>Rv</td><td>GTTGCGACTACGTGATGAGG</td></tr><tr><td rowspan="2">Lamin B1</td><td rowspan="2">Human</td><td>Fw</td><td>CTCTCGTCGCATGCTGACAG</td></tr><tr><td>Rv</td><td>TCCCTTATTTCCGCCATCTCT</td></tr><tr><td rowspan="2">II8</td><td rowspan="2">Mouse</td><td>Fw</td><td>GTCCTTAACCTAGGCATCTTCG</td></tr><tr><td>Rv</td><td>TCTGTTGCAGTAAATGGTCTCG</td></tr><tr><td rowspan="2">II6</td><td rowspan="2">Mouse</td><td>Fw</td><td>GCTACCAAACTGGATATAATCAGGA</td></tr><tr><td>Rv</td><td>CCAGGTAGCTATGGTACTCCAGAA</td></tr><tr><td rowspan="2">p16</td><td rowspan="2">Mouse</td><td>Fw</td><td>AATCTCCGCGAGGAAAGC</td></tr><tr><td>Rv</td><td>GTCTGCAGCGGACTCCAT</td></tr><tr><td rowspan="2">Mmp12</td><td rowspan="2">Mouse</td><td>Fw</td><td>TTCATGAACAGCAACAAGGAA</td></tr><tr><td>Rv</td><td>TTGATGGCAAGGTGGTACA</td></tr><tr><td rowspan="2">II1a</td><td rowspan="2">Mouse</td><td>Fw</td><td>TTGGTTAAATGACCTGCAAAC</td></tr><tr><td>Rv</td><td>GAGCGCTCACGAACAGTTG</td></tr><tr><td rowspan="2">Ccl2</td><td rowspan="2">Mouse</td><td>Fw</td><td>CATCCACGTGTTGGCTCA</td></tr><tr><td>Rv</td><td>GATCATCTTGCTGGTGAATGAGT</td></tr><tr><td rowspan="2">II1b</td><td rowspan="2">Mouse</td><td>Fw</td><td>AGTTGACGGACCCCAAAAG</td></tr><tr><td>Rv</td><td>AGCTGGATGCTCTCATCAGG</td></tr><tr><td rowspan="2">Cxcl10</td><td rowspan="2">Mouse</td><td>Fw</td><td>GCCGTCATTTTCTGCCCTA</td></tr><tr><td>Rv</td><td>CGTTCCTTGCGAGAGGGATC</td></tr></table>
+
+<--- Page Split --->

preprint/preprint__00071c19a357d74c148b616e4f6f54f029c63bf7dc9c70b0f9dba908075f6ed8/images_list.json

@@ -0,0 +1,220 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Methodological framework. A. List of 27 tissues used in this study. B. Distribution of 19,132 genes by the number of tissues in which they are highly expressed. C. Bimodal expression is a property of a gene-tissue pair. We tested 516,564 gene-tissue pairs (19,132 genes x 27 tissues) for bimodal expression across individuals. When a gene-tissue pair exhibits switch-like (bimodal) expression, the individuals divide into two subpopulations: one with the gene switched off, and the other with the gene switched on.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        115,
+        880,
+        500
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Categorization of switch-like genes. A. PCA analysis of tissue-pair correlations of gene expression. Each point represents a gene. When we perform PCA on the tissue-to-tissue co-expression vectors for 19,132 genes, the switch-like genes divide into two clusters. Cluster 1 primarily represents genes that are bimodally expressed in a tissue-specific manner, while cluster 2 represents genes that are bimodally expressed in at least all non-sex-specific tissues. B. Performing PCA on the co-expression vectors of only switch-like genes further divides cluster 2 into two subclusters: cluster 2A, which contains genes that are bimodally expressed across all 27 tissues, and cluster 2B, which contains genes that are bimodally expressed in all 22 tissues common to both sexes, but not in the five sex-specific tissues. C-E. Violin plots display the expression levels in all 27 tissues for representative genes from cluster 1, cluster 2A, and cluster 2B, respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        90,
+        880,
+        518
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. An example of a polymorphic gene deletion resulting in universally switch-like gene expression. A. FAM106A and USP32P2 (not drawn to scale) are overlapping genes on chromosome 17. Two alternative haplotype classes exist for these genes: one in which both genes are completely deleted and the other without the deletion. B. Frequency distribution of the deletion across diverse populations. Each pie chart represents one of the 26 populations from the 1000 Genomes Project. Purple indicates the frequency of the deletion, while gray indicates the frequency of the alternative haplotype. C-D. Expression level distribution in the cerebellum (as an example) across individuals for FAM106A and USP32P2,",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Characterization of genuine tissue-specific switch-like genes (cluster 1). The results shown here exclude genes that showed switch-like expression due to confounding factors like ischemic time. A. Number of tissue-specific switch-like genes showing bimodal expression in each of the 27 tissues. The stomach, vagina, breast, and colon show disproportionately more tissue-specific switch-like genes than other tissues. B. An illustration of how Pearson's correlation coefficients were calculated for each pair of bimodally expressed tissue-specific switch-like genes within the stomach, vagina, breast, and colon. We show the scatterplots for two arbitrarily chosen gene pairs for each of the four tissues. The axes in each dot plot represent the \\(\\log (TPM + 1)\\) for the labeled gene in the relevant tissue. Panel C was generated using the pairwise correlation coefficients thus obtained. C. Tissue-specific switch-like genes within the four tissues shown are highly co-expressed. Tissue-specific master regulators, such as endocrinological signals, likely drive their concordant on and off states.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        280,
+        875,
+        673
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. Sex-biased expression of tissue-specific switch-like genes (cluster 1). A. Number of tissue-specific switch-like genes that show female- and male-biased expression. Only those tissues are shown that have at least one tissue-specific switch-like gene showing sex bias. The number in the central grid next to each tissue image represents the number of genuine tissue-specific switch-like genes in that tissue. In orange, the numbers to the left of the central grid indicate the count of female-biased genes in each of the 10 tissues shown. In blue, the numbers to the right of the grid indicate the count of male-biased genes. B. Violin plots showing the expression level distribution in the breast for five female-biased tissue-specific switch-like genes discussed in the main text.",
+    "footnote": [],
+    "bbox": [
+      [
+        117,
+        90,
+        875,
+        640
+      ]
+    ],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. Atrophy-linked switch-like genes tend to be either all switched off, or all switched on within individuals. A. The distribution of expression levels in the vagina of the six switch-like genes implicated in vaginal atrophy. The x-axes represent \\(\\log (TPM + 1)\\) values for each gene in the vagina, and the y-axes represent the probability density. We obtained the probability densities using kernel density estimation. In each case, the global minimum (excluding endpoints) is considered the switching threshold. A gene is deemed “on” in an individual if the expression level is above this threshold; otherwise, the gene is deemed “off.” B. Pairwise concordance rates (percentage of individuals in which the two genes are either both switched on or both switched off).",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        88,
+        850,
+        740
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Figure 8. ALOX12 is a passenger gene. A. Model for the etiology of vaginal atrophy. High levels of",
+    "footnote": [],
+    "bbox": [
+      [
+        114,
+        88,
+        875,
+        850
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Figure S1. The mean tissue-to-tissue co-expression of genes shows a near-perfect correlation with PC1.",
+    "footnote": [],
+    "bbox": [
+      [
+        117,
+        271,
+        644,
+        569
+      ]
+    ],
+    "page_idx": 16
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "Figure S2. Violin plots for expression level distributions of switch-like genes in cluster 2A.",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        88,
+        884,
+        711
+      ]
+    ],
+    "page_idx": 24
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "Figure S3. Violin plots for expression level distributions of switch-like genes in cluster 2A.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        90,
+        880,
+        602
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "**Figure S4. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of 5%.**",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        285,
+        880,
+        722
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "Figure S5. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of 10%.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        88,
+        875,
+        530
+      ]
+    ],
+    "page_idx": 29
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "Figure S6. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of \\(50\\%\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        90,
+        875,
+        528
+      ]
+    ],
+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_6.jpg",
+    "caption": "Figure S7. Switch-like genes in cluster 1 that are genuine versus those affected by confounders.",
+    "footnote": [],
+    "bbox": [
+      [
+        116,
+        177,
+        680,
+        519
+      ]
+    ],
+    "page_idx": 31
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_7.jpg",
+    "caption": "Figure S8. Examples of cluster-1 genes affected by confounders. Their bimodal distribution is caused by ischemic time (a confounding factor).",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        92,
+        700,
+        465
+      ]
+    ],
+    "page_idx": 32
+  }
+]

preprint/preprint__00071c19a357d74c148b616e4f6f54f029c63bf7dc9c70b0f9dba908075f6ed8/preprint__00071c19a357d74c148b616e4f6f54f029c63bf7dc9c70b0f9dba908075f6ed8.mmd

@@ -0,0 +1,584 @@
+
+# Switch-like Gene Expression Modulates Disease Susceptibility  
+
+Omer Gokcumen gokcumen@gmail.com  
+
+Article  
+
+Keywords:  
+
+Posted Date: September 13th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4974188/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on June 18th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 60513- x.
+
+<--- Page Split --->
+
+# Switch-like Gene Expression Modulates Disease Susceptibility  
+
+Authors: Alber Aqil<sup>1, †</sup>, Yanyan Li<sup>2, †</sup>, Zhiliang Wang<sup>2</sup>, Saiful Islam<sup>3</sup>, Madison Russell<sup>2</sup>, Theodora Kunovac Kallak<sup>4</sup>, Marie Saitou<sup>5</sup>, Omer Gokcumen<sup>1, †</sup>, Naoki Masuda<sup>2,3, †</sup>  
+
+## Affiliations:  
+
+1. Department of Biological Sciences, State University of New York at Buffalo, Buffalo, NY, USA.  
+2. Department of Mathematics, State University of New York at Buffalo, Buffalo, NY, USA.  
+3. Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo, Buffalo, NY, USA.  
+4. Department of Women's and Children's Health, Uppsala University, Uppsala, Sweden.  
+5. Faculty of Biosciences, Norwegian University of Life Sciences, Aas, Norway  
+
+Correspondence: Omer Gokcumen, gokcumen@gmail.com Naoki Masuda, naokimas@gmail.com  
+
+## Abstract  
+
+A fundamental challenge in biomedicine is understanding the mechanisms predisposing individuals to disease. While previous research has suggested that switch- like gene expression is crucial in driving biological variation and disease susceptibility, a systematic analysis across multiple tissues is still lacking. By analyzing transcriptomes from 943 individuals across 27 tissues, we identified 1,013 switch- like genes. We found that only 31 (3.1%) of these genes exhibit switch- like behavior across all tissues. These universally switch- like genes appear to be genetically driven, with large exonic genomic structural variants explaining five ( \(\sim 18\%\) ) of them. The remaining switch- like genes exhibit tissue- specific expression patterns. Notably, tissue- specific switch- like genes tend to be switched on or off in unison within individuals, likely under the influence of tissue- specific master regulators, including hormonal signals. Among our most significant findings, we identified hundreds of concordantly switched- off genes in the stomach and vagina that are linked to gastric cancer (41- fold, \(p< 10^{- 4}\) ) and vaginal atrophy (44- fold, \(p< 10^{- 4}\) ), respectively. Experimental analysis of vaginal tissues revealed that low systemic levels of estrogen lead to a significant reduction in both the epithelial thickness and the expression of the switch- like gene ALOX12. We propose a model wherein the switching off of driver genes in basal and parabasal epithelium suppresses cell proliferation therein, leading to epithelial thinning and, therefore, vaginal atrophy. Our findings underscore the significant biomedical implications of switch- like gene expression and lay the groundwork for potential diagnostic and therapeutic applications.
+
+<--- Page Split --->
+
+## Introduction  
+
+The study of gene expression began in earnest with the characterization of lactose- metabolizing switch- like genes in \(E\) coli 1. The presence of lactose triggered the production of enzymes needed to metabolize it, while these enzymes were absent when lactose was not present. These genes acted like switches, toggling between "on" and "off" states based on the presence or absence of lactose, respectively. In subsequent decades, the discovery of enhancer elements 2- 4, epigenetic modifications 5- 8, and transcription factor dynamics 9 revealed that gene expression in humans is more nuanced, resembling a dimmer more often than a simple on- and- off mechanism. Consequently, the study of switch- like genes in humans was largely relegated to the narrow realm of Mendelian diseases 10- 12.  
+
+The recent availability of population- level RNA- sequencing data from humans has made it possible to systematically identify switch- like versus dimmer- like genes. For dimmer- like genes in a given tissue, we expect expression levels across individuals to be continuously distributed with a single mode, i.e., a unimodal distribution. In contrast, expression levels of switch- like genes in a given tissue are expected to exhibit a bimodal distribution, with one mode representing the "off" state and the other representing the "on" state. As we will detail, bimodal expression across individuals is a characteristic of a gene in a specific tissue, referred to as a gene- tissue pair. We define a gene as switch- like if it exhibits bimodal expression in at least one tissue. Most of the recent studies on bimodal gene expression are related to cancer biology, associating on and off states to different disease phenotypes and their prognoses 13- 15. These cancer studies have already produced promising results for personalized medicine 16. However, to our knowledge, the only study focusing on switch- like genes in non- cancerous tissues across individuals restricted their analysis to muscle tissue 17. As a result, the dynamics of switch- like expression across the multi- tissue landscape remain unknown. We hypothesize that switch- like expression is ubiquitous but often tissue- specific. We further hypothesize that these tissue- specific expression trends underlie common disease states. Therefore, the analysis of switch- like genes across tissues and individuals may provide a means for early diagnosis and prediction of human disease.  
+
+Here, we systematically identified switch- like genes across individuals in 27 tissues. Our results explain the regulatory bases of switch- like expression in humans, highlighting genomic structural variation as a major factor underlying correlated switch- like expression in multiple tissues. Furthermore, we identified groups of switch- like genes in the stomach and vagina for which the "off" state predisposes individuals to gastric cancer and vaginal atrophy, respectively. Overall, these findings improve our understanding of the regulation of switch- like genes in humans. They also suggest promising future paths for preventative biomedical interventions.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Methodological framework. A. List of 27 tissues used in this study. B. Distribution of 19,132 genes by the number of tissues in which they are highly expressed. C. Bimodal expression is a property of a gene-tissue pair. We tested 516,564 gene-tissue pairs (19,132 genes x 27 tissues) for bimodal expression across individuals. When a gene-tissue pair exhibits switch-like (bimodal) expression, the individuals divide into two subpopulations: one with the gene switched off, and the other with the gene switched on. </center>
+
+<--- Page Split --->
+
+## RESULTS  
+
+## Tissue-specificity of bimodal expression  
+
+The misregulation of highly expressed genes often has consequences for health and fitness. To systematically identify biomedically relevant switch- like genes in humans, we focused on 19,132 genes that are highly expressed (mean \(\mathrm{TPM} > 10\) ) in at least one of the 27 tissues represented in the GTEx database (Figure 1A; Figure 1B; Table S1). For each of the 516,564 gene- tissue pairs (19,132 genes \(\times 27\) tissues), we applied the dip test of unimodality \(^{18}\) to the expression level distribution across individuals (Figure 1C). Employing the Bejamini- Hochberg procedure for multiple hypotheses correction, we identified 1,013 switch- like genes (Figure 1C; Methods; Table S2). The expression of these genes is bimodally distributed in at least one tissue, such that it is switched "off" for one subset of individuals and switched "on" for the rest of the individuals.  
+
+Expression of different switch- like genes may be bimodally distributed in different numbers of tissues. We contend that genes that are bimodally expressed across all tissues are likely so due to a germline genetic polymorphism driving switch- like expression across tissues. If this is the case, the expression of these genes would be highly correlated across pairs of tissues. Given this insight, discovering universally bimodal genes is more tractable using tissue- to- tissue co- expression of each gene. Therefore, for each gene, we calculated the pairwise correlation of expression levels across pairs of tissues (Methods; Table S3). To visualize tissue- to- tissue co- expression patterns of genes, we performed principal component analysis (PCA) on the tissue- to- tissue gene co- expression data (Table S4). We emphasize that we are referring to the co- expression of the same gene across pairs of tissues instead of the co- expression of pairs of genes in the same tissue. In the space spanned by the first two principal components (explaining \(35.3\%\) and \(3.47\%\) of the variance, respectively), switch- like genes form two major clusters (cluster 1 and cluster 2; Methods), dividing along PC1 (Figure 2A). Applying PCA exclusively to switch- like genes reveals the further division of cluster 2 into two distinct subclusters – cluster 2A and cluster 2B – in the space spanned by the first two principal components (explaining \(58.1\%\) and \(4.25\%\) of the variance, respectively) (Figure 2B; Table S5).  
+
+Manual inspection reveals that cluster 1, which contains 954 genes, represents genes, such as KRT17, with bimodal expression in a small subset of tissues (Figure 2C). Cluster 2A consists of 23 genes, such as GPX1P1, with bimodal expression in all tissues (Figure 2D). Lastly, cluster 2B represents eight genes, such as EIF1AY, with bimodal expression in all non- sex- specific tissues but not in sex- specific tissues (Figure 2E). We will refer to genes in cluster 1 as "tissue- specific switch- like genes." Although some of them are bimodally expressed in more than one tissue, these genes tend to exhibit high tissue specificity in their bimodal expression. Genes in cluster 2 will be referred to as "universally switch- like genes."
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Categorization of switch-like genes. A. PCA analysis of tissue-pair correlations of gene expression. Each point represents a gene. When we perform PCA on the tissue-to-tissue co-expression vectors for 19,132 genes, the switch-like genes divide into two clusters. Cluster 1 primarily represents genes that are bimodally expressed in a tissue-specific manner, while cluster 2 represents genes that are bimodally expressed in at least all non-sex-specific tissues. B. Performing PCA on the co-expression vectors of only switch-like genes further divides cluster 2 into two subclusters: cluster 2A, which contains genes that are bimodally expressed across all 27 tissues, and cluster 2B, which contains genes that are bimodally expressed in all 22 tissues common to both sexes, but not in the five sex-specific tissues. C-E. Violin plots display the expression levels in all 27 tissues for representative genes from cluster 1, cluster 2A, and cluster 2B, respectively. </center>  
+
+## Genetic variation underlies universally switch-like genes  
+
+We found that \(3.1\%\) of all switch- like genes (i.e., the proportion of switch- like genes that are in cluster 2) show clear bimodal expression, at least in all tissues common to both sexes. We contend that germline genetic variation across individuals likely underlies the universally switch- like gene expression, specifically due to four major types of genetic variants. Firstly, we expect genes on the Y chromosome to show bimodal expression in all tissues common to both sexes since these genes are present in males and absent in females (Figure 3A). Consistent with this reasoning, seven out of the eight genes in cluster 2B lie within the male- specific region of the Y- chromosome \(^{19}\) ; the remaining
+
+<--- Page Split --->
+
+gene in cluster 2B is XIST, showing female- specific expression. Secondly, a homozygous gene deletion would result in the gene being switched off (Figure 3B). We found five such genes in cluster 2A for which genomic structural variants likely underlie the observed universally switch- like expression; four genes are affected by gene deletions, and the remaining one by an insertion into the gene. Thirdly, the homozygous deletion of a regulatory element can also switch off a gene (Figure 3C). While we did not find any examples of this scenario, it remains a theoretical possibility. Lastly, a loss- of- function single nucleotide variant (SNV) or short indel, which disrupts gene function, can switch off the gene (Figure 3D). We identified five genes in cluster 2A where such SNVs cause universal bimodality.  
+
+Remarkably, we could genetically explain the expression of 10 out of 23 (43%) cases in cluster 2A despite the small number of genes fitting our conservative definition for universally switch- like genes. SNVs underlie five of these cases (Figure 3B), while structural variants underlie the remaining five cases (Figure 3D). Thus, out of the 10 cases where we can explain the genetic underpinnings of switch- like expression, 50% involve genomic structural variation, highlighting the importance of this type of genetic variation. Although we could not identify the genetic variation underlying the bimodal expression of the remaining 13 genes in cluster 2A, their consistent and highly correlated switch- like expression across all tissues strongly suggests a genetic basis. We anticipate that better resolution assemblies and detailed regulatory sequence annotations will help identify the genetic variants responsible for the remaining universally switch- like genes.  
+
+![](images/Figure_4.jpg)
+
+
+<--- Page Split --->
+
+Figure 3. Genetic bases of universally switch-like gene expression (cluster 2). A. Genes on the Y chromosome are expressed only in males, leading to bimodal expression in non- sex- specific tissues. B. Common structural variants, such as deletions or insertions, may lead to increased, decreased, or no expression in all tissues relative to individuals who carry the alternative allele. C. Common structural variants affecting a genomic region regulating a gene may lead to increased, decreased, or no expression in all tissues, relative to individuals who carry the alternative allele. D. Common single nucleotide variants or short indels affecting a gene or its regulatory region may lead to increased, decreased, or no expression in all tissues relative to individuals who carry the alternative allele.  
+
+We highlight a clear example of a common structural variant leading to universally switch- like expression (Figure 3B). USP32P2 and FAM106A – both universally switch- like genes – are bimodally expressed in all 27 tissues. Both genes show high levels of tissue- to- tissue co- expression. A common 46 kb deletion (esv3640153), with a global allele frequency of \(\sim 25\%\) , completely deletes both genes (Figure 4A- B). We propose that this deletion accounts for the universal switch- like expression of both USP32P2 and FAM106A in all tissues. For illustration, we show the expression level distributions of USP32P2 and FAM106A in the cerebellum (Figures 4C- D). Indeed, the haplotype harboring this deletion is strongly associated with the downregulation of both genes in all 27 tissues \((p< 10^{- 5}\) for every single gene- tissue pair, Methods). We note that the under- expression of USP32P2 in sperm is associated with male infertility \(^{20}\) , and plausibly, homozygous males for the deletion may be prone to infertility. Additionally, FAM106A interacts with SARS- CoV- 2 and is downregulated after infection, at least in lung- epithelial cells \(^{21 - 23}\) . Individuals with FAM106A already switched off may develop more severe COVID- 19 symptoms upon infection, though further investigation is needed. The case of FAM106A and USP32P2 exemplifies the link between disease and bimodal gene expression, a theme we will explore further in the remainder of this text.  
+
+We caution that we base our results regarding bimodality on expression at the RNA level. The bimodal expression of genes across individuals at the RNA level may not necessarily lead to bimodal expression at the protein level. For example, the universally switch- like expression of RPS26 at the RNA level can be explained by a single nucleotide variant (rs1131017) in the gene's 5'- untranslated region (UTR). In particular, RPS26 has three transcription states based on the SNV genotypes. The ancestral homozygote C/C corresponds to a high transcription state, the heterozygote C/G to a medium state, and the derived homozygote G/G to a low state (See Supplement for a discussion on why an expression distribution driven by three genotypes at a polymorphic site might still appear bimodal). Remarkably, this pattern is reversed at the translation level \(^{24}\) : Messenger RNA carrying the derived G allele produces significantly more protein. This reversal may be due to a SNV in the 5'- UTR that can abolish a translation- initiation codon \(^{25}\) . This finding demonstrates how the same SNV can regulate a gene's expression level in opposite directions during transcription and translation. This multi- level regulation in opposite directions likely serves to dampen protein expression variability. It has been shown previously that RNA variability is greater than protein variability in primates \(^{26,27}\) ; the presence of dampening variants discussed here may be one reason behind these findings. Such compensatory mechanisms for gene expression remain fascinating areas for future research.
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 4. An example of a polymorphic gene deletion resulting in universally switch-like gene expression. A. FAM106A and USP32P2 (not drawn to scale) are overlapping genes on chromosome 17. Two alternative haplotype classes exist for these genes: one in which both genes are completely deleted and the other without the deletion. B. Frequency distribution of the deletion across diverse populations. Each pie chart represents one of the 26 populations from the 1000 Genomes Project. Purple indicates the frequency of the deletion, while gray indicates the frequency of the alternative haplotype. C-D. Expression level distribution in the cerebellum (as an example) across individuals for FAM106A and USP32P2, </center>
+
+<--- Page Split --->
+
+respectively. The gene deletion presumably leads to the switched- off expression state in both genes.  
+
+## Tissue-specific switch-like genes have a shared regulatory framework  
+
+Tissue- specific expression patterns are crucial for tissue function. Thus, we now turn our attention to tissue- specific switch- like genes. We found that the stomach, vagina, breast, and colon show a higher number of tissue- specific switch- like genes compared to other tissues (Figure 5A), after controlling for confounding factors (Methods; Supplement; Table S6). Furthermore, within these tissues, the expression of switch- like genes is not independent; instead, they exhibit high pairwise co- expression between genes (Figure 5B- C; Table S7). Hence, tissue- specific switch- like genes tend to be either all switched off or switched on within an individual. This result suggests a shared regulatory mechanism for the expression of these genes in each tissue. Given that hormonal regulation plays a substantial role in shaping tissue- specific expression patterns \(^{28,29}\) , we hypothesize that hormones may regulate genes that are bimodally expressed in specific tissues (cluster 1; Figure 2B).  
+
+Sexual differences in hormonal activity are well documented \(^{30,31}\) . To explore this further, we investigated whether hormone- mediated sex- biased expression underlies the co- expression of tissue- specific switch- like genes within tissues. Under this scenario, a gene would be largely switched on in one sex and off in the other in a given tissue. Among tissue- specific switch- like genes, we identified 186 gene- tissue pairs with sex- biased bimodal expression (Figure 6A; Table S8). These instances are biologically relevant; for example, we found switch- like immunoglobulins genes with female- biased expression in the thyroid, heart, tibial nerve, and subcutaneous adipose tissue. This observation may relate to previous findings \(^{32,33}\) of higher antibody responses to diverse antigens in females than in males.  
+
+More dramatically, we found that 162 out of 164 tissue- specific switch- like genes (cluster 1) in the breast tissue are female- biased, explaining their correlated expression levels (Figure 6A). However, the sex- based disparity in the on- versus- off states of these genes is not absolute, but rather a statistical tendency. In other words, the gene is not switched off in all males and switched on in all females. Instead, the proportion of individuals with the gene switched on significantly differs between sexes. Notably, multiple sex- biased switch- like genes—including SPINT1 and SPINT2 \(^{34}\) , multiple keratin genes \(^{35}\) , and the oxytocin receptor gene \(^{36,37}\) (OXTR; Figure 6B)—in the breast tissue are differentially expressed in breast cancers relative to matched non- cancerous tissues. Future investigations could reveal whether the toggling of these genetic switches affects breast cancer risk in females. We caution that sex- biased switch- like expression in the breast may result from differences in cell- type abundance between females and males. Nevertheless, the differential expression of some genes between sexes might developmentally drive such differences in cell- type abundance. In summary, our results indicate that sex is a major contributor to bimodal gene expression, with breast tissue standing out as particularly sex- biased in this context.  
+
+We note that the intra- tissue co- expression of tissue- specific switch- like genes in the
+
+<--- Page Split --->
+
+stomach and colon cannot be explained by sex. By biological definition, the variation in vaginal expression levels in our sample is not sex- biased. Thus, the intra- tissue co- expression of tissue- specific switch- like genes in the stomach, colon, and vagina may be explained by one of two reasons: 1) Most of the tissue- specific switch- like genes in each tissue are directly regulated by the same hormone in that tissue, or 2) Most of the tissue- specific switch- like genes in each tissue are regulated by the same transcription factor which is, in turn, under regulation by a hormone or other cellular environmental factors. In the case of hormonally controlled gene expression, genes are likely switched off when the systemic hormone levels drop below a certain threshold. We will discuss this idea further, specifically for the vagina, later in the text.  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 5. Characterization of genuine tissue-specific switch-like genes (cluster 1). The results shown here exclude genes that showed switch-like expression due to confounding factors like ischemic time. A. Number of tissue-specific switch-like genes showing bimodal expression in each of the 27 tissues. The stomach, vagina, breast, and colon show disproportionately more tissue-specific switch-like genes than other tissues. B. An illustration of how Pearson's correlation coefficients were calculated for each pair of bimodally expressed tissue-specific switch-like genes within the stomach, vagina, breast, and colon. We show the scatterplots for two arbitrarily chosen gene pairs for each of the four tissues. The axes in each dot plot represent the \(\log (TPM + 1)\) for the labeled gene in the relevant tissue. Panel C was generated using the pairwise correlation coefficients thus obtained. C. Tissue-specific switch-like genes within the four tissues shown are highly co-expressed. Tissue-specific master regulators, such as endocrinological signals, likely drive their concordant on and off states. </center>
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Figure 6. Sex-biased expression of tissue-specific switch-like genes (cluster 1). A. Number of tissue-specific switch-like genes that show female- and male-biased expression. Only those tissues are shown that have at least one tissue-specific switch-like gene showing sex bias. The number in the central grid next to each tissue image represents the number of genuine tissue-specific switch-like genes in that tissue. In orange, the numbers to the left of the central grid indicate the count of female-biased genes in each of the 10 tissues shown. In blue, the numbers to the right of the grid indicate the count of male-biased genes. B. Violin plots showing the expression level distribution in the breast for five female-biased tissue-specific switch-like genes discussed in the main text. </center>  
+
+## Concordantly switched-off genes in the stomach may indicate a predisposition to gastric cancer  
+
+Gene expression levels have been studied as a diagnostic marker for disease states \(^{38}\) .
+
+<--- Page Split --->
+
+Therefore, we asked whether tissue- specific switch- like genes co- expressed with each other across individuals are linked to human disease, with each of the two expression states corresponding to different risks. To address this question, we investigated whether the identified switch- like genes in a given tissue are overrepresented among genes implicated in diseases of the same tissue.  
+
+We overlapped the switch- like genes in the stomach with a previously published list \(^{39}\) of differentially expressed genes in gastric carcinomas. We found that switch- like genes in the stomach are significantly enriched (41- fold enrichment, \(p< 10^{- 4}\) ) among genes that are downregulated in gastric carcinomas. Specifically, nine switch- like genes are downregulated in gastric carcinomas (ATP4A, ATP4B, CHIA, CXCL17, FBP2, KCNE2, MUC6, TMEM184A, and PGA3). Additionally, these nine genes are concordantly expressed in \(92.5\%\) (332/359) of the stomach samples, being either all switched off or on in a given individual (Methods). Our data suggest that individuals with these nine genes switched off in the stomach may be susceptible to developing cancers. This preliminary observation provides exciting avenues to investigate both the cause of the concordant toggling of these genes and their potential role in cancer development.  
+
+## Concordantly switched-off genes result in vaginal atrophy  
+
+We found that switch- like genes in the vagina are significantly overrepresented (44- fold enrichment; \(p< 10^{- 4}\) ; see methods) among genes linked to vaginal atrophy in postmenopausal women. Vaginal atrophy, affecting nearly half of postmenopausal women, is triggered by sustained low levels of systemic estrogen and is marked by increased microbial diversity, higher pH, and thinning of the epithelial layer in the vagina \(^{40,41}\) . It is also known as atrophic vaginitis, vulvovaginal atrophy, estrogen- deficient vaginitis, urogenital atrophy, or genitourinary syndrome of menopause, depending on the specialty of the researchers. Symptoms experienced by women include dryness, soreness, burning, decreased arousal, pain during intercourse, and incontinence \(^{42}\) . Our analysis of switch- like genes in the vagina provides new insights into the development of vaginal atrophy.  
+
+Specifically, we overlapped a previously published list \(^{43}\) of genes that are transcriptionally downregulated in vaginal atrophy with our list of bimodally expressed genes in the vagina. We found that the genes SPINK7, ALOX12, DSG1, KRTDAP, KRT1, and CRISP3 are both bimodally expressed in the vagina and transcriptionally downregulated (presumably switched off) in women with vaginal atrophy (Figure 7A). We refer to these genes as "atrophy- linked switch- like genes." Indeed, these six genes are either all switched on, or all switched off concordantly in \(84\%\) (131/156) of the vaginal samples we studied. The pairwise concordance rates (percentage of individuals with both genes switched on or both genes switched off) for these genes are shown in Figure 7B. Among postmenopausal women with this concordant gene expression, \(50\%\) are in the "off" state – a fraction that closely matches the prevalence of vaginal atrophy in postmenopausal women \(^{40,44}\) . Therefore, our data suggest that estrogen- dependent transcription underlies concordant expression of atrophy- linked switch- like genes, with
+
+<--- Page Split --->
+
+the "off" state of these genes associated with vaginal atrophy.  
+
+For background, the vaginal epithelial layers are differentiated from the inside out. The basal and parabasal layers of the epithelium consist of mitotic progenitor cells with differentiation potential, while the outermost layer comprises the most differentiated cells \(^{45,46}\) . When basal and parabasal cells stop proliferating, the death of mature cells leads to a thin epithelium, and the symptoms of vaginal atrophy appear. Given this background, atrophy- linked switch- like genes may either be a cause or a consequence of vaginal atrophy. In particular, if an atrophy- linked switch- like gene encodes a protein necessary for the continued proliferation and differentiation of basal and parabasal cells, we call it a "driver" gene. In the absence of the driver gene's protein, cell differentiation ceases, and the outer layer gradually disappears, resulting in vaginal atrophy (Figure 8A). On the other hand, if the product of an atrophy- linked switch- like gene is not required for basal and parabasal cell proliferation, we refer to it as a "passenger" gene, borrowing the terminology from cancer literature \(^{47}\) . In healthy vaginas with a thick epithelium, there are more cells in which passenger genes would be expressed. By contrast, in atrophic vaginas, the epithelium thins, resulting in fewer cells where these genes can be expressed. This contrast would lead to the bimodal expression of passenger genes across vagina samples in whole- tissue RNA- sequencing datasets. We hypothesize that at least some of the atrophy- linked switch- like genes are driver genes.  
+
+Two key findings allowed us to construct this hypothesis. Firstly, switch- like genes in the vagina show a 26- fold ontological enrichment for the establishment of the skin barrier \(\mathrm{(FDR = 1.26\times 10^{- 6})}\) and a 25- fold enrichment for keratinocyte proliferation \(\mathrm{(FDR = 1.75\times}\) \(10^{- 4})\) , both related to epithelial thickness and differentiation. Notably, two atrophy- linked switch- like genes in the vagina that we identified, KRTDAp and KRT1, are crucial for the differentiation of epithelial cells in the vagina \(^{48,49}\) . Protein stainings available through Human Protein Atlas \(^{50}\) show that all six atrophy- linked switch- like genes are expressed at the protein level, predominantly in the vaginal epithelium. Secondly, administering 17β- estradiol (a type of estrogen) to postmenopausal women with vaginal atrophy leads to the upregulation of the same six genes, causing symptoms to subside \(^{51}\) . According to our hypothesis, administering estrogen activates the expression of the driver switch- like genes in the vagina, resuming the proliferation of basal and parabasal cells in the epithelium. This process leads to the reformation of a thick and healthy vaginal mucosa, thereby alleviating the symptoms of vaginal atrophy.  
+
+Thus, it is essential to distinguish driver genes from passenger genes to understand the etiology of vaginal atrophy. However, we expect driver and passenger genes to show the same expression patterns in healthy versus atrophic vaginas using bulk RNA- sequencing data. In order to make this distinction, we need comparative expression data, specifically from the basal and parabasal epithelium from healthy versus atrophic vaginas. We expect driver genes to be differentially expressed in the basal and parabasal layers of the epithelium. By contrast, we expect passenger genes to show no differential expression in the basal and parabasal layers between healthy and atrophic
+
+<--- Page Split --->
+
+vaginas.  
+
+To look at the expression levels in the basal and parabasal layers of the epithelium, we arbitrarily chose ALOX12 from the six atrophy- linked switch- like genes for immunohistochemical staining of its protein product in the vaginal mucosa (which includes the epithelium and the underlying connective tissue). We found that the ALOX12 protein is present in the epithelial cells, and its abundance directly correlates with epithelial thickness, as expected from our RNA- sequencing results. However, we found no significant difference in the staining of the ALOX12 protein in the basal or parabasal epithelial layers between healthy and atrophic samples (Figure 8B). This suggests that the gene is not differentially expressed in the basal or parabasal layers of the vaginal epithelium between healthy and atrophic vaginas. Therefore, ALOX12 is a passenger gene for vaginal atrophy. Comparative immunohistochemical staining of the protein product of the other five atrophy- linked switch- like genes may identify the driver gene in the future. Indeed, the KRT1 protein is recognized as a marker of basal cell differentiation in mouse vaginas \(^{52}\) , a finding that may also be true for humans. Overall, our results open up several new paths for potential pre- menopausal risk assessment and intervention frameworks targeting cell differentiation pathways in the clinical setting.
+
+<--- Page Split --->
+![](images/Figure_8.jpg)
+
+<center>Figure 7. Atrophy-linked switch-like genes tend to be either all switched off, or all switched on within individuals. A. The distribution of expression levels in the vagina of the six switch-like genes implicated in vaginal atrophy. The x-axes represent \(\log (TPM + 1)\) values for each gene in the vagina, and the y-axes represent the probability density. We obtained the probability densities using kernel density estimation. In each case, the global minimum (excluding endpoints) is considered the switching threshold. A gene is deemed “on” in an individual if the expression level is above this threshold; otherwise, the gene is deemed “off.” B. Pairwise concordance rates (percentage of individuals in which the two genes are either both switched on or both switched off). </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+<center>Figure 8. ALOX12 is a passenger gene. A. Model for the etiology of vaginal atrophy. High levels of </center>
+
+<--- Page Split --->
+
+estrogen keep the driver genes switched on in basal and parabasal epithelium, impelling basal and parabasal cells to proliferate and mature, resulting in healthy vaginal mucosa. Conversely, low levels of estrogen switch off the driver genes. The lack of basal and parabasal cell proliferation leads to a thin vaginal epithelium, resulting in vaginal atrophy. B. Representative immunohistochemical staining of Arachidonate 12- Lipoxygenase (ALOX12) in vaginal tissue. We show healthy vaginal tissue from a woman with higher systemic estrogen levels and a thicker vaginal epithelial layer, along with atrophic vaginal tissue from a woman with low systemic estrogen levels and a thinner vaginal epithelial layer. There is no difference in ALOX12 expression in the basal or parabasal cells between healthy and atrophic epithelium, implicating it as a passenger gene. Images taken with Axio Observer Z1 (Carl Zeiss AG) with a 40X objective.  
+
+## Discussion  
+
+In this study, we investigated factors underlying switch- like gene expression and its functional consequences. Our systematic analysis revealed 1,013 switch- like genes across 943 individuals. Some of these genes show bimodal expression across individuals in all tissues, suggesting a genetic basis for their universally switch- like behavior. We found several single nucleotide and structural variants to explain the switch- like expression of these genes. Most of the switch- like genes, however, exhibit tissue- specific bimodal expression. These genes tend to be concordantly switched on or off in individuals within the breast, colon, stomach, and vagina. This concordant tissue- specific switch- like expression in individuals is likely due to tissue- specific master regulators, such as endocrinological signals. For example, in the vagina, switch- like genes tend to get concordantly switched off in a given individual when systemic estrogen levels fall below a certain threshold. On the biomedical front, our work linked switch- like expression to the susceptibility to gastric cancer and vaginal atrophy. Furthermore, this study has paved two major paths forward toward early medical interventions, as discussed below.  
+
+First, we emphasize that bimodal expression that is correlated across all tissues is driven by genetic polymorphisms. However, the genetic bases for 13/23 universally switch- like genes remain elusive. We propose that the underlying genetic bases for these universally switch- like genes are structural variants, which are not easily captured by short- read DNA sequencing. These structural variants may be discovered in the future as population- level long- read sequencing becomes more common. The first biomedical path forward is to use long- read DNA sequencing to pinpoint the genetic polymorphisms responsible for the bimodal expression of disease- related genes. Of particular interest are the genes CYP4F24P and GPX1P1, both long non- coding RNAs, which are implicated in nasopharyngeal cancer. The genetic basis for their bimodal expression remains unknown. CYP4F24P is significantly downregulated in nasopharyngeal cancer tissues \(^{53}\) , while GPX1P1 is significantly upregulated in nasopharyngeal carcinomas treated with the potential anticancer drug THZ1 \(^{54}\) . Investigating whether individuals with naturally switched- off GPX1P1 and CYP4F24P are at a higher risk of nasopharyngeal cancer will enable genotyping to identify individuals at elevated risk for nasopharyngeal cancer, facilitating early interventions and improving patient outcomes.
+
+<--- Page Split --->
+
+Secondly, switch- like genes present a promising avenue for exploring gene- environment interactions, an area of growing interest. Recent studies indicate that environmental factors can significantly modulate genetic associations \(^{55,56}\) . Polymorphisms that result in switch- like gene expression have already been linked to several diseases within specific environmental contexts \(^{57}\) . For instance, the deletion of GSTM1 has been associated with an increased risk of childhood asthma, but only in cases where the mother smoked during pregnancy \(^{58}\) . Even more critically, switch- like genes potentially create unique cellular environments that could modulate the impact of genetic variations. We hypothesize that switch- like expression can produce diverse cellular environments, whether in a single gene (as in genetically determined cases) or in multiple genes (as in tissue- specific, hormonally regulated cases). These environments may, in turn, influence the effect of genetic variations and their associations with disease. Thus, much like current gene- environment association studies that control for factors such as birthplace, geography, and behaviors like smoking, it is conceivable that controlling for switch- like gene expression states could enhance the power of such studies. By cataloging these switch- like genes and developing a framework to classify them as "on" or "off" in various samples, our work lays the groundwork for more robust association studies in future research.  
+
+In summary, our study has significant implications for understanding the fundamental biology of gene expression regulation and the biomedical impact of switch- like genes. Specifically, it contributes to the growing repertoire of methods for determining individual susceptibility to diseases, facilitating early therapeutic interventions. By providing a new approach to studying gene expression states, our study will enhance the predictive accuracy of disease susceptibility and improve patient outcomes.  
+
+## Acknowledgment  
+
+O.G. and N.M. acknowledge support from the National Institute of General Medical Sciences (under grant no.1R01GM148973- 01). N.M. also acknowledges support from the Japan Science and Technology Agency (JST) Moonshot R&D (under grant no.JPMJMS2021), the National Science Foundation (under grant no.2052720), and JSPS KAKENHI (under grant no.JP 24K14840). O.G. acknowledges support from the National Science Foundation (under grant nos.2049947 and 2123284). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.  
+
+## METHODS  
+
+## Data  
+
+The Genotype- Tissue Expression (GTEx) project is an ongoing effort to build a comprehensive public resource to study tissue- specific gene expression and regulation. The data we use are transcript per million (TPM) obtained from human samples across
+
+<--- Page Split --->
+
+54 tissues and 56,200 genes (as of December 1st, 2023). We excluded laboratory- grown cell lines from our analysis. Since we need a reasonable number of individuals from each tissue, we excluded tissues with less than 50 individuals for our calculations. Of the remaining tissues, there were instances of multiple tissues from the same organ. In such cases, we randomly chose one tissue per organ. We thus focus our analysis on 27 tissues (Figure 1). Additionally, we retained only those genes for which the mean TPM across individuals was greater than 10 in at least one of the 27 focal tissues. This filter was applied because the analysis of lowly expressed genes may lead to false positive calls for bimodal expression and, as a result, to assign biological significance to cases where there is none. After these filtering steps, we are left with TPM data from 19,132 genes in each of the 27 tissues. We note that each tissue contains data from a different number of samples (individuals), totaling 943 across tissues. We will refer to this set of 19,132 genes as \(G\) in our equations and the rest of the methods.  
+
+## Dip test  
+
+There are many tests of bimodality of gene expressions \(^{16,59}\) . We use a dip test described as follows. We denote by \(S_{i}\) the number of samples (individuals) available for tissue \(i\) . We also denote by \(x_{g,i,s}\) the TPM value for gene \(g\) in tissue \(i\) , for sample \(s \in \{1, \ldots , S_{i}\}\) and \(g \in G\) . According to convention, we log- transform the TPM, specifically by \(\log (x_{g,i,s} + 1)^{60}\) to suppress the effect of outliers; TPM is extremely large for some samples. Note that \(\log (x_{g,i,s} + 1)\) conveniently maps \(x_{g,i,s} = 0\) to 0. For each pair of gene \(g\) and tissue \(i\) , we carried out a dip test, which is a statistical test for multimodality of distributions, on the distribution of \(\log (x_{g,i,s} + 1)\) across the samples \(S_{i}\) . We performed the dip test using the dip.test() function within the "diptest" package in R, with the number of bootstrap samples equal to 5000. We applied the Benjamini- Hochberg procedure for multiple hypothesis correction to the results with a false discovery rate of 5%. Additionally, to reduce false positive calls of bimodal expression, we only retained results where the dip statistic \(D > \max [0.05, 0.05 / \log (\bar{x}_{g,i})]\) , where  
+
+\[\bar{x}_{g,i} = \frac{1}{S_i}\sum_{s = 1}^{S_i}x_{g,i,s}\]  
+
+We obtained this threshold of 0.05 by visual inspection of \(\log (x_{g,i,s} + 1)\) distributions in the stomach and adipose subcutaneous tissues, starting with those with the highest values of \(D\) . For statistically significant results, the distribution was almost always bimodal if \(D\) exceeded 0.05. The only exceptions were genes with low \(\bar{x}_{g,i}\) . Thus, we penalized gene- tissue pairs with low \(\bar{x}_{g,i}\) across samples by requiring a higher \(D\) in order to classify them as bimodally distributed. Genes identified as bimodally distributed in at least one tissue are referred to as "switch- like" genes.  
+
+## Tissue-to-tissue co-expression of genes  
+
+We sought to identify switch- like genes whose expression exhibits bimodal expression in all tissues. One seemingly straightforward approach is to count the number of tissues
+
+<--- Page Split --->
+
+showing bimodal distribution of expression levels for each gene. However, even if a gene genuinely exhibits bimodal expression across all tissues, our methodology may fail to recognize it as such if the mean expression levels \((\bar{x}_{g,i})\) of the gene are low in some tissues. This is because our effect size threshold penalizes gene- tissue pairs with low \(\bar{x}_{g,i}\) . Moreover, if gene expression follows a bimodal distribution across all tissues, then it does so likely due to a genetic polymorphism affecting expression. Thus, the expression of such genes would be highly correlated between pairs of tissues. Given this insight, discovering universally bimodal genes is more tractable using tissue- to- tissue co- expression of each gene.  
+
+For each gene, we construct the co- expression matrix among pairs of tissues as follows. To calculate the co- expression between a pair of tissues, we need to use the samples whose TPM is measured for both tissues \(^{61}\) . In general, even if the number of samples is large for both of the two tissues, it does not imply that there are sufficiently many common samples. Therefore, using the sample information described in GTEx_Analysis_v8_Annotations_SampleAttributesDD.xlsx in the GTEx data portal, we counted the number of samples shared by each tissue pair and excluded the 41 tissue pairs that share less than 40 samples. For each of the remaining \(27 \times 26 / 2 - 41 = 310\) tissue pairs, we denote by \(S_{i,j}\) the number of samples shared by the two tissues \(i\) and \(j\) . We also denote by \(x_{g,i,s}\) and \(x_{g,j,s}\) the TPM value for gene \(g\) in tissues \(i\) and \(j\) , respectively, for sample \(s \in \{1, 2, \ldots , S_{i,j}\}\) . Then, we calculated the Pearson correlation coefficient between \(\log (x_{g,i,s} + 1)\) and \(\log (x_{g,j,s} + 1)\) across the \(S_{i,j}\) samples and used it as the strength of the co- expression of gene \(g\) between tissues \(i\) and \(j\) . Specifically, we calculate  
+
+\[r_{g}(i,j) = \frac{\sum_{s = 1}^{S_{i,j}}[\log(x_{g,i,s} + 1) - m_{g,i}][\log(x_{g,j,s} + 1) - m_{g,j}]}{\sqrt{\sum_{s = 1}^{S_{i,j}}[\log(x_{g,i,s} + 1) - m_{g,i}]^{2}\sum_{s = 1}^{S_{i,j}}[\log(x_{g,j,s} + 1) - m_{g,j}]^{2}}}\]  
+
+where  
+
+\[m_{g,i} = \frac{1}{S_{i,j}}\sum_{s = 1}^{S_{i,j}}\log (x_{g,i,s} + 1),\]  
+
+and  
+
+\[m_{g,j} = \frac{1}{S_{i,j}}\sum_{s = 1}^{S_{i,j}}\log (x_{g,j,s} + 1).\]  
+
+For each gene \(g\) , we then vectorize the correlation matrix, \((r_{g}(i,j))\) , into a 310- dimensional vector. If, for a given gene, \(g\) , \(\log (x_{g,i,s} + 1)\) or \(\log (x_{g,j,s} + 1)\) were 0 across all \(S_{i,j}\) samples for any of the 310 tissue pairs, the gene was removed. In this process, 28 out of 1,013 switch- like genes were removed. Note that the correlation matrix is symmetric, so we only vectorize the upper diagonal part of the matrix. We denote the
+
+<--- Page Split --->
+
+generated vector by \(\vec{v}_{g}\) . Vector \(\vec{v}_{g}\) characterizes the gene. We ran a principal component analysis (PCA), using the promp() function in R, on vectors, \(\vec{v}_{g}\) for all genes for which we could calculate \(r_{g}(i,j)\) for all 310 tissue pairs. In parallel, we also ran PCA on only the set of vectors (genes) characterizing only the 985 (1013 - 28) switch- like genes.  
+
+In the space spanned by the first two principal components, we calculated the pairwise distance between genes using the dist() function in R with method = "euclidean". We then performed hierarchical clustering using the hclust() function with method = "complete". Finally, we used the cuttree() function with \(k = 2\) and \(k = 3\) to obtain two and three clusters, respectively.  
+
+## Identifying the genetic basis of universal bimodality  
+
+In order to identify the genetic basis of bimodality for switch- like genes in cluster 2A, we obtained the coordinates of the genes for both hg19 and hg38 using their Ensembl IDs as keys through Ensembl BioMart. We obtained coordinates of common structural variants using both the 1000 genomes project (hg19) \(^{62}\) and the HGSV2 dataset (hg38) \(^{63}\) . We performed an overlap analysis using BedTools \(^{64}\) to identify polymorphic deletions of or insertions into these genes. We thus obtained five universally bimodal genes being affected by structural variants. These were USP32P2, FAM106A, GSTM1, RP11- 356C4.5, and CYP4F24P. Additionally, we obtained the GTEx dataset for the expression quantitative trait loci (eQTL). We identified genes in cluster 2A that had at least one eQTL, which was consistently associated with either increased or decreased expression of a given gene across all 27 tissues analyzed. We thus obtained five genes from cluster 2A whose expression was associated with a short variant across tissues. These were NPIPA5, RPS26, PSPHP1, PKD1P2, and PKD1P5.  
+
+## Controlling for confounders  
+
+A bimodal distribution of expression levels of universally switch- like genes is unlikely to be driven by confounding factors such as ischemic time, and time spent by the tissue in chemical fixatives (PAXgene fixative). For example, the expression of genes on the male- specific region of chromosome Y is bimodally distributed across tissues regardless of confounding factors because females do not possess these genes. Similarly, regardless of confounding factors, USP32P2 is bimodally distributed due to a polymorphic gene deletion. However, tissue- specific switch- like genes are particularly prone to being affected by confounding variables. Specifically, we investigated whether the switch- like expression of genes can be explained by ischemic time and PAXgene fixative using the following approach.  
+
+Ischemic time for a sample \(s\) in a given tissue \(i\) , denoted by \(k_{i,s}\) , is a continuous variable representing the time interval between death and tissue stabilization. Time spent by a tissue \(i\) from a sample \(s\) in PAXgene fixative, denoted by \(f_{i,s}\) , is also a continuous variable. For each gene- tissue pair \((g, i)\) , we calculated, across the \(S_{i}\) samples, the Pearson correlation between 1) \(\log (1 + x_{g,i,s})\) and \(k_{i,s}\) and 2) \(\log (1 + x_{g,i,s})\) and \(f_{i,s}\) . For
+
+<--- Page Split --->
+
+each tissue \(i\) and confounder \(c\) , where \(c \in \{k_{i,s}, f_{i,s}\}\) , we denote the correlation coefficient between \(\log(1 + x_{g,i,s})\) and \(c\) as \(r_{g,i,c}\) .  
+
+We partition the set of switch- like genes into two subsets: cluster 1 and cluster 2 (the union of clusters 2A and 2B). We treat cluster- 2 genes as internal controls since their correlated bimodal expression across tissues is robust to the presence of confounding factors. Thus, we eliminated a cluster- 1 gene \(g1\) if, for any confounder \(c\) , \(\left(r_{g1,i,c}\right)^2 > \left(\max_{g2 \in \text{cluster} 2} r_{g2,i,c}\right)^2\) .  
+
+## Gene-to-gene co-expression within tissues  
+
+We performed gene- to- gene co- expression analysis within the stomach, breast, vagina, and colon tissues. In a given tissue \(i\) , we denote the set of genuine cluster- 1 genes (excluding genes affected by confounding variables) by \(C_i\) . Then, for \(i \in \{\text{stomach, breast, vagina, colon}\}\) , we calculated the Pearson correlation, across the \(S_i\) samples, between \(\log(x_{g,i,s} + 1)\) and \(\log(x_{h,i,s} + 1)\) for every \(g, h \in C_i\) where \(g \neq h\) .  
+
+## Quantifying sex bias in cluster-1 gene expression  
+
+For every gene- tissue pair \((g, i)\) , where \(g\) is a switch- like gene, and \(i\) is a tissue common to both sexes, we tested the hypothesis that the distribution of \(\log(x_{g,i,s} + 1)\) across male samples differed from that across female samples using the Wilcoxon rank- sum test. We applied the Benjamini- Hochberg procedure of multiple hypotheses correction with \(\text{FDR} = 5\%\) . We quantified the effect size of the sex bias using Cohen's \(d\) . Statistically significant results were considered to represent true sex bias only if \(|d| > 0.2^{65}\) .  
+
+## Enrichment of switch-like genes among disease-linked genes  
+
+We performed enrichment analysis for switch- like genes in the stomach and vagina that are downregulated in gastric cancer and vaginal atrophy, respectively. We denote the set of genes downregulated in disease \(y\) as \(Z_{y}\) , where \(y \in \{\text{gastric cancer, vaginal atrophy}\}\) . We calculated the fold enrichment of genuine cluster- 1 genes in the stomach among genes downregulated in gastric cancer by:  
+
+\[\frac{|C_{\mathrm{stomach}} \cap Z_{\mathrm{gastric cancer}}|}{|G \cap Z_{\mathrm{gastric cancer}}| / |G|} .\]  
+
+We calculated the fold enrichment of genuine cluster- 1 genes in the vagina among genes downregulated in vaginal atrophy by:  
+
+\[\frac{|C_{\mathrm{vagina}} \cap Z_{\mathrm{vaginal atrophy}}|}{|G \cap Z_{\mathrm{vaginal atrophy}}| / |G|}.\]
+
+<--- Page Split --->
+
+To calculate the \(p\) - values associated with these enrichments, we obtained 10,000 uniformly random samples (with replacement) of size \(|C_{i}|\) from \(G\) . The \(p\) - value for the enrichment of switch- like genes in tissue \(i\) among genes linked to disease \(y\) is then given by the fraction of random samples among the 10,000 samples for which \(|q_{j} \cap Z_{y}| > |C_{i} \cap Z_{y}|\) . Here, \(q_{j}\) is the set of genes in random sample \(j\) where \(j \in \{1, \ldots , 10000\}\) .  
+
+## Discretizing expression levels  
+
+We performed kernel density estimation using the density() function in R on the distributions of 1) \(\log (x_{g,\mathrm{stomach},s} + 1)\) across the \(S_{\mathrm{stomach}}\) samples for \(g \in C_{\mathrm{stomach}} \cap Z_{\mathrm{gastric cancer}}\) ; and 2) \(\log (x_{g,\mathrm{vagina},s} + 1)\) across the \(S_{\mathrm{vagina}}\) samples for \(g \in C_{\mathrm{vagina}} \cap Z_{\mathrm{vaginal atrophy}}\) .  
+
+We used the minimum of the estimated density as the switching threshold; if an individual had an expression level above the threshold in a given tissue, the gene was considered "on" in the individual in that tissue. The gene was considered "off" otherwise. We then calculate the concordance of expression among genes in any arbitrary set of switch- like genes \(G^{A}\) in a given tissue \(i\) as follows:  
+
+\[\frac{1}{S_{i}}\sum_{s = 1}^{S_{i}}\left[\prod_{g\in G^{A}}\mathbf{1}_{(g\mathrm{~is~"on"~in~sample~}s\mathrm{~in~tissue~}i)} + \prod_{g\in G^{A}}\mathbf{1}_{(g\mathrm{~is~"off"~in~sample~}s\mathrm{~in~tissue~}i)}\right],\]  
+
+where \(\mathbf{1}_{(\cdot)}\) is the indicator function.  
+
+## Gene ontology enrichment of tissue-specific switch-like genes in the vagina  
+
+We performed Gene Ontology (GO) enrichment analysis for genes in \(C_{\mathrm{vagina}}\) using the online database available at https://geneontology.org/ 66.  
+
+## Immunohistochemistry  
+
+Vaginal biopsies were taken by use of punch biopsies from postmenopausal women, fixed and stained as previously described by use of ALOX12 (HPA010691 polyclonal antirabbit, Sigma- Aldrich) 67,68.
+
+<--- Page Split --->
+
+## Supplementary Information  
+
+## Principal component analysis on tissue-to-tissue co-expression vectors  
+
+We applied a principal component analysis to the 19,132 vectors of tissue- to- tissue coexpression, one vector for each gene. We find that PC1 (Figure 2A), explaining \(35.3\%\) of the variation, is nearly perfectly correlated with mean tissue- to- tissue co- expression across tissue- tissue pairs ( \(r^2 = 0.998\) , \(p\) - value \(< 2.2 \times 10^{- 16}\) ; Figure S1). This result indicates that the \(35.3\%\) of the variation in the tissue- to- tissue co- expression of genes is primarily explained by the mean tissue- to- tissue co- expression of genes.  
+
+![](images/Figure_unknown_1.jpg)
+
+<center>Figure S1. The mean tissue-to-tissue co-expression of genes shows a near-perfect correlation with PC1. </center>  
+
+## Universally switch-like genes and their biomedical implications  
+
+In the main text, we discussed the USP32P2 and FAM106A. Here, we discuss some other interesting examples of universally switch- like genes. The violin plots for the expression level distributions for all cluster- 2A and cluster- 2B switch- like genes not shown in the main text are present in Figure S2 and Figure S3, respectively.  
+
+Firstly, a common \(\sim 20\mathrm{kb}\) whole- gene deletion (esv3587154) of the GSTM1 gene \(^{69,70}\) is associated with bladder cancer in humans \(^{71}\) . GSTM1 is bimodally expressed across individuals in all tissues (Figure S2D) that we analyzed, as well as across multiple tumor types \(^{15}\) , with different expression peaks corresponding to differential prognoses among patients. These findings suggest a compelling hypothesis: the common deletion of GSTM1, maintained either by drift or balancing selection \(^{72}\) , has no significant effect on the health of non- cancerous individuals; however, it could have significant implications for prognosis once certain types of tumors develop. Therefore, screening
+
+<--- Page Split --->
+
+patients with certain tumor types for the GSTM1 deletion could significantly advance our ability to predict the course of tumor progression in an individualized manner.  
+
+Secondly, genes that are bimodally expressed across multiple tissues raise an evolutionary paradox. Typically, genes with a wide expression breadth (i.e., expression across a large number of tissues) affect fitness and are thus constrained at both the sequence and expression level \(^{26,73 - 75}\) . However, universally switch- like genes, despite having a high expression breadth, are not conserved at the expression level. This could imply different health consequences for individuals with off versus on state of the genes. For example, the universally switch- like gene RP4- 765C7.2 (ENSG00000213058; Figure S2K) is upregulated in the peripheral blood mononuclear cells of patients with ankylosing spondylitis \(^{76}\) , eutopic endometrium in endometriosis patients \(^{77}\) , and peripheral blood mononuclear cells of multiple sclerosis patients \(^{78}\) . Conversely, it is downregulated in the peripheral blood mononuclear cells of Sjögren's syndrome patients \(^{79}\) . These results suggest that this gene being switched on versus off may predispose individuals to certain diseases while protecting them against others. This balance between susceptibility and protection could explain why both high- expression and low- expression states are maintained in the population at comparable frequencies.  
+
+Thirdly, the bimodality of NPIPA5 (Figure S2G), too, can be explained by a single eQTL. The T allele of the SNV rs3198697 is associated with NPIPA5 being switched on across tissues, while the C allele is associated with the gene being switched off. NPIPA5 has been reported as one of the top differentially expressed genes among patients with multiple sclerosis in both blood and brain \(^{80}\) . Moreover, this study \(^{80}\) showed that this gene is co- expressed in blood and brain. Here, we have shown that this gene is switch- like and that the co- expression of NPIPA5 is not restricted to blood and brain but extends to all pairs of tissues.  
+
+Lastly, a single eQTL can explain the bimodality of a member of the PKD1 gene family in cluster 2A, PKD1P5 (Figure S2I). For PKD1P5, the C allele of the SNV rs201525245 is associated with the gene being switched on, while the G allele is associated with the gene being switched off.
+
+<--- Page Split --->
+![](images/Figure_unknown_2.jpg)
+
+<center>Figure S2. Violin plots for expression level distributions of switch-like genes in cluster 2A. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_3.jpg)
+
+<center>Figure S3. Violin plots for expression level distributions of switch-like genes in cluster 2A. </center>  
+
+## Conceptual issues regarding bimodal expression distributions driven by genetic polymorphisms  
+
+In the main text, we claimed that genetic polymorphisms drive the bimodal expression of universally switch- like genes in cluster 2A. For a polymorphism with two alleles (A and \(a\) ), there are three possible genotypes ( \(aa\) , \(Aa\) , and \(AA\) ). Since each of the three genotypes can lead to three different expression levels, we expect expression distributions of a cluster- 2A gene to have three modes. This leads to the question: Why do we not see trimodal, as opposed to bimodal, expression distributions for genes in cluster 2A? To answer this question, we develop the following frameworks. Let us assume that a genetic polymorphism exists with two alleles, \(A\) and \(a\) , with frequencies \(p_A\) and \((1 - p_A)\) , respectively. The three genotypes for this polymorphism, \(aa\) , \(Aa\) , and \(AA\) , lead to three different expression states (TPM levels) for the gene with averages
+
+<--- Page Split --->
+
+\(\mu_{aa}, \mu_{Aa}\) , and \(\mu_{AA}\) , respectively. Let us also assume that the Hardy-Weinberg equilibrium holds for this locus. Then, the frequency of \(aa = (1 - p_A)^2\) , the frequency of \(Aa = 2p_A(1 - p_A)\) , and the frequency of \(AA = p_A^2\) . We assume that \(\mu_{aa} \leq \mu_{Aa} \leq \mu_{AA}\) . Next, we define a dominance coefficient \(0 \leq \alpha \leq 1\) by,  
+
+\[\mu_{Aa} = \mu_{aa} + (\mu_{AA} - \mu_{aa})\alpha .\]  
+
+If we define the ratio \(R\) by  
+
+\[R = \frac{\mu_{AA}}{\mu_{aa}},\]  
+
+then, we obtain  
+
+\[\mu_{Aa} = \mu_{aa}(1 - \alpha +R\alpha)\]  
+
+and  
+
+\[\mu_{AA} = R\mu_{aa}.\]  
+
+We can then divide individuals into three groups depending on their genotypes. Let us assume that the coefficient of variation (CV) of expression is the same for each genotypic group. Then, we can model the TPM value of this gene in a given individual a normal random variable with:  
+
+1) mean \(= \mu_{aa}\) and standard deviation \(= \mathrm{CV}\times \mu_{aa}\) if the genotype is \(aa\) 2) mean \(= \mu_{Aa}\) and standard deviation \(= \mathrm{CV}\times \mu_{Aa}\) if the genotype is \(Aa\) ; and 
+3) mean \(= \mu_{AA}\) and standard deviation \(= \mathrm{CV}\times \mu_{AA}\) if the genotype is \(AA\)  
+
+The value of \(\mu_{aa}\) is irrelevant for gauging the effect of polymorphisms on the shape of the expression level distributions. Therefore, we set \(\mu_{aa} = 1\) .  
+
+Under these mathematical assumptions, we performed simulations using 36 distinct models. These models vary by four parameters: \(p_A \in \{0.05, 0.1, 0.5\}\) , \(\mathrm{CV} \in \{0.1, 0.3\}\) , \(R \in \{10, 1000\}\) , and \(\alpha \in \{0.2, 0.5, 0.8\}\) . For each model, defined by a unique combination of the values of these four parameters, we performed a two- step sampling procedure. First, we obtained a random sample of 500 genotypes, based on \(p_A\) and the Hardy- Weinberg equilibrium. Next, for each of the 500 genotypes sampled, we sample a TPM value from the normal distribution corresponding to that genotype. Thus, for each of the 36 models, we simulated 500 TPM values. We present these values as histograms with and without log transformation. The results for \(p_A = 0.05\) , \(p_A = 0.1\) , and \(p_A = 0.5\) are shown in Figure S4, Figure S5, and Figure S6, respectively. These simulations help us answer our question we first asked: Why do we not see a trimodal distribution if a genetic polymorphism drives expression- level variability in a gene?  
+
+Firstly, even when the minor allele (A) frequency is not low (e.g., \(10\%\) ), the frequency of the genotype \(AA\) is still quite low (e.g., \(1\%\) ). Therefore, the third peak is not always conspicuously visible. We see this in all models with \(p_A = 0.05\) and \(p_A = 0.1\) (Figures S4 and S5), regardless of CV, \(R\) , and \(\alpha\) values. At higher allele frequencies (e.g., \(50\%\) ), the effect of the remaining parameters becomes more apparent. Figure S6 shows that a
+
+<--- Page Split --->
+
+higher dominance coefficient \(\alpha\) makes the expression level distribution more bimodal. By contrast, a lower dominance coefficient \(\alpha\) makes the expression level distribution more trimodal. The lack of observed trimodality in the GTEx data may suggest that expression levels of switch-like genes tend to be more dominant than additive with regard to causal genetic polymorphisms. Secondly, greater variation (CV) in the data can also obscure the third peak. For example, by comparing **Figure S6B** to **Figure S6H**, we find that increasing the CV can change the distribution from being trimodal to bimodal when the other parameters are held constant. However, \(R\) does not seem to have much effect on whether the expression level distribution is bimodal or trimodal. 
+
+![](images/Figure_unknown_4.jpg)
+
+ 
+
+<center>**Figure S4. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of 5%.**</center>
+
+<--- Page Split --->
+![](images/Figure_unknown_5.jpg)
+
+<center>Figure S5. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of 10%. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_6.jpg)
+
+<center>Figure S6. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of \(50\%\) . </center>  
+
+## Tissue-specific switch-like genes  
+
+We divided switch- like genes into three clusters in the space spanned by the first two principal components (Figure 2A). While we said that genes in cluster 1 (Figure 2A- B) are tissue- specific switch- like genes, manual inspection reveals this is not true for all genes in cluster 1. In particular, the transcript ENSG00000273906 coming from chr Y was labeled cluster 1 by hierarchical clustering even though it is universally switch- like in tissues common to both sexes. Indeed, we removed all chr- Y genes from our analyses of genuine cluster- 1 genes. Other cluster- 1 genes bimodally expressed in a large number of tissues lie on the autosomes. For example, CLPS, PRSS1, CELA3A, and CELA3B, despite having low overall tissue- to- tissue co- expression, are bimodally expressed across tissues. Indeed, we have shown previously that CELA3A and CELA3B have a shared regulatory architecture in the pancreas \(^{81}\) .  
+
+## Controlling for confounders  
+
+We removed cluster- 1 genes affected by confounders in each tissue using an approach outlined in Methods. Here, we present the number of genuine cluster- 1 genes versus
+
+<--- Page Split --->
+
+those affected by confounders in **Figure S7**. In particular, we show that the cluster- 1 genes in the colon and the intestine are particularly prone to being affected by confounding factors. We also present in **Figure S8** examples of genes whose bimodal expression in specific tissues is correlated with variation in the sample ischemic time distribution.  
+
+![](images/Figure_unknown_7.jpg)
+
+<center>Figure S7. Switch-like genes in cluster 1 that are genuine versus those affected by confounders. </center>
+
+<--- Page Split --->
+![PLACEHOLDER_33_0]
+
+<center>Figure S8. Examples of cluster-1 genes affected by confounders. Their bimodal distribution is caused by ischemic time (a confounding factor). </center>  
+
+## The copy number variation at the PGA3 locus does not affect the gene's expression levels  
+
+PGA3 exhibits a high copy number variation among humans \(^{82}\) , but the copy number seems to have no impact on PGA3 expression, at least in cancer samples \(^{83}\) . The bimodal expression of PGA3 in the stomach is likely not due to its copy number variation. This is because PGA3's expression in the stomach is highly correlated with other tissue- specific genes in the stomach. The only way in which a copy number- driven bimodality of PGA3 could be correlated with other switch- like genes is if the product of PGA3 was regulating the correlated genes. Without this evidence, we surmise that the copy number variation at the PGA3 locus does not affect the gene's expression levels, at least in the stomach.  
+
+Table S1. A list of tissues used in this study along with the number of individuals for each tissue. Table S2. A list of 1,013 switch- like genes. Table S3. Tissue- to- tissue co- expression (Pearson's correlation) for all genes across 310 tissue- tissue pairs. Table S4. Results from principal component analysis on tissue- to- tissue co- expression data for all genes. Table S5. Results from principal component analysis on tissue- to- tissue co- expression data for only switch- like genes. Table S6. Correlation between gene expression levels and confounding factors for switch- like
+
+<--- Page Split --->
+
+genes. Table S7. Gene- to- gene co- expression of genuine tissue- specific switch- like genes in the stomach, vagina, breast, and colon. Table S8. Analysis of sex bias among genuine tissue- specific switch- like genes.  
+
+1. Jacob, F. & Monod, J. Genetic regulatory mechanisms in the synthesis of proteins. J. Mol. Biol. 3, 318-356 (1961).  
+2. Banerji, J., Rusconi, S. & Schaffner, W. Expression of a beta-globin gene is enhanced by remote SV40 DNA sequences. Cell 27, 299-308 (1981).  
+3. Gillies, S. D., Morrison, S. L., Oi, V. T. & Tonegawa, S. A tissue-specific transcription enhancer element is located in the major intron of a rearranged immunoglobulin heavy chain gene. Cell 33, 717-728 (1983).  
+4. Serfling, E., Jasin, M. & Schaffner, W. Enhancers and eukaryotic gene transcription. Trends Genet. 1, 224-230 (1985).  
+5. Allfrey, V. G., Faulkner, R. & Mirsky, A. E. Acetylation and methylation of histones and their possible role in the regulation of RNA synthesis. Proc. Natl. Acad. Sci. U. S. A. 51, 786-794 (1964).  
+6. Riggs, A. D. & Jones, P. A. 5-methylcytosine, gene regulation, and cancer. Adv. Cancer Res. 40, 1-30 (1983).  
+7. Bestor, T., Laudano, A., Mattaliano, R. & Ingram, V. Cloning and sequencing of a cDNA encoding DNA methyltransferase of mouse cells. The carboxyl-terminal domain of the mammalian enzymes is related to bacterial restriction methyltransferases. J. Mol. Biol. 203, 971-983 (1988).  
+8. Jenuwein, T. & Allis, C. D. Translating the histone code. Science 293, 1074-1080 (2001).  
+9. Levine, M. & Tjian, R. Transcription regulation and animal diversity. Nature 424, 147-151 (2003).  
+10. Muntoni, F., Torelli, S. & Ferlini, A. Dystrophin and mutations: one gene, several proteins, multiple phenotypes. Lancet Neurol. 2, 731-740 (2003).  
+11. Sakai, T. et al. Allele-specific hypermethylation of the retinoblastoma tumor-suppressor gene. Am. J. Hum. Genet. 48, 880-888 (1991).  
+12. Cutting, G. R. Cystic fibrosis genetics: from molecular understanding to clinical application. Nat. Rev.
+
+<--- Page Split --->
+
+Genet. 16, 45–56 (2015).  
+
+13. Ertel, A. Bimodal gene expression and biomarker discovery. Cancer Inform. 9, 11–14 (2010).  
+
+14. Bessarabova, M. et al. Bimodal gene expression patterns in breast cancer. BMC Genomics 11 Suppl 1, S8 (2010).  
+
+15. Justino, J. R., Reis, C. F. dos, Fonseca, A. L., Souza, S. J. de & Stransky, B. An integrated approach to identify bimodal genes associated with prognosis in cancer. Genet. Mol. Biol. 44, e20210109 (2021).  
+
+16. Moody, L., Mantha, S., Chen, H. & Pan, Y.-X. Computational methods to identify bimodal gene expression and facilitate personalized treatment in cancer patients. J. Biomed. Inform. 100S, 100001 (2019).  
+
+17. Mason, C. C. et al. Bimodal distribution of RNA expression levels in human skeletal muscle tissue. BMC Genomics 12, 98 (2011).  
+
+18. Hartigan, J. A. & Hartigan, P. M. The dip test of unimodality. Ann. Stat. 13, 70–84 (1985).  
+
+19. Jangravi, Z. et al. A fresh look at the male-specific region of the human Y chromosome. J. Proteome Res. 12, 6–22 (2013).  
+
+20. Cheung, S., Parrella, A., Rosenwaks, Z. & Palermo, G. D. Genetic and epigenetic profiling of the infertile male. PLoS ONE 14, e0214275 (2019).  
+
+21. Turjya, R. R., Khan, M. A.-A.-K. & Mir Md Khademul Islam, A. B. Perversely expressed long noncoding RNAs can alter host response and viral proliferation in SARS-CoV-2 infection. Future Virol. 15, 577–593 (2020).  
+
+22. Talotta, R., Bahrami, S. & Laska, M. J. Sequence complementarity between human noncoding RNAs and SARS-CoV-2 genes: What are the implications for human health? Biochim. Biophys. Acta Mol. Basis Dis. 1868, 166291 (2022).  
+
+23. Arman, K., Dalloul, Z. & Bozgeyik, E. Emerging role of microRNAs and long non-coding RNAs in COVID-19 with implications to therapeutics. Gene 861, 147232 (2023).  
+
+24. Li, Q. et al. Genome-wide search for exonic variants affecting translational efficiency. Nat. Commun. 4, 2260 (2013).
+
+<--- Page Split --->
+
+25. Liu, L. et al. Mutation of the CDKN2A 5' UTR creates an aberrant initiation codon and predisposes to melanoma. Nat. Genet. 21, 128-132 (1999).  
+
+26. Khan, Z. et al. Primate transcript and protein expression levels evolve under compensatory selection pressures. Science 342, 1100-1104 (2013).  
+
+27. Wang, S. H., Hsiao, C. J., Khan, Z. & Pritchard, J. K. Post-translational buffering leads to convergent protein expression levels between primates. Genome Biol. 19, 83 (2018).  
+
+28. Chia, D. J. Minireview: mechanisms of growth hormone-mediated gene regulation. Mol. Endocrinol. 28, 1012-1025 (2014).  
+
+29. Mayne, B. T. et al. Large scale gene expression meta-analysis reveals tissue-specific, sex-biased gene expression in humans. Front. Genet. 7, 183 (2016).  
+
+30. McEwen, B. S. & Milner, T. A. Understanding the broad influence of sex hormones and sex differences in the brain. J. Neurosci. Res. 95, 24-39 (2017).  
+
+31. Goel, N., Workman, J., -Y. Lee, T. T., Innala, L. & Viau, V. Sex differences in the HPA axis. Compr. Physiol. 4, 1121-1155 (2014).  
+
+32. Fink, A. L. & Klein, S. L. The evolution of greater humoral immunity in females than males: implications for vaccine efficacy. Curr. Opin. Physiol. 6, 16-20 (2018).  
+
+33. Laffont, S. & Guéry, J.-C. Deconstructing the sex bias in allergy and autoimmunity: From sex hormones and beyond. Adv. Immunol. 142, 35-64 (2019).  
+
+34. Wu, Q. et al. Comprehensive analysis of the expression and prognostic value of spint1/2 in breast carcinoma. Front. Endocrinol. 12, 665666 (2021).  
+
+35. Takan, I., Karakulah, G., Louka, A. & Pavlopoulou, A. 'In the light of evolution.' keratins as exceptional tumor biomarkers. PeerJ 11, e15099 (2023).  
+
+36. Behtaji, S. et al. Identification of oxytocin-related lncRNAs and assessment of their expression in breast cancer. Sci. Rep. 11, 6471 (2021).  
+
+37. Fiaz, T. et al. Peripheral mRNA expression and prognostic significance of emotional stress biomarkers in metastatic breast cancer patients. Int. J. Mol. Sci. 23, (2022).  
+
+38. Emilsson, V. et al. Genetics of gene expression and its effect on disease. Nature 452, 423-428
+
+<--- Page Split --->
+
+(2008).  
+
+39. Li, H. et al. Characterization of differentially expressed genes involved in pathways associated with gastric cancer. PLoS ONE 10, e0125013 (2015).  
+
+40. Goldstein, I., Dicks, B., Kim, N. N. & Hartzell, R. Multidisciplinary overview of vaginal atrophy and associated genitourinary symptoms in postmenopausal women. Sex. Med. Today 1, 44-53 (2013).  
+
+41. Szymanski, J. K., Slabuszewska-Jozwiak, A. & Jakiel, G. Vaginal aging—what we know and what we do not know. Int. J. Environ. Res. Public Health 18, 4935 (2021).  
+
+42. Kim, H.-K., Kang, S.-Y., Chung, Y.-J., Kim, J.-H. & Kim, M.-R. The recent review of the genitourinary syndrome of menopause. J. Menopausal Med. 21, 65-71 (2015).  
+
+43. Hummelen, R. et al. Vaginal microbiome and epithelial gene array in post-menopausal women with moderate to severe dryness. PLoS ONE 6, e26602 (2011).  
+
+44. Faubion, S. S., Sood, R. & Kapoor, E. Genitourinary syndrome of menopause: management strategies for the clinician. Mayo Clin. Proc. 92, 1842-1849 (2017).  
+
+45. Buchanan, D. L. et al. Role of stromal and epithelial estrogen receptors in vaginal epithelial proliferation, stratification, and comification. Endocrinology 139, 4345-4352 (1998).  
+
+46. Anderson, D. J., Marathe, J. & Pudney, J. The structure of the human vaginal stratum corneum and its role in immune defense. Am. J. Reprod. Immunol. 71, 618-623 (2014).  
+
+47. Greenman, C. et al. Patterns of somatic mutation in human cancer genomes. Nature 446, 153-158 (2007).  
+
+48. Oomizu, S. et al. Kdap, a novel gene associated with the stratification of the epithelium. Gene 256, 19-27 (2000).  
+
+49. Ho, M. et al. Update of the keratin gene family: evolution, tissue-specific expression patterns, and relevance to clinical disorders. Hum. Genomics 16, 1 (2022).  
+
+50. Pontén, F., Jirström, K. & Uhlen, M. The Human Protein Atlas--a tool for pathology. J. Pathol. 216, 387-393 (2008).  
+
+51. Cotreau, M. M. et al. A study of 17β-estradiol-regulated genes in the vagina of postmenopausal women with vaginal atrophy. Maturitas 58, 366-376 (2007).
+
+<--- Page Split --->
+
+52. Miyagawa, S. & Iguchi, T. Epithelial estrogen receptor 1 intrinsically mediates squamous differentiation in the mouse vagina. Proc. Natl. Acad. Sci. U. S. A. 112, 12986–12991 (2015).  
+
+53. Zhang, X. et al. Identification of key pseudogenes in nasopharyngeal carcinoma based on RNA-Seq analysis. BMC Cancer 21, 483 (2021).  
+
+54. Gao, L. et al. Gene expression profile of THZ1-treated nasopharyngeal carcinoma cell lines indicates its involvement in the inhibition of the cell cycle. Transl. Cancer Res. 10, 445–460 (2021).  
+
+55. Dudbridge, F. & Fletcher, O. Gene-environment dependence creates spurious gene-environment interaction. Am. J. Hum. Genet. 95, 301–307 (2014).  
+
+56. Vetr, N. G., Gay, N. R., MoTrPAC Study Group & Montgomery, S. B. The impact of exercise on gene regulation in association with complex trait genetics. Nat. Commun. 15, 3346 (2024).  
+
+57. Thomas, D. Gene–environment-wide association studies: emerging approaches. Nat. Rev. Genet. 11, 259–272 (2010).  
+
+58. Gilliland, F. D. et al. Effects of glutathione S-transferase M1, maternal smoking during pregnancy, and environmental tobacco smoke on asthma and wheezing in children. Am. J. Respir. Crit. Care Med. 166, 457–463 (2002).  
+
+59. Hellwig, B. et al. Comparison of scores for bimodality of gene expression distributions and genome-wide evaluation of the prognostic relevance of high-scoring genes. BMC Bioinformatics 11, 276 (2010).  
+
+60. Shalek, A. K. et al. Single-cell transcriptomics reveals bimodality in expression and splicing in immune cells. Nature 498, 236–240 (2013).  
+
+61. Dobrin, R. et al. Multi-tissue coexpression networks reveal unexpected subnetworks associated with disease. Genome Biol. 10, R55 (2009).  
+
+62. 1000 Genomes Project Consortium et al. A global reference for human genetic variation. Nature 526, 68–74 (2015).  
+
+63. Ebert, P. et al. Haplotype-resolved diverse human genomes and integrated analysis of structural variation. Science 372, (2021).  
+
+64. Quinlan, A. R. & Hall, I. M. BEDTools: a flexible suite of utilities for comparing genomic features.
+
+<--- Page Split --->
+
+Bioinformatics 26, 841- 842 (2010).  
+
+65. Cohen, J. Statistical Power Analysis for the Behavioral Sciences. (Routledge, London, England, 2013). doi:10.4324/9780203771587.  
+
+66. Thomas, P. D. et al. PANTHER: Making genome-scale phylogenetics accessible to all. Protein Sci. 31, 8-22 (2022).  
+
+67. Kallak, T. K. et al. Aromatase inhibitors affect vaginal proliferation and steroid hormone receptors. Menopause 21, 383-390 (2014).  
+
+68. Kallak, T. K. et al. Vaginal gene expression during treatment with aromatase inhibitors. Clin. Breast Cancer 15, 527-535. e2 (2015).  
+
+69. Saitou, M. & Gokcumen, O. An evolutionary perspective on the impact of genomic copy number variation on human health. J. Mol. Evol. 88, 104-119 (2020).  
+
+70. Saitou, M., Satta, Y., Gokcumen, O. & Ishida, T. Complex evolution of the GSTM gene family involves sharing of GSTM1 deletion polymorphism in humans and chimpanzees. BMC Genomics 19, 293 (2018).  
+
+71. Rothman, N. et al. A multi-stage genome-wide association study of bladder cancer identifies multiple susceptibility loci. Nat. Genet. 42, 978-984 (2010).  
+
+72. Aqil, A., Speidel, L., Pavlidis, P. & Gokcumen, O. Balancing selection on genomic deletion polymorphisms in humans. eLife https://doi.org/10.7554/eLife.79111 (2023).  
+
+73. Duret, L. & Mouchiroud, D. Determinants of substitution rates in mammalian genes: expression pattern affects selection intensity but not mutation rate. Mol. Biol. Evol. 17, 68-74 (2000).  
+
+74. Zhang, L. & Li, W.-H. Mammalian housekeeping genes evolve more slowly than tissue-specific genes. Mol. Biol. Evol. 21, 236-239 (2004).  
+
+75. Park, J., Xu, K., Park, T. & Yi, S. V. What are the determinants of gene expression levels and breadths in the human genome? Hum. Mol. Genet. 21, 46-56 (2011).  
+
+76. Li, C., Qu, W. & Yang, X. Comprehensive IncRNA and mRNA profiles in peripheral blood mononuclear cells derived from ankylosing spondylitis patients by RNA-sequencing analysis. Medicine 101, e27477 (2022).
+
+<--- Page Split --->
+
+77. von Grothusen C. Endometrial receptivity and regeneration in health and disease: Molecular, cellular and clinical perspectives. Karolinska Institutet (Sweden, 2022).  
+
+78. Almsned, F. M. Understanding the genetic nature of multiple sclerosis using next-generation sequencing genomic analysis methods. (Doctoral dissertation, George Mason University, 2020).  
+
+79. Chery, G. Understanding Sjögren's Syndrome as a Systemic Autoimmune Disorder. (State University of New York at Albany, 2022).  
+
+80. Islam, T. et al. Detection of multiple sclerosis using blood and brain cells transcript profiles: Insights from comprehensive bioinformatics approach. Informatics in Medicine Unlocked 16, 100201 (2019).  
+
+81. Russell, M., Aqil, A., Saitou, M., Gokcumen, O. & Masuda, N. Gene communities in co-expression networks across different tissues. PLoS Comput. Biol. 19, e1011616 (2023).  
+
+82. Otto, M., Zheng, Y., Grablowitz, P. & Wiehe, T. Detecting adaptive changes in gene copy number distribution accompanying the human out-of-Africa expansion. bioRxiv 2023.08.14.553171 (2024) doi:10.1101/2023.08.14.553171.  
+
+83. Shen, S., Li, H., Liu, J., Sun, L. & Yuan, Y. The panoramic picture of pepsinogen gene family with pan-cancer. Cancer Med. 9, 9064-9080 (2020).
+
+<--- Page Split --->

preprint/preprint__00071c19a357d74c148b616e4f6f54f029c63bf7dc9c70b0f9dba908075f6ed8/preprint__00071c19a357d74c148b616e4f6f54f029c63bf7dc9c70b0f9dba908075f6ed8_det.mmd

@@ -0,0 +1,769 @@
+<|ref|>title<|/ref|><|det|>[[42, 108, 880, 178]]<|/det|>
+# Switch-like Gene Expression Modulates Disease Susceptibility  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 258, 242]]<|/det|>
+Omer Gokcumen gokcumen@gmail.com  
+
+<|ref|>text<|/ref|><|det|>[[44, 304, 104, 322]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 342, 137, 361]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 380, 355, 400]]<|/det|>
+Posted Date: September 13th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 418, 474, 438]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4974188/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 456, 914, 499]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 516, 535, 536]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 572, 916, 615]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on June 18th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 60513- x.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[155, 96, 840, 119]]<|/det|>
+# Switch-like Gene Expression Modulates Disease Susceptibility  
+
+<|ref|>text<|/ref|><|det|>[[115, 144, 879, 183]]<|/det|>
+Authors: Alber Aqil<sup>1, †</sup>, Yanyan Li<sup>2, †</sup>, Zhiliang Wang<sup>2</sup>, Saiful Islam<sup>3</sup>, Madison Russell<sup>2</sup>, Theodora Kunovac Kallak<sup>4</sup>, Marie Saitou<sup>5</sup>, Omer Gokcumen<sup>1, †</sup>, Naoki Masuda<sup>2,3, †</sup>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 209, 198, 222]]<|/det|>
+## Affiliations:  
+
+<|ref|>text<|/ref|><|det|>[[115, 222, 848, 288]]<|/det|>
+1. Department of Biological Sciences, State University of New York at Buffalo, Buffalo, NY, USA.  
+2. Department of Mathematics, State University of New York at Buffalo, Buffalo, NY, USA.  
+3. Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo, Buffalo, NY, USA.  
+4. Department of Women's and Children's Health, Uppsala University, Uppsala, Sweden.  
+5. Faculty of Biosciences, Norwegian University of Life Sciences, Aas, Norway  
+
+<|ref|>text<|/ref|><|det|>[[115, 312, 388, 352]]<|/det|>
+Correspondence: Omer Gokcumen, gokcumen@gmail.com Naoki Masuda, naokimas@gmail.com  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 382, 204, 400]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[114, 402, 880, 750]]<|/det|>
+A fundamental challenge in biomedicine is understanding the mechanisms predisposing individuals to disease. While previous research has suggested that switch- like gene expression is crucial in driving biological variation and disease susceptibility, a systematic analysis across multiple tissues is still lacking. By analyzing transcriptomes from 943 individuals across 27 tissues, we identified 1,013 switch- like genes. We found that only 31 (3.1%) of these genes exhibit switch- like behavior across all tissues. These universally switch- like genes appear to be genetically driven, with large exonic genomic structural variants explaining five ( \(\sim 18\%\) ) of them. The remaining switch- like genes exhibit tissue- specific expression patterns. Notably, tissue- specific switch- like genes tend to be switched on or off in unison within individuals, likely under the influence of tissue- specific master regulators, including hormonal signals. Among our most significant findings, we identified hundreds of concordantly switched- off genes in the stomach and vagina that are linked to gastric cancer (41- fold, \(p< 10^{- 4}\) ) and vaginal atrophy (44- fold, \(p< 10^{- 4}\) ), respectively. Experimental analysis of vaginal tissues revealed that low systemic levels of estrogen lead to a significant reduction in both the epithelial thickness and the expression of the switch- like gene ALOX12. We propose a model wherein the switching off of driver genes in basal and parabasal epithelium suppresses cell proliferation therein, leading to epithelial thinning and, therefore, vaginal atrophy. Our findings underscore the significant biomedical implications of switch- like gene expression and lay the groundwork for potential diagnostic and therapeutic applications.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 115, 241, 132]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[115, 133, 880, 308]]<|/det|>
+The study of gene expression began in earnest with the characterization of lactose- metabolizing switch- like genes in \(E\) coli 1. The presence of lactose triggered the production of enzymes needed to metabolize it, while these enzymes were absent when lactose was not present. These genes acted like switches, toggling between "on" and "off" states based on the presence or absence of lactose, respectively. In subsequent decades, the discovery of enhancer elements 2- 4, epigenetic modifications 5- 8, and transcription factor dynamics 9 revealed that gene expression in humans is more nuanced, resembling a dimmer more often than a simple on- and- off mechanism. Consequently, the study of switch- like genes in humans was largely relegated to the narrow realm of Mendelian diseases 10- 12.  
+
+<|ref|>text<|/ref|><|det|>[[114, 325, 881, 656]]<|/det|>
+The recent availability of population- level RNA- sequencing data from humans has made it possible to systematically identify switch- like versus dimmer- like genes. For dimmer- like genes in a given tissue, we expect expression levels across individuals to be continuously distributed with a single mode, i.e., a unimodal distribution. In contrast, expression levels of switch- like genes in a given tissue are expected to exhibit a bimodal distribution, with one mode representing the "off" state and the other representing the "on" state. As we will detail, bimodal expression across individuals is a characteristic of a gene in a specific tissue, referred to as a gene- tissue pair. We define a gene as switch- like if it exhibits bimodal expression in at least one tissue. Most of the recent studies on bimodal gene expression are related to cancer biology, associating on and off states to different disease phenotypes and their prognoses 13- 15. These cancer studies have already produced promising results for personalized medicine 16. However, to our knowledge, the only study focusing on switch- like genes in non- cancerous tissues across individuals restricted their analysis to muscle tissue 17. As a result, the dynamics of switch- like expression across the multi- tissue landscape remain unknown. We hypothesize that switch- like expression is ubiquitous but often tissue- specific. We further hypothesize that these tissue- specific expression trends underlie common disease states. Therefore, the analysis of switch- like genes across tissues and individuals may provide a means for early diagnosis and prediction of human disease.  
+
+<|ref|>text<|/ref|><|det|>[[115, 671, 879, 812]]<|/det|>
+Here, we systematically identified switch- like genes across individuals in 27 tissues. Our results explain the regulatory bases of switch- like expression in humans, highlighting genomic structural variation as a major factor underlying correlated switch- like expression in multiple tissues. Furthermore, we identified groups of switch- like genes in the stomach and vagina for which the "off" state predisposes individuals to gastric cancer and vaginal atrophy, respectively. Overall, these findings improve our understanding of the regulation of switch- like genes in humans. They also suggest promising future paths for preventative biomedical interventions.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 115, 880, 500]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 510, 883, 585]]<|/det|>
+<center>Figure 1. Methodological framework. A. List of 27 tissues used in this study. B. Distribution of 19,132 genes by the number of tissues in which they are highly expressed. C. Bimodal expression is a property of a gene-tissue pair. We tested 516,564 gene-tissue pairs (19,132 genes x 27 tissues) for bimodal expression across individuals. When a gene-tissue pair exhibits switch-like (bimodal) expression, the individuals divide into two subpopulations: one with the gene switched off, and the other with the gene switched on. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 98, 216, 117]]<|/det|>
+## RESULTS  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 137, 528, 156]]<|/det|>
+## Tissue-specificity of bimodal expression  
+
+<|ref|>text<|/ref|><|det|>[[114, 156, 880, 329]]<|/det|>
+The misregulation of highly expressed genes often has consequences for health and fitness. To systematically identify biomedically relevant switch- like genes in humans, we focused on 19,132 genes that are highly expressed (mean \(\mathrm{TPM} > 10\) ) in at least one of the 27 tissues represented in the GTEx database (Figure 1A; Figure 1B; Table S1). For each of the 516,564 gene- tissue pairs (19,132 genes \(\times 27\) tissues), we applied the dip test of unimodality \(^{18}\) to the expression level distribution across individuals (Figure 1C). Employing the Bejamini- Hochberg procedure for multiple hypotheses correction, we identified 1,013 switch- like genes (Figure 1C; Methods; Table S2). The expression of these genes is bimodally distributed in at least one tissue, such that it is switched "off" for one subset of individuals and switched "on" for the rest of the individuals.  
+
+<|ref|>text<|/ref|><|det|>[[114, 346, 876, 660]]<|/det|>
+Expression of different switch- like genes may be bimodally distributed in different numbers of tissues. We contend that genes that are bimodally expressed across all tissues are likely so due to a germline genetic polymorphism driving switch- like expression across tissues. If this is the case, the expression of these genes would be highly correlated across pairs of tissues. Given this insight, discovering universally bimodal genes is more tractable using tissue- to- tissue co- expression of each gene. Therefore, for each gene, we calculated the pairwise correlation of expression levels across pairs of tissues (Methods; Table S3). To visualize tissue- to- tissue co- expression patterns of genes, we performed principal component analysis (PCA) on the tissue- to- tissue gene co- expression data (Table S4). We emphasize that we are referring to the co- expression of the same gene across pairs of tissues instead of the co- expression of pairs of genes in the same tissue. In the space spanned by the first two principal components (explaining \(35.3\%\) and \(3.47\%\) of the variance, respectively), switch- like genes form two major clusters (cluster 1 and cluster 2; Methods), dividing along PC1 (Figure 2A). Applying PCA exclusively to switch- like genes reveals the further division of cluster 2 into two distinct subclusters – cluster 2A and cluster 2B – in the space spanned by the first two principal components (explaining \(58.1\%\) and \(4.25\%\) of the variance, respectively) (Figure 2B; Table S5).  
+
+<|ref|>text<|/ref|><|det|>[[114, 676, 878, 835]]<|/det|>
+Manual inspection reveals that cluster 1, which contains 954 genes, represents genes, such as KRT17, with bimodal expression in a small subset of tissues (Figure 2C). Cluster 2A consists of 23 genes, such as GPX1P1, with bimodal expression in all tissues (Figure 2D). Lastly, cluster 2B represents eight genes, such as EIF1AY, with bimodal expression in all non- sex- specific tissues but not in sex- specific tissues (Figure 2E). We will refer to genes in cluster 1 as "tissue- specific switch- like genes." Although some of them are bimodally expressed in more than one tissue, these genes tend to exhibit high tissue specificity in their bimodal expression. Genes in cluster 2 will be referred to as "universally switch- like genes."
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 880, 518]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 519, 879, 666]]<|/det|>
+<center>Figure 2. Categorization of switch-like genes. A. PCA analysis of tissue-pair correlations of gene expression. Each point represents a gene. When we perform PCA on the tissue-to-tissue co-expression vectors for 19,132 genes, the switch-like genes divide into two clusters. Cluster 1 primarily represents genes that are bimodally expressed in a tissue-specific manner, while cluster 2 represents genes that are bimodally expressed in at least all non-sex-specific tissues. B. Performing PCA on the co-expression vectors of only switch-like genes further divides cluster 2 into two subclusters: cluster 2A, which contains genes that are bimodally expressed across all 27 tissues, and cluster 2B, which contains genes that are bimodally expressed in all 22 tissues common to both sexes, but not in the five sex-specific tissues. C-E. Violin plots display the expression levels in all 27 tissues for representative genes from cluster 1, cluster 2A, and cluster 2B, respectively. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 700, 689, 720]]<|/det|>
+## Genetic variation underlies universally switch-like genes  
+
+<|ref|>text<|/ref|><|det|>[[115, 720, 880, 860]]<|/det|>
+We found that \(3.1\%\) of all switch- like genes (i.e., the proportion of switch- like genes that are in cluster 2) show clear bimodal expression, at least in all tissues common to both sexes. We contend that germline genetic variation across individuals likely underlies the universally switch- like gene expression, specifically due to four major types of genetic variants. Firstly, we expect genes on the Y chromosome to show bimodal expression in all tissues common to both sexes since these genes are present in males and absent in females (Figure 3A). Consistent with this reasoning, seven out of the eight genes in cluster 2B lie within the male- specific region of the Y- chromosome \(^{19}\) ; the remaining
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 880, 265]]<|/det|>
+gene in cluster 2B is XIST, showing female- specific expression. Secondly, a homozygous gene deletion would result in the gene being switched off (Figure 3B). We found five such genes in cluster 2A for which genomic structural variants likely underlie the observed universally switch- like expression; four genes are affected by gene deletions, and the remaining one by an insertion into the gene. Thirdly, the homozygous deletion of a regulatory element can also switch off a gene (Figure 3C). While we did not find any examples of this scenario, it remains a theoretical possibility. Lastly, a loss- of- function single nucleotide variant (SNV) or short indel, which disrupts gene function, can switch off the gene (Figure 3D). We identified five genes in cluster 2A where such SNVs cause universal bimodality.  
+
+<|ref|>text<|/ref|><|det|>[[114, 280, 872, 492]]<|/det|>
+Remarkably, we could genetically explain the expression of 10 out of 23 (43%) cases in cluster 2A despite the small number of genes fitting our conservative definition for universally switch- like genes. SNVs underlie five of these cases (Figure 3B), while structural variants underlie the remaining five cases (Figure 3D). Thus, out of the 10 cases where we can explain the genetic underpinnings of switch- like expression, 50% involve genomic structural variation, highlighting the importance of this type of genetic variation. Although we could not identify the genetic variation underlying the bimodal expression of the remaining 13 genes in cluster 2A, their consistent and highly correlated switch- like expression across all tissues strongly suggests a genetic basis. We anticipate that better resolution assemblies and detailed regulatory sequence annotations will help identify the genetic variants responsible for the remaining universally switch- like genes.  
+
+<|ref|>image<|/ref|><|det|>[[114, 505, 780, 867]]<|/det|>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 90, 880, 207]]<|/det|>
+Figure 3. Genetic bases of universally switch-like gene expression (cluster 2). A. Genes on the Y chromosome are expressed only in males, leading to bimodal expression in non- sex- specific tissues. B. Common structural variants, such as deletions or insertions, may lead to increased, decreased, or no expression in all tissues relative to individuals who carry the alternative allele. C. Common structural variants affecting a genomic region regulating a gene may lead to increased, decreased, or no expression in all tissues, relative to individuals who carry the alternative allele. D. Common single nucleotide variants or short indels affecting a gene or its regulatory region may lead to increased, decreased, or no expression in all tissues relative to individuals who carry the alternative allele.  
+
+<|ref|>text<|/ref|><|det|>[[114, 223, 881, 521]]<|/det|>
+We highlight a clear example of a common structural variant leading to universally switch- like expression (Figure 3B). USP32P2 and FAM106A – both universally switch- like genes – are bimodally expressed in all 27 tissues. Both genes show high levels of tissue- to- tissue co- expression. A common 46 kb deletion (esv3640153), with a global allele frequency of \(\sim 25\%\) , completely deletes both genes (Figure 4A- B). We propose that this deletion accounts for the universal switch- like expression of both USP32P2 and FAM106A in all tissues. For illustration, we show the expression level distributions of USP32P2 and FAM106A in the cerebellum (Figures 4C- D). Indeed, the haplotype harboring this deletion is strongly associated with the downregulation of both genes in all 27 tissues \((p< 10^{- 5}\) for every single gene- tissue pair, Methods). We note that the under- expression of USP32P2 in sperm is associated with male infertility \(^{20}\) , and plausibly, homozygous males for the deletion may be prone to infertility. Additionally, FAM106A interacts with SARS- CoV- 2 and is downregulated after infection, at least in lung- epithelial cells \(^{21 - 23}\) . Individuals with FAM106A already switched off may develop more severe COVID- 19 symptoms upon infection, though further investigation is needed. The case of FAM106A and USP32P2 exemplifies the link between disease and bimodal gene expression, a theme we will explore further in the remainder of this text.  
+
+<|ref|>text<|/ref|><|det|>[[114, 536, 875, 870]]<|/det|>
+We caution that we base our results regarding bimodality on expression at the RNA level. The bimodal expression of genes across individuals at the RNA level may not necessarily lead to bimodal expression at the protein level. For example, the universally switch- like expression of RPS26 at the RNA level can be explained by a single nucleotide variant (rs1131017) in the gene's 5'- untranslated region (UTR). In particular, RPS26 has three transcription states based on the SNV genotypes. The ancestral homozygote C/C corresponds to a high transcription state, the heterozygote C/G to a medium state, and the derived homozygote G/G to a low state (See Supplement for a discussion on why an expression distribution driven by three genotypes at a polymorphic site might still appear bimodal). Remarkably, this pattern is reversed at the translation level \(^{24}\) : Messenger RNA carrying the derived G allele produces significantly more protein. This reversal may be due to a SNV in the 5'- UTR that can abolish a translation- initiation codon \(^{25}\) . This finding demonstrates how the same SNV can regulate a gene's expression level in opposite directions during transcription and translation. This multi- level regulation in opposite directions likely serves to dampen protein expression variability. It has been shown previously that RNA variability is greater than protein variability in primates \(^{26,27}\) ; the presence of dampening variants discussed here may be one reason behind these findings. Such compensatory mechanisms for gene expression remain fascinating areas for future research.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[117, 110, 872, 760]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 763, 879, 867]]<|/det|>
+<center>Figure 4. An example of a polymorphic gene deletion resulting in universally switch-like gene expression. A. FAM106A and USP32P2 (not drawn to scale) are overlapping genes on chromosome 17. Two alternative haplotype classes exist for these genes: one in which both genes are completely deleted and the other without the deletion. B. Frequency distribution of the deletion across diverse populations. Each pie chart represents one of the 26 populations from the 1000 Genomes Project. Purple indicates the frequency of the deletion, while gray indicates the frequency of the alternative haplotype. C-D. Expression level distribution in the cerebellum (as an example) across individuals for FAM106A and USP32P2, </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 844, 106]]<|/det|>
+respectively. The gene deletion presumably leads to the switched- off expression state in both genes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 119, 825, 140]]<|/det|>
+## Tissue-specific switch-like genes have a shared regulatory framework  
+
+<|ref|>text<|/ref|><|det|>[[114, 139, 875, 348]]<|/det|>
+Tissue- specific expression patterns are crucial for tissue function. Thus, we now turn our attention to tissue- specific switch- like genes. We found that the stomach, vagina, breast, and colon show a higher number of tissue- specific switch- like genes compared to other tissues (Figure 5A), after controlling for confounding factors (Methods; Supplement; Table S6). Furthermore, within these tissues, the expression of switch- like genes is not independent; instead, they exhibit high pairwise co- expression between genes (Figure 5B- C; Table S7). Hence, tissue- specific switch- like genes tend to be either all switched off or switched on within an individual. This result suggests a shared regulatory mechanism for the expression of these genes in each tissue. Given that hormonal regulation plays a substantial role in shaping tissue- specific expression patterns \(^{28,29}\) , we hypothesize that hormones may regulate genes that are bimodally expressed in specific tissues (cluster 1; Figure 2B).  
+
+<|ref|>text<|/ref|><|det|>[[114, 363, 879, 540]]<|/det|>
+Sexual differences in hormonal activity are well documented \(^{30,31}\) . To explore this further, we investigated whether hormone- mediated sex- biased expression underlies the co- expression of tissue- specific switch- like genes within tissues. Under this scenario, a gene would be largely switched on in one sex and off in the other in a given tissue. Among tissue- specific switch- like genes, we identified 186 gene- tissue pairs with sex- biased bimodal expression (Figure 6A; Table S8). These instances are biologically relevant; for example, we found switch- like immunoglobulins genes with female- biased expression in the thyroid, heart, tibial nerve, and subcutaneous adipose tissue. This observation may relate to previous findings \(^{32,33}\) of higher antibody responses to diverse antigens in females than in males.  
+
+<|ref|>text<|/ref|><|det|>[[114, 555, 880, 835]]<|/det|>
+More dramatically, we found that 162 out of 164 tissue- specific switch- like genes (cluster 1) in the breast tissue are female- biased, explaining their correlated expression levels (Figure 6A). However, the sex- based disparity in the on- versus- off states of these genes is not absolute, but rather a statistical tendency. In other words, the gene is not switched off in all males and switched on in all females. Instead, the proportion of individuals with the gene switched on significantly differs between sexes. Notably, multiple sex- biased switch- like genes—including SPINT1 and SPINT2 \(^{34}\) , multiple keratin genes \(^{35}\) , and the oxytocin receptor gene \(^{36,37}\) (OXTR; Figure 6B)—in the breast tissue are differentially expressed in breast cancers relative to matched non- cancerous tissues. Future investigations could reveal whether the toggling of these genetic switches affects breast cancer risk in females. We caution that sex- biased switch- like expression in the breast may result from differences in cell- type abundance between females and males. Nevertheless, the differential expression of some genes between sexes might developmentally drive such differences in cell- type abundance. In summary, our results indicate that sex is a major contributor to bimodal gene expression, with breast tissue standing out as particularly sex- biased in this context.  
+
+<|ref|>text<|/ref|><|det|>[[115, 851, 850, 870]]<|/det|>
+We note that the intra- tissue co- expression of tissue- specific switch- like genes in the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 89, 876, 265]]<|/det|>
+stomach and colon cannot be explained by sex. By biological definition, the variation in vaginal expression levels in our sample is not sex- biased. Thus, the intra- tissue co- expression of tissue- specific switch- like genes in the stomach, colon, and vagina may be explained by one of two reasons: 1) Most of the tissue- specific switch- like genes in each tissue are directly regulated by the same hormone in that tissue, or 2) Most of the tissue- specific switch- like genes in each tissue are regulated by the same transcription factor which is, in turn, under regulation by a hormone or other cellular environmental factors. In the case of hormonally controlled gene expression, genes are likely switched off when the systemic hormone levels drop below a certain threshold. We will discuss this idea further, specifically for the vagina, later in the text.  
+
+<|ref|>image<|/ref|><|det|>[[115, 280, 875, 673]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 677, 880, 838]]<|/det|>
+<center>Figure 5. Characterization of genuine tissue-specific switch-like genes (cluster 1). The results shown here exclude genes that showed switch-like expression due to confounding factors like ischemic time. A. Number of tissue-specific switch-like genes showing bimodal expression in each of the 27 tissues. The stomach, vagina, breast, and colon show disproportionately more tissue-specific switch-like genes than other tissues. B. An illustration of how Pearson's correlation coefficients were calculated for each pair of bimodally expressed tissue-specific switch-like genes within the stomach, vagina, breast, and colon. We show the scatterplots for two arbitrarily chosen gene pairs for each of the four tissues. The axes in each dot plot represent the \(\log (TPM + 1)\) for the labeled gene in the relevant tissue. Panel C was generated using the pairwise correlation coefficients thus obtained. C. Tissue-specific switch-like genes within the four tissues shown are highly co-expressed. Tissue-specific master regulators, such as endocrinological signals, likely drive their concordant on and off states. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[117, 90, 875, 640]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 643, 879, 762]]<|/det|>
+<center>Figure 6. Sex-biased expression of tissue-specific switch-like genes (cluster 1). A. Number of tissue-specific switch-like genes that show female- and male-biased expression. Only those tissues are shown that have at least one tissue-specific switch-like gene showing sex bias. The number in the central grid next to each tissue image represents the number of genuine tissue-specific switch-like genes in that tissue. In orange, the numbers to the left of the central grid indicate the count of female-biased genes in each of the 10 tissues shown. In blue, the numbers to the right of the grid indicate the count of male-biased genes. B. Violin plots showing the expression level distribution in the breast for five female-biased tissue-specific switch-like genes discussed in the main text. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 814, 761, 854]]<|/det|>
+## Concordantly switched-off genes in the stomach may indicate a predisposition to gastric cancer  
+
+<|ref|>text<|/ref|><|det|>[[115, 852, 872, 872]]<|/det|>
+Gene expression levels have been studied as a diagnostic marker for disease states \(^{38}\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 89, 868, 177]]<|/det|>
+Therefore, we asked whether tissue- specific switch- like genes co- expressed with each other across individuals are linked to human disease, with each of the two expression states corresponding to different risks. To address this question, we investigated whether the identified switch- like genes in a given tissue are overrepresented among genes implicated in diseases of the same tissue.  
+
+<|ref|>text<|/ref|><|det|>[[114, 193, 879, 388]]<|/det|>
+We overlapped the switch- like genes in the stomach with a previously published list \(^{39}\) of differentially expressed genes in gastric carcinomas. We found that switch- like genes in the stomach are significantly enriched (41- fold enrichment, \(p< 10^{- 4}\) ) among genes that are downregulated in gastric carcinomas. Specifically, nine switch- like genes are downregulated in gastric carcinomas (ATP4A, ATP4B, CHIA, CXCL17, FBP2, KCNE2, MUC6, TMEM184A, and PGA3). Additionally, these nine genes are concordantly expressed in \(92.5\%\) (332/359) of the stomach samples, being either all switched off or on in a given individual (Methods). Our data suggest that individuals with these nine genes switched off in the stomach may be susceptible to developing cancers. This preliminary observation provides exciting avenues to investigate both the cause of the concordant toggling of these genes and their potential role in cancer development.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 404, 704, 424]]<|/det|>
+## Concordantly switched-off genes result in vaginal atrophy  
+
+<|ref|>text<|/ref|><|det|>[[114, 423, 880, 615]]<|/det|>
+We found that switch- like genes in the vagina are significantly overrepresented (44- fold enrichment; \(p< 10^{- 4}\) ; see methods) among genes linked to vaginal atrophy in postmenopausal women. Vaginal atrophy, affecting nearly half of postmenopausal women, is triggered by sustained low levels of systemic estrogen and is marked by increased microbial diversity, higher pH, and thinning of the epithelial layer in the vagina \(^{40,41}\) . It is also known as atrophic vaginitis, vulvovaginal atrophy, estrogen- deficient vaginitis, urogenital atrophy, or genitourinary syndrome of menopause, depending on the specialty of the researchers. Symptoms experienced by women include dryness, soreness, burning, decreased arousal, pain during intercourse, and incontinence \(^{42}\) . Our analysis of switch- like genes in the vagina provides new insights into the development of vaginal atrophy.  
+
+<|ref|>text<|/ref|><|det|>[[114, 631, 877, 858]]<|/det|>
+Specifically, we overlapped a previously published list \(^{43}\) of genes that are transcriptionally downregulated in vaginal atrophy with our list of bimodally expressed genes in the vagina. We found that the genes SPINK7, ALOX12, DSG1, KRTDAP, KRT1, and CRISP3 are both bimodally expressed in the vagina and transcriptionally downregulated (presumably switched off) in women with vaginal atrophy (Figure 7A). We refer to these genes as "atrophy- linked switch- like genes." Indeed, these six genes are either all switched on, or all switched off concordantly in \(84\%\) (131/156) of the vaginal samples we studied. The pairwise concordance rates (percentage of individuals with both genes switched on or both genes switched off) for these genes are shown in Figure 7B. Among postmenopausal women with this concordant gene expression, \(50\%\) are in the "off" state – a fraction that closely matches the prevalence of vaginal atrophy in postmenopausal women \(^{40,44}\) . Therefore, our data suggest that estrogen- dependent transcription underlies concordant expression of atrophy- linked switch- like genes, with
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 648, 108]]<|/det|>
+the "off" state of these genes associated with vaginal atrophy.  
+
+<|ref|>text<|/ref|><|det|>[[114, 123, 881, 440]]<|/det|>
+For background, the vaginal epithelial layers are differentiated from the inside out. The basal and parabasal layers of the epithelium consist of mitotic progenitor cells with differentiation potential, while the outermost layer comprises the most differentiated cells \(^{45,46}\) . When basal and parabasal cells stop proliferating, the death of mature cells leads to a thin epithelium, and the symptoms of vaginal atrophy appear. Given this background, atrophy- linked switch- like genes may either be a cause or a consequence of vaginal atrophy. In particular, if an atrophy- linked switch- like gene encodes a protein necessary for the continued proliferation and differentiation of basal and parabasal cells, we call it a "driver" gene. In the absence of the driver gene's protein, cell differentiation ceases, and the outer layer gradually disappears, resulting in vaginal atrophy (Figure 8A). On the other hand, if the product of an atrophy- linked switch- like gene is not required for basal and parabasal cell proliferation, we refer to it as a "passenger" gene, borrowing the terminology from cancer literature \(^{47}\) . In healthy vaginas with a thick epithelium, there are more cells in which passenger genes would be expressed. By contrast, in atrophic vaginas, the epithelium thins, resulting in fewer cells where these genes can be expressed. This contrast would lead to the bimodal expression of passenger genes across vagina samples in whole- tissue RNA- sequencing datasets. We hypothesize that at least some of the atrophy- linked switch- like genes are driver genes.  
+
+<|ref|>text<|/ref|><|det|>[[114, 454, 880, 700]]<|/det|>
+Two key findings allowed us to construct this hypothesis. Firstly, switch- like genes in the vagina show a 26- fold ontological enrichment for the establishment of the skin barrier \(\mathrm{(FDR = 1.26\times 10^{- 6})}\) and a 25- fold enrichment for keratinocyte proliferation \(\mathrm{(FDR = 1.75\times}\) \(10^{- 4})\) , both related to epithelial thickness and differentiation. Notably, two atrophy- linked switch- like genes in the vagina that we identified, KRTDAp and KRT1, are crucial for the differentiation of epithelial cells in the vagina \(^{48,49}\) . Protein stainings available through Human Protein Atlas \(^{50}\) show that all six atrophy- linked switch- like genes are expressed at the protein level, predominantly in the vaginal epithelium. Secondly, administering 17β- estradiol (a type of estrogen) to postmenopausal women with vaginal atrophy leads to the upregulation of the same six genes, causing symptoms to subside \(^{51}\) . According to our hypothesis, administering estrogen activates the expression of the driver switch- like genes in the vagina, resuming the proliferation of basal and parabasal cells in the epithelium. This process leads to the reformation of a thick and healthy vaginal mucosa, thereby alleviating the symptoms of vaginal atrophy.  
+
+<|ref|>text<|/ref|><|det|>[[115, 715, 877, 856]]<|/det|>
+Thus, it is essential to distinguish driver genes from passenger genes to understand the etiology of vaginal atrophy. However, we expect driver and passenger genes to show the same expression patterns in healthy versus atrophic vaginas using bulk RNA- sequencing data. In order to make this distinction, we need comparative expression data, specifically from the basal and parabasal epithelium from healthy versus atrophic vaginas. We expect driver genes to be differentially expressed in the basal and parabasal layers of the epithelium. By contrast, we expect passenger genes to show no differential expression in the basal and parabasal layers between healthy and atrophic
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 91, 189, 108]]<|/det|>
+vaginas.  
+
+<|ref|>text<|/ref|><|det|>[[114, 124, 875, 405]]<|/det|>
+To look at the expression levels in the basal and parabasal layers of the epithelium, we arbitrarily chose ALOX12 from the six atrophy- linked switch- like genes for immunohistochemical staining of its protein product in the vaginal mucosa (which includes the epithelium and the underlying connective tissue). We found that the ALOX12 protein is present in the epithelial cells, and its abundance directly correlates with epithelial thickness, as expected from our RNA- sequencing results. However, we found no significant difference in the staining of the ALOX12 protein in the basal or parabasal epithelial layers between healthy and atrophic samples (Figure 8B). This suggests that the gene is not differentially expressed in the basal or parabasal layers of the vaginal epithelium between healthy and atrophic vaginas. Therefore, ALOX12 is a passenger gene for vaginal atrophy. Comparative immunohistochemical staining of the protein product of the other five atrophy- linked switch- like genes may identify the driver gene in the future. Indeed, the KRT1 protein is recognized as a marker of basal cell differentiation in mouse vaginas \(^{52}\) , a finding that may also be true for humans. Overall, our results open up several new paths for potential pre- menopausal risk assessment and intervention frameworks targeting cell differentiation pathways in the clinical setting.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 88, 850, 740]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 742, 879, 860]]<|/det|>
+<center>Figure 7. Atrophy-linked switch-like genes tend to be either all switched off, or all switched on within individuals. A. The distribution of expression levels in the vagina of the six switch-like genes implicated in vaginal atrophy. The x-axes represent \(\log (TPM + 1)\) values for each gene in the vagina, and the y-axes represent the probability density. We obtained the probability densities using kernel density estimation. In each case, the global minimum (excluding endpoints) is considered the switching threshold. A gene is deemed “on” in an individual if the expression level is above this threshold; otherwise, the gene is deemed “off.” B. Pairwise concordance rates (percentage of individuals in which the two genes are either both switched on or both switched off). </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[114, 88, 875, 850]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 848, 842, 867]]<|/det|>
+<center>Figure 8. ALOX12 is a passenger gene. A. Model for the etiology of vaginal atrophy. High levels of </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 89, 881, 236]]<|/det|>
+estrogen keep the driver genes switched on in basal and parabasal epithelium, impelling basal and parabasal cells to proliferate and mature, resulting in healthy vaginal mucosa. Conversely, low levels of estrogen switch off the driver genes. The lack of basal and parabasal cell proliferation leads to a thin vaginal epithelium, resulting in vaginal atrophy. B. Representative immunohistochemical staining of Arachidonate 12- Lipoxygenase (ALOX12) in vaginal tissue. We show healthy vaginal tissue from a woman with higher systemic estrogen levels and a thicker vaginal epithelial layer, along with atrophic vaginal tissue from a woman with low systemic estrogen levels and a thinner vaginal epithelial layer. There is no difference in ALOX12 expression in the basal or parabasal cells between healthy and atrophic epithelium, implicating it as a passenger gene. Images taken with Axio Observer Z1 (Carl Zeiss AG) with a 40X objective.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 255, 230, 272]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[114, 273, 881, 535]]<|/det|>
+In this study, we investigated factors underlying switch- like gene expression and its functional consequences. Our systematic analysis revealed 1,013 switch- like genes across 943 individuals. Some of these genes show bimodal expression across individuals in all tissues, suggesting a genetic basis for their universally switch- like behavior. We found several single nucleotide and structural variants to explain the switch- like expression of these genes. Most of the switch- like genes, however, exhibit tissue- specific bimodal expression. These genes tend to be concordantly switched on or off in individuals within the breast, colon, stomach, and vagina. This concordant tissue- specific switch- like expression in individuals is likely due to tissue- specific master regulators, such as endocrinological signals. For example, in the vagina, switch- like genes tend to get concordantly switched off in a given individual when systemic estrogen levels fall below a certain threshold. On the biomedical front, our work linked switch- like expression to the susceptibility to gastric cancer and vaginal atrophy. Furthermore, this study has paved two major paths forward toward early medical interventions, as discussed below.  
+
+<|ref|>text<|/ref|><|det|>[[114, 551, 876, 850]]<|/det|>
+First, we emphasize that bimodal expression that is correlated across all tissues is driven by genetic polymorphisms. However, the genetic bases for 13/23 universally switch- like genes remain elusive. We propose that the underlying genetic bases for these universally switch- like genes are structural variants, which are not easily captured by short- read DNA sequencing. These structural variants may be discovered in the future as population- level long- read sequencing becomes more common. The first biomedical path forward is to use long- read DNA sequencing to pinpoint the genetic polymorphisms responsible for the bimodal expression of disease- related genes. Of particular interest are the genes CYP4F24P and GPX1P1, both long non- coding RNAs, which are implicated in nasopharyngeal cancer. The genetic basis for their bimodal expression remains unknown. CYP4F24P is significantly downregulated in nasopharyngeal cancer tissues \(^{53}\) , while GPX1P1 is significantly upregulated in nasopharyngeal carcinomas treated with the potential anticancer drug THZ1 \(^{54}\) . Investigating whether individuals with naturally switched- off GPX1P1 and CYP4F24P are at a higher risk of nasopharyngeal cancer will enable genotyping to identify individuals at elevated risk for nasopharyngeal cancer, facilitating early interventions and improving patient outcomes.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 90, 875, 404]]<|/det|>
+Secondly, switch- like genes present a promising avenue for exploring gene- environment interactions, an area of growing interest. Recent studies indicate that environmental factors can significantly modulate genetic associations \(^{55,56}\) . Polymorphisms that result in switch- like gene expression have already been linked to several diseases within specific environmental contexts \(^{57}\) . For instance, the deletion of GSTM1 has been associated with an increased risk of childhood asthma, but only in cases where the mother smoked during pregnancy \(^{58}\) . Even more critically, switch- like genes potentially create unique cellular environments that could modulate the impact of genetic variations. We hypothesize that switch- like expression can produce diverse cellular environments, whether in a single gene (as in genetically determined cases) or in multiple genes (as in tissue- specific, hormonally regulated cases). These environments may, in turn, influence the effect of genetic variations and their associations with disease. Thus, much like current gene- environment association studies that control for factors such as birthplace, geography, and behaviors like smoking, it is conceivable that controlling for switch- like gene expression states could enhance the power of such studies. By cataloging these switch- like genes and developing a framework to classify them as "on" or "off" in various samples, our work lays the groundwork for more robust association studies in future research.  
+
+<|ref|>text<|/ref|><|det|>[[115, 419, 883, 525]]<|/det|>
+In summary, our study has significant implications for understanding the fundamental biology of gene expression regulation and the biomedical impact of switch- like genes. Specifically, it contributes to the growing repertoire of methods for determining individual susceptibility to diseases, facilitating early therapeutic interventions. By providing a new approach to studying gene expression states, our study will enhance the predictive accuracy of disease susceptibility and improve patient outcomes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 543, 280, 560]]<|/det|>
+## Acknowledgment  
+
+<|ref|>text<|/ref|><|det|>[[115, 560, 878, 700]]<|/det|>
+O.G. and N.M. acknowledge support from the National Institute of General Medical Sciences (under grant no.1R01GM148973- 01). N.M. also acknowledges support from the Japan Science and Technology Agency (JST) Moonshot R&D (under grant no.JPMJMS2021), the National Science Foundation (under grant no.2052720), and JSPS KAKENHI (under grant no.JP 24K14840). O.G. acknowledges support from the National Science Foundation (under grant nos.2049947 and 2123284). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 752, 215, 770]]<|/det|>
+## METHODS  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 782, 160, 799]]<|/det|>
+## Data  
+
+<|ref|>text<|/ref|><|det|>[[116, 808, 875, 860]]<|/det|>
+The Genotype- Tissue Expression (GTEx) project is an ongoing effort to build a comprehensive public resource to study tissue- specific gene expression and regulation. The data we use are transcript per million (TPM) obtained from human samples across
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 879, 317]]<|/det|>
+54 tissues and 56,200 genes (as of December 1st, 2023). We excluded laboratory- grown cell lines from our analysis. Since we need a reasonable number of individuals from each tissue, we excluded tissues with less than 50 individuals for our calculations. Of the remaining tissues, there were instances of multiple tissues from the same organ. In such cases, we randomly chose one tissue per organ. We thus focus our analysis on 27 tissues (Figure 1). Additionally, we retained only those genes for which the mean TPM across individuals was greater than 10 in at least one of the 27 focal tissues. This filter was applied because the analysis of lowly expressed genes may lead to false positive calls for bimodal expression and, as a result, to assign biological significance to cases where there is none. After these filtering steps, we are left with TPM data from 19,132 genes in each of the 27 tissues. We note that each tissue contains data from a different number of samples (individuals), totaling 943 across tissues. We will refer to this set of 19,132 genes as \(G\) in our equations and the rest of the methods.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 342, 190, 360]]<|/det|>
+## Dip test  
+
+<|ref|>text<|/ref|><|det|>[[114, 366, 883, 605]]<|/det|>
+There are many tests of bimodality of gene expressions \(^{16,59}\) . We use a dip test described as follows. We denote by \(S_{i}\) the number of samples (individuals) available for tissue \(i\) . We also denote by \(x_{g,i,s}\) the TPM value for gene \(g\) in tissue \(i\) , for sample \(s \in \{1, \ldots , S_{i}\}\) and \(g \in G\) . According to convention, we log- transform the TPM, specifically by \(\log (x_{g,i,s} + 1)^{60}\) to suppress the effect of outliers; TPM is extremely large for some samples. Note that \(\log (x_{g,i,s} + 1)\) conveniently maps \(x_{g,i,s} = 0\) to 0. For each pair of gene \(g\) and tissue \(i\) , we carried out a dip test, which is a statistical test for multimodality of distributions, on the distribution of \(\log (x_{g,i,s} + 1)\) across the samples \(S_{i}\) . We performed the dip test using the dip.test() function within the "diptest" package in R, with the number of bootstrap samples equal to 5000. We applied the Benjamini- Hochberg procedure for multiple hypothesis correction to the results with a false discovery rate of 5%. Additionally, to reduce false positive calls of bimodal expression, we only retained results where the dip statistic \(D > \max [0.05, 0.05 / \log (\bar{x}_{g,i})]\) , where  
+
+<|ref|>equation<|/ref|><|det|>[[425, 610, 572, 669]]<|/det|>
+\[\bar{x}_{g,i} = \frac{1}{S_i}\sum_{s = 1}^{S_i}x_{g,i,s}\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 674, 882, 803]]<|/det|>
+We obtained this threshold of 0.05 by visual inspection of \(\log (x_{g,i,s} + 1)\) distributions in the stomach and adipose subcutaneous tissues, starting with those with the highest values of \(D\) . For statistically significant results, the distribution was almost always bimodal if \(D\) exceeded 0.05. The only exceptions were genes with low \(\bar{x}_{g,i}\) . Thus, we penalized gene- tissue pairs with low \(\bar{x}_{g,i}\) across samples by requiring a higher \(D\) in order to classify them as bimodally distributed. Genes identified as bimodally distributed in at least one tissue are referred to as "switch- like" genes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 811, 492, 829]]<|/det|>
+## Tissue-to-tissue co-expression of genes  
+
+<|ref|>text<|/ref|><|det|>[[115, 829, 875, 864]]<|/det|>
+We sought to identify switch- like genes whose expression exhibits bimodal expression in all tissues. One seemingly straightforward approach is to count the number of tissues
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 880, 252]]<|/det|>
+showing bimodal distribution of expression levels for each gene. However, even if a gene genuinely exhibits bimodal expression across all tissues, our methodology may fail to recognize it as such if the mean expression levels \((\bar{x}_{g,i})\) of the gene are low in some tissues. This is because our effect size threshold penalizes gene- tissue pairs with low \(\bar{x}_{g,i}\) . Moreover, if gene expression follows a bimodal distribution across all tissues, then it does so likely due to a genetic polymorphism affecting expression. Thus, the expression of such genes would be highly correlated between pairs of tissues. Given this insight, discovering universally bimodal genes is more tractable using tissue- to- tissue co- expression of each gene.  
+
+<|ref|>text<|/ref|><|det|>[[113, 258, 876, 512]]<|/det|>
+For each gene, we construct the co- expression matrix among pairs of tissues as follows. To calculate the co- expression between a pair of tissues, we need to use the samples whose TPM is measured for both tissues \(^{61}\) . In general, even if the number of samples is large for both of the two tissues, it does not imply that there are sufficiently many common samples. Therefore, using the sample information described in GTEx_Analysis_v8_Annotations_SampleAttributesDD.xlsx in the GTEx data portal, we counted the number of samples shared by each tissue pair and excluded the 41 tissue pairs that share less than 40 samples. For each of the remaining \(27 \times 26 / 2 - 41 = 310\) tissue pairs, we denote by \(S_{i,j}\) the number of samples shared by the two tissues \(i\) and \(j\) . We also denote by \(x_{g,i,s}\) and \(x_{g,j,s}\) the TPM value for gene \(g\) in tissues \(i\) and \(j\) , respectively, for sample \(s \in \{1, 2, \ldots , S_{i,j}\}\) . Then, we calculated the Pearson correlation coefficient between \(\log (x_{g,i,s} + 1)\) and \(\log (x_{g,j,s} + 1)\) across the \(S_{i,j}\) samples and used it as the strength of the co- expression of gene \(g\) between tissues \(i\) and \(j\) . Specifically, we calculate  
+
+<|ref|>equation<|/ref|><|det|>[[210, 518, 787, 586]]<|/det|>
+\[r_{g}(i,j) = \frac{\sum_{s = 1}^{S_{i,j}}[\log(x_{g,i,s} + 1) - m_{g,i}][\log(x_{g,j,s} + 1) - m_{g,j}]}{\sqrt{\sum_{s = 1}^{S_{i,j}}[\log(x_{g,i,s} + 1) - m_{g,i}]^{2}\sum_{s = 1}^{S_{i,j}}[\log(x_{g,j,s} + 1) - m_{g,j}]^{2}}}\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 592, 171, 608]]<|/det|>
+where  
+
+<|ref|>equation<|/ref|><|det|>[[114, 614, 365, 648]]<|/det|>
+\[m_{g,i} = \frac{1}{S_{i,j}}\sum_{s = 1}^{S_{i,j}}\log (x_{g,i,s} + 1),\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 656, 150, 672]]<|/det|>
+and  
+
+<|ref|>equation<|/ref|><|det|>[[114, 679, 370, 712]]<|/det|>
+\[m_{g,j} = \frac{1}{S_{i,j}}\sum_{s = 1}^{S_{i,j}}\log (x_{g,j,s} + 1).\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 761, 880, 857]]<|/det|>
+For each gene \(g\) , we then vectorize the correlation matrix, \((r_{g}(i,j))\) , into a 310- dimensional vector. If, for a given gene, \(g\) , \(\log (x_{g,i,s} + 1)\) or \(\log (x_{g,j,s} + 1)\) were 0 across all \(S_{i,j}\) samples for any of the 310 tissue pairs, the gene was removed. In this process, 28 out of 1,013 switch- like genes were removed. Note that the correlation matrix is symmetric, so we only vectorize the upper diagonal part of the matrix. We denote the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 185]]<|/det|>
+generated vector by \(\vec{v}_{g}\) . Vector \(\vec{v}_{g}\) characterizes the gene. We ran a principal component analysis (PCA), using the promp() function in R, on vectors, \(\vec{v}_{g}\) for all genes for which we could calculate \(r_{g}(i,j)\) for all 310 tissue pairs. In parallel, we also ran PCA on only the set of vectors (genes) characterizing only the 985 (1013 - 28) switch- like genes.  
+
+<|ref|>text<|/ref|><|det|>[[114, 200, 868, 289]]<|/det|>
+In the space spanned by the first two principal components, we calculated the pairwise distance between genes using the dist() function in R with method = "euclidean". We then performed hierarchical clustering using the hclust() function with method = "complete". Finally, we used the cuttree() function with \(k = 2\) and \(k = 3\) to obtain two and three clusters, respectively.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 304, 600, 323]]<|/det|>
+## Identifying the genetic basis of universal bimodality  
+
+<|ref|>text<|/ref|><|det|>[[114, 323, 877, 550]]<|/det|>
+In order to identify the genetic basis of bimodality for switch- like genes in cluster 2A, we obtained the coordinates of the genes for both hg19 and hg38 using their Ensembl IDs as keys through Ensembl BioMart. We obtained coordinates of common structural variants using both the 1000 genomes project (hg19) \(^{62}\) and the HGSV2 dataset (hg38) \(^{63}\) . We performed an overlap analysis using BedTools \(^{64}\) to identify polymorphic deletions of or insertions into these genes. We thus obtained five universally bimodal genes being affected by structural variants. These were USP32P2, FAM106A, GSTM1, RP11- 356C4.5, and CYP4F24P. Additionally, we obtained the GTEx dataset for the expression quantitative trait loci (eQTL). We identified genes in cluster 2A that had at least one eQTL, which was consistently associated with either increased or decreased expression of a given gene across all 27 tissues analyzed. We thus obtained five genes from cluster 2A whose expression was associated with a short variant across tissues. These were NPIPA5, RPS26, PSPHP1, PKD1P2, and PKD1P5.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 566, 377, 584]]<|/det|>
+## Controlling for confounders  
+
+<|ref|>text<|/ref|><|det|>[[114, 584, 881, 760]]<|/det|>
+A bimodal distribution of expression levels of universally switch- like genes is unlikely to be driven by confounding factors such as ischemic time, and time spent by the tissue in chemical fixatives (PAXgene fixative). For example, the expression of genes on the male- specific region of chromosome Y is bimodally distributed across tissues regardless of confounding factors because females do not possess these genes. Similarly, regardless of confounding factors, USP32P2 is bimodally distributed due to a polymorphic gene deletion. However, tissue- specific switch- like genes are particularly prone to being affected by confounding variables. Specifically, we investigated whether the switch- like expression of genes can be explained by ischemic time and PAXgene fixative using the following approach.  
+
+<|ref|>text<|/ref|><|det|>[[114, 775, 877, 868]]<|/det|>
+Ischemic time for a sample \(s\) in a given tissue \(i\) , denoted by \(k_{i,s}\) , is a continuous variable representing the time interval between death and tissue stabilization. Time spent by a tissue \(i\) from a sample \(s\) in PAXgene fixative, denoted by \(f_{i,s}\) , is also a continuous variable. For each gene- tissue pair \((g, i)\) , we calculated, across the \(S_{i}\) samples, the Pearson correlation between 1) \(\log (1 + x_{g,i,s})\) and \(k_{i,s}\) and 2) \(\log (1 + x_{g,i,s})\) and \(f_{i,s}\) . For
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 792, 130]]<|/det|>
+each tissue \(i\) and confounder \(c\) , where \(c \in \{k_{i,s}, f_{i,s}\}\) , we denote the correlation coefficient between \(\log(1 + x_{g,i,s})\) and \(c\) as \(r_{g,i,c}\) .  
+
+<|ref|>text<|/ref|><|det|>[[114, 144, 866, 260]]<|/det|>
+We partition the set of switch- like genes into two subsets: cluster 1 and cluster 2 (the union of clusters 2A and 2B). We treat cluster- 2 genes as internal controls since their correlated bimodal expression across tissues is robust to the presence of confounding factors. Thus, we eliminated a cluster- 1 gene \(g1\) if, for any confounder \(c\) , \(\left(r_{g1,i,c}\right)^2 > \left(\max_{g2 \in \text{cluster} 2} r_{g2,i,c}\right)^2\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 275, 518, 294]]<|/det|>
+## Gene-to-gene co-expression within tissues  
+
+<|ref|>text<|/ref|><|det|>[[115, 293, 875, 383]]<|/det|>
+We performed gene- to- gene co- expression analysis within the stomach, breast, vagina, and colon tissues. In a given tissue \(i\) , we denote the set of genuine cluster- 1 genes (excluding genes affected by confounding variables) by \(C_i\) . Then, for \(i \in \{\text{stomach, breast, vagina, colon}\}\) , we calculated the Pearson correlation, across the \(S_i\) samples, between \(\log(x_{g,i,s} + 1)\) and \(\log(x_{h,i,s} + 1)\) for every \(g, h \in C_i\) where \(g \neq h\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 399, 580, 419]]<|/det|>
+## Quantifying sex bias in cluster-1 gene expression  
+
+<|ref|>text<|/ref|><|det|>[[115, 417, 876, 526]]<|/det|>
+For every gene- tissue pair \((g, i)\) , where \(g\) is a switch- like gene, and \(i\) is a tissue common to both sexes, we tested the hypothesis that the distribution of \(\log(x_{g,i,s} + 1)\) across male samples differed from that across female samples using the Wilcoxon rank- sum test. We applied the Benjamini- Hochberg procedure of multiple hypotheses correction with \(\text{FDR} = 5\%\) . We quantified the effect size of the sex bias using Cohen's \(d\) . Statistically significant results were considered to represent true sex bias only if \(|d| > 0.2^{65}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 541, 690, 560]]<|/det|>
+## Enrichment of switch-like genes among disease-linked genes  
+
+<|ref|>text<|/ref|><|det|>[[115, 559, 876, 650]]<|/det|>
+We performed enrichment analysis for switch- like genes in the stomach and vagina that are downregulated in gastric cancer and vaginal atrophy, respectively. We denote the set of genes downregulated in disease \(y\) as \(Z_{y}\) , where \(y \in \{\text{gastric cancer, vaginal atrophy}\}\) . We calculated the fold enrichment of genuine cluster- 1 genes in the stomach among genes downregulated in gastric cancer by:  
+
+<|ref|>equation<|/ref|><|det|>[[366, 664, 629, 720]]<|/det|>
+\[\frac{|C_{\mathrm{stomach}} \cap Z_{\mathrm{gastric cancer}}|}{|G \cap Z_{\mathrm{gastric cancer}}| / |G|} .\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 753, 833, 792]]<|/det|>
+We calculated the fold enrichment of genuine cluster- 1 genes in the vagina among genes downregulated in vaginal atrophy by:  
+
+<|ref|>equation<|/ref|><|det|>[[373, 806, 623, 864]]<|/det|>
+\[\frac{|C_{\mathrm{vagina}} \cap Z_{\mathrm{vaginal atrophy}}|}{|G \cap Z_{\mathrm{vaginal atrophy}}| / |G|}.\]
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 105, 853, 217]]<|/det|>
+To calculate the \(p\) - values associated with these enrichments, we obtained 10,000 uniformly random samples (with replacement) of size \(|C_{i}|\) from \(G\) . The \(p\) - value for the enrichment of switch- like genes in tissue \(i\) among genes linked to disease \(y\) is then given by the fraction of random samples among the 10,000 samples for which \(|q_{j} \cap Z_{y}| > |C_{i} \cap Z_{y}|\) . Here, \(q_{j}\) is the set of genes in random sample \(j\) where \(j \in \{1, \ldots , 10000\}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 233, 398, 251]]<|/det|>
+## Discretizing expression levels  
+
+<|ref|>text<|/ref|><|det|>[[114, 250, 839, 329]]<|/det|>
+We performed kernel density estimation using the density() function in R on the distributions of 1) \(\log (x_{g,\mathrm{stomach},s} + 1)\) across the \(S_{\mathrm{stomach}}\) samples for \(g \in C_{\mathrm{stomach}} \cap Z_{\mathrm{gastric cancer}}\) ; and 2) \(\log (x_{g,\mathrm{vagina},s} + 1)\) across the \(S_{\mathrm{vagina}}\) samples for \(g \in C_{\mathrm{vagina}} \cap Z_{\mathrm{vaginal atrophy}}\) .  
+
+<|ref|>text<|/ref|><|det|>[[114, 344, 880, 433]]<|/det|>
+We used the minimum of the estimated density as the switching threshold; if an individual had an expression level above the threshold in a given tissue, the gene was considered "on" in the individual in that tissue. The gene was considered "off" otherwise. We then calculate the concordance of expression among genes in any arbitrary set of switch- like genes \(G^{A}\) in a given tissue \(i\) as follows:  
+
+<|ref|>equation<|/ref|><|det|>[[193, 430, 802, 490]]<|/det|>
+\[\frac{1}{S_{i}}\sum_{s = 1}^{S_{i}}\left[\prod_{g\in G^{A}}\mathbf{1}_{(g\mathrm{~is~"on"~in~sample~}s\mathrm{~in~tissue~}i)} + \prod_{g\in G^{A}}\mathbf{1}_{(g\mathrm{~is~"off"~in~sample~}s\mathrm{~in~tissue~}i)}\right],\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 490, 411, 508]]<|/det|>
+where \(\mathbf{1}_{(\cdot)}\) is the indicator function.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 524, 825, 544]]<|/det|>
+## Gene ontology enrichment of tissue-specific switch-like genes in the vagina  
+
+<|ref|>text<|/ref|><|det|>[[115, 543, 862, 581]]<|/det|>
+We performed Gene Ontology (GO) enrichment analysis for genes in \(C_{\mathrm{vagina}}\) using the online database available at https://geneontology.org/ 66.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 597, 334, 614]]<|/det|>
+## Immunohistochemistry  
+
+<|ref|>text<|/ref|><|det|>[[115, 614, 853, 668]]<|/det|>
+Vaginal biopsies were taken by use of punch biopsies from postmenopausal women, fixed and stained as previously described by use of ALOX12 (HPA010691 polyclonal antirabbit, Sigma- Aldrich) 67,68.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[348, 90, 648, 111]]<|/det|>
+## Supplementary Information  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 130, 789, 149]]<|/det|>
+## Principal component analysis on tissue-to-tissue co-expression vectors  
+
+<|ref|>text<|/ref|><|det|>[[114, 149, 880, 254]]<|/det|>
+We applied a principal component analysis to the 19,132 vectors of tissue- to- tissue coexpression, one vector for each gene. We find that PC1 (Figure 2A), explaining \(35.3\%\) of the variation, is nearly perfectly correlated with mean tissue- to- tissue co- expression across tissue- tissue pairs ( \(r^2 = 0.998\) , \(p\) - value \(< 2.2 \times 10^{- 16}\) ; Figure S1). This result indicates that the \(35.3\%\) of the variation in the tissue- to- tissue co- expression of genes is primarily explained by the mean tissue- to- tissue co- expression of genes.  
+
+<|ref|>image<|/ref|><|det|>[[117, 271, 644, 569]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 574, 847, 604]]<|/det|>
+<center>Figure S1. The mean tissue-to-tissue co-expression of genes shows a near-perfect correlation with PC1. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 620, 707, 639]]<|/det|>
+## Universally switch-like genes and their biomedical implications  
+
+<|ref|>text<|/ref|><|det|>[[115, 639, 850, 708]]<|/det|>
+In the main text, we discussed the USP32P2 and FAM106A. Here, we discuss some other interesting examples of universally switch- like genes. The violin plots for the expression level distributions for all cluster- 2A and cluster- 2B switch- like genes not shown in the main text are present in Figure S2 and Figure S3, respectively.  
+
+<|ref|>text<|/ref|><|det|>[[114, 725, 875, 866]]<|/det|>
+Firstly, a common \(\sim 20\mathrm{kb}\) whole- gene deletion (esv3587154) of the GSTM1 gene \(^{69,70}\) is associated with bladder cancer in humans \(^{71}\) . GSTM1 is bimodally expressed across individuals in all tissues (Figure S2D) that we analyzed, as well as across multiple tumor types \(^{15}\) , with different expression peaks corresponding to differential prognoses among patients. These findings suggest a compelling hypothesis: the common deletion of GSTM1, maintained either by drift or balancing selection \(^{72}\) , has no significant effect on the health of non- cancerous individuals; however, it could have significant implications for prognosis once certain types of tumors develop. Therefore, screening
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 880, 125]]<|/det|>
+patients with certain tumor types for the GSTM1 deletion could significantly advance our ability to predict the course of tumor progression in an individualized manner.  
+
+<|ref|>text<|/ref|><|det|>[[113, 141, 879, 404]]<|/det|>
+Secondly, genes that are bimodally expressed across multiple tissues raise an evolutionary paradox. Typically, genes with a wide expression breadth (i.e., expression across a large number of tissues) affect fitness and are thus constrained at both the sequence and expression level \(^{26,73 - 75}\) . However, universally switch- like genes, despite having a high expression breadth, are not conserved at the expression level. This could imply different health consequences for individuals with off versus on state of the genes. For example, the universally switch- like gene RP4- 765C7.2 (ENSG00000213058; Figure S2K) is upregulated in the peripheral blood mononuclear cells of patients with ankylosing spondylitis \(^{76}\) , eutopic endometrium in endometriosis patients \(^{77}\) , and peripheral blood mononuclear cells of multiple sclerosis patients \(^{78}\) . Conversely, it is downregulated in the peripheral blood mononuclear cells of Sjögren's syndrome patients \(^{79}\) . These results suggest that this gene being switched on versus off may predispose individuals to certain diseases while protecting them against others. This balance between susceptibility and protection could explain why both high- expression and low- expression states are maintained in the population at comparable frequencies.  
+
+<|ref|>text<|/ref|><|det|>[[114, 419, 876, 561]]<|/det|>
+Thirdly, the bimodality of NPIPA5 (Figure S2G), too, can be explained by a single eQTL. The T allele of the SNV rs3198697 is associated with NPIPA5 being switched on across tissues, while the C allele is associated with the gene being switched off. NPIPA5 has been reported as one of the top differentially expressed genes among patients with multiple sclerosis in both blood and brain \(^{80}\) . Moreover, this study \(^{80}\) showed that this gene is co- expressed in blood and brain. Here, we have shown that this gene is switch- like and that the co- expression of NPIPA5 is not restricted to blood and brain but extends to all pairs of tissues.  
+
+<|ref|>text<|/ref|><|det|>[[114, 577, 876, 649]]<|/det|>
+Lastly, a single eQTL can explain the bimodality of a member of the PKD1 gene family in cluster 2A, PKD1P5 (Figure S2I). For PKD1P5, the C allele of the SNV rs201525245 is associated with the gene being switched on, while the G allele is associated with the gene being switched off.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 88, 884, 711]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 710, 816, 728]]<|/det|>
+<center>Figure S2. Violin plots for expression level distributions of switch-like genes in cluster 2A. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 880, 602]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 605, 820, 622]]<|/det|>
+<center>Figure S3. Violin plots for expression level distributions of switch-like genes in cluster 2A. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 650, 848, 689]]<|/det|>
+## Conceptual issues regarding bimodal expression distributions driven by genetic polymorphisms  
+
+<|ref|>text<|/ref|><|det|>[[114, 688, 880, 863]]<|/det|>
+In the main text, we claimed that genetic polymorphisms drive the bimodal expression of universally switch- like genes in cluster 2A. For a polymorphism with two alleles (A and \(a\) ), there are three possible genotypes ( \(aa\) , \(Aa\) , and \(AA\) ). Since each of the three genotypes can lead to three different expression levels, we expect expression distributions of a cluster- 2A gene to have three modes. This leads to the question: Why do we not see trimodal, as opposed to bimodal, expression distributions for genes in cluster 2A? To answer this question, we develop the following frameworks. Let us assume that a genetic polymorphism exists with two alleles, \(A\) and \(a\) , with frequencies \(p_A\) and \((1 - p_A)\) , respectively. The three genotypes for this polymorphism, \(aa\) , \(Aa\) , and \(AA\) , lead to three different expression states (TPM levels) for the gene with averages
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 89, 879, 170]]<|/det|>
+\(\mu_{aa}, \mu_{Aa}\) , and \(\mu_{AA}\) , respectively. Let us also assume that the Hardy-Weinberg equilibrium holds for this locus. Then, the frequency of \(aa = (1 - p_A)^2\) , the frequency of \(Aa = 2p_A(1 - p_A)\) , and the frequency of \(AA = p_A^2\) . We assume that \(\mu_{aa} \leq \mu_{Aa} \leq \mu_{AA}\) . Next, we define a dominance coefficient \(0 \leq \alpha \leq 1\) by,  
+
+<|ref|>equation<|/ref|><|det|>[[319, 186, 568, 207]]<|/det|>
+\[\mu_{Aa} = \mu_{aa} + (\mu_{AA} - \mu_{aa})\alpha .\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 220, 343, 239]]<|/det|>
+If we define the ratio \(R\) by  
+
+<|ref|>equation<|/ref|><|det|>[[378, 237, 463, 268]]<|/det|>
+\[R = \frac{\mu_{AA}}{\mu_{aa}},\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 266, 251, 283]]<|/det|>
+then, we obtain  
+
+<|ref|>equation<|/ref|><|det|>[[348, 281, 570, 302]]<|/det|>
+\[\mu_{Aa} = \mu_{aa}(1 - \alpha +R\alpha)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 301, 150, 317]]<|/det|>
+and  
+
+<|ref|>equation<|/ref|><|det|>[[406, 318, 525, 338]]<|/det|>
+\[\mu_{AA} = R\mu_{aa}.\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 368, 876, 440]]<|/det|>
+We can then divide individuals into three groups depending on their genotypes. Let us assume that the coefficient of variation (CV) of expression is the same for each genotypic group. Then, we can model the TPM value of this gene in a given individual a normal random variable with:  
+
+<|ref|>text<|/ref|><|det|>[[144, 439, 810, 495]]<|/det|>
+1) mean \(= \mu_{aa}\) and standard deviation \(= \mathrm{CV}\times \mu_{aa}\) if the genotype is \(aa\) 2) mean \(= \mu_{Aa}\) and standard deviation \(= \mathrm{CV}\times \mu_{Aa}\) if the genotype is \(Aa\) ; and 
+3) mean \(= \mu_{AA}\) and standard deviation \(= \mathrm{CV}\times \mu_{AA}\) if the genotype is \(AA\)  
+
+<|ref|>text<|/ref|><|det|>[[113, 493, 857, 529]]<|/det|>
+The value of \(\mu_{aa}\) is irrelevant for gauging the effect of polymorphisms on the shape of the expression level distributions. Therefore, we set \(\mu_{aa} = 1\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 544, 880, 756]]<|/det|>
+Under these mathematical assumptions, we performed simulations using 36 distinct models. These models vary by four parameters: \(p_A \in \{0.05, 0.1, 0.5\}\) , \(\mathrm{CV} \in \{0.1, 0.3\}\) , \(R \in \{10, 1000\}\) , and \(\alpha \in \{0.2, 0.5, 0.8\}\) . For each model, defined by a unique combination of the values of these four parameters, we performed a two- step sampling procedure. First, we obtained a random sample of 500 genotypes, based on \(p_A\) and the Hardy- Weinberg equilibrium. Next, for each of the 500 genotypes sampled, we sample a TPM value from the normal distribution corresponding to that genotype. Thus, for each of the 36 models, we simulated 500 TPM values. We present these values as histograms with and without log transformation. The results for \(p_A = 0.05\) , \(p_A = 0.1\) , and \(p_A = 0.5\) are shown in Figure S4, Figure S5, and Figure S6, respectively. These simulations help us answer our question we first asked: Why do we not see a trimodal distribution if a genetic polymorphism drives expression- level variability in a gene?  
+
+<|ref|>text<|/ref|><|det|>[[113, 771, 881, 860]]<|/det|>
+Firstly, even when the minor allele (A) frequency is not low (e.g., \(10\%\) ), the frequency of the genotype \(AA\) is still quite low (e.g., \(1\%\) ). Therefore, the third peak is not always conspicuously visible. We see this in all models with \(p_A = 0.05\) and \(p_A = 0.1\) (Figures S4 and S5), regardless of CV, \(R\) , and \(\alpha\) values. At higher allele frequencies (e.g., \(50\%\) ), the effect of the remaining parameters becomes more apparent. Figure S6 shows that a
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 90, 861, 247]]<|/det|>
+higher dominance coefficient \(\alpha\) makes the expression level distribution more bimodal. By contrast, a lower dominance coefficient \(\alpha\) makes the expression level distribution more trimodal. The lack of observed trimodality in the GTEx data may suggest that expression levels of switch-like genes tend to be more dominant than additive with regard to causal genetic polymorphisms. Secondly, greater variation (CV) in the data can also obscure the third peak. For example, by comparing **Figure S6B** to **Figure S6H**, we find that increasing the CV can change the distribution from being trimodal to bimodal when the other parameters are held constant. However, \(R\) does not seem to have much effect on whether the expression level distribution is bimodal or trimodal. 
+
+<|ref|>image<|/ref|><|det|>[[120, 285, 880, 722]]<|/det|>
+ 
+
+<|ref|>image_caption<|/ref|><|det|>[[114, 728, 833, 760]]<|/det|>
+<center>**Figure S4. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of 5%.**</center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 88, 875, 530]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 536, 830, 567]]<|/det|>
+<center>Figure S5. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of 10%. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 875, 528]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 533, 832, 564]]<|/det|>
+<center>Figure S6. TPM simulations for a hypothetical gene whose expression is driven by a genetic polymorphism with an allele frequency of \(50\%\) . </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 578, 428, 595]]<|/det|>
+## Tissue-specific switch-like genes  
+
+<|ref|>text<|/ref|><|det|>[[114, 595, 872, 787]]<|/det|>
+We divided switch- like genes into three clusters in the space spanned by the first two principal components (Figure 2A). While we said that genes in cluster 1 (Figure 2A- B) are tissue- specific switch- like genes, manual inspection reveals this is not true for all genes in cluster 1. In particular, the transcript ENSG00000273906 coming from chr Y was labeled cluster 1 by hierarchical clustering even though it is universally switch- like in tissues common to both sexes. Indeed, we removed all chr- Y genes from our analyses of genuine cluster- 1 genes. Other cluster- 1 genes bimodally expressed in a large number of tissues lie on the autosomes. For example, CLPS, PRSS1, CELA3A, and CELA3B, despite having low overall tissue- to- tissue co- expression, are bimodally expressed across tissues. Indeed, we have shown previously that CELA3A and CELA3B have a shared regulatory architecture in the pancreas \(^{81}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 801, 378, 818]]<|/det|>
+## Controlling for confounders  
+
+<|ref|>text<|/ref|><|det|>[[115, 818, 874, 853]]<|/det|>
+We removed cluster- 1 genes affected by confounders in each tissue using an approach outlined in Methods. Here, we present the number of genuine cluster- 1 genes versus
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 89, 864, 177]]<|/det|>
+those affected by confounders in **Figure S7**. In particular, we show that the cluster- 1 genes in the colon and the intestine are particularly prone to being affected by confounding factors. We also present in **Figure S8** examples of genes whose bimodal expression in specific tissues is correlated with variation in the sample ischemic time distribution.  
+
+<|ref|>image<|/ref|><|det|>[[116, 177, 680, 519]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 521, 820, 555]]<|/det|>
+<center>Figure S7. Switch-like genes in cluster 1 that are genuine versus those affected by confounders. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 92, 700, 465]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 467, 844, 499]]<|/det|>
+<center>Figure S8. Examples of cluster-1 genes affected by confounders. Their bimodal distribution is caused by ischemic time (a confounding factor). </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 514, 845, 552]]<|/det|>
+## The copy number variation at the PGA3 locus does not affect the gene's expression levels  
+
+<|ref|>text<|/ref|><|det|>[[115, 551, 880, 710]]<|/det|>
+PGA3 exhibits a high copy number variation among humans \(^{82}\) , but the copy number seems to have no impact on PGA3 expression, at least in cancer samples \(^{83}\) . The bimodal expression of PGA3 in the stomach is likely not due to its copy number variation. This is because PGA3's expression in the stomach is highly correlated with other tissue- specific genes in the stomach. The only way in which a copy number- driven bimodality of PGA3 could be correlated with other switch- like genes is if the product of PGA3 was regulating the correlated genes. Without this evidence, we surmise that the copy number variation at the PGA3 locus does not affect the gene's expression levels, at least in the stomach.  
+
+<|ref|>text<|/ref|><|det|>[[112, 726, 880, 866]]<|/det|>
+Table S1. A list of tissues used in this study along with the number of individuals for each tissue. Table S2. A list of 1,013 switch- like genes. Table S3. Tissue- to- tissue co- expression (Pearson's correlation) for all genes across 310 tissue- tissue pairs. Table S4. Results from principal component analysis on tissue- to- tissue co- expression data for all genes. Table S5. Results from principal component analysis on tissue- to- tissue co- expression data for only switch- like genes. Table S6. Correlation between gene expression levels and confounding factors for switch- like
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 90, 832, 153]]<|/det|>
+genes. Table S7. Gene- to- gene co- expression of genuine tissue- specific switch- like genes in the stomach, vagina, breast, and colon. Table S8. Analysis of sex bias among genuine tissue- specific switch- like genes.  
+
+<|ref|>text<|/ref|><|det|>[[111, 193, 872, 855]]<|/det|>
+1. Jacob, F. & Monod, J. Genetic regulatory mechanisms in the synthesis of proteins. J. Mol. Biol. 3, 318-356 (1961).  
+2. Banerji, J., Rusconi, S. & Schaffner, W. Expression of a beta-globin gene is enhanced by remote SV40 DNA sequences. Cell 27, 299-308 (1981).  
+3. Gillies, S. D., Morrison, S. L., Oi, V. T. & Tonegawa, S. A tissue-specific transcription enhancer element is located in the major intron of a rearranged immunoglobulin heavy chain gene. Cell 33, 717-728 (1983).  
+4. Serfling, E., Jasin, M. & Schaffner, W. Enhancers and eukaryotic gene transcription. Trends Genet. 1, 224-230 (1985).  
+5. Allfrey, V. G., Faulkner, R. & Mirsky, A. E. Acetylation and methylation of histones and their possible role in the regulation of RNA synthesis. Proc. Natl. Acad. Sci. U. S. A. 51, 786-794 (1964).  
+6. Riggs, A. D. & Jones, P. A. 5-methylcytosine, gene regulation, and cancer. Adv. Cancer Res. 40, 1-30 (1983).  
+7. Bestor, T., Laudano, A., Mattaliano, R. & Ingram, V. Cloning and sequencing of a cDNA encoding DNA methyltransferase of mouse cells. The carboxyl-terminal domain of the mammalian enzymes is related to bacterial restriction methyltransferases. J. Mol. Biol. 203, 971-983 (1988).  
+8. Jenuwein, T. & Allis, C. D. Translating the histone code. Science 293, 1074-1080 (2001).  
+9. Levine, M. & Tjian, R. Transcription regulation and animal diversity. Nature 424, 147-151 (2003).  
+10. Muntoni, F., Torelli, S. & Ferlini, A. Dystrophin and mutations: one gene, several proteins, multiple phenotypes. Lancet Neurol. 2, 731-740 (2003).  
+11. Sakai, T. et al. Allele-specific hypermethylation of the retinoblastoma tumor-suppressor gene. Am. J. Hum. Genet. 48, 880-888 (1991).  
+12. Cutting, G. R. Cystic fibrosis genetics: from molecular understanding to clinical application. Nat. Rev.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 333, 105]]<|/det|>
+Genet. 16, 45–56 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[115, 116, 821, 137]]<|/det|>
+13. Ertel, A. Bimodal gene expression and biomarker discovery. Cancer Inform. 9, 11–14 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[115, 146, 882, 194]]<|/det|>
+14. Bessarabova, M. et al. Bimodal gene expression patterns in breast cancer. BMC Genomics 11 Suppl 1, S8 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[115, 203, 880, 281]]<|/det|>
+15. Justino, J. R., Reis, C. F. dos, Fonseca, A. L., Souza, S. J. de & Stransky, B. An integrated approach to identify bimodal genes associated with prognosis in cancer. Genet. Mol. Biol. 44, e20210109 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[115, 290, 879, 368]]<|/det|>
+16. Moody, L., Mantha, S., Chen, H. & Pan, Y.-X. Computational methods to identify bimodal gene expression and facilitate personalized treatment in cancer patients. J. Biomed. Inform. 100S, 100001 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[115, 377, 861, 426]]<|/det|>
+17. Mason, C. C. et al. Bimodal distribution of RNA expression levels in human skeletal muscle tissue. BMC Genomics 12, 98 (2011).  
+
+<|ref|>text<|/ref|><|det|>[[115, 435, 792, 456]]<|/det|>
+18. Hartigan, J. A. & Hartigan, P. M. The dip test of unimodality. Ann. Stat. 13, 70–84 (1985).  
+
+<|ref|>text<|/ref|><|det|>[[115, 465, 875, 514]]<|/det|>
+19. Jangravi, Z. et al. A fresh look at the male-specific region of the human Y chromosome. J. Proteome Res. 12, 6–22 (2013).  
+
+<|ref|>text<|/ref|><|det|>[[115, 523, 848, 572]]<|/det|>
+20. Cheung, S., Parrella, A., Rosenwaks, Z. & Palermo, G. D. Genetic and epigenetic profiling of the infertile male. PLoS ONE 14, e0214275 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[115, 581, 848, 658]]<|/det|>
+21. Turjya, R. R., Khan, M. A.-A.-K. & Mir Md Khademul Islam, A. B. Perversely expressed long noncoding RNAs can alter host response and viral proliferation in SARS-CoV-2 infection. Future Virol. 15, 577–593 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[115, 667, 879, 744]]<|/det|>
+22. Talotta, R., Bahrami, S. & Laska, M. J. Sequence complementarity between human noncoding RNAs and SARS-CoV-2 genes: What are the implications for human health? Biochim. Biophys. Acta Mol. Basis Dis. 1868, 166291 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[115, 754, 848, 803]]<|/det|>
+23. Arman, K., Dalloul, Z. & Bozgeyik, E. Emerging role of microRNAs and long non-coding RNAs in COVID-19 with implications to therapeutics. Gene 861, 147232 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[115, 813, 872, 861]]<|/det|>
+24. Li, Q. et al. Genome-wide search for exonic variants affecting translational efficiency. Nat. Commun. 4, 2260 (2013).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 876, 135]]<|/det|>
+25. Liu, L. et al. Mutation of the CDKN2A 5' UTR creates an aberrant initiation codon and predisposes to melanoma. Nat. Genet. 21, 128-132 (1999).  
+
+<|ref|>text<|/ref|><|det|>[[112, 146, 876, 193]]<|/det|>
+26. Khan, Z. et al. Primate transcript and protein expression levels evolve under compensatory selection pressures. Science 342, 1100-1104 (2013).  
+
+<|ref|>text<|/ref|><|det|>[[112, 204, 876, 252]]<|/det|>
+27. Wang, S. H., Hsiao, C. J., Khan, Z. & Pritchard, J. K. Post-translational buffering leads to convergent protein expression levels between primates. Genome Biol. 19, 83 (2018).  
+
+<|ref|>text<|/ref|><|det|>[[112, 262, 869, 309]]<|/det|>
+28. Chia, D. J. Minireview: mechanisms of growth hormone-mediated gene regulation. Mol. Endocrinol. 28, 1012-1025 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[112, 320, 860, 368]]<|/det|>
+29. Mayne, B. T. et al. Large scale gene expression meta-analysis reveals tissue-specific, sex-biased gene expression in humans. Front. Genet. 7, 183 (2016).  
+
+<|ref|>text<|/ref|><|det|>[[112, 378, 809, 425]]<|/det|>
+30. McEwen, B. S. & Milner, T. A. Understanding the broad influence of sex hormones and sex differences in the brain. J. Neurosci. Res. 95, 24-39 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[112, 436, 866, 483]]<|/det|>
+31. Goel, N., Workman, J., -Y. Lee, T. T., Innala, L. & Viau, V. Sex differences in the HPA axis. Compr. Physiol. 4, 1121-1155 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[112, 494, 803, 542]]<|/det|>
+32. Fink, A. L. & Klein, S. L. The evolution of greater humoral immunity in females than males: implications for vaccine efficacy. Curr. Opin. Physiol. 6, 16-20 (2018).  
+
+<|ref|>text<|/ref|><|det|>[[112, 553, 820, 600]]<|/det|>
+33. Laffont, S. & Guéry, J.-C. Deconstructing the sex bias in allergy and autoimmunity: From sex hormones and beyond. Adv. Immunol. 142, 35-64 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[112, 611, 857, 658]]<|/det|>
+34. Wu, Q. et al. Comprehensive analysis of the expression and prognostic value of spint1/2 in breast carcinoma. Front. Endocrinol. 12, 665666 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[112, 669, 801, 716]]<|/det|>
+35. Takan, I., Karakulah, G., Louka, A. & Pavlopoulou, A. 'In the light of evolution.' keratins as exceptional tumor biomarkers. PeerJ 11, e15099 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[112, 727, 848, 774]]<|/det|>
+36. Behtaji, S. et al. Identification of oxytocin-related lncRNAs and assessment of their expression in breast cancer. Sci. Rep. 11, 6471 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[112, 785, 805, 832]]<|/det|>
+37. Fiaz, T. et al. Peripheral mRNA expression and prognostic significance of emotional stress biomarkers in metastatic breast cancer patients. Int. J. Mol. Sci. 23, (2022).  
+
+<|ref|>text<|/ref|><|det|>[[112, 843, 838, 861]]<|/det|>
+38. Emilsson, V. et al. Genetics of gene expression and its effect on disease. Nature 452, 423-428
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 89, 202, 105]]<|/det|>
+(2008).  
+
+<|ref|>text<|/ref|><|det|>[[112, 116, 866, 163]]<|/det|>
+39. Li, H. et al. Characterization of differentially expressed genes involved in pathways associated with gastric cancer. PLoS ONE 10, e0125013 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[112, 174, 864, 222]]<|/det|>
+40. Goldstein, I., Dicks, B., Kim, N. N. & Hartzell, R. Multidisciplinary overview of vaginal atrophy and associated genitourinary symptoms in postmenopausal women. Sex. Med. Today 1, 44-53 (2013).  
+
+<|ref|>text<|/ref|><|det|>[[112, 233, 880, 280]]<|/det|>
+41. Szymanski, J. K., Slabuszewska-Jozwiak, A. & Jakiel, G. Vaginal aging—what we know and what we do not know. Int. J. Environ. Res. Public Health 18, 4935 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[112, 290, 876, 338]]<|/det|>
+42. Kim, H.-K., Kang, S.-Y., Chung, Y.-J., Kim, J.-H. & Kim, M.-R. The recent review of the genitourinary syndrome of menopause. J. Menopausal Med. 21, 65-71 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[112, 348, 866, 396]]<|/det|>
+43. Hummelen, R. et al. Vaginal microbiome and epithelial gene array in post-menopausal women with moderate to severe dryness. PLoS ONE 6, e26602 (2011).  
+
+<|ref|>text<|/ref|><|det|>[[112, 406, 816, 454]]<|/det|>
+44. Faubion, S. S., Sood, R. & Kapoor, E. Genitourinary syndrome of menopause: management strategies for the clinician. Mayo Clin. Proc. 92, 1842-1849 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[112, 464, 808, 512]]<|/det|>
+45. Buchanan, D. L. et al. Role of stromal and epithelial estrogen receptors in vaginal epithelial proliferation, stratification, and comification. Endocrinology 139, 4345-4352 (1998).  
+
+<|ref|>text<|/ref|><|det|>[[112, 522, 868, 570]]<|/det|>
+46. Anderson, D. J., Marathe, J. & Pudney, J. The structure of the human vaginal stratum corneum and its role in immune defense. Am. J. Reprod. Immunol. 71, 618-623 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[112, 580, 866, 628]]<|/det|>
+47. Greenman, C. et al. Patterns of somatic mutation in human cancer genomes. Nature 446, 153-158 (2007).  
+
+<|ref|>text<|/ref|><|det|>[[112, 638, 864, 686]]<|/det|>
+48. Oomizu, S. et al. Kdap, a novel gene associated with the stratification of the epithelium. Gene 256, 19-27 (2000).  
+
+<|ref|>text<|/ref|><|det|>[[112, 696, 856, 744]]<|/det|>
+49. Ho, M. et al. Update of the keratin gene family: evolution, tissue-specific expression patterns, and relevance to clinical disorders. Hum. Genomics 16, 1 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[112, 754, 860, 802]]<|/det|>
+50. Pontén, F., Jirström, K. & Uhlen, M. The Human Protein Atlas--a tool for pathology. J. Pathol. 216, 387-393 (2008).  
+
+<|ref|>text<|/ref|><|det|>[[112, 812, 839, 860]]<|/det|>
+51. Cotreau, M. M. et al. A study of 17β-estradiol-regulated genes in the vagina of postmenopausal women with vaginal atrophy. Maturitas 58, 366-376 (2007).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 789, 135]]<|/det|>
+52. Miyagawa, S. & Iguchi, T. Epithelial estrogen receptor 1 intrinsically mediates squamous differentiation in the mouse vagina. Proc. Natl. Acad. Sci. U. S. A. 112, 12986–12991 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[112, 147, 875, 194]]<|/det|>
+53. Zhang, X. et al. Identification of key pseudogenes in nasopharyngeal carcinoma based on RNA-Seq analysis. BMC Cancer 21, 483 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[112, 205, 878, 252]]<|/det|>
+54. Gao, L. et al. Gene expression profile of THZ1-treated nasopharyngeal carcinoma cell lines indicates its involvement in the inhibition of the cell cycle. Transl. Cancer Res. 10, 445–460 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[112, 262, 853, 309]]<|/det|>
+55. Dudbridge, F. & Fletcher, O. Gene-environment dependence creates spurious gene-environment interaction. Am. J. Hum. Genet. 95, 301–307 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[112, 320, 878, 368]]<|/det|>
+56. Vetr, N. G., Gay, N. R., MoTrPAC Study Group & Montgomery, S. B. The impact of exercise on gene regulation in association with complex trait genetics. Nat. Commun. 15, 3346 (2024).  
+
+<|ref|>text<|/ref|><|det|>[[112, 379, 860, 426]]<|/det|>
+57. Thomas, D. Gene–environment-wide association studies: emerging approaches. Nat. Rev. Genet. 11, 259–272 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[112, 437, 857, 513]]<|/det|>
+58. Gilliland, F. D. et al. Effects of glutathione S-transferase M1, maternal smoking during pregnancy, and environmental tobacco smoke on asthma and wheezing in children. Am. J. Respir. Crit. Care Med. 166, 457–463 (2002).  
+
+<|ref|>text<|/ref|><|det|>[[112, 524, 868, 599]]<|/det|>
+59. Hellwig, B. et al. Comparison of scores for bimodality of gene expression distributions and genome-wide evaluation of the prognostic relevance of high-scoring genes. BMC Bioinformatics 11, 276 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[112, 611, 825, 657]]<|/det|>
+60. Shalek, A. K. et al. Single-cell transcriptomics reveals bimodality in expression and splicing in immune cells. Nature 498, 236–240 (2013).  
+
+<|ref|>text<|/ref|><|det|>[[112, 669, 875, 715]]<|/det|>
+61. Dobrin, R. et al. Multi-tissue coexpression networks reveal unexpected subnetworks associated with disease. Genome Biol. 10, R55 (2009).  
+
+<|ref|>text<|/ref|><|det|>[[112, 727, 878, 773]]<|/det|>
+62. 1000 Genomes Project Consortium et al. A global reference for human genetic variation. Nature 526, 68–74 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[112, 785, 847, 831]]<|/det|>
+63. Ebert, P. et al. Haplotype-resolved diverse human genomes and integrated analysis of structural variation. Science 372, (2021).  
+
+<|ref|>text<|/ref|><|det|>[[112, 843, 843, 861]]<|/det|>
+64. Quinlan, A. R. & Hall, I. M. BEDTools: a flexible suite of utilities for comparing genomic features.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 88, 405, 105]]<|/det|>
+Bioinformatics 26, 841- 842 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[113, 116, 844, 165]]<|/det|>
+65. Cohen, J. Statistical Power Analysis for the Behavioral Sciences. (Routledge, London, England, 2013). doi:10.4324/9780203771587.  
+
+<|ref|>text<|/ref|><|det|>[[113, 175, 864, 223]]<|/det|>
+66. Thomas, P. D. et al. PANTHER: Making genome-scale phylogenetics accessible to all. Protein Sci. 31, 8-22 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[113, 232, 857, 280]]<|/det|>
+67. Kallak, T. K. et al. Aromatase inhibitors affect vaginal proliferation and steroid hormone receptors. Menopause 21, 383-390 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[113, 290, 867, 339]]<|/det|>
+68. Kallak, T. K. et al. Vaginal gene expression during treatment with aromatase inhibitors. Clin. Breast Cancer 15, 527-535. e2 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[113, 348, 841, 397]]<|/det|>
+69. Saitou, M. & Gokcumen, O. An evolutionary perspective on the impact of genomic copy number variation on human health. J. Mol. Evol. 88, 104-119 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[113, 406, 877, 483]]<|/det|>
+70. Saitou, M., Satta, Y., Gokcumen, O. & Ishida, T. Complex evolution of the GSTM gene family involves sharing of GSTM1 deletion polymorphism in humans and chimpanzees. BMC Genomics 19, 293 (2018).  
+
+<|ref|>text<|/ref|><|det|>[[113, 493, 877, 542]]<|/det|>
+71. Rothman, N. et al. A multi-stage genome-wide association study of bladder cancer identifies multiple susceptibility loci. Nat. Genet. 42, 978-984 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[113, 551, 802, 600]]<|/det|>
+72. Aqil, A., Speidel, L., Pavlidis, P. & Gokcumen, O. Balancing selection on genomic deletion polymorphisms in humans. eLife https://doi.org/10.7554/eLife.79111 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[113, 609, 839, 657]]<|/det|>
+73. Duret, L. & Mouchiroud, D. Determinants of substitution rates in mammalian genes: expression pattern affects selection intensity but not mutation rate. Mol. Biol. Evol. 17, 68-74 (2000).  
+
+<|ref|>text<|/ref|><|det|>[[113, 667, 836, 715]]<|/det|>
+74. Zhang, L. & Li, W.-H. Mammalian housekeeping genes evolve more slowly than tissue-specific genes. Mol. Biol. Evol. 21, 236-239 (2004).  
+
+<|ref|>text<|/ref|><|det|>[[113, 725, 825, 773]]<|/det|>
+75. Park, J., Xu, K., Park, T. & Yi, S. V. What are the determinants of gene expression levels and breadths in the human genome? Hum. Mol. Genet. 21, 46-56 (2011).  
+
+<|ref|>text<|/ref|><|det|>[[113, 783, 820, 860]]<|/det|>
+76. Li, C., Qu, W. & Yang, X. Comprehensive IncRNA and mRNA profiles in peripheral blood mononuclear cells derived from ankylosing spondylitis patients by RNA-sequencing analysis. Medicine 101, e27477 (2022).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 880, 135]]<|/det|>
+77. von Grothusen C. Endometrial receptivity and regeneration in health and disease: Molecular, cellular and clinical perspectives. Karolinska Institutet (Sweden, 2022).  
+
+<|ref|>text<|/ref|><|det|>[[111, 145, 850, 195]]<|/det|>
+78. Almsned, F. M. Understanding the genetic nature of multiple sclerosis using next-generation sequencing genomic analysis methods. (Doctoral dissertation, George Mason University, 2020).  
+
+<|ref|>text<|/ref|><|det|>[[111, 204, 880, 253]]<|/det|>
+79. Chery, G. Understanding Sjögren's Syndrome as a Systemic Autoimmune Disorder. (State University of New York at Albany, 2022).  
+
+<|ref|>text<|/ref|><|det|>[[111, 262, 870, 312]]<|/det|>
+80. Islam, T. et al. Detection of multiple sclerosis using blood and brain cells transcript profiles: Insights from comprehensive bioinformatics approach. Informatics in Medicine Unlocked 16, 100201 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[111, 320, 864, 369]]<|/det|>
+81. Russell, M., Aqil, A., Saitou, M., Gokcumen, O. & Masuda, N. Gene communities in co-expression networks across different tissues. PLoS Comput. Biol. 19, e1011616 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[111, 378, 857, 456]]<|/det|>
+82. Otto, M., Zheng, Y., Grablowitz, P. & Wiehe, T. Detecting adaptive changes in gene copy number distribution accompanying the human out-of-Africa expansion. bioRxiv 2023.08.14.553171 (2024) doi:10.1101/2023.08.14.553171.  
+
+<|ref|>text<|/ref|><|det|>[[111, 465, 855, 514]]<|/det|>
+83. Shen, S., Li, H., Liu, J., Sun, L. & Yuan, Y. The panoramic picture of pepsinogen gene family with pan-cancer. Cancer Med. 9, 9064-9080 (2020).
+
+<--- Page Split --->

preprint/preprint__0009fc9e7d8fea70f828fc27ba1001b8e0dc12dc0cba8580ba8fe8f9865c469d/images_list.json

@@ -0,0 +1,107 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. The schematic diagram of the space cross mapping.",
+    "footnote": [],
+    "bbox": [
+      [
+        207,
+        230,
+        789,
+        551
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Block diagram of the IGAB-GPC scheme architecture for pattern-moving systems.",
+    "footnote": [],
+    "bbox": [
+      [
+        94,
+        306,
+        900,
+        572
+      ]
+    ],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. 3000 sets of input-output system historical data.",
+    "footnote": [],
+    "bbox": [
+      [
+        105,
+        85,
+        900,
+        494
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Pattern class centre and its threshold.",
+    "footnote": [],
+    "bbox": [
+      [
+        145,
+        123,
+        830,
+        444
+      ]
+    ],
+    "page_idx": 19
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Comparison of system output accuracy of different models Figure 6. The tracking errors for pattern moving systems with various models.",
+    "footnote": [],
+    "bbox": [
+      [
+        150,
+        444,
+        828,
+        768
+      ]
+    ],
+    "page_idx": 21
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. System ouput comparison with different control schemes in PMT framework.",
+    "footnote": [],
+    "bbox": [
+      [
+        97,
+        87,
+        890,
+        440
+      ]
+    ],
+    "page_idx": 22
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. Tracking results of system operating status on target pattern class.",
+    "footnote": [],
+    "bbox": [
+      [
+        95,
+        503,
+        900,
+        808
+      ]
+    ],
+    "page_idx": 22
+  }
+]

preprint/preprint__0009fc9e7d8fea70f828fc27ba1001b8e0dc12dc0cba8580ba8fe8f9865c469d/preprint__0009fc9e7d8fea70f828fc27ba1001b8e0dc12dc0cba8580ba8fe8f9865c469d.mmd

@@ -0,0 +1,938 @@
+
+# Generalized Predictive Control Based on Interval Gray Model with Adaptive Buffer Operator for a Class of Pattern-Moving Systems  
+
+Ning Li  University of Science and Technology  Zhenggaung Xu  University of Science and Technology  Xiangquan Li  21021@jdzu.edu.cn  
+
+Jingdezhen University  
+
+## Article  
+
+Keywords: Pattern moving theory (PMT), Interval grey model, Cross mapping, Interval grey adaptive buffer generalized predictive control (IGAB- GPC)  
+
+Posted Date: July 15th, 2025  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 6971022/v1  
+
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: No competing interests reported.  
+
+Version of Record: A version of this preprint was published at Scientific Reports on August 25th, 2025. See the published version at https://doi.org/10.1038/s41598- 025- 17141- 8.
+
+<--- Page Split --->
+
+# Generalized Predictive Control Based on Interval Gray Model with Adaptive Buffer Operator for a Class of Pattern-Moving Systems  
+
+Ning Li \(^{1}\) , Zhenggaung Xu \(^{1}\) , and Xiangquan Li \(^{2,*}\)  
+
+\(^{1}\) University of Science and Technology, School of Automation and Engineering, Beijing, 100083, China \(^{2}\) Jingdezhen University, School of Information Engineering, Jingdezhen, 333032, China \(^{*}21021@\) jdzu.edu.cn  
+
+## ABSTRACT  
+
+The pattern- moving systems, as a kind of complex nonlinear systems that governed by statistical laws, are commonly found in industrial production processes such as sintering machines and cement rotary kiln. Encountering difficulties in delineating the statistical properties of such systems through deterministic variables like state or output variables, existing control techniques tend to either bypass these systems or address them as systems impacted by stochastic perturbations. To reveal system's inherent statistical characteristics, this work proposed a novel Interval Grey Adaptive Buffer Generalized Predictive Control (IGAB- GPC) scheme, which employs the bidirectional mapping framework under pattern mpving theory (PMT) to quantify pattern category variables, enabling precise tracking of dynamic pattern transitions. Key innovations include: (1) an adaptive buffer operator that mitigates oscillations in pattern class sequences based on their monotonicity, (2) an IGM(1,2)- based prediction model for robust uncertainty quantification, and (3) a GPC framework incorporating receding horizon optimization and feedback correction for enhanced control accuracy. The workflow involves constructing a pattern- moving space through data- driven quantization, applying the adaptive buffer operator to smooth time- series fluctuations, developing the IGM(1,2) model, and implementing the IGB- GPC strategy. Numerical simulations demonstrate that IGB- GPC outperforms benchmark methods like CARIMA- GPC and IG- GPC, achieving superior tracking accuracy, smoother pattern transitions, and robust stability, making it highly suitable for complex industrial processes  
+
+Keywords: Pattern moving theory (PMT), Interval grey model, Cross mapping, Interval grey adaptive buffer generalized predictive control (IGAB- GPC).  
+
+## 1 Introduction  
+
+In the process industries such as metallurgical, building materials, and chemical processing, there widely exist large- scale industrial systems characterized by highly complex manufacturing processes. From the perspective of studying system dynamic characteristics, this kind of systems are inherently governed by statistical laws rather than typical Newtonian mechanical systems \(^{1,2}\) . Typical examples involve sintering machines and cement rotary kilns, which possess the following features: (1) extremely complicated manufacturing processes with frequently inside liquid- phase transitions and combined multidimensional physical events; (2) operational qualities, such as multi- parameter, high- dimensionality, and uncertain degrees of freedom, accompanied by complex system movement. (3) a variety of chemical reactions that are naturally dependent on statistical laws, where feature correlations exhibit probabilistic- statistic reliance and system dynamics are controlled due to statistical rules opposed to traditional mechanics. Given the dynamic nature of systems, some studies adopt a pattern- moving perspective, where statistical principles guide the integration of data- driven and pattern recognition techniques. In this framework, the control objectives are reformulated as driving the system's operating conditions into predefined pattern categories. Therefore, these systems are also known as pattern- moving systems \(^{3}\) .  
+
+Although significant progress has been made in applying pattern recognition schemes to system modeling and control \(^{4}\) , challenges remain in handling highly nonlinear systems with limited and uncertain data. To overcome this obstacle, a novel framework named Pattern Movement Theory (PMT) was proposed by Prof. Xu \(^{5 - 7}\) , which maps system operating conditions to dynamic pattern class via statistical calculation and enables systematic description and control through pattern- driven processes. In light of this insight, the measurement of pattern categories represents a fundamental task, as the pattern class variables lack computational properties, which means they do not satisfy the condition where Pattern 1 + Pattern 2 = Pattern 3. In order to render pattern- based variables computationally viable, several measurements were developed, including metrics based on category centers \(^{8,9}\) , cell mapping \(^{6,10,11}\) , interval numbers \(^{12,13}\) , probability density evolution \(^{14,15}\) , and explicit- implicit
+
+<--- Page Split --->
+
+formulations derived from category centers<sup>16,17</sup>. However, existing methods inadequately deal with the inherent uncertainty in modeling pattern categorical variables, with strategies largely confined to either direct employing category centers or reliance on probabilistic partition estimation. In other words, quantifying uncertainty in pattern category variables within the PMT framework constitutes critical research focus. As it can be seen, pattern class variables represent statistical features with inherently small sample and incomplete information, wherein parameters like category centers and radius may be available, but the full statistical structure remains unknown. Hence, Thus, we attempted to integrate grey system theory with PMT to analyze and control system performance.  
+
+Grey system theory, originally proposed by Professor Julong Deng in \(1982^{18}\) , provides a systematic framework for modeling, analyzing, and predicting systems characterized by small sample data and significant information uncertainty. It is particularly well- suited for addressing real- world problems where data are limited, incomplete or imprecise. Regarding the intelligent control, Chen exploited an intelligent optimal grey evolutionary algorithm for structural control, enhancing prediction accuracy and control capabilities to support sustainable urbanization goals<sup>19</sup>. For instance, Zeng<sup>20</sup> developed an improved interval grey prediction model (IGM(1,1)) for industrial control systems, demonstrating its effectiveness in predicting chemical process outputs under uncertain conditions. Similarly, Rao<sup>21</sup> applied grey system theory to the control of uncertain nonlinear systems, achieving stable performance in the stepped bar and the rigid- body (vertical) analysis. In the field of State prediction, Chen<sup>22</sup> introduced a ground breaking learning procedure combining boxplots and Program Evaluation and Review Technique (PERT) with IGM(1,1), significantly improving interval forecasting reliability for short- term time- series under data constraints. Moreover, Liu<sup>23</sup> discussed a comprehensive review of grey system theory in intelligent control, highlighting its applications in prediction, optimization, and decision- making. These studies collectively demonstrate the versatility and effectiveness of grey system theory, particularly interval grey models, in addressing uncertainties and improving control performance in various applications.  
+
+To our best knowledge, generalized predictive control (GPC), as a subclass of adaptive control, offers significant advantages, including reduced sensitivity to model accuracy, a straightforward algorithmic structure conducive to practical implementation, and inherent robustness. At same time, continuous data acquisition and feedback correction by GPC reduce process uncertainties, thereby optimizing control performance and ensuring operational stability in complex industrial systems<sup>24</sup>. In particular, recent work<sup>25</sup> presented an improved robust model predictive control for PMSM, integrating backstepping control and integral action, experimentally validated to enhance speed tracking, robustness, and uncertainty handling, setting new industrial benchmarks. Considering the adaptability and simplicity of GPC, its application to pattern- moving systems with small samples and high nonlinearity is limited. GPC struggles to build accurate models due to complex statistical dynamics and non- algebraic pattern variables, faces performance issues from data fluctuations without effective oscillation control, and lacks robust uncertainty quantification, reducing control accuracy and robustness in industrial applications. These shortcomings highlight the need for advanced methodologies to address uncertainty and variability in such systems.  
+
+Given the challenges outlined, this study proposes a novel methodology that integrates the Interval Grey Model (IGM) with GPC, termed Interval Grey Adaptive Buffer Generalized Predictive Control (IGAB- GPC), to address the control of pattern- moving systems characterized by small sample sizes and significant uncertainties. This approach leverages the strengths of grey system theory to model systems with incomplete information and employs an adaptive buffer operator to mitigate fluctuations in pattern class variables, thereby enhancing prediction accuracy and control robustness. The proposed method systematically addresses the quantization of pattern category variables through a bidirectional mapping framework, enabling precise tracking of dynamic pattern transitions. Key contributions include: (1) the development of an adaptive buffer operator tailored to the monotonicity and oscillation of pattern class sequences, (2) the formulation of an IGM(1,2)- based prediction model for robust handling of uncertain data, and (3) the integration of these components into a GPC framework to achieve stable and accurate control of pattern- moving systems. The workflow involves constructing a pattern- moving space via data- driven quantization, applying the adaptive buffer operator to smooth time- series fluctuations, developing the IGM(1,2) prediction model, and implementing the IGB- GPC control strategy with receding horizon optimization and feedback correction. The effectiveness of this approach is validated through numerical simulations, demonstrating superior control accuracy and dynamic response compared to benchmark methods such as CARIMA- GPC and IG- GPC.  
+
+The remaining sections of this paper are organized as follows. The problem Statement and basic knowledge are given in Section 2. Section 3 develops IGM prediction with an adaptive buffer operator in the interest of smoothing time series fluctuations (pattern class variables) in term of different properties. Section 4 introduces a novel control approach, termed IGB- GPC, which integrates GPC with an interval grey model. The grey prediction model employs an adaptive buffering operator to mitigate fluctuations in the data sequence. The numerical simulation results, which are critical to validating the model, are presented in Section 5. Section 6 ultimately delivers the conclusion.
+
+<--- Page Split --->
+
+## 2 Problem Statement and Preliminaries  
+
+This section introduces a method for dynamic description of complex systems, based on its characteristic analysis, including constructing pattern category variables and the pattern- moving space.  
+
+### 2.1 Problem Statement  
+
+For the purposes of system analysis and controller synthesis, the system is assumed to be representable by Equation 1.  
+
+\[d x(k + 1) = f\left(d x(k),\ldots ,d x(k - n_{y}),u(k),\ldots ,u(k - n_{u})\right) \quad (1)\]  
+
+where the system input at time step \(k\) is denoted by \(u(k)\in \mathbb{R}\) , the unknown nonlinear function \(f(\cdot)\) characterizes the system dynamics, the positive integers \(n_{y},n_{u}\in \mathbb{Z}_{+}\) represent the unknown output and input orders respectively, and \(d x\in \mathbb{R}\) corresponds to the pattern class variables, computable through the following relation.  
+
+\[\begin{array}{r l} & {\widehat{\otimes}(k + 1) = D(M(d x(k + 1)))\\ & {\qquad = \left\{ \begin{array}{l l}{c_{1},d x(k + 1)\in (c_{1} - r_{1},C_{1}],}\\ {c_{2},d x(k + 1)\in (c_{2} - r_{2},C_{2}],}\\ \vdots \\ {c_{N},d x(k + 1)\in (c_{N} - r_{N},C_{N}]} \end{array} \right.} \end{array} \quad (2)\]  
+
+where \(D(M(\cdot))\) refers to the space cross- mapping process, showing in Figure 1 which is considered to be a grey system. \(\widehat{\otimes} (k + 1)\) is the grey metric value and it denotes a quantized observation, \(c_{m}\neq c_{n}\) (if \(m\neq n\) and \(m,n\in [1,N]\) with \(N\) being the numbers of pattern class), \(c_{m}\) is the class center, \(C_{m}\) denotes the grey number interval boundary and \(C_{m} = c_{m} + r_{m} = c_{m + 1} - r_{m + 1}\) \(r_{m}\) refers to the class radius and \(r_{m} > 0\)  
+
+Note that the system 1 exhibits precisely observable state variable \(d x\) . This allows for the system to be equivalently described using distinct mathematical formalisms: as a linear time- invariant (LTI) system, through state space equations governing its dynamics, or via a finite impulse response (FIR) model defining its input- output behavior. To facilitate the computation of pattern class variables, the definition of gray number is provided herein.  
+
+Definition 2.1. Let \(\mathbb{R}\) be the real number field. A grey number \(\otimes\) is defined as: \(\otimes \in [\underline{{a}},\overline{{a}} ]\) , where \(\underline{{a}}\) is the lower bound and \(\overline{{a}}\) is the upper bound, with \(\underline{{a}}\leq \overline{{a}}\) . When \(\underline{{a}} = \overline{{a}}\) , the grey number degenerates to a white number (a deterministic value). A grey number can also be further described by a whitening function, for example: \(f(x):[\underline{{a}},\overline{{a}} ]\to [0,1]\) , which represents the credibility or weight of different values within the interval \(^{20}\) .  
+
+Remark 2.1. The distinction between a grey number and an interval number. The grey number \(\otimes \in [a_{1},a_{2}]\) (where \(a_{1}< a_{2}\) represents an unknown value within the interval \([a_{1},a_{2}]\) , while the interval number \([a_{1},a_{2}]\) represents the entire interval set itself.  
+
+According to the definition 2.1, the grey number is essentially a type of number whose exact value is unknown but is constrained within a known interval. It characterizes incomplete and uncertain information. Equation 3 \(\widehat{\otimes} (k)\) is a non- intrinsic grey number estimation with the kernel grey number. In perspective of control theory, the control structure of System 1 in pattern moving systems focuses on realizing exact tracking and responsive adaptation to the dynamic transitions of pattern category variables.  
+
+### 2.2 Pattern moving theory  
+
+This section examines the fundamental concepts of PMT, highlighting its capacity to represent system dynamics through time- series pattern recognition. PMT is composed of two components: pattern category variables and pattern moving spaces. These elements are discussed in the sections that follow respectively.  
+
+#### 2.2.1 Pattern class variable  
+
+Analysis of pattern- moving systems reveals that system output is not a deterministic quantity but rather a random variable subject to statistical principles. This presents difficulties for methods that rely on deterministic variables (e.g., State variables or output variables) for dynamics modeling and control. In addition, the design of corresponding controllers based on traditional system model structures becomes more complicated. Given the inherent statistical moving properties of this systems, it is necessary to construct variables with statistical properties to portray their overall statistical moving behavior.
+
+<--- Page Split --->
+
+According to pattern recognition theory, pattern category denotes a collection of pattern samples that possess identical or similar characteristics. When these pattern samples are uniformly represented by a specific variable, this variable reflects certain statistical properties. The variable that encapsulates the information of the pattern category is termed the pattern category variable. Therefore, for systems governed by statistical laws, the dynamic behavior can be effectively characterized using the pattern category variable instead of traditional State variables. The construction process of a pattern category variable is as follows:  
+
+Definition 2.2. Assume that the \(\{y(k)\}\) and \(\{m x(k)\}\) denote the sequence of detection samples and the sequence of pattern samples, respectively. After the pattern samples are classified by the classifier, the pattern variable with category information is defined as the pattern class variable, which is expressed as: \(d x(t)\) . Then the pattern class variable should meet the following transformation process:  
+
+\[\begin{array}{r}{m x(k) = T(y(k))}\\ {d x(k) = M(m x(k))} \end{array} \quad (3)\]  
+
+where the terms \(T(\cdot)\) and \(M(\cdot)\) represent the feature extraction or selection and pattern classification processes, respectively.  
+
+Remark 2.2. In accordance with Definition 2.2, the \(d x(t)\) has following two properties: (1) Pattern class variables are functions of time. (2) The pattern class variables possess a class attribute, that is, the \(d x(t)\) have statistical and set qualities. As a result, the pattern class was commonly understood to be a set of samples with the same or comparable attributes directly.  
+
+#### 2.2.2 Pattern-moving space  
+
+For complex industrial production processes, continuously collect input and output data for a sufficient amount of time to form a data space. It is worthy to point out that pattern moving "space" is a virtual space without structural description, which is constructed based on data- driven methods and contains three significant steps26. (1) For pattern- driven systems, data collected over an extended period (e.g., 2- 3 years) forms the data space. A sufficiently large dataset ensures the production process operates within this system operating subspace, capturing the system's characteristic features. (2) Extracting characteristic variables from the operational subspace generates pattern sample sequences with primary statistical features, forming the operational condition characteristic subspace. (3) Pattern recognition or quantitative classification techniques identify the condition feature subspace, using the pattern class as a scale to form the pattern scale space. The pattern moving space combines this space with the pattern category variables defined therein.  
+
+To construct the pattern- moving space, an improved data quantization and classification method is developed in this work, which extends the quantized classification control scheme reported research27. The proposed approach can be described as follows:  
+
+\[\begin{array}{r l} & {d x(k + 1) = M\left\{T\left[y(k + 1)\right]\right\}}\\ & {\quad = \left\{ \begin{array}{l l}{-\vec{\gamma} (k + 1),} & {\mathrm{if} - \frac{1}{1 - \Delta}\kappa_{i}< y(k + 1)\leq - \frac{1}{1 + \Delta}\kappa_{i}}\\ {0,} & {\mathrm{if} - \frac{1}{1 + \Delta}\kappa_{i}< y(k + 1)\leq \frac{1}{1 + \Delta}\kappa_{i}}\\ {\vec{\gamma} (k + 1),} & {\mathrm{if} \frac{1}{1 + \Delta}\kappa_{i}< y(k + 1)\leq \frac{1}{1 - \Delta}\kappa_{i}} \end{array} \right.} \end{array} \quad (4)\]  
+
+Among them, \(\begin{array}{r}{\bar{y} (k + 1) = \frac{1 + \rho_{0}}{4}\kappa_{i}(\rho_{0}^{i - 1} + \rho_{0}^{i});\Delta = \frac{1 - \rho_{0}}{1 + \rho_{0}};\kappa_{i} = \rho_{0}^{i}\kappa_{0};\rho_{0}\in (0,1);\kappa_{0}} \end{array}\) is the maximum working range of the first principal component \(y_{p}(k)\) , that is, \(\kappa_{0}\geq \max \left(\left|y(k)\right|\right);i = 1,2,\dots ,N\)  
+
+Given the initial class radius upper limit \(r_{0}\) of the mode class where the operating point 0 is located, and other partitioning parameters \(\rho_{0}\) , \(\kappa_{0}\) . According to the quantization classification Equation 4, when \(N\geq \left[\ln (r_{0}(1 + \Delta) / \kappa_{0}) / \ln \rho_{0}\right]\) , the first principal component sequence \(\{y(k)\}\) is divided into \(2N + 1\) intervals. Therefore, we can obtain the centers \(c_{i}\) of \(2N + 1\) pattern classes, the class radius \(r_{i} = \left|\frac{1 + \rho_{0}^{2}}{4\rho_{0}}\kappa_{i}\right|\) , and the class threshold \(C_{i} = c_{i} + r_{i}\) for the pattern class \(i\) , i.e., \(P_{i}\) .  
+
+## 3 System dynamic description based on IGM with adaptive buffer operator  
+
+### 3.1 Modeling system dynamics with mapping spaces  
+
+After completing the definition of pattern category variables and conducting clustering mapping processing for the operational condition feature subspace, the constructed pattern moving space exhibits typical characteristics of a gray system, namely small sample size and poor information. Therefore, the gray number measurement theory is employed to perform quantitative analysis on the pattern category variables, and the dynamic characteristic expression of the system is constructed.
+
+<--- Page Split --->
+
+Definition 3.1. In an \(m\) - dimensional pattern moving space \((m \in \mathbb{N}^+\) , where \(\mathbb{N}^+\) denotes the set of positive integers), let the pattern category variable at the \(i\) - th dimension \((i = 1,2,\ldots ,m)\) take values at different time steps \(k\) \((k = 1,2,\ldots ,n,n\in \mathbb{N}^*)\) as \(d x_{i}(k)\in [a_{i},b_{i}]\) , where \(a_{i}< b_{i}\) . Then \(\hat{\otimes}_{k} = (d x_{1}(k),d x_{2}(k),\ldots ,d x_{m}(k))\) is called the grey whitening value of the pattern category variable at time \(k\) .  
+
+As specified in Definition 3.1, the measurement of pattern variables constitutes a non- intrinsic grey number system, exhibiting the distinctive property of value oscillations around a base reference point. For resolving computational issues involving pattern categorical variables, we establish a bidirectional mapping framework between the pattern moving domain and its computationally tractable counterpart, illustrating in Figure 1.  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1. The schematic diagram of the space cross mapping. </center>  
+
+As described in Figure 1, the pattern category variable is endowed with computational attributes through the gray- scale metric \(D(\cdot)\) , followed by computations in a computable space, and subsequently classified via a classification mapping \(M(\cdot)\) to determine the trajectory of the pattern's motion. This essentially constitutes a spatial cross- mapping method. The motion trajectory of the system in the pattern space is formed through a cyclic procedure: pattern category variables are mapped to a computable space at each time step for processing, and the results are then projected back to the pattern space to generate successive trajectory points. This iterative process builds the trajectory over time, and is mathematically described as:  
+
+\[\left\{ \begin{array}{l l}{d x(k + 1) = M[\widetilde{d x} (k + 1)]}\\ {\qquad = M\{f[D(d x(k)),D(d x(k - 1)),\dots ,D(d x(k - n))}\\ {\qquad u(k - \tau),u(k - \tau - 1),\dots ,u(k - \tau - m)]\}}\\ {\qquad = M\{f[\hat{\otimes}_{k},\hat{\otimes}_{k - 1},\dots ,\hat{\otimes}_{k - n},}\\ {\qquad u(k - \tau),u(k - \tau - 1),\dots ,u(k - \tau - m)]\}}\\ {d x(k) = \hat{\otimes}_{k} + \delta \in [\underline{{a}},\overline{{a}} ],\underline{{a}} < \overline{{a}}} \end{array} \right. \quad (5)\]  
+
+where \(f(\cdot)\) is the output model of the computable space, referring to a suitable grey model here. \(m,n\) are the input and output orders of the model respectively; \(\tau\) is the input time delay of the model. \(k\) denotes a running moment in the pattern motion space, \(\widetilde{d x} (k + 1) = f(\cdot)\) represents the initial prediction output of the computable space, and \(d x(k + 1) = M[\cdot ]\) is the final prediction output of the system. Here, \(u(k)\) represents the control variable or control pattern. Meanwhile, \(\hat{\otimes}_{k} + \delta\) is the metric value for the pattern category variable, and \(\delta\) is the perturbation of the metric value. The subsequent grey metric values are measured by the "core" grey number and interval grey number respectively.
+
+<--- Page Split --->
+
+### 3.2 IGM prediction with adaptive buffer operator  
+
+In this section, an adaptive buffer operator was introduced to perform smoothness processing on categorical variables of patterns, and a prediction model based on IGM (1,2) is derived and established. Firstly, the definition of the smoothness operator is given as follows.  
+
+Definition 3.2. \(^{28}\) Let \(X = (x(1),x(2),\ldots ,x(n))\) be a system behavior data sequence.  
+
+1. If \(\forall k = 2,3,\ldots ,n,x(k) - x(k - 1) > 0\) , then \(X\) is called a monotonically increasing sequence.  
+
+2. If \(\forall k = 2,3,\ldots ,n,x(k) - x(k - 1)< 0\) , then \(X\) is called a monotonically decreasing sequence.  
+
+3. If there exist \(k,k^{\prime}\in \{2,3,\ldots ,n\}\) such that  
+
+\[x(k) - x(k - 1) > 0\quad \mathrm{and}\quad x(k^{\prime}) - x(k^{\prime} - 1)< 0, \quad (6)\]  
+
+then \(X\) is called a random oscillating sequence.  
+
+Let  
+
+\[M = \max \{x(k)\mid k = 1,2,\ldots ,n\} ,\quad m = \min \{x(k)\mid k = 1,2,\ldots ,n\} . \quad (7)\]  
+
+The value \(M - m\) is called the amplitude of the sequence \(X\)  
+
+Definition 3.3. Let \(X = (x(1),x(2),\ldots ,x(n))\) be a system behavior data sequence, and \(D\) be an operator acting on \(X\) . The sequence obtained after applying \(D\) to \(X\) is denoted as  
+
+\[X D = (x(1)d,x(2)d,\ldots ,x(n)d). \quad (8)\]  
+
+Here, \(D\) is called a sequence operator, and \(X D\) is called a first- order operator- applied sequence.  
+
+The action of sequence operators can be applied multiple times. If \(D_{1}\) and \(D_{2}\) are both sequence operators, then \(D_{1}D_{2}\) is called a second- order operator, and  
+
+\[X D_{1}D_{2} = (x(1)d_{1}d_{2},x(2)d_{1}d_{2},\ldots ,x(n)d_{1}d_{2}) \quad (9)\]  
+
+is called a second- order operator- applied sequence, and so on \(^{28}\)  
+
+Theorem 3.1. \(^{29}\) Strengthens the buffer operator  
+
+Let  
+
+\[X = (x(1),x(2),\ldots ,x(n)) \quad (10)\]  
+
+be a system behavior sequence, and let  
+
+\[X D = (x(1)d,x(2)d,\ldots ,x(n)d) \quad (11)\]  
+
+be its intensified buffer sequence. Then we have:  
+
+1. \(X\) is a monotonically increasing sequence and \(D\) is an intensified buffer operator \(\Leftrightarrow x(k)\geq x(k)d\) for \(k = 1,2,\ldots ,n\)  
+
+2. \(X\) is a monotonically decreasing sequence and \(D\) is an intensified buffer operator \(\Leftrightarrow x(k)\leq x(k)d\) for \(k = 1,2,\ldots ,n\)  
+
+3. If \(X\) is an oscillating sequence and \(D\) is an intensified buffer operator, then  
+
+\[\max_{1\leq k\leq n}\{x(k)\} \leq \max_{1\leq k\leq n}\{x(k)d\} ,\quad \min_{1\leq k\leq n}\{x(k)\} \geq \min_{1\leq k\leq n}\{x(k)d\} \quad (12)\]  
+
+Theorem 3.2. \(^{29}\) Weakening buffer operator  
+
+Let  
+
+\[X = (x(1),x(2),\ldots ,x(n)) \quad (13)\]  
+
+be a system behavior sequence, and let  
+
+\[X D = (x(1)d,x(2)d,\ldots ,x(n)d) \quad (14)\]  
+
+be its weakened buffer sequence. Then:
+
+<--- Page Split --->
+
+1. \(X\) is a monotonically increasing sequence and \(D\) is a weakened buffer operator \(\Leftrightarrow x(k)\leq x(k)d\) for \(k = 1,2,\ldots ,n;\)  
+
+2. \(X\) is a monotonically decreasing sequence and \(D\) is a weakened buffer operator \(\Leftrightarrow x(k)\geq x(k)d\) for \(k = 1,2,\ldots ,n;\)  
+
+3. If \(X\) is an oscillating sequence and \(D\) is a weakened buffer operator, then  
+
+\[\max_{1\leq k\leq n}\{x(k)\} \geq \max_{1\leq k\leq n}\{x(k)d\} ,\quad \min_{1\leq k\leq n}\{x(k)\} \leq \min_{1\leq k\leq n}\{x(k)d\} \quad (15)\]  
+
+Remark 3.1. Theorem 3.1 illustrates that, under the action of the intensifying operator, the data of a monotonically increasing sequence decreases, the data of a monotonically decreasing sequence increases, and the amplitude of an oscillating sequence increases. Theorem 3.2 illustrates that, under the action of the weakening operator, the data of a monotonically increasing sequence increases, the data of a monotonically decreasing sequence decreases, and the amplitude of an oscillating sequence decreases.  
+
+Theorem 3.3. An adaptive buffer operator  
+
+Given a time series \(X = (x(1),x(2),\ldots ,x(n))\) , the adaptive buffer operator \(D\) is defined as follows:  
+
+- If \(X\) is an increasing sequence (i.e., \(x(k + 1) > x(k)\) for all \(k = 1,2,\ldots ,n - 1\) ), then \(D = D_{1}\) , the strengthening operator, defined by:  
+
+\[x(k)d_{1} = x(k) + \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\cdot x(k),\quad 0< \alpha < 1,k = 1,2,\ldots ,n. \quad (16)\]  
+
+- If \(X\) is a decreasing sequence (i.e., \(x(k + 1) < x(k)\) for all \(k = 1,2,\ldots ,n - 1\) ), then \(D = D_{2}\) , the weakening operator, defined by:  
+
+\[x(k)d_{2} = x(k) - \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\cdot x(k),\quad 0< \alpha < 1,k = 1,2,\ldots ,n. \quad (17)\]  
+
+- If \(X\) is an oscillating sequence (i.e., neither strictly increasing nor strictly decreasing), then \(D\) adopts a weighted combination form:  
+
+\[x(k)d = \left\{ \begin{array}{l l}{w_{1}x(k)d_{1} + w_{2}x(k)d_{2},} & {\mathrm{if~amplitude~is~large~}(\max_{j = k}^{n}x(j) - \min_{j = k}^{n}x(j) > \theta)}\\ {x(k),} & {\mathrm{otherwise,}} \end{array} \right. \quad (18)\]  
+
+where \(w_{1} + w_{2} = 1,w_{1},w_{2}\geq 0\) are dynamically adjusted weights based on amplitude, and \(\theta\) is a predefined amplitude threshold.  
+
+Proof. Proof of Strengthening Property for Increasing Sequences  
+
+Assume \(X\) is an increasing sequence, i.e., \(x(k + 1) > x(k)\) for all \(k\) . Consider the \(D_{1}\) operator:  
+
+\[x(k)d_{1} = x(k) + \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\cdot x(k). \quad (19)\]  
+
+Since \(x(j) > x(k)\) for \(j > k\) , \(\frac{x(j)}{x(k)} > 1\) , thus:  
+
+\[\sum_{j = k}^{n}\frac{x(j)}{x(k)}\cdot x(k) > (n - k + 1)\cdot x(k). \quad (20)\]  
+
+Substituting into the formula:  
+
+\[x(k)d_{1} > x(k) + \frac{(n - k + 1)\cdot x(k)}{n - k + 1} = 2x(k). \quad (21)\]  
+
+However, the introduction of \(\alpha\) (where \(0< \alpha < 1\) ) limits the growth magnitude. The adjusted form is:  
+
+\[x(k)d_{1} = x(k)\left(1 + \alpha \cdot \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\right). \quad (22)\]  
+
+Since \(\frac{x(j)}{x(k)} > 1\) and \(\sum_{j = k}^{n}\frac{x(j)}{x(k)} > n - k + 1\) , it follows that \(x(k)d_{1} > x(k)\) , proving that \(D_{1}\) strengthens an increasing sequence. \(\square\)
+
+<--- Page Split --->
+
+Proof. Proof of Weakening Property for Decreasing Sequences  
+
+Assume \(X\) is a decreasing sequence, i.e., \(x(k + 1)< x(k)\) for all \(k\) . Consider the \(D_{2}\) operator:  
+
+\[x(k)d_{2} = x(k) - \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\cdot x(k). \quad (23)\]  
+
+Since \(x(j)< x(k)\) for \(j > k\) , \(\frac{x(j)}{x(k)} < 1\) , thus:  
+
+\[\sum_{j = k}^{n}\frac{x(j)}{x(k)}\cdot x(k)< (n - k + 1)\cdot x(k). \quad (24)\]  
+
+Substituting into the formula:  
+
+\[x(k)d_{2}< x(k) - \frac{(n - k + 1)\cdot x(k)}{n - k + 1} = 0. \quad (25)\]  
+
+However, \(\alpha\) ensures moderate weakening. The adjusted form is:  
+
+\[x(k)d_{2} = x(k)\left(1 - \alpha \cdot \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\right). \quad (26)\]  
+
+Since \(\frac{x(j)}{x(k)} < 1\) and \(\sum_{j = k}^{n}\frac{x(j)}{x(k)} < n - k + 1\) , it follows that \(x(k)d_{2}< x(k)\) , proving that \(D_{2}\) weakens a decreasing sequence. \(\square\)  
+
+Proof. Proof of Weighted Combination for Oscillating Sequences Let the amplitude of a sequence \(\{x(k)\}_{k = 1}^{n}\) be defined as  
+
+\[\Delta = \max_{k\leq j\leq n}x(j) - \min_{k\leq j\leq n}x(j). \quad (27)\]  
+
+Given a threshold \(\theta >0\) , define the adjusted value \(x(k)^{d}\) as follows:  
+
+If \(\Delta >\theta\) , let  
+
+\[x(k)^{d} = w_{1}x(k)^{d_{1}} + w_{2}x(k)^{d_{2}},\]  
+
+where  
+
+\[w_{1} = \frac{\sum_{j = 1}^{n - 1}\max (0,x(j + 1) - x(j))}{\sum_{j = 1}^{n - 1}|x(j + 1) - x(j)|},w_{2} = 1 - w_{1}. \quad (28)\]  
+
+If \(\Delta \leq \theta\) , set  
+
+\[x(k)^{d} = x(k), \quad (29)\]  
+
+to avoid unnecessary adjustment.  
+
+This weighted formulation dynamically balances the influence of strengthening and weakening trends in response to the degree of oscillation. \(\square\)  
+
+Remark 3.2. The adaptive buffer operator \(D\) intelligently adjusts to the nature of the sequence (increasing, decreasing, or oscillating) by adapting \(D_{1}\) , \(D_{2}\) , or a weighted combination, effectively accommodating the sequence's trend. In addition, common methods for sequence trend detection encompass differential statistical analysis, cumulative sum method for difference series, and extremum- based feature identification \(^{30}\) .  
+
+- Here is the complete step-by-step procedure for constructing the Interval Grey Number Prediction IGM(1,2).
+
+<--- Page Split --->
+
+Interval Grey Number: Denoted as \(\otimes = [\otimes ,\otimes ]\) , where \(\otimes\) and \(\otimes\) are the lower and upper bounds of the grey number. Form of IGM(1,2) Model: Based on a first- order differential equation:  
+
+\[\frac{d\otimes_{1}(t)}{dt} +a\otimes_{1}(t) = b\otimes_{2}(t) \quad (30)\]  
+
+Here, \(\otimes_{1}(t)\) is the dependent variable sequence, \(\otimes_{2}(t)\) is the independent variable sequence, and \(a,b\) are parameters to be estimated by least- squares regression.  
+
+## Data Preprocessing  
+
+For the dependent interval grey number sequence \(\otimes_{1}(0) = [\underline{{x}}_{1}(0),\bar{x}_{1}(0)],\otimes_{1}(1) = [\underline{{x}}_{1}(1),\bar{x}_{1}(1)],\dots ,\otimes_{1}(n) = [\underline{{x}}_{1}(n),\bar{x}_{1}(n)]\) and the independent one \(\otimes_{2}(0) = [\underline{{x}}_{2}(0),\bar{x}_{2}(0)],\otimes_{2}(1) = [\underline{{x}}_{2}(1),\bar{x}_{2}(1)],\dots ,\otimes_{2}(n) = [\underline{{x}}_{2}(n),\bar{x}_{2}(n)]\) , check equidistance and monotonicity. If data fluctuates, use First- Order Accumulated Generation (1- AGO):  
+
+\[\left\{ \begin{array}{l l}{\underline{{X}}_{i}(1) = \underline{{x}}_{i}(1),} & {\overline{{X}}_{i}(1) = \overline{{x}}_{i}(1)}\\ {\underline{{X}}_{i}(k) = \underline{{X}}_{i}(k - 1) + \underline{{x}}_{i}(k),} & {\overline{{X}}_{i}(k) = \overline{{X}}_{i}(k - 1) + \overline{{x}}_{i}(k)} & {(k = 2,3,\ldots ,n)} \end{array} \right. \quad (31)\]  
+
+Denote the result as \(\otimes_{1}^{(1)}(k) = [\underline{{X}}_{i}(k),\overline{{X}}_{i}(k)]\)  
+
+## Constructing the IGM(1,2) Model  
+
+Generate the adjacent mean sequence \(Z_{1}(k)\) for \(\otimes_{1}^{(1)}(k)\) :  
+
+\[Z_{1}(k) = [\underline{{z}}_{1}(k),\bar{z}_{1}(k)] = \alpha \otimes_{1}^{(1)}(k) + (1 - \alpha)\otimes_{1}^{(1)}(k - 1)\quad (\alpha \in [0,1],\mathrm{usually}\alpha = 0.5) \quad (32)\]  
+
+Approximately, for \(k = 2,3,\ldots ,n\) :  
+
+\[\frac{d\otimes_{1}^{(1)}(t)}{dt}\bigg|_{t = k} +a\otimes_{1}^{(1)}(k)\approx b\otimes_{2}^{(1)}(k) \quad (33)\]  
+
+The discrete form is:  
+
+\[Z_{1}(k) + a\otimes_{1}^{(1)}(k) = b\otimes_{2}^{(1)}(k) \quad (34)\]  
+
+In matrix form:  
+
+\[\begin{array}{r}{\left[ \begin{array}{c c}{-Z_{1}(2)} & {\otimes_{1}^{(1)}(2)}\\ {-Z_{1}(3)} & {\otimes_{2}^{(1)}(3)}\\ \vdots & \vdots \\ {-Z_{1}(n)} & {\otimes_{2}^{(1)}(n)} \end{array} \right]\left[ \begin{array}{c}{\otimes_{1}^{(1)}(2) - \otimes_{1}^{(1)}(1)}\\ {\otimes_{1}^{(1)}(3) - \otimes_{1}^{(1)}(2)}\\ \vdots \\ {\otimes_{1}^{(1)}(n) - \otimes_{1}^{(1)}(n - 1)} \end{array} \right]} \end{array} \quad (35)\]  
+
+Solve \(\hat{\pmb{\theta}} = [a,b]^{T}\) in \(\mathbf{B}\cdot \hat{\pmb{\theta}} = \mathbf{Y}\) by interval grey number least squares:  
+
+\[\hat{\pmb{\theta}} = (\mathbf{B}^{T}\cdot \mathbf{B})^{-1}\cdot \mathbf{B}^{T}\cdot \mathbf{Y} \quad (36)\]  
+
+Split into lower and upper bounds to get \(a = [\underline{{a}},\overline{{a}} ]\) and \(b = [\underline{{b}},\overline{{b}} ]\)  
+
+Model Prediction: The predicted value of the accumulated sequence  
+
+\[\otimes_{1}^{(1)}(k + 1) = [\underline{{X}}_{1}(k + 1),\overline{{X}}_{1}(k + 1)] = \left(\otimes_{1}^{(1)}(1) - \frac{b}{a}\right)e^{-a k} + \frac{b}{a} \quad (37)\]  
+
+Use Inverse Accumulated Generation (IAGO) to get:  
+
+\[\left\{ \begin{array}{l l}{\underline{{x}}_{1}(k + 1) = \underline{{X}}_{1}(k + 1) - \underline{{X}}_{1}(k)}\\ {\overline{{x}}_{1}(k + 1) = \overline{{X}}_{1}(k + 1) - \overline{{X}}_{1}(k)} \end{array} \right. \quad (38)\]  
+
+The prediction interval is \(\otimes_{1}(k + 1) = [\underline{{x}}_{1}(k + 1),\overline{{x}}_{1}(k + 1)]\)  
+
+## Model Validation  
+
+Calculate the residual interval:  
+
+\[\mathrm{Residual~Interval} = [\underline{{x}}_{1}(k) - \underline{{x}}_{1}(k),\overline{{x}}_{1}(k) - \overline{{x}}_{1}(k)] \quad (39)\]
+
+<--- Page Split --->
+
+Ensure the mean absolute value of residuals is less than a threshold. Calculate \(S_{1}\) , \(S_{2}\) , where \(S_{1} = \frac{1}{n}\sum_{k = 1}^{n}\left[x_{1}(k) - \bar{x}_{1}\right]^{2}\) (variance of the original sequence \(\{x_{1}(k)\}\) , where \(\bar{x}_{1} = \frac{1}{n}\sum_{k = 1}^{n}x_{1}(k)\) ) and \(S_{2} = \frac{1}{n}\sum_{k = 1}^{n}\left[e(k) - \bar{e}\right]^{2}\) (variance of residuals \(e(k) = x_{1}(k) - \hat{x}_{1}(k)\) , with \(\bar{e} = \frac{1}{n}\sum_{k = 1}^{n}e(k)\) ) quantify data dispersion and model error, respectively. The posterior difference ratio \(C = \frac{S_{2}}{S_{1}}\) ( \(C< 0.35\) is excellent, \(C< 0.5\) is qualified), and the small error probability \(P = P\{|e(k) - \bar{e}|< 0.6745S_{1}\}\) ( \(P > 0.95\) is excellent). Also, the grey correlation degree between the predicted and original sequences should be greater than 0.6.  
+
+## 4 Controller design and performance analysis  
+
+This section demonstrates that Interval Grey Adaptive Buffer Generalized Predictive Control (IGAB- GPC) not only guarantees the convergence of system tracking error but also ensures bounded- input bounded- output (BIBO) stability under certain conditions. Based on the mentioned background and issues, the following will systematically elaborate on the control design and conduct an in- depth analysis and evaluation of its performance.  
+
+### 4.1 Controller design  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Block diagram of the IGAB-GPC scheme architecture for pattern-moving systems. </center>  
+
+As illustrated in Figure 2, IGAB- GPC incorporates the fundamental components GPC, including the prediction model, receding horizon optimization, and feedback correction mechanism. The flowchart illustrates a control system architecture based on Generalized Predictive Control (GPC) integrated with an IGM prediction using an adaptive buffer operator. The detailed description of the components and their interactions is as follows:  
+
+- Reference Trajectory \((y_{r}(k))\) : The control system begins with a reference trajectory, denoted as \(y_{r}(k)\) , which represents the desired output or setpoint that the system aims to achieve at time step \(k\) . Consider the measurement uncertainty of pattern-class variables, the reference output is represented as follows.  
+
+\[y_{r}(k) = \left\{ \begin{array}{l l}{y_{d}(k)\cap r_{1}^{k},} & {\mathrm{if}\exists i\in \{1,2,\ldots ,l\} \models |y(k) - y_{d}(k)|\leq r_{1}^{k},}\\ {r_{t + 1}^{k} = \mathcal{R}_{n e w}(k),} & {\mathrm{otherwise}.} \end{array} \right. \quad (40)\]  
+
+where \(l = 2N + 1\) , \(r_{t}^{k}\) refers to the category radius calculated by Equation 4. \(\mathcal{R}_{new}(k)\) denotes a new pattern class variable which can be computed by automatic category expansion strategy \(^{31}\) .  
+
+- Output Error Calculation \((e(k))\) : The reference trajectory \(y_{r}(k)\) is compared with the predicted output \(y_{p}(k)\) (obtained from the revising feedback loop). The difference between these two signals is computed as the error signal:  
+
+\[e(k) = y_{r}(k) - y_{p}(k) \quad (41)\]  
+
+This error \(e(k)\) is then passed to the optimization algorithm.
+
+<--- Page Split --->
+
+- Pattern-Moving Systems: This part represents the controlled system or plant, which receives the control input \(u(k)\) and produces the actual output \(y(k)\) . The pattern-moving systems could represent a dynamic process with specific characteristics in Equation 32 (e.g., linear or nonlinear dynamics).  
+
+- Event-Triggered IGM Prediction with Adaptive Buffer Operator: The actual system output \(y(k)\) is processed by a module integrating Interval Grey Model (IGM) prediction with an adaptive buffer operator, as depicted in Figure 2. This component manages uncertainties and fluctuations in pattern-moving systems by combining interval grey modeling with adaptive buffering. The formalized procedure is as follows:  
+
+1. Monotonicity Event Detection: At each time step \(k\) , the monotonicity of the interval grey number sequence \(\widehat{\otimes} (k) = [\underline{{x}} (k),\overline{{x}} (k)]\) , derived from \(y(k)\) Definition 2.1, is evaluated over a detection window of size \(\tau \in \mathbb{Z}_{+}\) (e.g., \(\tau = 5\) ). The event \(\mathcal{E}_{k}\) is defined based on the monotonicity of \(\{\widehat{\otimes} (i)\}_{i = k - 1}^{k - 1}\) :  
+
+\[\mathcal{E}_{k}=\left\{\begin{array}{l l}{\mathrm{increasing}}&{\mathrm{if~}\underline{{x}}(i+1)>\underline{{x}}(i)\mathrm{~and~}\overline{{x}}(i+1)>\overline{{x}}(i),~\forall i\in[k-\tau,k-1],}\\ {\mathrm{decreasing}}&{\mathrm{if~}\underline{{x}}(i+1)< \underline{{x}}(i)\mathrm{~and~}\overline{{x}}(i+1)< \overline{{x}}(i),~\forall i\in[k-\tau,k-1],}\\ {\mathrm{oscillating}}&{\mathrm{otherwise},}\end{array}\right. \quad (42)\]  
+
+where comparisons are applied component- wise to the lower and upper bounds, ensuring consistency with Definition 2.1. The window size \(\tau\) captures sufficient historical data for reliable trend detection.  
+
+2. Adaptive Buffering: Based on \(\mathcal{E}_{k}\) , the adaptive buffer operator \(D\) , as defined in Theorem 3, is applied to the sequence \(\{\widehat{\otimes} (i)\}_{i = 1}^{k}\) :  
+
+\[\begin{array}{r}{\widehat{\otimes} (k) = D(\widehat{\otimes} (k)) = \left\{ \begin{array}{l l}{D_{1}(\widehat{\otimes} (k)),} & {\mathrm{if~}\mathcal{E}_{k} = \mathrm{increasing},}\\ {D_{2}(\widehat{\otimes} (k)),} & {\mathrm{if~}\mathcal{E}_{k} = \mathrm{decreasing},}\\ {w_{1}D_{1}(\widehat{\otimes} (k)) + w_{2}D_{2}(\widehat{\otimes} (k)),} & {\mathrm{if~}\mathcal{E}_{k} = \mathrm{oscillating~and~}\Delta_{k} > \theta ,}\\ {\widehat{\otimes} (k),} & {\mathrm{otherwise},} \end{array} \right.} \end{array} \quad (43)\]  
+
+where \(D_{1}\) and \(D_{2}\) are the strengthening and weakening buffer operators, respectively, defined as:  
+
+\[x(k)d_{1} = x(k)\left(1 + \alpha \cdot \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\right),\quad 0< \alpha < 1, \quad (44)\]  
+
+\[x(k)d_{2} = x(k)\left(1 - \alpha \cdot \frac{1}{n - k + 1}\sum_{j = k}^{n}\frac{x(j)}{x(k)}\right),\quad 0< \alpha < 1, \quad (45)\]  
+
+applied component- wise to \(\underline{{x}} (k)\) and \(\overline{{x}} (k)\) of \(\widehat{\otimes} (k) = [\underline{{x}} (k),\overline{{x}} (k)]\) . The amplitude \(\Delta_{k}\) is:  
+
+\[\Delta_{k} = \max_{i\in [k - \tau ,k]}\overline{{x}} (i) - \min_{i\in [k - \tau ,k]}\underline{{x}} (i), \quad (46)\]  
+
+with \(\theta = 0.1\cdot (\max_{i = 1}^{k}\overline{{x}} (i) - \min_{i = 1}^{k}\underline{{x}} (i))\) as the threshold. The weights \(w_{1}\) and \(w_{2}\) are:  
+
+\[w_{1} = \frac{\sum_{j = k - \tau}^{k - 1}\max (0,\overline{{x}} (j + 1) - \overline{{x}} (j))}{\sum_{j = k - \tau}^{k - 1}|\overline{{x}} (j + 1) - \overline{{x}} (j)| + \epsilon},\quad w_{2} = 1 - w_{1}, \quad (47)\]  
+
+where \(\epsilon = 10^{- 6}\) prevents division by zero, and \(w_{1},w_{2}\geq 0\) satisfy \(w_{1} + w_{2} = 1\)
+
+<--- Page Split --->
+
+3. Accumulated Generation (1-AGO): The buffered sequence \(\{\hat{\otimes} (i)\}_{i = 1}^{k}\) undergoes First-Order Accumulated Generation (1-AGO) to reduce noise and enhance stability:  
+
+\[\hat{\otimes}^{(1)}(k) = \left\{ \begin{array}{ll}\hat{\otimes}(1), & k = 1,\\ \hat{\otimes}^{(1)}(k - 1) + \hat{\otimes}(k), & k > 1, \end{array} \right. \quad (48)\]  
+
+where \(\hat{\otimes}^{(1)}(k) = [\underline{{X}} (k),\overline{{X}} (k)]\) , with:  
+
+\[\underline{{X}} (k) = \sum_{i = 1}^{k}\underline{{x}} (i),\quad \overline{{X}} (k) = \sum_{i = 1}^{k}\overline{{x}} (i). \quad (49)\]  
+
+4. Parameter Update for IGM(1,2): The IGM(1,2) parameters \(\hat{\theta}_{k} = [a,b]^{T}\) are updated only when monotonicity changes \((\hat{\mathcal{E}}_{k}\neq \hat{\mathcal{E}}_{k - 1})\) to enhance efficiency:  
+
+\[\hat{\theta}_{k} = \left\{ \begin{array}{ll}(\mathbf{B}^{T}\mathbf{B})^{-1}\mathbf{B}^{T}\mathbf{Y}, & \mathrm{if} \hat{\mathcal{E}}_{k}\neq \hat{\mathcal{E}}_{k - 1},\\ \hat{\theta}_{k - 1}, & \mathrm{otherwise}, \end{array} \right. \quad (50)\]  
+
+where \(\mathbf{B}\) and \(\mathbf{Y}\) are constructed using the adjacent mean sequence \(Z_{1}(k)\) :  
+
+\[Z_{1}(k) = 0.5\hat{\otimes}^{(1)}(k) + 0.5\hat{\otimes}^{(1)}(k - 1), \quad (51)\]  
+
+and for \(k = 2,\ldots ,n\) :  
+
+\[\mathbf{B} = \left[ \begin{array}{c c c}{-Z_{1}(2)} & {\hat{\otimes}_{1}^{(1)}(2)}\\ {-Z_{1}(3)} & {\hat{\otimes}_{2}^{(1)}(3)}\\ \vdots & \vdots \\ {-Z_{1}(n)} & {\hat{\otimes}_{2}^{(1)}(n)} \end{array} \right],\quad \mathbf{Y} = \left[ \begin{array}{c}{\hat{\otimes}_{1}^{(1)}(2) - \hat{\otimes}_{1}^{(1)}(1)}\\ {\hat{\otimes}_{1}^{(1)}(3) - \hat{\otimes}_{1}^{(1)}(2)}\\ \vdots \\ {\hat{\otimes}_{1}^{(1)}(n) - \hat{\otimes}_{1}^{(1)}(n - 1)} \end{array} \right], \quad (52)\]  
+
+where \(\hat{\otimes}_{1}^{(1)}\) and \(\hat{\otimes}_{2}^{(1)}\) are the 1- AGO sequences for dependent and independent variables, respectively. Parameters \(a = [a,\bar{a} ]\) and \(b = [b,\bar{b} ]\) are computed for interval bounds.  
+
+5. Prediction and Correction: The predicted output \(y_{m}(k + 1)\) is computed using the IGM(1,2) model with a correction term:  
+
+\[y_{m}(k + 1) = \left(\hat{\otimes}^{(1)}(1) - \frac{b}{a}\right)e^{-a k} + \frac{b}{a} +\gamma (D(y(k)) - \hat{y}_{m}(k)), \quad (53)\]  
+
+where \(\hat{\otimes}^{(1)}(1) = [\underline{{X}} (1),\overline{{X}} (1)]\) , \(a,b\) are from \(\hat{\theta}_{k}\) , and \(\gamma = 0.1\) is the correction gain. The buffered output \(D(y(k))\) follows Equation (43), and \(\hat{y}_{m}(k)\) is the prior prediction. The interval grey number is recovered via Inverse Accumulated Generation (IAGO):  
+
+\[\hat{\otimes}(k + 1) = \hat{\otimes}^{(1)}(k + 1) - \hat{\otimes}^{(1)}(k), \quad (54)\]  
+
+yielding \(\hat{\otimes}(k + 1) = [\underline{{x}} (k + 1),\overline{{x}} (k + 1)]\) , which is mapped to the pattern- moving space using \(M(\cdot)\) in Equation (3).  
+
+The following pseudocode describes the event- triggered Interval Grey Model (IGM) prediction with an adaptive buffer operator, which processes system outputs to handle uncertainties and fluctuations in pattern- moving systems, seeing Algorithm 1
+
+<--- Page Split --->
+
+Input: Time range \(T\) , Window size \(\tau\) , Buffer parameters (Eqs. (44), (45)), IGM(1,2) parameters (Eqs. (53), (54)), \(\gamma = 0.1\) , \(\theta\) factor \(= 0.1\) , \(\epsilon = 10^{- 6}\)  
+
+Output: Predicted output \(y_{m}(k + 1)\) , Parameters \(\hat{\theta}_{k} = [a,b]^{T}\)  
+
+Initialize: \(\mathcal{E}_{\mathrm{prev}}\gets \theta\) , \(\hat{\theta}_{1}\gets \mathbf{0}\)  
+
+for \(k\gets 2\) to \(T\) do  
+
+1. Get output: \(y(k)\gets\) System output  
+
+2. Form interval: \(\hat{\otimes} (k)\gets [x(k),\bar{x} (k)]\) (Def. 2.1)  
+
+3. Detect event: \(\mathcal{E}_{k}\gets\) Monotonicity of \(\{\hat{\otimes} (i)\}_{i = k - \tau}^{k - 1}\) (Eq. (42))  
+
+if \(\mathcal{E}_{k}\neq \mathcal{E}_{\mathrm{prev}}\) then  
+
+3.1 Buffer operation:  
+
+\[\Delta_{k}\gets \max_{i\in [k - \tau ,k]}\bar{x} (i) - \min_{i\in [k - \tau ,k]}\underline{{x}} (i) \quad (Eq. (46))\]  
+
+\[\theta \gets 0.1\cdot (\max_{i = 1}^{k}\bar{x} (i) - \min_{i = 1}^{k}\underline{{x}} (i))\]  
+
+if \(\mathcal{E}_{k} =\) increasing then  
+
+\[\hat{\otimes} (k)\gets D_{1}(\hat{\otimes} (k)) \quad (\mathrm{Eq.} (44))\]  
+
+else if \(\mathcal{E}_{k} =\) decreasing then  
+
+\[\hat{\otimes} (k)\gets D_{2}(\hat{\otimes} (k)) \quad (\mathrm{Eq.} (45))\]  
+
+else if \(\mathcal{E}_{k} =\) oscillating and \(\Delta_{k} > \theta\) then  
+
+\[w_{1}\leftarrow \frac{\Sigma_{j = k - \tau}^{k - 1}\max (0,\bar{x} (j + 1) - \bar{x} (j))}{\Sigma_{j = k - \tau}^{k - 1}\bar{x} (j + 1) - \bar{x} (j) + \epsilon},w_{2}\leftarrow 1 - w_{1} \quad (\mathrm{Eq.} (47))\]  
+
+else  
+
+\[\hat{\otimes} (k)\gets \hat{\otimes} (k)\]  
+
+end if  
+
+3.2 Compute 1- AGO: \(\hat{\otimes}^{(1)}(i)\gets 1 - \mathrm{AGO}(\hat{\otimes}(i)),i = 1,\ldots ,k\) (Eq. (48))  
+
+3.3 Build matrices: \(\mathbf{B},\mathbf{Y}\gets \mathrm{Using}Z_{1}(k) = 0.5\hat{\otimes}^{(1)}(k) + 0.5\hat{\otimes}^{(1)}(k - 1)\) (Eqs. (51), (52))  
+
+3.4 Update parameters: \(\hat{\theta}_{k}\gets (\mathbf{B}^{T}\mathbf{B})^{- 1}\mathbf{B}^{T}\mathbf{Y}\) (Eq. (50))  
+
+3.5 Set \(\mathcal{E}_{\mathrm{prev}}\gets \mathcal{E}_{k}\)  
+
+else  
+
+\[\hat{\theta}_{k}\gets \hat{\theta}_{k - 1}\]  
+
+end if  
+
+4. Predict: \(y_{m}(k + 1)\gets \left(\hat{\otimes}^{(1)}(1) - \frac{a}{b}\right)e^{-a k} + \frac{b}{a}\) , IAGO (Eqs. (53), (54)), map via \(M(\cdot)\) (Eq. (3))  
+
+5. Correct: \(y_{m}(k + 1)\gets y_{m}(k + 1) + \gamma (D(y(k)) - \hat{y}_{m}(k))\) (Eq. (53))  
+
+end for  
+
+- Optimization Algorithm: The optimization algorithm block takes the error signal \(e(k)\) as input and computes the optimal control input \(u(k)\) . The optimization process typically minimizes a cost function that balances the tracking error and control effort, a hallmark of GPC. The control input \(u(k)\) is then applied to the pattern-moving systems. The cost function is designed as follows.  
+
+\[J(N_{1},N_{y},N_{u}) = \sum_{j = N_{1}}^{N_{y}}[\hat{y} (k + j|k) - y_{r}(k + j)|_{Q_{j}}^{2} + \sum j = 1^{N_{u}}|\Delta u(k + j - 1)|_{R_{j}}^{2} \quad (55)\]  
+
+where \(N_{1}\) is the minimum costing horizon (typically \(N_{1} = 1\) ), \(N_{y}\) is the prediction horizon, \(N_{u}\) is the control horizon \((N_{u}\leq N_{y})\) , \(\hat{y} (k + j|k)\) is the predicted output at step \(k + j\) based on information at step \(k\) , \(y_{r}(k + j)\) is the reference trajectory at step \(k + j\) , \(\Delta u(k + j - 1) = u(k + j - 1) - u(k + j - 2)\) is the control increment, \(\mathbf{Q}_{j}\succeq 0\) is the output weighting matrix, and \(\mathbf{R}_{j}\succ 0\) is the control weighting matrix. The reference trajectory is generated through setpoint smoothing: \(y_{r}(k + j) = \alpha y_{r}(k + j - 1) + (1 - \alpha)w(k + j)\) with \(\alpha \in [0,1)\) , where \(w(k + j)\) is the desired setpoint.  
+
+The optimal control sequence is derived by expressing predictions in vector form:  
+
+\[\hat{\mathbf{Y}} = \mathbf{G}\Delta \mathbf{U} + \mathbf{F} \quad (56)\]  
+
+where \(\hat{\mathbf{Y}} = [\hat{y} (k + N_{1}|k),\ldots ,\hat{y} (k + N_{y}|k)]^{T}\) , \(\Delta \mathbf{U} = [\Delta u(k),\ldots ,\Delta u(k + N_{u} - 1)]^{T}\) , \(\mathbf{F}\) is the free response vector (prediction
+
+<--- Page Split --->
+
+with \(\Delta u = 0\) ), and \(\mathbf{G}\) is the dynamic matrix containing step response coefficients. The cost function then becomes:  
+
+\[J = (\mathbf{G}\Delta \mathbf{U} + \mathbf{F} - \mathbf{Y}_{r})^{T}\mathbf{Q}(\mathbf{G}\Delta \mathbf{U} + \mathbf{F} - \mathbf{Y}_{r}) + \Delta \mathbf{U}^{T}\mathbf{R}\Delta \mathbf{U} \quad (57)\]  
+
+with \(\mathbf{Q} = \mathrm{diag}(\mathbf{Q}_{N_{1}},\dots ,\mathbf{Q}_{N_{s}})\) and \(\mathbf{R} = \mathrm{diag}(\mathbf{R}_{1},\dots ,\mathbf{R}_{N_{u}})\) . The optimal solution is obtained by solving:  
+
+\[\frac{\partial J}{\partial\Delta\mathbf{U}} = 2\mathbf{G}^{T}\mathbf{Q}(\mathbf{G}\Delta \mathbf{U} + \mathbf{F} - \mathbf{Y}_{r}) + 2\mathbf{R}\Delta \mathbf{U} = 0 \quad (58)\]  
+
+yielding:  
+
+\[\Delta \mathbf{U}^{*} = (\mathbf{G}^{T}\mathbf{Q}\mathbf{G} + \mathbf{R})^{-1}\mathbf{G}^{T}\mathbf{Q}(\mathbf{Y}_{r} - \mathbf{F}) \quad (59)\]  
+
+Only the first element is implemented: \(u(k) = u(k - 1) + [1,0,\dots ,0]\Delta \mathbf{U}^{*}\) .  
+
+Key implementation aspects include: (1) Dynamic matrix \(\mathbf{G}\) construction using step response coefficients from IGM(1,2): \(g_{i} = \partial \hat{y} (k + i|k) / \partial \Delta u(k)\approx [\hat{y} (k + i|k,\Delta u(k) = \delta) - \hat{y} (k + i|k,\Delta u(k) = 0)] / \delta\) ; (2) Free response \(\mathbf{F}\) calculation by propagating IGM(1,2) with \(\Delta u = 0\) : \(\hat{y}_{0}(k + j|k) = [\hat{\otimes}^{(1)}(1) - b / a]e^{-a(k + j - 1)} + b / a\) ; (3) Physical constraints handling \((u_{\mathrm{min}}\leq u(k + j)\leq u_{\mathrm{max}}\) , \(\Delta u_{\mathrm{min}}\leq \Delta u(k + j)\leq \Delta u_{\mathrm{max}}\) , \(\mathrm{y}_{\mathrm{min}}\leq \hat{y} (k + j|k)\leq \mathrm{y}_{\mathrm{max}})\) transforming the problem into constrained QP; and (4) Recalculation of optimization each time step with updated parameters.  
+
+# Algorithm 2 IGB-GPC Optimization Procedure  
+
+Input: Current state \(\mathbf{x}(k)\) , Reference \(\mathbf{Y}_{r}\) , Model \(\{a,b\}\) , Weights \(\mathbf{Q}\) , \(\mathbf{R}\)  
+
+Output: Optimal control \(u(k)\)  
+
+procedure OPTIMIZE  
+
+1. Compute \(\mathbf{Y}_{r}\gets [y_{r}(k + N_{1}),\dots ,y_{r}(k + N_{y})]^{T}\)  
+
+2. Calculate free response \(\mathbf{F}\) via IGM(1,2) with \(\Delta u = 0\)  
+
+3. Construct \(\mathbf{G}\) using step response coefficients  
+
+4. Solve \(\Delta \mathbf{U}^{*}\leftarrow (\mathbf{G}^{T}\mathbf{Q}\mathbf{G} + \mathbf{R})^{-1}\mathbf{G}^{T}\mathbf{Q}(\mathbf{Y}_{r} - \mathbf{F})\)  
+
+5. Extract \(\Delta u^{*}(k)\gets [1,0,\dots ,0]\Delta \mathbf{U}^{*}\)  
+
+6. Apply \(u(k)\gets u(k - 1) + \Delta u^{*}(k)\)  
+
+return \(u(k)\)  
+
+end procedure  
+
+- Summation Block for Predicted Output Adjustment: The predicted output \(y_{m}(k)\) is compared with the actual output \(y(k)\) in another summation block. The difference between these two signals is calculated as:  
+
+\[y_{p}(k) = y_{m}(k) + (y(k) - y_{m}(k)) \quad (60)\]  
+
+However, in practice, this step may involve additional correction mechanisms to refine the predicted output \(y_{p}(k)\) . \(p\) represents the optimized time domain parameter, satisfying the condition that \(m < p\)  
+
+- Revising Feedback \((y_{p}(k))\) : The adjusted predicted output \(y_{p}(k)\) is fed back into the system through a revising feedback loop. This feedback is used to compute the error \(e(k)\) in the first summation block, closing the control loop.  
+
+Figure 2 represents the GPC control system using IGM prediction with adaptive buffer operators to manage dynamic uncertainties; real- time feedback enables continuous output correction for pattern- moving systems with uncertain behavior. Algorithm 3 details the signal flow process within this control system.  
+
+In summary, this diagram depicts a GPC- based control system featuring IGM prediction named as IGB- GPC for handling uncertainty and limited data, an adaptive buffer operator for robustness against disturbances, and a feedback loop for continuous adjustment. It is tailored for complex, dynamic pattern- moving systems.  
+
+### 4.2 Performance analysis  
+
+This section rigorously analyzes the stability and convergence properties of the proposed IGB- GPC framework. We establish formal guarantees for bounded- input bounded- output (BIBO) stability and tracking error convergence under specified conditions. The analysis leverages Lyapunov stability theory and incorporates the effects of the adaptive buffer operator on prediction accuracy.
+
+<--- Page Split --->
+
+Input: Reference trajectory \(y_{r}(k)\) , System parameters  
+
+Output: Control input \(u(k)\) , Actual output \(y(k)\)  
+
+Initialize: \(y_{p}(0) \leftarrow\) initial value  
+
+for each time step \(k\) do  
+
+1. Compute error between reference and predicted output: \(e(k) \leftarrow y_{r}(k) - y_{p}(k)\)  
+
+2. Generate control input through optimization \(u(k) \leftarrow\) Optimization Algorithm \((e(k))\)  
+
+3. Apply control to the system \(y(k) \leftarrow\) Pattern Moving System \((u(k))\)  
+
+4. Predict output using IGM and adaptive buffer \(y_{m}(k) \leftarrow\) IGMP prediction \((y(k))\) using Adaptive Buffer Operator  
+
+5. Revise prediction with actual output \(y_{p}(k + 1) \leftarrow\) Revise Prediction \((y_{m}(k), y(k))\)  
+
+end for  
+
+Theorem 4.1. (Bounded prediction error) For the interval grey prediction model with adaptive buffer operator, the prediction error \(e_{p}(k) = y(k) - y_{m}(k)\) satisfies:  
+
+\[|e_{p}(k)|\leq \epsilon_{1} + \epsilon_{2}\exp (-\lambda k) \quad (61)\]  
+
+where \(\epsilon_{1} = \sup_{k}|\delta (k)|\) is the supremum of metric perturbation, \(\epsilon_{2}\) depends on initial conditions, and \(\lambda >0\) is the convergence rate of the grey model.  
+
+Proof. From Definition 3.1, the pattern class variable satisfies \(d x(k) = \tilde{\otimes}_{k} + \delta\) where \(|\delta |\leq \tilde{\delta}\) . The buffered sequence \(\tilde{\otimes} (k) = D(\tilde{\otimes} (k))\) reduces amplitude \(\Delta_{k}\) according to Theorems 3.1 and 3.2. For the IGM(1,2) solution:  
+
+\[\tilde{\otimes}^{(1)}(k + 1) = \left(\tilde{\otimes}^{(1)}(1) - \frac{b}{a}\right)e^{-a k} + \frac{b}{a} \quad (62)\]  
+
+The prediction error dynamics follow:  
+
+\[e_{p}(k + 1) = y(k + 1) - y_{m}(k + 1)\] \[\qquad = \left[f(\cdot) - \left(\tilde{\otimes}^{(1)}(1) - \frac{b}{a}\right)e^{-a k} - \frac{b}{a}\right] - \gamma (D(y(k)) - \hat{y}_{m}(k))\]  
+
+Applying the adaptive buffer operator bounds the high- frequency components, yielding exponentially stable error dynamics. The correction term \(\gamma (\cdot)\) further attenuates residual errors. \(\square\)  
+
+Theorem 4.2. (BIBO stability) The closed- loop system under IGAB- GPC is BIBO stable if: 1. The prediction horizon \(N_{y}\) exceeds the system's degree of freedom 2. Control weighting matrix \(\mathbf{R} > 0\) 3. The class radius satisfies \(r_{i}< \min_{j\neq i}|c_{i} - c_{j}| / 2\)  
+
+Proof. Consider the Lyapunov function candidate:  
+
+\[V(k) = \Delta \mathbf{U}^{T}(k)\mathbf{\Delta}\mathbf{U}(k) + \sum_{i = k - N_{u} + 1}^{k}e_{p}^{2}(i) \quad (63)\]  
+
+where \(\mathbf{\delta} = \mathbf{G}^{T}\mathbf{Q}\mathbf{G} + \mathbf{R} > 0\) . The difference \(\Delta V(k) = V(k + 1) - V(k)\) satisfies:  
+
+\[\Delta V(k)\leq -\Delta \mathbf{U}^{T}(k)\mathbf{R}\Delta \mathbf{U}(k) + 2L_{g}\| \Delta \mathbf{U}(k)\| |e_{p}(k)|\] \[\qquad +L_{f}e_{p}^{2}(k) - e_{p}^{2}(k - N_{u})\]  
+
+where \(L_{g}\) and \(L_{f}\) are Lipschitz constants for \(\mathbf{G}\) and system dynamics \(f(\cdot)\) . From Theorem 4.1, \(\| e_{p}(k)\| \leq \bar{e}_{p}\) . Selecting \(\mathbf{R}\) such that \(\lambda_{\min}(\mathbf{R}) > L_{g}^{2} / L_{f}\) ensures:  
+
+\[\Delta V(k)\leq -\eta \| \Delta \mathbf{U}(k)\|^{2} - \mu e_{p}^{2}(k)\quad (\eta ,\mu >0) \quad (64)\]  
+
+Thus \(V(k)\) decreases monotonically, proving bounded states and outputs.
+
+<--- Page Split --->
+
+Theorem 4.3. (Tracking error convergence) The tracking error \(e(k) = y_{r}(k) - y(k)\) converges exponentially to a bounded set:  
+
+\[\lim_{k\to \infty}\sup |e(k)|\leq \frac{\epsilon_{1} + \bar{w}}{1 - \alpha} \quad (65)\]  
+
+where \(\alpha\) is the reference trajectory smoothing factor and \(\bar{w}\) is the disturbance bound.  
+
+Proof. The optimized control increment \(\Delta \mathbf{U}^{*}\) from Eq. (59) minimizes:  
+
+\[J(k) = \| \mathbf{G}\Delta \mathbf{U} + \mathbf{F} - \mathbf{Y}_{r}\|_{\mathbf{Q}}^{2} + \| \Delta \mathbf{U}\|_{\mathbf{R}}^{2}\] \[\qquad = \| \mathbf{G}(\Delta \mathbf{U} - \Delta \mathbf{U}^{*})\|_{\mathbf{Q}}^{2} + \| \Delta \mathbf{U} - \Delta \mathbf{U}^{*}\|_{\mathbf{P}}^{2} + J^{*}(k)\]  
+
+where \(\mathbf{P} = \mathbf{G}^{T}\mathbf{Q}\mathbf{G} + \mathbf{R}\) . The error dynamics satisfy:  
+
+\[e(k + 1) = \alpha e(k) + (1 - \alpha)[w(k) - y(k)] + \Delta f(\cdot) \quad (66)\]  
+
+with \(\| \Delta f(\cdot)\| \leq L_{\delta}\) due to metric perturbation. From Lemma 4.1 and Theorem 4.2, we have:  
+
+\[|y(k) - w(k)|\leq |y(k) - y_{m}(k)| + |y_{m}(k) - w(k)|\] \[\qquad \leq \epsilon_{1} + \kappa \| \Delta \mathbf{U}^{*}(k)\|\]  
+
+where \(\kappa = \| \mathbf{G}(1, \cdot)\|\) . Since \(\| \Delta \mathbf{U}^{*}(k)\|\) decays exponentially, the error converges to the stated bound.  
+
+Remark 4.1. The adaptive buffer operator enhances performance by: 1. Reducing prediction error amplitude by \(30 - 50\%\) compared to unbuffered models 2. Decreasing the Lipschitz constant \(L_{f}\) by smoothing system dynamics 3. Accelerating the convergence rate \(\lambda\) in Lemma 4.1  
+
+Corollary 1. (Pattern convergence) The system operating point converges to the target pattern class \(P_{d}\) within finite steps \(K\) satisfying:  
+
+\[K\leq \frac{1}{\mu}\log \left(\frac{\|d x(0) - c_{d}\|}{\min_{i\neq d}r_{i}}\right) \quad (67)\]  
+
+where \(\mu\) is the convergence rate from Theorem 4.3, and \(c_{d}\) is the target class center.  
+
+Proof. From quantization properties in Eq. (4), convergence to \(P_{d}\) occurs when \(\| d x(k) - c_{d}\| < r_{d}\) . Theorem 4.3 ensures \(\| d x(k) - c_{d}\|\) decreases exponentially, yielding the step bound.  
+
+The analysis demonstrates that IGAB- GPC guarantees closed- loop stability and pattern convergence while accommodating inherent uncertainties in pattern- moving systems through grey modeling and adaptive buffering.  
+
+## 5 Simulation results  
+
+An numerical simulation case are given in this section to illustrate the effectiveness of the proposed IGAB- GPC scheme. In order to properly assess its efficacy and applicability of the proposed method, the classical CARIMA- GPC \(^{24}\) (controlled autoregressive integral moving average generalized predictive control) and IG- GPC \(^{32}\) (interval grey generalized predictive control) are selected as the benchmark comparison methods. By constructing simulation experiments, the control accuracy, dynamic response characteristics are compared and analyzed. Furthermore, the advantages and potential disadvantages of this method in practical applications are comprehensively revealed.  
+
+Consider the the nonlinear discrete- time system with one input and three outputs as follows.  
+
+\[\left\{ \begin{array}{l l}{y_{1}(k) = 0.3y_{1}(k - 1) + \frac{u(k - 1)}{1 + u^{2}(k - 1)} +u(k - 2) + d(k)}\\ {y_{2}(k) = 0.2y_{2}(k - 1) + 0.4y_{2}(k - 2) + \frac{u(k - 1)}{1 + u^{2}(k - 1)} +u(k - 3) + d(k)}\\ {y_{3}(k) = 0.3y_{3}(k - 1) + 0.1y_{3}(k - 2) + \frac{u(k - 1)}{1 + u^{2}(k - 1)} +u(k - 2) + d(k)} \end{array} \right.. \quad (68)\]  
+
+Among them, the system input \(u(k) \in [- 4, 4]\) ; the system noise satisfies \(d(k) \sim N(0, 0.1^{2})\) and is assumed to be known.  
+
+Through the following 3 steps, first, construct the description mode of system dynamics; then, complete the system tracking control by using the designed control algorithm; finally, compare the accuracy with CARIMA- GPC and IG- GPC, respectively.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. 3000 sets of input-output system historical data. </center>  
+
+Step 1: Constructing the pattern moving space and system output prediction with IGAB. Based on the construction process described in Section 2.2.2, the input signals \(u(k)\) are introduced to the system, generating 3000 sets of historical input- output data (Figure 3) that form the moving subspace.  
+
+After normalizing the output data, dimensionality reduction was performed via Principal Component Analysis (PCA) to a one- dimensional feature space, with the contribution rate reaching \(87.23\%\) . Subsequently, for quantitative evaluation using the class - specific metric defined in Equation 4, we set the initial parameters of the improved quantization classification algorithm as \(\kappa_{0} = 5\) , \(\rho_{0} = 0.6\) , and \(r_{0} = 0.4\) . By taking \(N = 5\) , the number of classes can be obtained as \(2N + 1 = 11\) . Meanwhile, the center values, class interval values and class radius of each class are acquired. The detailed results are found in Table 1.  
+
+Table 1 shows the construction of the pattern moving space over time, with the variations of the pattern center and threshold illustrated in Figure 4. As indicated in the Definition 2.2, the variation scope of the pattern class variable aligns with the class threshold, involving epistemic uncertainty, exhibiting inherent uncertainty, whereas the grey measure can utilize the variables center as measurement basis. After the quantization algorithm produces category divisions, the first 11 input variables and \(dx(k)\) measures are used to construct IGM(1,2), and the process is as follows.  
+
+1) The adaptive buffer operator is applied to the interval sequence \(\otimes_{1}(k)\) , resulting in a smoothed sequence \(\hat{\otimes}_{1}(k)\) . This process reduces oscillations and enhances the stability of the subsequent IGM(1,2) modeling steps.  
+
+\[\frac{d\otimes_{1}^{(1)}(t)}{dt} +a\otimes_{1}^{(1)}(t) = b\otimes_{2}^{(1)}(t) \quad (69)\]  
+
+where \(\otimes_{1}^{(1)}(t)\) is the first- order accumulated generation (1- AGO) sequence of the buffered output interval \(\hat{\otimes}_{1}(k),\hat{\otimes}_{2}^{(1)}(t)\) is the 1- AGO sequence of the input interval \(\otimes_{2}(k)\) , \(a\) and \(b\) are parameters to be estimated.  
+
+2) With estimated parameters \(a = [0.12, 0.15]\) and \(b = [0.08, 0.10]\) , the specific differential equations for the lower and upper bounds are formulated as follows:
+
+<--- Page Split --->
+
+
+Table 1. Results of pattern class and pattern moving space by Equation 4.   
+
+<table><tr><td>Class No</td><td>Class Center</td><td>Class Radius</td><td>Class Threshold</td><td>Class Interval</td></tr><tr><td>1</td><td>4.533</td><td>1.500</td><td>6.033</td><td>[3.033, 6.033]</td></tr><tr><td>2</td><td>2.730</td><td>0.303</td><td>3.033</td><td>[2.427, 3.033]</td></tr><tr><td>3</td><td>1.932</td><td>0.495</td><td>2.427</td><td>[1.437, 2.427]</td></tr><tr><td>4</td><td>0.979</td><td>0.458</td><td>1.437</td><td>[0.521, 1.437]</td></tr><tr><td>5</td><td>0.288</td><td>0.233</td><td>0.521</td><td>[0.055, 0.521]</td></tr><tr><td>6</td><td>0</td><td>0.521</td><td>0.521</td><td>[-0.521, 0.521]</td></tr><tr><td>7</td><td>-0.288</td><td>0.233</td><td>-0.055</td><td>[-0.521, -0.055]</td></tr><tr><td>8</td><td>-0.979</td><td>0.458</td><td>-0.521</td><td>[-1.437, -0.521]</td></tr><tr><td>9</td><td>-1.932</td><td>0.495</td><td>-1.437</td><td>[-2.427, -1.437]</td></tr><tr><td>10</td><td>-2.730</td><td>0.303</td><td>-2.427</td><td>[-3.033, -2.427]</td></tr><tr><td>11</td><td>-4.533</td><td>1.500</td><td>-3.033</td><td>[-6.033, -3.033]</td></tr></table>  
+
+\[\left\{ \begin{array}{l}\frac{dX_1(t)}{dt} +0.12X_1(t) = 0.08X_2(t)\quad (Lower\ Bounded)\\ \displaystyle \frac{d\overline{X}_1(t)}{dt} +0.15\overline{X}_1(t) = 0.10\overline{X}_2(t)\quad (Upper\ Bounded) \end{array} \right. \quad (70)\]  
+
+3) The prediction formulas for the accumulated sequences are derived as:  
+
+\[\left\{ \begin{array}{l}\underline{X}_1(k + 1) = -1.443e^{-0.12k} + 0.667\quad (Lower\ Bounded)\\ \overline{X}_1(k + 1) = -1.369e^{-0.15k} + 0.125\quad (Upper\ Bounded) \end{array} \right. \quad (71)\]  
+
+Finally, the predicted interval for the pattern class variable is then obtained via inverse accumulated generation operation (IAGO):  
+
+\[\hat{\otimes}_{1}(k + 1) = \left[\underline{X}_{1}(k + 1) - \underline{X}_{1}(k),\overline{X}_{1}(k + 1) - \overline{X}_{1}(k)\right]\]  
+
+The IGM(1,2) model, constructed with parameters \(a = [0.12, 0.15]\) and \(b = [0.08, 0.10]\) , effectively predicts \(y_{1}(k)\) using \(u(k)\) in pattern- moving systems.  
+
+Step 2: Design of IGB- GPC controller and comparison of control effects for pattern moving system. Differing from the control targets of traditional purpose control systems, the objective of pattern moving regulation is to assign the system output to the specified product quality. The expected pattern class are respectively established as category 2 (2.739) and category 5 (0.288), i.e.,  
+
+\[y_{d} = \left\{ \begin{array}{ll}2, & 0\leq k\leq 100\\ 5, & 100< k\leq 200 \end{array} \right. \quad (72)\]  
+
+we proceed to elaborate the design of the control input \(u(k)\) , the optimization process for determining the optimal control sequence, and a comparative simulation framework to evaluate the performance of the proposed IGB- GPC against benchmark methods, namely CARIMA- GPC and IG- GPC.  
+
+The control objective in this pattern- moving system is to drive the system output \(y(k)\) to match the specified pattern class centers corresponding to \(y_{d}\) , which represent the desired product quality indices. Specifically, \(y_{d} = 2\) corresponds to pattern class 2 with center \(c_{2} = 2.739\) for \(0 \leq k \leq 100\) , and \(y_{d} = 5\) corresponds to pattern class 5 with center \(c_{5} = 0.288\) for \(100 < k \leq 200\) (see Table 1). To simplify the control design, we assume \(y_{d}\) directly approximates these center values, i.e., \(y_{d}(k) = 2.739\) and \(y_{d}(k) = 0.288\) .
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Pattern class centre and its threshold. </center>  
+
+Using the IGM(1,2) parameters estimated in Step 1 \((a = [0.12,0.15],b = [0.08,0.10])\) , the predicted output at step \(k + j\) is expressed as:  
+
+\[\hat{y} (k + j|k) = \left(\hat{\otimes}^{(1)}(1) - \frac{b}{a}\right)e^{-a\cdot j} + \frac{b}{a} \quad (73)\]  
+
+With initial conditions \(\underline{{X}}_{1}(1) = \underline{{x}}_{1}(1) = 2.739\) (for \(y_{d} = 2\) ) and \(\overline{{X}}_{1}(1) = \overline{{x}}_{1}(1) = 2.739 + r_{2} = 3.033\) , the predicted interval at \(j = 1\) is:  
+
+\[\hat{y} (k + 1|k) = [2.739\cdot e^{-0.12} + 0.667,3.033\cdot e^{-0.15} + 0.667]\approx [2.435,2.712] \quad (74)\]  
+
+The dynamic matrix \(\mathbf{G}\) is constructed using step response coefficients. For a prediction horizon \(N_{\mathrm{y}} = 5\) and control horizon \(N_{u} = 3\) , each element \(g_{i,j}\) represents the effect of a unit control increment at step \(k + j - 1\) on the output at step \(k + i\) :  
+
+\[g_{i,j} = \frac{\partial\hat{y} (k + i|k)}{\partial\Delta u(k + j - 1)}\approx \frac{\hat{y} (k + i|k,\Delta u = 1) - \hat{y} (k + i|k,\Delta u = 0)}{1} \quad (75)\]  
+
+For \(i = 1,j = 1\) :  
+
+\[g_{1,1} = \left[\left(\underline{{X}}_{1}(1) - \frac{0.08}{0.12} +\frac{0.08}{0.12}\right)e^{-0.12\cdot 1} + \frac{0.08}{0.12}\right] - \hat{y} (k + 1|k) = e^{-0.12}\approx 0.886 \quad (76)\]  
+
+Subsequent elements yield:  
+
+\[\mathbf{G} = \left[ \begin{array}{lll}0.886 & 0 & 0\\ 0.789 & 0.886 & 0\\ 0.703 & 0.789 & 0.886\\ 0.627 & 0.703 & 0.789\\ 0.560 & 0.627 & 0.703 \end{array} \right] \quad (77)\]
+
+<--- Page Split --->
+
+The free response vector \(\mathbf{F}\) under zero control increments:  
+
+\[\mathbf{F} = [\hat{y} (k + 1|k,\Delta u = 0),\hat{y} (k + 2|k,\Delta u = 0),\dots ,\hat{y} (k + N_{y}|k,\Delta u = 0)]^{T} \quad (78)\]  
+
+For \(k = 0\) and \(y_{d} = 2.739\) :  
+
+\[\begin{array}{r l} & {\hat{y} (1|0,\Delta u = 0) = 2.739\cdot e^{-0.12} + 0.667\approx 2.435}\\ & {\hat{y} (2|0,\Delta u = 0) = 2.739\cdot e^{-0.24} + 0.667\approx 2.160} \end{array} \quad (80)\]  
+
+Thus:  
+
+\[\mathbf{F} = [2.435,2.160,1.911,1.686,1.483]^{T} \quad (81)\]  
+
+With weighting matrices \(\mathbf{Q} = \mathrm{diag}(10,8,6,4,2)\) and \(\mathbf{R} = \mathrm{diag}(1,1,1)\) , the reference trajectory is:  
+
+\[\mathbf{Y}_{r} = [2.739,2.739,2.739,2.739,2.739]^{T} \quad (82)\]  
+
+The optimal control increment is solved via:  
+
+\[\Delta \mathbf{U}^{*} = (\mathbf{G}^{T}\mathbf{Q}\mathbf{G} + \mathbf{R})^{-1}\mathbf{G}^{T}\mathbf{Q}(\mathbf{Y}_{r} - \mathbf{F}) \quad (83)\]  
+
+Matrix computations:  
+
+\[\begin{array}{r l} & {\mathbf{G}^{T}\mathbf{Q}\mathbf{G} = \left[ \begin{array}{l l l}{23.25} & {18.64} & {14.08}\\ {18.64} & {15.76} & {12.28}\\ {14.08} & {12.28} & {9.78} \end{array} \right]}\\ & {\mathbf{G}^{T}\mathbf{Q}(\mathbf{Y}_{r} - \mathbf{F}) = \left[ \begin{array}{l}{10.24}\\ {8.32}\\ {6.41} \end{array} \right]} \end{array} \quad (84)\]  
+
+Solution:  
+
+\[\Delta \mathbf{U}^{*} = \left[ \begin{array}{l}{0.32}\\ {0.25}\\ {0.18} \end{array} \right],\quad u(0) = u(- 1) + \Delta u^{*}(0) = 0 + 0.32 = 0.32 \quad (86)\]  
+
+The control input update rule:  
+
+\[u(k) = u(k - 1) + \Delta u^{*}(k),\quad \Delta u^{*}(k) = [1,0,0]\Delta \mathbf{U}^{*}(k) \quad (87)\]  
+
+At \(k = 100\) , switching to \(y_{d} = 0.288\) with \(\underline{{X}}_{1}(1) = 0.288\) , \(\overline{{X}}_{1}(1) = 0.521\) , the calculation yields \(u(101)\approx - 0.25\)  
+
+In summary, the procedure of proposed method was demonstrated in Algorithm 4. Moreover, the tracking results and its errors were shown in Figures 5 and 6, respectively.
+
+<--- Page Split --->
+
+Input: \(a, b, \tilde{\otimes}^{(1)}(1), \mathbf{Y}_r, \mathbf{Q}, \mathbf{R}, N_y, N_u\)  
+
+Output: Control input \(u(k)\)  
+
+Initialize \(u(- 1) = 0, \Delta \mathbf{U} = \mathbf{0}\)  
+
+for \(k = 0\) to 199 do  
+
+if \(k \leq 100\) then  
+
+\(y_d \leftarrow 2.739\)  
+
+else  
+
+\(y_d \leftarrow 0.288\)  
+
+end if  
+
+Construct \(\mathbf{Y}_r = [y_d]^{N_y \times 1}\)  
+
+Compute \(\mathbf{F}\) via IGM(1,2) with \(\Delta u = 0\)  
+
+Build \(\mathbf{G}\) using step responses  
+
+Solve \(\Delta \mathbf{U}^* = (\mathbf{G}^T \mathbf{Q} \mathbf{G} + \mathbf{R})^{- 1} \mathbf{G}^T \mathbf{Q}(\mathbf{Y}_r - \mathbf{F})\)  
+
+\(\Delta u(k) \leftarrow \Delta \mathbf{U}^* (1)\)  
+
+\(u(k) \leftarrow u(k - 1) + \Delta u(k)\)  
+
+\(u(k) \leftarrow \text{saturate}(u(k), [- 4, 4])\)  
+
+end for  
+
+![](images/Figure_6.jpg)
+
+<center>Comparison of system output accuracy of different models  Figure 6. The tracking errors for pattern moving systems with various models. </center>  
+
+Figure 5 indicates that IGB- GPC maintains the output closest to the reference trajectory over the time change. Notably, around the transition point at 100, where the reference shifts from 2.739 to 0.288, IGB- GPC exhibits a smoother and faster response, minimizing overshoot and stabilizing more quickly compared to CARIMA- GPC and IG- GPC. Meanwhile, Figure 6 indicates IGB- GPC has the lowest median error and smallest interquartile range, while CARIMA- GPC and IG- GPC show higher errors and greater variability, highlighting IGB- GPC's superior accuracy and consistency.
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5. System ouput comparison with different control schemes in PMT framework. </center>  
+
+![](images/Figure_7.jpg)
+
+<center>Figure 7. Tracking results of system operating status on target pattern class. </center>  
+
+For this comparison, CARIMA- GPC shows a significant drop and oscillatory behavior post- transition, while IG- GPC also struggles with stability, particularly after 100, with larger fluctuations. This suggests that IGAB- GPC's adaptive buffer operator and interval grey modeling enhance tracking accuracy and robustness against dynamic changes. The results can be attributed to two main reasons. The superior performance of IGAB- GPC can be attributed to two key factors. First, the adaptive buffer
+
+<--- Page Split --->
+
+operator reduces fluctuations in pattern class variables by \(30 - 50\%\) (Remark following Theorem 4.3), enhancing prediction accuracy for small- sample, uncertain data compared to CARIMA- GPC and IG- GPC, as shown in Figure 6. Second, integrating IGM(1,2) (Equation (70)) with GPC's receding horizon optimization (Equations (55), (59)) ensures robust tracking of pattern transitions (e.g., class 2 to class 5 at \(k = 100\) ), outperforming CARIMA- GPC's deterministic approach and IG- GPC's less adaptive buffer operator, as evidenced by smoother responses and lower errors in Figures 5.  
+
+Additionally, Figure 7 presents the actual pattern class using IGB- GPC by space cross mapping \((M(\cdot))\) , which indicates the system's ability to accurately track the target pattern classes (class 2 with center \(c_{2} = 2.739\) for \(0 \leq k \leq 100\) and class 5 with center \(c_{5} = 0.288\) for \(100 < k \leq 200\) ). The figure demonstrates that IGB- GPC successfully drives the system operating condition to the desired pattern classes with minimal deviation, maintaining the output within the corresponding class intervals as defined in Table 1. Specifically, the system remains within the class threshold of \([2.427, 3.033)\) for class 2 and \([0.055, 0.521)\) for class 5, with rapid convergence to the target class centers post- transition at \(k = 100\) . Compared to CARIMA- GPC and IG- GPC, IGB- GPC exhibits fewer misclassifications and smoother transitions between pattern classes, underscoring the effectiveness of the adaptive buffer operator and interval grey modeling in handling the inherent uncertainties and dynamic shifts in pattern- moving systems.  
+
+## 6 Conclusions  
+
+This study introduces a novel Interval Grey Adaptive Buffer Generalized Predictive Control (IGAB- GPC) framework specifically designed for pattern- moving systems characterized by limited sample sizes, pronounced nonlinearity, and significant uncertainties. By synergistically integrating the Interval Grey Model (IGM(1,2)) with an adaptive buffer operator and Generalized Predictive Control (GPC), the proposed methodology effectively addresses the challenges associated with modeling and controlling complex industrial systems governed by statistical dynamics. The primary contributions of this work encompass: (1) the development of an adaptive buffer operator to mitigate oscillations in pattern class variables, (2) the formulation of an IGM(1,2)- based predictive model for robust handling of epistemic uncertainties, and (3) the seamless integration of these components within a GPC framework to achieve precise, stable, and robust control performance.  
+
+Theoretical analysis, grounded in Lyapunov stability theory, rigorously establishes that IGB- GPC guarantees bounded- input bounded- output (BIBO) stability and exponential convergence of tracking errors under well- defined conditions. The adaptive buffer operator reduces the amplitude of prediction errors by \(30 - 50\%\) , thereby enhancing robustness against dynamic fluctuations, while the IGM(1,2) model provides a reliable framework for quantifying uncertainties inherent in pattern category variables. Numerical simulations substantiate the superiority of IGB- GPC over established benchmark methods, namely Controlled AutoRegressive Integrated Moving Average Generalized Predictive Control (CARIMA- GPC) and Interval Grey Generalized Predictive Control (IG- GPC). The results demonstrate that IGB- GPC achieves smoother transitions, significantly lower tracking errors, and reduced misclassifications during pattern class shifts, as evidenced by its performance on a nonlinear discrete- time system.  
+
+The proposed IGB- GPC framework holds considerable promise for applications in process industries, such as metallurgy and chemical engineering, where pattern- moving systems are prevalent. Future research directions include extending the framework to accommodate multi- input multi- output systems, incorporating real- time adaptive parameter estimation to further enhance robustness, and conducting experimental validation on industrial platforms to bridge the gap between simulation and practical deployment. Additionally, exploring hybrid methodologies that combine IGB- GPC with advanced machine learning techniques could further elevate prediction accuracy and control efficacy in highly dynamic and uncertain environments.  
+
+## Data availability  
+
+The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.  
+
+## References  
+
+1. Xu, Z. Pattern recognition method of intelligent automation and its implementation in engineering. Univ. Sci. Technol. Beijing, Beijing, China (2001).  
+2. Shoude, J. Pattern recognition approach to intelligent automation for complex industrial processes. Chin. J. Eng. 20, 385-389 (1998).  
+3. Han, C., Xu, Z. & Deng, N. Minimum entropy control for non-newtonian mechanical systems based on pattern moving probability density evolution. J. Frankl. Inst. 362, 107597 (2025).  
+4. Nandy, D. & Padariya, R. An overview of pattern recognition. Int. J. for Innov. Res. Sci. & Technol. 2 (2016).  
+5. Han, C. & Xu, Z. Pattern-moving-based dynamic description for a class of nonlinear systems using the generalized probability density evolution. Probabilistic Eng. Mech. 74, 103543 (2023).
+
+<--- Page Split --->
+
+6. Guo, L., Xu, Z. & Wang, Y. Dynamic modeling and optimal control for complex systems with statistical trajectory. Discret. Dyn. Nat. Soc. 2015, 245685 (2015).  
+
+7. Sun, C. & Xu, Z. Multi-dimensional moving pattern prediction based on multi-dimensional interval ts fuzzy model. Control. Decis. 31, 1569-1576 (2016).  
+
+8. Wu, J. & Li, J. System asymptotic stability analysis of a kind of complex production processes based on multi-dimensional moving pattern. SN Appl. Sci. 5, 32 (2023).  
+
+9. Wang, M., Pan, W. & Lu, Y. A pattern-based controller for a class of production processes with input delay. Asian J. Control. 25, 1074-1085 (2023).  
+
+10. Guo, L. L. & Wang, Y. The application of cell mapping to dynamic modeling and control. Appl. Mech. Mater. 687, 661-664 (2014).  
+
+11. Li, N., Xu, Z. & Li, X. Pattern-moving-modelling and analysis based on clustered generalized cell mapping for a class of complex systems. Processes 12, 492 (2024).  
+
+12. Changping, S. & Zhengguang, X. Extended ts fuzzy model based on interval arithmetic and its application to interval nonlinear regression analysis. In 2009 IEEE International Conference on Fuzzy Systems, 1773-1778 (IEEE, 2009).  
+
+13. Zhengguang, X. & Changping, S. Moving pattern-based approach to modeling of a class of complex production processes. In 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), 2282-2287 (IEEE, 2011).  
+
+14. Han, C. & Xu, Z. Prediction and output estimation of pattern moving in non-newtonian mechanical systems based on probability density evolution. CMES-Computer Model. Eng. & Sci. 139 (2024).  
+
+15. Han, C. & Xu, Z. Pattern-moving based data-driven control for multi-input continuous-time non-newtonian mechanical systems. Int. J. Syst. Sci. 1-25 (2025).  
+
+16. Li, X., Xu, Z., Lu, Y., Cui, J. & Zhang, L. Modified model free adaptive control for a class of nonlinear systems with multi-threshold quantized observations. Int. J. Control. Autom. Syst. 19, 3285-3296 (2021).  
+
+17. Li, X., Xu, Z., Han, C. & Li, N. Pattern-moving-based parameter identification of output error models with multi-threshold quantized observations. CMES-Computer Model. Eng. & Sci. 130 (2022).  
+
+18. Ju-Long, D. Control problems of grey systems. Syst. & control letters 1, 288-294 (1982).  
+
+19. Chen, Z., Meng, Y., Wang, R.-Y. & Chen, T. Intelligent optimal grey evolutionary algorithm for structural control and analysis. Smart Struct. Syst. 33, 365-374 (2024).  
+
+20. Zeng, B., Li, C., Zhou, X.-Y. & Long, X.-J. Prediction model of interval grey numbers with a real parameter and its application. In Abstract and Applied Analysis, vol. 2014, 939404 (Wiley Online Library, 2014).  
+
+21. Rao, S. S. & Liu, X. Universal grey system theory for analysis of uncertain structural systems. AIAA journal 55, 3966-3979 (2017).  
+
+22. Chen, C.-C. & Tsai, C. M. Interval forecasting with grey models: a novel learning procedure for improved decision-making. Grey Syst. Theory Appl. (2025).  
+
+23. Liu, S., Yang, Y., Xie, N. & Forrest, J. New progress of grey system theory in the new millennium. Grey Syst. Theory Appl. 6, 2-31 (2016).  
+
+24. Schwenzer, M., Ay, M., Bergs, T. & Abel, D. Review on model predictive control: An engineering perspective. The Int. J. Adv. Manuf. Technol. 117, 1327-1349 (2021).  
+
+25. Djouadi, H. et al. Improved robust model predictive control for pmsm using backstepping control and incorporating integral action with experimental validation. Results Eng. 23, 102416 (2024).  
+
+26. Li, N., Xu, Z. G., Zhao, C. T. & Li, X. Q. Pattern-moving-based dynamic description and optimal control for non-newtonian mechanical systems with generalized cell mapping. The Can. J. Chem. Eng. 103, 3208-3229 (2025).  
+
+27. Liu, G., Pan, Y., Lam, H.-K. & Liang, H. Event-triggered fuzzy adaptive quantized control for nonlinear multi-agent systems in nonaffine pure-feedback form. Fuzzy Sets Syst. 416, 27-46 (2021).  
+
+28. Liu, S., Yang, Y. & Forrest, J. Y.-L. Grey systems analysis: Methods, models and applications (Springer, 2022).  
+
+29. Liu, S.-H. A new grey buffer operator and its application. J. Intell. & Fuzzy Syst. 1-9 (2024).  
+
+30. Yu, X. & Cheng, Y. A comprehensive review and comparison of cusum and change-point-analysis methods to detect test speededness. Multivar. Behav. Res. 57, 112-133 (2022).
+
+<--- Page Split --->
+
+31. Xu, Z., Wu, J. & Qu, S. Prediction model based on moving pattern. J. Comput. 7, 2695–2701 (2012).  
+
+32. Xie, N. & Liu, S. Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model. J. Syst. Eng. Electron. 26, 96–102 (2015).  
+
+## Author contributions Statement  
+
+Ning Li: Writing original draft, Methodology, Conceptualization, Formal analysis. Zhenggaung Xu: Methodology, Conceptualization, Data Collection, Validation. Xiangquan Li: Writing - review & editing, Visualization, Supervision, Project administration.  
+
+## Funding  
+
+Open access funding provided by Natural Science Foundation Project of Guizhou Province, Grant Number ZK[2023] Genera004; Science and Technology Project of Jiangxi Provincial Department of Education, Grant Number GJJ2202404; Natural Science Foundation Project of JiangXi Province, Grant Number 20242BAB25091.
+
+<--- Page Split --->

preprint/preprint__001ce7d757b4396ce7f19d0548d511beacdaa8866b8ea15323e2c67a11e2b04d/images_list.json

@@ -0,0 +1,92 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1: CD-XRMS experiments. (a) Experimental configuration with the incident beams of the IR pump and the x-ray probe. (b) Magnetic diffraction pattern, (CL+CR) (c) Dichroic pattern (CL-CR), displaying the typical signature of clockwise Néel",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        702,
+        860,
+        860
+      ]
+    ],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2: Evolution of the XRMS signal over the first 5 ps: (a) intensity of integrated diffraction ring \\((CL + CR)\\) and dichroism \\((CL - CR)\\) normalized at their values at negative time delays; (b) experimental asymmetry ratio \\((CL - CR) / (CL + CR)\\) normalized by its value at \\(t< 0\\) in grey circles and black dots. The simulations for different models discussed in the main text appear as colored lines (see Supplementary Materials S3 for details). (c) Full width at half maximum (FWHM) (red dots) and the position (blue circles) in reciprocal space of the magnetic dichroic peak as a function of time.",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        90,
+        486,
+        556
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3: Magnetization texture modification by hot electrons. (a) Schematic representation of the torque (black arrows) imposed by the 'hot spins' flowing from the domains to the DWs resulting in transient mixed Bloch/Neel/Bloch contributions. (b) Transient DW shape. (c) Precession angles (red) and DW magnetization normalized by Domain one (blue) used in the simulations of the asymmetry ratio shown in Fig. 2(b).",
+    "footnote": [],
+    "bbox": [
+      [
+        118,
+        421,
+        876,
+        608
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
+    "footnote": [],
+    "bbox": [
+      [
+        45,
+        97,
+        944,
+        303
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2",
+    "footnote": [],
+    "bbox": [
+      [
+        50,
+        52,
+        551,
+        775
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3",
+    "footnote": [],
+    "bbox": [
+      [
+        45,
+        92,
+        940,
+        333
+      ]
+    ],
+    "page_idx": 15
+  }
+]

preprint/preprint__001ce7d757b4396ce7f19d0548d511beacdaa8866b8ea15323e2c67a11e2b04d/preprint__001ce7d757b4396ce7f19d0548d511beacdaa8866b8ea15323e2c67a11e2b04d.mmd

@@ -0,0 +1,204 @@
+
+# Ultrafast time-evolution of chiral Néel magnetic domain walls probed by circular dichroism in x-ray resonant magnetic scattering.  
+
+Cyril Lévéillé  Synchrotron SOLEIL  
+
+Erick Burgos- Parra  Synchrotron SOLEIL  
+
+Yanis Sassi  Unité Mixte de Physique, CNRS, Thales, Université Paris- Saclay  https://orcid.org/0000- 0003- 0703- 6068  
+
+Fernando Ajejas  Unité Mixte de Physique CNRS/Thales  https://orcid.org/0000- 0001- 8980- 4475  
+
+Valentin Chardonnet  Sorbonne Université, CNRS, Laboratoire Chimie Physique – Matière et Rayonnement, LCPMR  
+
+Emanuele Pedersoli  Elettra- Sincrotrone Trieste  https://orcid.org/0000- 0003- 0572- 6735  
+
+Flavio Capotondi  Elettra Sincrotrone Trieste  https://orcid.org/0000- 0003- 1980- 6162  
+
+Giovanni De Ninno  University of Nova Gorica and Elettra- Sincrotrone Trieste  https://orcid.org/0000- 0002- 4648- 4413  
+
+Francesco Maccherozzi  Diamond Light Source, Chilton, Didcot, Oxfordshire, OX11 0DE, UK.  
+
+Samjeet Dhesi  Diamond Light Source  https://orcid.org/0000- 0003- 4966- 0002  
+
+David Bum  Diamond Light Source (United Kingdom)  https://orcid.org/0000- 0001- 7540- 1616  
+
+Gerrit van der Laan  Diamond Light Source  https://orcid.org/0000- 0001- 6852- 2495  
+
+Oliver Latcham  University of Exeter  
+
+Andrei Shytov  University of Exeter  
+
+Volodymyr Kruglyak  University of Exeter  https://orcid.org/0000- 0001- 6607- 0886  
+
+Emmanuelle Jal
+
+<--- Page Split --->
+
+Sorbonne Université https://orcid.org/0000- 0001- 5297- 9124  
+
+## Vincent Cros  
+
+Unité Mixte de Physique CNRS,Thales, Université Paris- Saclay https://orcid.org/0000- 0003- 0272- 3651  
+
+## Jean-Yves Chauleau  
+
+Service de Physique de l'Etat Condensé  
+
+## Nicolas Reyren  
+
+Unité Mixte de Physique CNRS/Thales https://orcid.org/0000- 0002- 7745- 7282  
+
+## Michel Viret  
+
+SPEC, CEA,CNRS, Université Paris- Saclay, 91191 Gif- sur- Yvette https://orcid.org/0000- 0001- 6320- 6100  
+
+Nicolas Jaouen ( Nicolas.jaouen@synchrotron- soleil.fr)  
+
+Synchrotron SOLEIL https://orcid.org/0000- 0003- 1781- 7669  
+
+## Article  
+
+Keywords: Dzyaloshinskii- Moriya interaction, chiral Néel magnetic domain walls  
+
+Posted Date: March 3rd, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 271463/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 17th, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 28899- 0.
+
+<--- Page Split --->
+
+1 Ultrafast time-evolution of chiral Néel magnetic domain walls 2 probed by circular dichroism in x-ray resonant magnetic 3 scattering.  
+
+6 Cyril Léveillé \(^{1}\) , Erick Burgos-Parra \(^{1,2}\) , Yanis Sassi \(^{2}\) , Fernando Ajejas \(^{2}\) , Valentin Chardonnet \(^{3}\) , Emanuele Pedersoli \(^{4}\) , Flavio Capotondi \(^{4}\) , Giovanni De Ninno \(^{4,5}\) , Francesco Maccherozzi \(^{6}\) , Sarnjeet Dhesi \(^{6}\) , David M. Burn \(^{6}\) , Gerrit van der Laan \(^{6}\) , Oliver S. Latcham \(^{7}\) , Andrey V. Shytov \(^{7}\) , Volodymyr V. Kruglyak \(^{7}\) , Emmanuelle Jal \(^{3}\) , Vincent Cros \(^{2}\) , Jean-Yves Chauleau \(^{8}\) , Nicolas Reyren \(^{2}\) , Michel Viret \(^{8}\) and Nicolas Jaouen \(^{1}\)  
+
+\(^{1}\) Synchrotron SOLEIL, Saint-Aubin, Boite Postale 48, 91192 Gif-sur-Yvette Cedex, France  
+
+\(^{2}\) Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France  
+
+\(^{3}\) Sorbonne Université, CNRS, Laboratoire Chimie Physique – Matière et Rayonnement, LCPMR, 75005 Paris, France  
+
+\(^{4}\) Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy  
+
+\(^{5}\) University of Nova Gorica, 5000 Nova Gorica, Slovenia  
+
+\(^{6}\) Diamond Light Source, Didcot OX11 0DE, United Kingdom.  
+
+\(^{7}\) University of Exeter, Stocker road, Exeter, EX4 4QL, United Kingdom.  
+
+\(^{8}\) SPEC, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France  
+
+Non- collinear spin textures in ferromagnetic ultrathin films are attracting a renewed interest fueled by possible fine engineering of several magnetic interactions, notably the interfacial Dzyaloshinskii- Moriya interaction. This allows the stabilization of complex chiral spin textures such as chiral magnetic domain walls (DWs), spin spirals, and magnetic skyrmions. We report here on the ultrafast behavior of chiral DWs after optical pumping in perpendicularly magnetized asymmetric multilayers, probed using time- resolved circular dichroism in x- ray resonant magnetic scattering (CD- XRMS). We observe a picosecond transient reduction of the CD- XRMS, which is attributed to the spin current- induced coherent and incoherent torques within the continuously dependent spin texture of the DWs. We argue that a specific demagnetization of the inner structure of the DW induces a flow of spins from the interior of the neighboring magnetic domains. We identify this time- varying change of the DW texture shortly after the laser pulse as
+
+<--- Page Split --->
+
+a distortion of the homochiral Néel shape toward a transient mixed Bloch- Néel- Bloch texture along a direction transverse to the DW.  
+
+Ultrafast demagnetization of a ferromagnet by an optical pulse was first demonstrated in 1996 in the seminal study by Beaurepaire et al [Beaurepaire96], which is widely considered as the birth of the research field of femtomagnetism, i.e., the magnetism modulated ("pumped") by femtosecond long laser pulses. While several underlying mechanisms are considered to explain these ultrafast processes, the central role of spin dependent transport of hot electrons has been clearly evidenced [Melnikov11, Siegrist19]. Such phenomena were first experimentally demonstrated in spin valves, in which the demagnetization process is faster for antiparallel alignment of the magnetization in the magnetic layers [Malinowski08]. Models based on polarized electron transport in the superdiffusive regime have been subsequently developed [Battiat0o]. The optically excited hot electrons, initially ballistic, with spin- dependent lifetimes and velocities, generate non- equilibrium spin currents either within a ferromagnetic layer or in adjacent non- magnetic layer. The induced loss of angular momentum greatly participates in ultrafast dynamical behavior of the magnetization [vodungbo16]. The existence of this phenomenon has also been tested in single magnetic layers with a heterogeneous magnetization configuration, i.e., containing a large density of magnetic domains and DWs, albeit with different conclusions [Moisan14, vodungbo16, Pfau2012]. X- ray diffraction experiments are in this latter case more powerful for probing the behavior of DWs [zusin2020, Kerber20, Hennes20b]. For example, Pfau et al. [Pfau2012] inferred that the DW size changes in the first few ps by investigating the variations of the first- order Bragg peak of the magnetic configuration. More recently, the studies of Zuzin et al. [Zuzin2020] and Hennes et al. [hennes2020b] have shown that a more precise way to extract insights about DWs is to study the position and width of higher order diffraction peaks.  
+
+In this Letter, we use circular dichroism in x- ray resonant magnetic scattering (CD- XRMS) to gain access to the internal spin texture of the domain walls. This technique permits indeed a direct determination of the type (Néel or Bloch) as well as of the effective chirality of the DWs [Dürr99, chauleau2018]. Magnetic multilayers with homochiral Néel DWs stabilized by a large interfacial Dzyaloshinskii- Moriya (DM) interaction [Fert80, Fert90] are ideal systems to study DW dynamics at the fs timescales. In recent studies, this approach was used [Zhang17, chauleau2018, Legrand2018, Zhang20] to investigate the intrinsic nature of DWs and skyrmionic systems, which is currently a topic of the utmost relevance from both fundamental and technological viewpoints [Thiaville12, Ruy13, Nagoasa13, Fert17, Yang15]. The degree of circular dichroism in these experiments is not only related to the homochiral nature of the magnetic textures but also to the intrinsic DW configuration and allows us to probe the size and magnetization ratio of domain/domain- wall with unprecedented sensitivity. We hence unveil the ultrafast dynamics of these domain walls, unambiguously showing a specific behavior compared to that of the domains.
+
+<--- Page Split --->
+
+The system under study is an asymmetric magnetic multilayer \(\mathrm{[Pt(3nm)|Co(1.5nm)|Al(1.4nm)|x_5}\) grown by sputtering on a thermally oxidized Si wafer buffered by \(\mathrm{Ta(5)|Pt(5)}\) (see Supplementary Sec. S1 for details) presenting perpendicular magnetic anisotropy and large interfacial DM interaction. At remanence, domains adopt a typical disordered labyrinthine structure, but with a narrow distribution of domain widths. The magnetization and anisotropy are measured by SQUID magnetometry, while the DM amplitude is determined by comparing the experimentally measured (by magnetic force microscopy) domain periodicity to those simulated using micromagnetic calculations with MuMax3 [Vansteenkiste14] (see Supplemental Material S1 for details about the magnetic preparation and the simulations). From these calculations, we can also estimate the DW width to be \(\sim 20 \mathrm{nm}\) . The micromagnetic simulations are also used as inputs in the empirical XRMS model with accurate values for the width of the DW.  
+
+The time- resolved XRMS experiments have been performed on the DiProI beam line [Capotondi13] at the FERMI free electron laser [Allaria12] (Trieste, Italy). Time resolution is achieved using a standard pump- probe approach [Fig. 1(a)] in which the probe is a 60 fs XUV pulse at the Co \(M\) edge energy (photon energy \(\sim 60 \mathrm{eV}\) ) and the pump is a 100 fs infrared laser pulse (780 nm). The overall time resolution is therefore \(\sim 120 \mathrm{fs}\) . The scattering experiments have been conducted under reflectivity condition at \(45^{\circ}\) incidence for circularly left (CL) and right (CR) x- ray polarization allowing to acquire ultrafast snapshots of diffraction diagrams (Fig. 1b) and their corresponding circular dichroism (Fig. 1c) at each delay time of the infrared (IR) excitation (see S2 for details). Noteworthy, the degree of x- ray circular polarization is between \(92 - 95\%\) [Allaria14]. Regarding the probe and pump energy densities, the IR fluence was set to \(4.8 \mathrm{mJ / cm^2}\) (at a repetition rate of \(50 \mathrm{Hz}\) ) and the FEL fluence was set to \(0.5 \mathrm{mJ / cm^2}\) . At the Co \(M\) edge, with \(45^{\circ}\) photon incidence angle, the penetration depth is \(\sim 10 \mathrm{nm}\) , therefore most of the scattered signal comes from the uppermost Co layers. Such a small penetration depth also ensures that the expected tilting of the Ewald sphere is negligible in our experiment. Finally, we decided to perform the experiment at the peak of the absorption resonance to avoid any spurious effect caused by the energy shift of the XAS edge at ultrafast timescales [yao20, hennes20].  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1: CD-XRMS experiments. (a) Experimental configuration with the incident beams of the IR pump and the x-ray probe. (b) Magnetic diffraction pattern, (CL+CR) (c) Dichroic pattern (CL-CR), displaying the typical signature of clockwise Néel </center>
+
+<--- Page Split --->
+
+domain walls. The images in panels b and c have been geometrically corrected to account for the projection related to the photon incidence angle \(\theta = 45^{\circ}\) , and the scale corresponds to the sum of the counts (500 XFEL pulse of each polarization) for \((CL + CR)\) (b) and \((CL - CR)\) (c).  
+
+A typical diffraction pattern of the magnetic system at negative time delays, i.e. before the laser pulse excitation, is displayed in Fig. 1(b) in which the diffracted intensity is the sum of the two circular polarizations (CL+CR). It results from the x- ray diffraction on the labyrinth structure with a period of \((330 \pm 20) \mathrm{nm}\) (estimated from the ring radius). The total magnetic scattering intensity mainly comes from the alternating out- of- plane magnetic domains. The diffraction intensity also displays circular dichroism (CL- CR) [Fig. 1(c)], which reverses its sign on each side (along \(Q_{y}\) ) of the specular reflection, and reaches about \(10\%\) . Such dichroic signal is known [Durr99] to be a signature of an uncompensated sense of rotation in non- collinear magnetic textures. In our experiment, the sign of the dichroism indeed reveals the stabilization of clockwise (CW) Néel DW as we recently demonstrated [Chauleau2018]. The observed features have been corroborated by static scattering measurements at the Co \(L\) edge performed at the SEXTANTS beamline at SOLEIL [Sacchi13], for which the interpretation is now well established (see Supplementary Materials S1).
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2: Evolution of the XRMS signal over the first 5 ps: (a) intensity of integrated diffraction ring \((CL + CR)\) and dichroism \((CL - CR)\) normalized at their values at negative time delays; (b) experimental asymmetry ratio \((CL - CR) / (CL + CR)\) normalized by its value at \(t< 0\) in grey circles and black dots. The simulations for different models discussed in the main text appear as colored lines (see Supplementary Materials S3 for details). (c) Full width at half maximum (FWHM) (red dots) and the position (blue circles) in reciprocal space of the magnetic dichroic peak as a function of time. </center>  
+
+The time dependence of both the magnetic intensity \((CL + CR)\) of the overall diffraction ring [Fig 2(a)] and the dichroism \((CL - CR)\) shows a typical signature of ultrafast demagnetization in metallic magnetic ultrathin layers: first, a quench of the magnetization reaching a minimum value after a few hundreds of fs, followed by a log- like recovery over a few ps. The experimental results are further analyzed by plotting the asymmetry ratio, i.e., \((CL - CR) / (CL + CR)\) as a function of time [see Fig. 2(b)], which represents the DW behavior normalized by the total magnetic moment. If the DW magnetization follows the same dynamics as that of the domains, this ratio should not vary. It is plotted in Fig. 2b (normalized by its value before the pump pulse) where one clearly observes a \(15\%\) dip at \(\sim 0.7\) ps. This has been reproducibly observed when repeating the experiment, as demonstrated by the overlapping series of black filled and open circles in Fig. 2(b) showing identical behavior within error bars (inferred
+
+<--- Page Split --->
+
+from the statistical fit of the background and peak intensity, see Supplemental Material Section S2). The normalized ratio remains below 1.0 up to 2 ps. The time evolution of the peak position defined by the maximum of its Gaussian fit, and of the full width at half maximum (FWHM) in reciprocal space of the magnetic dichroic peak are displayed in Fig. 2(c). Those two quantities generally correspond respectively to the variation of the domain size and their distribution. However, this apparent domain extension corresponds in fact to an expansion of the DW in the first ps after optical excitation, as reported by Pfau et al. [Pfau 2012]. When considering this expansion according to the value reported in Fig. 2(c), an increase of the asymmetry ratio is predicted as shown by the blue curve in Fig. 2(b).  
+
+To explain this ultrafast deviation of the dichroism asymmetry ratio, we first exclude an origin due to a change in the scattering factors induced by hot electrons filling the \(d\) band. Indeed, the IR laser fluence of our experiment is much lower ( \(\sim 10\%\) ) than the one used to probe the change of electron occupation induced by the IR pulse using x- ray absorption spectroscopy (XAS) [Mathieu18]. Thus, we explain our observation by the fact that during the demagnetization (resp. remagnetization), the magnetic moments do not decrease (resp. increase) by the same amount simultaneously inside the DWs and inside the domains. If the magnetization decreased uniformly, the expected asymmetry ratio would be constant, as shown by simulation using a model that is detailed in Supplemental Material S3 [magenta line in Fig. 2(b)]. As explained above, the sole expansion of the DW widths cannot explain our data [blue curve in Fig. 2(c)]. To explain an asymmetry ratio dropping below its initial value, we resort to a reduction of the degree of magnetic chirality. In other words, it corresponds to a change of the ratio between the out- of- plane and the in- plane magnetization. In our interpretation, the ultra- fast decrease of the asymmetry ratio below 1.0 is linked to a different demagnetization rate between the DWs and the domains. Note that a scenario that would correspond to a faster remagnetization of the DWs than the domains shall result into an asymmetry ratio larger than 1 (similarly to the expansion of the DW), and therefore can also be safely ruled out. In the following, in order to reproduce our experimental observations, the simulations include both coherent evolution of the hot electron spins that induce a spin torque on the DW and spin temperature (incoherent) variations within the DWs.  
+
+The understanding of the ultrafast DW width expansion requires considering the intense flow of spin currents in the ps regime. These can efficiently transfer angular momentum to and from the ferromagnetic material as shown, e.g., when Pt layers absorb it and generate ps electrical pulses [Kampfrath13]. Angular momentum transfer and dissipation often results in both enhanced demagnetization as well as a faster magnetization recovery. We argue that this is exactly what is happening with the non- collinear magnetic regions inside the DWs. The enhanced spin scattering within DWs is a rather old topic born with studies of the extra contribution to the static magnetoresistance [Viret96] or the induced spin transfer torques resulting in their current- induced displacement. To this aim, ballistic models have been developed and can be appropriately adapted for the ultrafast demagnetization scenario in which superdiffusive spin currents play a central role [Battiato10]. The
+
+<--- Page Split --->
+
+behavior of ballistic spin carriers can be described such as a classical spinned particle perceiving a time varying exchange field while crossing the wall [Viret96, Vanhaverbeke07]. Let us recaller salient features. First, these are band particles that are coupled by exchange to the localized spins (through the so- called \(s - d\) Hamiltonian). Their velocity perpendicular to the wall is related to their momentum in \(k\) space. With the appropriate parameter renormalization, the problem is equivalent to the "fast adiabatic passage" known, e.g., in NMR theory. The spin evolution is given by the Landau- Lifshitz equation:  
+
+\[\frac{d\vec{\mu}}{dt} = \frac{J_{ex}S}{\hbar}\vec{m}\times \vec{\mu}\]  
+
+where \(\vec{\mu}\) is the electron spin, \(J_{\mathrm{ex}}S\) the exchange energy with the localized moment \((S)\) and \(\vec{m}\) the direction of the time varying exchange field seen by the ballistic electrons. The localized moments are rotating in a Neel fashion within the DW and the problem is generally treated in this rotating frame [Vanhaverbeke07]. Basically, the electronic spins will precess around the localized moment effective field and thus acquire a component out of the plane of rotation, inducing a torque parallel to the chiral vector: \(S_{i}\times S_{j}\) . The electron spin precession angle \(\omega\) is proportional to the velocity \(v\) divided by exchange times and the DW width \(2\pi \Delta\) [Viret96]: \(< \omega > = \frac{\pi h\nu}{J_{\mathrm{ex}}S2\pi\Delta}\) . Typically, for electrons at the Fermi level, this precession angle is found to be around 7 degrees for a DW width \(2\pi \Delta\) of \(15\mathrm{nm}\) [Vanhaverbeke07]. However, it is to be noticed that this angle can be quite different for the hot electrons produced in the demagnetization process as the relevant parameter values are hard to quantify. Although their velocities should not be too far from those at the Fermi level (in the \(10^{6}\mathrm{m / s}\) range [Kampfrath13]), the exchange energies effective in bands over \(1\mathrm{eV}\) above the Fermi level can be dramatically reduced \((\sim 0.1\mathrm{eV})\) . Therefore, the expected mistracking angle could be significantly greater for a large part of the hot electrons' distribution. All these processes shall in turn generate a torque applied on the localized moments [Waintal04]. However, because the hot spin currents flow in all directions, mistracking angles can be both positive and negative, resulting in cancellation of the net torque acting on the DWs. The overall effect of the incoherent precession results in an average loss of angular momentum. This should speed up the spin relaxation processes within the DW so that after some \(100\mathrm{fs}\) , a net spin current is established from the domains into the interior of the DWs.  
+
+The new components of the spin- transfer torque resulting from this latter spin current originating from the coherent evolution of the hot electron spins are not cancelled out. Importantly such torques are of opposite sign on the two sides of the DW and should induce a sizeable tilting of the DW magnetization out of the Neel plane as illustrated in Fig. 3(a). This phenomenon is at the origin of a new transient DW shape, made of a Neel type center surrounded by opposite Bloch types as depicted in Fig. 3(b). Such a mixed Bloch/Neel/Bloch contribution will in turn lead to a transient reduction of the measured chirality as it adds two (opposite) Bloch components on both sides of the DW compared to the originally purely Neel character. In order to estimate the amplitude of this DW distortion, it is useful to realize that unlike small current- induced electron flows at the Fermi level, spin fluxes during demagnetization are
+
+<--- Page Split --->
+
+enormous as for each pulse, typically 0.5 electrons per Co atom are excited to higher bands for the used laser fluence [Kampfrath13]. The timescale for the onset of the induced torques is given by the exchange energy and falls in the 10- fs range, ensuring that the wall distortion does not lag from the population of hot electrons. For a spin temperature sufficiently different between domains and DWs, a quantitative estimate using the abovementioned parameters gives a precession angle of the magnetization inside the DW that is larger than 10 degrees. Moreover, the onset of this Bloch component in the DW must leaks out into the domains, thus slightly increasing the effective DW width as also observed experimentally. The measured expansion of the DW can be directly derived from the variation of the dichroic peak position and width shown in Fig. 2(c). We find that the DW width (slightly) increases rapidly and its magnetization reaches a minimum around 1 ps (blue curve), as reported previously for Bloch type DWs [Pfau2012]. Note that this DW expansion takes place when the quenched magnetization starts to recover (1 ps). After reaching it maximum expansion, the DW width then recovers its original (unpumped represented as dotted lines in Fig. 2(c) size at a timescale of \(\sim 5\) ps.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3: Magnetization texture modification by hot electrons. (a) Schematic representation of the torque (black arrows) imposed by the 'hot spins' flowing from the domains to the DWs resulting in transient mixed Bloch/Neel/Bloch contributions. (b) Transient DW shape. (c) Precession angles (red) and DW magnetization normalized by Domain one (blue) used in the simulations of the asymmetry ratio shown in Fig. 2(b). </center>  
+
+Using a 1D magnetization profile (described in Supplementary Material S3) and considering the experimental change of magnetization (extracted directly from the square root of the (CL+CR) intensity), the time evolution of the asymmetry ratio can be simulated. We consider a magnetization in the domains extracted from the (CL+CR) data, along with a further \(12\%\) reduction of the magnetization inside the DWs to account for incoherent effects, as well as a transient Bloch- Néel- Bloch wall as shown in Fig. 3(a) for coherent ones. With these simulations, we find that the precession angle can reach at the maximum about 8 degrees after a time delay of \(\sim 0.6\) ps [red curve in Fig. 3(c)] simultaneously with the reduction of the DW magnetization [relative to domain magnetization blue curve in Fig. 3(c)], The
+
+<--- Page Split --->
+
+resulting simulated asymmetry ratio using the described model is plotted as the green curve in Fig. 2(b), and is in excellent agreement with the experimental measurements. Even accounting for DW expansion [red curve in Fig. 2(b)], the agreement can be obtained for a \(\sim 10\) degrees tilt angle. Although the exchange driven DW distortion is established on a very short timescale, it should last for the nanosecond timescale of the micromagnetic evolution. On the other hand, the incoherent part of the spin current shall relax at the ps timescale of the remagnetization processes, similarly to what we have measured. Interestingly, enhanced spin relaxation existing inside the DWs should speed up remagnetization, explaining that the asymmetry ratio can exceed 1, again in agreement with the experimental results.  
+
+In conclusion, we report here about the experimental investigation of the ultra- short timescale evolution of complex chiral Néel spin textures after laser induced demagnetization. Circular dichroism in x- ray resonant magnetic scattering is used to obtain information in the time domain about both the magnetic domain configuration and the magnetic chirality. Beyond the evolution of the period of the magnetic domains in magnetic multilayers with large perpendicular anisotropy, we acquire new insights into the way that the chirality of the non- collinear spin textures, and their long- range ordering, is evolving in the few ps after demagnetization by a strong optical pulse. We observe that the magnetic difference CL- CR (reflecting the DW properties) reduces faster than the diffracted sum signal (associated to domain magnetization) in the first 2 ps after the laser pulse. To explain this unexpected change of XRMS chirality signal at this short timescale, we propose that angular momentum flowing from the interior of the domains inside the DWs associated to hot electrons induces an ultrafast distortion of the DW magnetization. This transient in- plane deformation of the DWs leads to a transient mixed Bloch- Néel- Bloch DW accompanied by an increase of the DWs width and a reduction of the magnetization inside the DW. These original experimental results are reproduced by calculations, considering a magnetization reduction of \(12\%\) with a 7.5 degrees distortion of the DW. On a longer timescale, i.e., after a few ps, the DWs return to their pure chiral Néel configuration preserving the original sense of rotation (i.e., chirality) together with a recovery of their magnetization. We emphasize that our approach using dichroism in x- ray resonant scattering is applicable to any other magnetic chiral texture and should provide a better understanding of the evolution of the chirality of spin textures on the ultrafast timescale.  
+
+Acknowledgment: We acknowledge Ivaylo Nikolov, Michele Manfredda, Luca Giannessi, and Giuseppe Penco for their inestimable help to set up the FEL and the laser for our experiment. NJ would like to thanks S. Flewett for discussion on XRMS simulations. Financial supports from FLAG- ERA SographMEM (ANR- 15- GRFL- 0005), funding from the Agence Nationale de la Recherche, France, under grant agreement no. ANR- 17- CE24- 0025 (TOPSKY) and 18- CE24- 0018- 01 (SANTA), the Horizon2020 Framework Program of the European Commission under FET- Proactive Grant agreement
+
+<--- Page Split --->
+
+268 no. 824123 (SKYTOP). E. J. is grateful for financial support received from the CNRS- MOMENTUM. 269 O. S. L., A. V. S., and V. V. K. acknowledge funding from the Engineering and Physical Sciences 270 Research Council (EPSRC) in the United Kingdom (Grant No. EP/T016574/1). 271 272 273 References: 274 [beaurepaire96] E. Beaurepaire et al., Ultrafast Spin Dynamics in Ferromagnetic Nickel 275 Phys. Rev. Lett. 76, 4250 (1996). 276 [Melnikov11] A. Melnikov et al. Ultrafast Transport of Laser- Excited Spin- Polarized Carriers 277 in Au/Fe/MgO(001). Phys. Rev. Lett. 107, 076601 (2011). 278 [Siegrist19] F. Siegrist, Light- wave dynamic control of magnetism. Nature 571, 240 (2019). 279 [Malinowski08] G. Malinowski, et al., Control of speed and efficiency of ultrafast demagnetization by 280 direct transfer of spin angular momentum. Nat. Phys. 4, 855 (2008) 281 [Battiato10] M. Battiato et al., Superdiffusive Spin Transport as a Mechanism of Ultrafast 282 Demagnetization. Phys. Rev. Lett. 105, 027203 (2010) 283 [vodungbo16] B. Vodungbo et al., Indirect excitation of ultrafast demagnetization. Sci. Rep. 6, 18970 284 (2016). 285 [Moisan14] N. Moisan et al., Investigating the role of superdiffusive currents in laser induced 286 demagnetization of ferromagnets with nanoscale magnetic domains. Sci. Rep. 4, 4658 (2014). 287 [Pfau2012] B. Pfau et al., Ultrafast optical demagnetization manipulates nanoscale spin structure in 288 domain walls, Nat. Commun. 3, 1100 (2012). 289 [zuzin2020] D. Zusin et al., Ultrafast domain dilation induced by optical pumping in ferromagnetic 290 CoFe/Ni multilayers. https://arxiv.org/abs/2001.11719 291 [Kerber20] N. Kerber et al., Faster chiral versus collinear magnetic order recovery after optical 292 excitation revealed by femtosecond XUV scattering. Nat. Commun. 11, 6304 (2020). 293 [Hennes20b] M. Hennes et al., Laser- induced ultrafast demagnetization and perpendicular magnetic 294 anisotropy reduction in a Co88Tb12 thin film with stripe domains. Phys. Rev. B 102, 174437 (2020) 295 [Durr99] H. A. Durr et al, Chiral Magnetic Domain Structures in Ultrathin FePd Films. Science 284, 296 (1999). 296 [Chauleau2018] J.- Y. Chauleau et al., Chirality in Magnetic Multilayers Probed by the Symmetry and 298 the Amplitude of Dichroism in X- Ray Resonant Magnetic Scattering. Phys. Rev. Lett. 120, 037202 299 (2018). 300 [Fert80] A. Fert and P.M. Levy. Role of Anisotropic Exchange Interactions in Determining the 301 Properties of Spin- Glasses. Phys. Rev. Lett. 44, 1538 (1980). 302 [Fert90] A. Fert, « Magnetic and Transport Properties of Metallic Multilayers », Materials Science 303 Forum, 59- 60, 439 (1990). 304 [Zhang17] S. L. Zhang et al. Direct experimental determination of the topological winding number of 305 skyrmions in Cu2OSeO3. Nat. Commun. 8, 14619 (2017). 306 [Legrand2018] W. Legrand et al., Hybrid chiral domain walls and skyrmions in magnetic multilayers. 307 Sci. Adv. 4 : eaat0415 (2018)
+
+<--- Page Split --->
+
+308 [Zhang20] S. L. Zhang et al., Robust Perpendicular Skyrmions and Their Surface Confinement. 309 NanoLett. 20 1428 (2020). 310 [Thiaville12] A. Thiaville et al., Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films. 311 Euro. Phys. Lett. 100, 57002 (2012). 312 [Ruy13] K. S. Ruy et al., Chiral spin torque at magnetic domain walls. Nat. Nanotech. 8, 527 (2013). 313 [Nagoasa13] N. Nagoasa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions. 314 Nat. Nanotech. 8, 899 (2013). 315 [Fert17] A. Fert, N. Reyren, V. Cros, Magnetic skyrmions: advances in physics and potential 316 applications. Nat. Rev. Mater. 2, 17031 (2017). 317 [Yang15] S. Yang, K., Ryu, and S. Parkin, Domain-wall velocities of up to \(750\mathrm{m s^{- 1}}\) driven by 318 exchange-coupling torque in synthetic antiferromagnets. Nat. Nanotech. 10, 221 (2015). 319 [Vansteenkiste14] A. Vansteenkiste et al. The design and verification of MuMax3. AIP Adv. 4, 320 107133 (2014). 321 [Capotondi13] F. Capotondi et al., Coherent imaging using seeded free-electron laser pulses with 322 variable polarization: First results and research opportunities. Rev. Sci. Instrum. 84, 051301 (2013). 323 [Allaria12] E. Allaria et al., Highly coherent and stable pulses from the FERMI seeded free-electron 324 laser in the extreme ultraviolet. Nat. Photonics 6, 699 (2012). 325 [Allaria14] E. Allaria et al., Control of the Polarization of a Vacuum-Ultraviolet, High-Gain, Free- 326 Electron Laser. Phys. Rev. X 4, 041040 (2014). 327 [yao2020] K. Yao et al., Distinct spectral response in M-edge magnetic circular dichroism. Phys. Rev. 328 B 102, 100405 (2020). 329 [hennes20] M. Hennes et al., Time-Resolved XUV absorption spectroscopy and magnetic circular 330 dichroism at the Ni M2,3-edges. https://arxiv.org/abs/2011.14352 331 [Sacchi13] M. Sacchi et al., The SEXTANTS beamline at SOLEIL: a new facility for elastic, 332 inelastic and coherent scattering of soft X-rays. J. Phys. Conf. Ser. 425, 072018 (2013). 333 [Mathieu18] B. Mathieu et al., Probing warm dense matter using femtosecond X-ray absorption 334 spectroscopy with a laser-produced betatron source. Nat. Commun. 9, 3276 (2018). 335 [Kampfrath13] T. Kampfrath et al., Terahertz spin current pulses controlled by magnetic 336 heterostructures. Nat. Nano. 8, 256 (2013). 337 [Viret96] M. Viret et al., Spin scattering in ferromagnetic thin films. Phys. Rev. B 53, 8464 (1996). 338 [Vanhaverbeke07] A. Vanhaverbeke and M. Viret, Simple model of current-induced spin torque in 339 domain walls. Phys. Rev. B 75, 024411 (2007). 340 [Waintal04] X. Waintal, and M. Viret, Current-induced distortion of a magnetic domain wall. 341 Europhys. Lett. 65, 427 (2004).
+
+<--- Page Split --->
+
+## Figures  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+CD- XRMS experiments. (a) Experimental configuration with the incident beams of the IR pump and the x- ray probe. (b) Magnetic diffraction pattern, (CL+CR) (c) Dichroic pattern (CL- CR), displaying the typical signature of clockwise Néel domain walls. The images in panels b and c have been geometrically corrected to account for the projection related to the photon incidence angle \(\theta = 45^{\circ}\) , and the scale corresponds to the sum of the counts (500 XFEL pulse of each polarization) for (CL+CR) (b) and (CL- CR) (c).
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+Evolution of the XRMS signal over the first 5 ps: (a) intensity of integrated diffraction ring (CL+CR) and dichroism (CL- CR) normalized at their values at negative time delays; (b) experimental asymmetry ratio (CL- CR)/(CL+CR) normalized by its value at \(t < 0\) in grey circles and black dots. The simulations for different models discussed in the main text appear as colored lines (see Supplementary Materials S3 for
+
+<--- Page Split --->
+
+details). (c) Full width at half maximum (FWHM) (red dots) and the position (blue circles) in reciprocal space of the magnetic dichroic peak as a function of time.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>  
+
+Magnetization texture modification by hot electrons. (a) Schematic representation of the torque (black arrows) imposed by the 'hot spins' flowing from the domains to the DWs resulting in transient mixed Bloch/Neel/Bloch contributions. (b) Transient DW shape. (c) Precession angles (red) and DW magnetization normalized by Domain one (blue) used in the simulations of the asymmetry ratio shown in Fig. 2(b).  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- trXRMSSupplementary.pdf
+
+<--- Page Split --->

preprint/preprint__001ce7d757b4396ce7f19d0548d511beacdaa8866b8ea15323e2c67a11e2b04d/preprint__001ce7d757b4396ce7f19d0548d511beacdaa8866b8ea15323e2c67a11e2b04d_det.mmd

@@ -0,0 +1,265 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 923, 210]]<|/det|>
+# Ultrafast time-evolution of chiral Néel magnetic domain walls probed by circular dichroism in x-ray resonant magnetic scattering.  
+
+<|ref|>text<|/ref|><|det|>[[44, 229, 231, 270]]<|/det|>
+Cyril Lévéillé  Synchrotron SOLEIL  
+
+<|ref|>text<|/ref|><|det|>[[44, 276, 231, 316]]<|/det|>
+Erick Burgos- Parra  Synchrotron SOLEIL  
+
+<|ref|>text<|/ref|><|det|>[[44, 323, 955, 364]]<|/det|>
+Yanis Sassi  Unité Mixte de Physique, CNRS, Thales, Université Paris- Saclay  https://orcid.org/0000- 0003- 0703- 6068  
+
+<|ref|>text<|/ref|><|det|>[[44, 368, 750, 410]]<|/det|>
+Fernando Ajejas  Unité Mixte de Physique CNRS/Thales  https://orcid.org/0000- 0001- 8980- 4475  
+
+<|ref|>text<|/ref|><|det|>[[44, 415, 857, 456]]<|/det|>
+Valentin Chardonnet  Sorbonne Université, CNRS, Laboratoire Chimie Physique – Matière et Rayonnement, LCPMR  
+
+<|ref|>text<|/ref|><|det|>[[44, 460, 639, 503]]<|/det|>
+Emanuele Pedersoli  Elettra- Sincrotrone Trieste  https://orcid.org/0000- 0003- 0572- 6735  
+
+<|ref|>text<|/ref|><|det|>[[44, 507, 639, 549]]<|/det|>
+Flavio Capotondi  Elettra Sincrotrone Trieste  https://orcid.org/0000- 0003- 1980- 6162  
+
+<|ref|>text<|/ref|><|det|>[[44, 554, 901, 596]]<|/det|>
+Giovanni De Ninno  University of Nova Gorica and Elettra- Sincrotrone Trieste  https://orcid.org/0000- 0002- 4648- 4413  
+
+<|ref|>text<|/ref|><|det|>[[44, 600, 630, 642]]<|/det|>
+Francesco Maccherozzi  Diamond Light Source, Chilton, Didcot, Oxfordshire, OX11 0DE, UK.  
+
+<|ref|>text<|/ref|><|det|>[[44, 647, 610, 689]]<|/det|>
+Samjeet Dhesi  Diamond Light Source  https://orcid.org/0000- 0003- 4966- 0002  
+
+<|ref|>text<|/ref|><|det|>[[44, 694, 767, 735]]<|/det|>
+David Bum  Diamond Light Source (United Kingdom)  https://orcid.org/0000- 0001- 7540- 1616  
+
+<|ref|>text<|/ref|><|det|>[[44, 740, 610, 782]]<|/det|>
+Gerrit van der Laan  Diamond Light Source  https://orcid.org/0000- 0001- 6852- 2495  
+
+<|ref|>text<|/ref|><|det|>[[44, 787, 225, 828]]<|/det|>
+Oliver Latcham  University of Exeter  
+
+<|ref|>text<|/ref|><|det|>[[44, 834, 225, 874]]<|/det|>
+Andrei Shytov  University of Exeter  
+
+<|ref|>text<|/ref|><|det|>[[44, 880, 580, 921]]<|/det|>
+Volodymyr Kruglyak  University of Exeter  https://orcid.org/0000- 0001- 6607- 0886  
+
+<|ref|>text<|/ref|><|det|>[[44, 926, 186, 944]]<|/det|>
+Emmanuelle Jal
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 45, 589, 64]]<|/det|>
+Sorbonne Université https://orcid.org/0000- 0001- 5297- 9124  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 70, 157, 88]]<|/det|>
+## Vincent Cros  
+
+<|ref|>text<|/ref|><|det|>[[50, 91, 944, 112]]<|/det|>
+Unité Mixte de Physique CNRS,Thales, Université Paris- Saclay https://orcid.org/0000- 0003- 0272- 3651  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 117, 223, 136]]<|/det|>
+## Jean-Yves Chauleau  
+
+<|ref|>text<|/ref|><|det|>[[55, 139, 397, 158]]<|/det|>
+Service de Physique de l'Etat Condensé  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 164, 176, 182]]<|/det|>
+## Nicolas Reyren  
+
+<|ref|>text<|/ref|><|det|>[[50, 185, 745, 205]]<|/det|>
+Unité Mixte de Physique CNRS/Thales https://orcid.org/0000- 0002- 7745- 7282  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 210, 150, 228]]<|/det|>
+## Michel Viret  
+
+<|ref|>text<|/ref|><|det|>[[50, 231, 950, 251]]<|/det|>
+SPEC, CEA,CNRS, Université Paris- Saclay, 91191 Gif- sur- Yvette https://orcid.org/0000- 0001- 6320- 6100  
+
+<|ref|>text<|/ref|><|det|>[[44, 255, 555, 275]]<|/det|>
+Nicolas Jaouen ( Nicolas.jaouen@synchrotron- soleil.fr)  
+
+<|ref|>text<|/ref|><|det|>[[55, 278, 590, 297]]<|/det|>
+Synchrotron SOLEIL https://orcid.org/0000- 0003- 1781- 7669  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 338, 102, 356]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 375, 735, 396]]<|/det|>
+Keywords: Dzyaloshinskii- Moriya interaction, chiral Néel magnetic domain walls  
+
+<|ref|>text<|/ref|><|det|>[[44, 414, 301, 433]]<|/det|>
+Posted Date: March 3rd, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 451, 463, 471]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 271463/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 489, 911, 533]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 567, 925, 610]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on March 17th, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 28899- 0.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[70, 82, 884, 172]]<|/det|>
+1 Ultrafast time-evolution of chiral Néel magnetic domain walls 2 probed by circular dichroism in x-ray resonant magnetic 3 scattering.  
+
+<|ref|>text<|/ref|><|det|>[[70, 228, 884, 345]]<|/det|>
+6 Cyril Léveillé \(^{1}\) , Erick Burgos-Parra \(^{1,2}\) , Yanis Sassi \(^{2}\) , Fernando Ajejas \(^{2}\) , Valentin Chardonnet \(^{3}\) , Emanuele Pedersoli \(^{4}\) , Flavio Capotondi \(^{4}\) , Giovanni De Ninno \(^{4,5}\) , Francesco Maccherozzi \(^{6}\) , Sarnjeet Dhesi \(^{6}\) , David M. Burn \(^{6}\) , Gerrit van der Laan \(^{6}\) , Oliver S. Latcham \(^{7}\) , Andrey V. Shytov \(^{7}\) , Volodymyr V. Kruglyak \(^{7}\) , Emmanuelle Jal \(^{3}\) , Vincent Cros \(^{2}\) , Jean-Yves Chauleau \(^{8}\) , Nicolas Reyren \(^{2}\) , Michel Viret \(^{8}\) and Nicolas Jaouen \(^{1}\)  
+
+<|ref|>text<|/ref|><|det|>[[110, 355, 840, 375]]<|/det|>
+\(^{1}\) Synchrotron SOLEIL, Saint-Aubin, Boite Postale 48, 91192 Gif-sur-Yvette Cedex, France  
+
+<|ref|>text<|/ref|><|det|>[[110, 383, 808, 404]]<|/det|>
+\(^{2}\) Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France  
+
+<|ref|>text<|/ref|><|det|>[[110, 412, 839, 454]]<|/det|>
+\(^{3}\) Sorbonne Université, CNRS, Laboratoire Chimie Physique – Matière et Rayonnement, LCPMR, 75005 Paris, France  
+
+<|ref|>text<|/ref|><|det|>[[110, 461, 568, 483]]<|/det|>
+\(^{4}\) Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy  
+
+<|ref|>text<|/ref|><|det|>[[110, 490, 548, 510]]<|/det|>
+\(^{5}\) University of Nova Gorica, 5000 Nova Gorica, Slovenia  
+
+<|ref|>text<|/ref|><|det|>[[110, 518, 579, 538]]<|/det|>
+\(^{6}\) Diamond Light Source, Didcot OX11 0DE, United Kingdom.  
+
+<|ref|>text<|/ref|><|det|>[[110, 545, 655, 565]]<|/det|>
+\(^{7}\) University of Exeter, Stocker road, Exeter, EX4 4QL, United Kingdom.  
+
+<|ref|>text<|/ref|><|det|>[[110, 572, 686, 593]]<|/det|>
+\(^{8}\) SPEC, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France  
+
+<|ref|>text<|/ref|><|det|>[[110, 630, 884, 877]]<|/det|>
+Non- collinear spin textures in ferromagnetic ultrathin films are attracting a renewed interest fueled by possible fine engineering of several magnetic interactions, notably the interfacial Dzyaloshinskii- Moriya interaction. This allows the stabilization of complex chiral spin textures such as chiral magnetic domain walls (DWs), spin spirals, and magnetic skyrmions. We report here on the ultrafast behavior of chiral DWs after optical pumping in perpendicularly magnetized asymmetric multilayers, probed using time- resolved circular dichroism in x- ray resonant magnetic scattering (CD- XRMS). We observe a picosecond transient reduction of the CD- XRMS, which is attributed to the spin current- induced coherent and incoherent torques within the continuously dependent spin texture of the DWs. We argue that a specific demagnetization of the inner structure of the DW induces a flow of spins from the interior of the neighboring magnetic domains. We identify this time- varying change of the DW texture shortly after the laser pulse as
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 880, 123]]<|/det|>
+a distortion of the homochiral Néel shape toward a transient mixed Bloch- Néel- Bloch texture along a direction transverse to the DW.  
+
+<|ref|>text<|/ref|><|det|>[[113, 144, 884, 592]]<|/det|>
+Ultrafast demagnetization of a ferromagnet by an optical pulse was first demonstrated in 1996 in the seminal study by Beaurepaire et al [Beaurepaire96], which is widely considered as the birth of the research field of femtomagnetism, i.e., the magnetism modulated ("pumped") by femtosecond long laser pulses. While several underlying mechanisms are considered to explain these ultrafast processes, the central role of spin dependent transport of hot electrons has been clearly evidenced [Melnikov11, Siegrist19]. Such phenomena were first experimentally demonstrated in spin valves, in which the demagnetization process is faster for antiparallel alignment of the magnetization in the magnetic layers [Malinowski08]. Models based on polarized electron transport in the superdiffusive regime have been subsequently developed [Battiat0o]. The optically excited hot electrons, initially ballistic, with spin- dependent lifetimes and velocities, generate non- equilibrium spin currents either within a ferromagnetic layer or in adjacent non- magnetic layer. The induced loss of angular momentum greatly participates in ultrafast dynamical behavior of the magnetization [vodungbo16]. The existence of this phenomenon has also been tested in single magnetic layers with a heterogeneous magnetization configuration, i.e., containing a large density of magnetic domains and DWs, albeit with different conclusions [Moisan14, vodungbo16, Pfau2012]. X- ray diffraction experiments are in this latter case more powerful for probing the behavior of DWs [zusin2020, Kerber20, Hennes20b]. For example, Pfau et al. [Pfau2012] inferred that the DW size changes in the first few ps by investigating the variations of the first- order Bragg peak of the magnetic configuration. More recently, the studies of Zuzin et al. [Zuzin2020] and Hennes et al. [hennes2020b] have shown that a more precise way to extract insights about DWs is to study the position and width of higher order diffraction peaks.  
+
+<|ref|>text<|/ref|><|det|>[[113, 619, 884, 911]]<|/det|>
+In this Letter, we use circular dichroism in x- ray resonant magnetic scattering (CD- XRMS) to gain access to the internal spin texture of the domain walls. This technique permits indeed a direct determination of the type (Néel or Bloch) as well as of the effective chirality of the DWs [Dürr99, chauleau2018]. Magnetic multilayers with homochiral Néel DWs stabilized by a large interfacial Dzyaloshinskii- Moriya (DM) interaction [Fert80, Fert90] are ideal systems to study DW dynamics at the fs timescales. In recent studies, this approach was used [Zhang17, chauleau2018, Legrand2018, Zhang20] to investigate the intrinsic nature of DWs and skyrmionic systems, which is currently a topic of the utmost relevance from both fundamental and technological viewpoints [Thiaville12, Ruy13, Nagoasa13, Fert17, Yang15]. The degree of circular dichroism in these experiments is not only related to the homochiral nature of the magnetic textures but also to the intrinsic DW configuration and allows us to probe the size and magnetization ratio of domain/domain- wall with unprecedented sensitivity. We hence unveil the ultrafast dynamics of these domain walls, unambiguously showing a specific behavior compared to that of the domains.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 104, 884, 349]]<|/det|>
+The system under study is an asymmetric magnetic multilayer \(\mathrm{[Pt(3nm)|Co(1.5nm)|Al(1.4nm)|x_5}\) grown by sputtering on a thermally oxidized Si wafer buffered by \(\mathrm{Ta(5)|Pt(5)}\) (see Supplementary Sec. S1 for details) presenting perpendicular magnetic anisotropy and large interfacial DM interaction. At remanence, domains adopt a typical disordered labyrinthine structure, but with a narrow distribution of domain widths. The magnetization and anisotropy are measured by SQUID magnetometry, while the DM amplitude is determined by comparing the experimentally measured (by magnetic force microscopy) domain periodicity to those simulated using micromagnetic calculations with MuMax3 [Vansteenkiste14] (see Supplemental Material S1 for details about the magnetic preparation and the simulations). From these calculations, we can also estimate the DW width to be \(\sim 20 \mathrm{nm}\) . The micromagnetic simulations are also used as inputs in the empirical XRMS model with accurate values for the width of the DW.  
+
+<|ref|>text<|/ref|><|det|>[[113, 355, 884, 693]]<|/det|>
+The time- resolved XRMS experiments have been performed on the DiProI beam line [Capotondi13] at the FERMI free electron laser [Allaria12] (Trieste, Italy). Time resolution is achieved using a standard pump- probe approach [Fig. 1(a)] in which the probe is a 60 fs XUV pulse at the Co \(M\) edge energy (photon energy \(\sim 60 \mathrm{eV}\) ) and the pump is a 100 fs infrared laser pulse (780 nm). The overall time resolution is therefore \(\sim 120 \mathrm{fs}\) . The scattering experiments have been conducted under reflectivity condition at \(45^{\circ}\) incidence for circularly left (CL) and right (CR) x- ray polarization allowing to acquire ultrafast snapshots of diffraction diagrams (Fig. 1b) and their corresponding circular dichroism (Fig. 1c) at each delay time of the infrared (IR) excitation (see S2 for details). Noteworthy, the degree of x- ray circular polarization is between \(92 - 95\%\) [Allaria14]. Regarding the probe and pump energy densities, the IR fluence was set to \(4.8 \mathrm{mJ / cm^2}\) (at a repetition rate of \(50 \mathrm{Hz}\) ) and the FEL fluence was set to \(0.5 \mathrm{mJ / cm^2}\) . At the Co \(M\) edge, with \(45^{\circ}\) photon incidence angle, the penetration depth is \(\sim 10 \mathrm{nm}\) , therefore most of the scattered signal comes from the uppermost Co layers. Such a small penetration depth also ensures that the expected tilting of the Ewald sphere is negligible in our experiment. Finally, we decided to perform the experiment at the peak of the absorption resonance to avoid any spurious effect caused by the energy shift of the XAS edge at ultrafast timescales [yao20, hennes20].  
+
+<|ref|>image<|/ref|><|det|>[[120, 702, 860, 860]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 867, 881, 901]]<|/det|>
+<center>Figure 1: CD-XRMS experiments. (a) Experimental configuration with the incident beams of the IR pump and the x-ray probe. (b) Magnetic diffraction pattern, (CL+CR) (c) Dichroic pattern (CL-CR), displaying the typical signature of clockwise Néel </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 81, 883, 135]]<|/det|>
+domain walls. The images in panels b and c have been geometrically corrected to account for the projection related to the photon incidence angle \(\theta = 45^{\circ}\) , and the scale corresponds to the sum of the counts (500 XFEL pulse of each polarization) for \((CL + CR)\) (b) and \((CL - CR)\) (c).  
+
+<|ref|>text<|/ref|><|det|>[[114, 161, 884, 430]]<|/det|>
+A typical diffraction pattern of the magnetic system at negative time delays, i.e. before the laser pulse excitation, is displayed in Fig. 1(b) in which the diffracted intensity is the sum of the two circular polarizations (CL+CR). It results from the x- ray diffraction on the labyrinth structure with a period of \((330 \pm 20) \mathrm{nm}\) (estimated from the ring radius). The total magnetic scattering intensity mainly comes from the alternating out- of- plane magnetic domains. The diffraction intensity also displays circular dichroism (CL- CR) [Fig. 1(c)], which reverses its sign on each side (along \(Q_{y}\) ) of the specular reflection, and reaches about \(10\%\) . Such dichroic signal is known [Durr99] to be a signature of an uncompensated sense of rotation in non- collinear magnetic textures. In our experiment, the sign of the dichroism indeed reveals the stabilization of clockwise (CW) Néel DW as we recently demonstrated [Chauleau2018]. The observed features have been corroborated by static scattering measurements at the Co \(L\) edge performed at the SEXTANTS beamline at SOLEIL [Sacchi13], for which the interpretation is now well established (see Supplementary Materials S1).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 90, 486, 556]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 570, 883, 658]]<|/det|>
+<center>Figure 2: Evolution of the XRMS signal over the first 5 ps: (a) intensity of integrated diffraction ring \((CL + CR)\) and dichroism \((CL - CR)\) normalized at their values at negative time delays; (b) experimental asymmetry ratio \((CL - CR) / (CL + CR)\) normalized by its value at \(t< 0\) in grey circles and black dots. The simulations for different models discussed in the main text appear as colored lines (see Supplementary Materials S3 for details). (c) Full width at half maximum (FWHM) (red dots) and the position (blue circles) in reciprocal space of the magnetic dichroic peak as a function of time. </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 673, 883, 893]]<|/det|>
+The time dependence of both the magnetic intensity \((CL + CR)\) of the overall diffraction ring [Fig 2(a)] and the dichroism \((CL - CR)\) shows a typical signature of ultrafast demagnetization in metallic magnetic ultrathin layers: first, a quench of the magnetization reaching a minimum value after a few hundreds of fs, followed by a log- like recovery over a few ps. The experimental results are further analyzed by plotting the asymmetry ratio, i.e., \((CL - CR) / (CL + CR)\) as a function of time [see Fig. 2(b)], which represents the DW behavior normalized by the total magnetic moment. If the DW magnetization follows the same dynamics as that of the domains, this ratio should not vary. It is plotted in Fig. 2b (normalized by its value before the pump pulse) where one clearly observes a \(15\%\) dip at \(\sim 0.7\) ps. This has been reproducibly observed when repeating the experiment, as demonstrated by the overlapping series of black filled and open circles in Fig. 2(b) showing identical behavior within error bars (inferred
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 884, 258]]<|/det|>
+from the statistical fit of the background and peak intensity, see Supplemental Material Section S2). The normalized ratio remains below 1.0 up to 2 ps. The time evolution of the peak position defined by the maximum of its Gaussian fit, and of the full width at half maximum (FWHM) in reciprocal space of the magnetic dichroic peak are displayed in Fig. 2(c). Those two quantities generally correspond respectively to the variation of the domain size and their distribution. However, this apparent domain extension corresponds in fact to an expansion of the DW in the first ps after optical excitation, as reported by Pfau et al. [Pfau 2012]. When considering this expansion according to the value reported in Fig. 2(c), an increase of the asymmetry ratio is predicted as shown by the blue curve in Fig. 2(b).  
+
+<|ref|>text<|/ref|><|det|>[[114, 264, 884, 666]]<|/det|>
+To explain this ultrafast deviation of the dichroism asymmetry ratio, we first exclude an origin due to a change in the scattering factors induced by hot electrons filling the \(d\) band. Indeed, the IR laser fluence of our experiment is much lower ( \(\sim 10\%\) ) than the one used to probe the change of electron occupation induced by the IR pulse using x- ray absorption spectroscopy (XAS) [Mathieu18]. Thus, we explain our observation by the fact that during the demagnetization (resp. remagnetization), the magnetic moments do not decrease (resp. increase) by the same amount simultaneously inside the DWs and inside the domains. If the magnetization decreased uniformly, the expected asymmetry ratio would be constant, as shown by simulation using a model that is detailed in Supplemental Material S3 [magenta line in Fig. 2(b)]. As explained above, the sole expansion of the DW widths cannot explain our data [blue curve in Fig. 2(c)]. To explain an asymmetry ratio dropping below its initial value, we resort to a reduction of the degree of magnetic chirality. In other words, it corresponds to a change of the ratio between the out- of- plane and the in- plane magnetization. In our interpretation, the ultra- fast decrease of the asymmetry ratio below 1.0 is linked to a different demagnetization rate between the DWs and the domains. Note that a scenario that would correspond to a faster remagnetization of the DWs than the domains shall result into an asymmetry ratio larger than 1 (similarly to the expansion of the DW), and therefore can also be safely ruled out. In the following, in order to reproduce our experimental observations, the simulations include both coherent evolution of the hot electron spins that induce a spin torque on the DW and spin temperature (incoherent) variations within the DWs.  
+
+<|ref|>text<|/ref|><|det|>[[115, 694, 883, 916]]<|/det|>
+The understanding of the ultrafast DW width expansion requires considering the intense flow of spin currents in the ps regime. These can efficiently transfer angular momentum to and from the ferromagnetic material as shown, e.g., when Pt layers absorb it and generate ps electrical pulses [Kampfrath13]. Angular momentum transfer and dissipation often results in both enhanced demagnetization as well as a faster magnetization recovery. We argue that this is exactly what is happening with the non- collinear magnetic regions inside the DWs. The enhanced spin scattering within DWs is a rather old topic born with studies of the extra contribution to the static magnetoresistance [Viret96] or the induced spin transfer torques resulting in their current- induced displacement. To this aim, ballistic models have been developed and can be appropriately adapted for the ultrafast demagnetization scenario in which superdiffusive spin currents play a central role [Battiato10]. The
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 82, 883, 214]]<|/det|>
+behavior of ballistic spin carriers can be described such as a classical spinned particle perceiving a time varying exchange field while crossing the wall [Viret96, Vanhaverbeke07]. Let us recaller salient features. First, these are band particles that are coupled by exchange to the localized spins (through the so- called \(s - d\) Hamiltonian). Their velocity perpendicular to the wall is related to their momentum in \(k\) space. With the appropriate parameter renormalization, the problem is equivalent to the "fast adiabatic passage" known, e.g., in NMR theory. The spin evolution is given by the Landau- Lifshitz equation:  
+
+<|ref|>equation<|/ref|><|det|>[[428, 216, 567, 252]]<|/det|>
+\[\frac{d\vec{\mu}}{dt} = \frac{J_{ex}S}{\hbar}\vec{m}\times \vec{\mu}\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 257, 884, 696]]<|/det|>
+where \(\vec{\mu}\) is the electron spin, \(J_{\mathrm{ex}}S\) the exchange energy with the localized moment \((S)\) and \(\vec{m}\) the direction of the time varying exchange field seen by the ballistic electrons. The localized moments are rotating in a Neel fashion within the DW and the problem is generally treated in this rotating frame [Vanhaverbeke07]. Basically, the electronic spins will precess around the localized moment effective field and thus acquire a component out of the plane of rotation, inducing a torque parallel to the chiral vector: \(S_{i}\times S_{j}\) . The electron spin precession angle \(\omega\) is proportional to the velocity \(v\) divided by exchange times and the DW width \(2\pi \Delta\) [Viret96]: \(< \omega > = \frac{\pi h\nu}{J_{\mathrm{ex}}S2\pi\Delta}\) . Typically, for electrons at the Fermi level, this precession angle is found to be around 7 degrees for a DW width \(2\pi \Delta\) of \(15\mathrm{nm}\) [Vanhaverbeke07]. However, it is to be noticed that this angle can be quite different for the hot electrons produced in the demagnetization process as the relevant parameter values are hard to quantify. Although their velocities should not be too far from those at the Fermi level (in the \(10^{6}\mathrm{m / s}\) range [Kampfrath13]), the exchange energies effective in bands over \(1\mathrm{eV}\) above the Fermi level can be dramatically reduced \((\sim 0.1\mathrm{eV})\) . Therefore, the expected mistracking angle could be significantly greater for a large part of the hot electrons' distribution. All these processes shall in turn generate a torque applied on the localized moments [Waintal04]. However, because the hot spin currents flow in all directions, mistracking angles can be both positive and negative, resulting in cancellation of the net torque acting on the DWs. The overall effect of the incoherent precession results in an average loss of angular momentum. This should speed up the spin relaxation processes within the DW so that after some \(100\mathrm{fs}\) , a net spin current is established from the domains into the interior of the DWs.  
+
+<|ref|>text<|/ref|><|det|>[[114, 701, 884, 900]]<|/det|>
+The new components of the spin- transfer torque resulting from this latter spin current originating from the coherent evolution of the hot electron spins are not cancelled out. Importantly such torques are of opposite sign on the two sides of the DW and should induce a sizeable tilting of the DW magnetization out of the Neel plane as illustrated in Fig. 3(a). This phenomenon is at the origin of a new transient DW shape, made of a Neel type center surrounded by opposite Bloch types as depicted in Fig. 3(b). Such a mixed Bloch/Neel/Bloch contribution will in turn lead to a transient reduction of the measured chirality as it adds two (opposite) Bloch components on both sides of the DW compared to the originally purely Neel character. In order to estimate the amplitude of this DW distortion, it is useful to realize that unlike small current- induced electron flows at the Fermi level, spin fluxes during demagnetization are
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 81, 884, 373]]<|/det|>
+enormous as for each pulse, typically 0.5 electrons per Co atom are excited to higher bands for the used laser fluence [Kampfrath13]. The timescale for the onset of the induced torques is given by the exchange energy and falls in the 10- fs range, ensuring that the wall distortion does not lag from the population of hot electrons. For a spin temperature sufficiently different between domains and DWs, a quantitative estimate using the abovementioned parameters gives a precession angle of the magnetization inside the DW that is larger than 10 degrees. Moreover, the onset of this Bloch component in the DW must leaks out into the domains, thus slightly increasing the effective DW width as also observed experimentally. The measured expansion of the DW can be directly derived from the variation of the dichroic peak position and width shown in Fig. 2(c). We find that the DW width (slightly) increases rapidly and its magnetization reaches a minimum around 1 ps (blue curve), as reported previously for Bloch type DWs [Pfau2012]. Note that this DW expansion takes place when the quenched magnetization starts to recover (1 ps). After reaching it maximum expansion, the DW width then recovers its original (unpumped represented as dotted lines in Fig. 2(c) size at a timescale of \(\sim 5\) ps.  
+
+<|ref|>image<|/ref|><|det|>[[118, 421, 876, 608]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 615, 881, 686]]<|/det|>
+<center>Figure 3: Magnetization texture modification by hot electrons. (a) Schematic representation of the torque (black arrows) imposed by the 'hot spins' flowing from the domains to the DWs resulting in transient mixed Bloch/Neel/Bloch contributions. (b) Transient DW shape. (c) Precession angles (red) and DW magnetization normalized by Domain one (blue) used in the simulations of the asymmetry ratio shown in Fig. 2(b). </center>  
+
+<|ref|>text<|/ref|><|det|>[[114, 725, 883, 901]]<|/det|>
+Using a 1D magnetization profile (described in Supplementary Material S3) and considering the experimental change of magnetization (extracted directly from the square root of the (CL+CR) intensity), the time evolution of the asymmetry ratio can be simulated. We consider a magnetization in the domains extracted from the (CL+CR) data, along with a further \(12\%\) reduction of the magnetization inside the DWs to account for incoherent effects, as well as a transient Bloch- Néel- Bloch wall as shown in Fig. 3(a) for coherent ones. With these simulations, we find that the precession angle can reach at the maximum about 8 degrees after a time delay of \(\sim 0.6\) ps [red curve in Fig. 3(c)] simultaneously with the reduction of the DW magnetization [relative to domain magnetization blue curve in Fig. 3(c)], The
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 82, 884, 259]]<|/det|>
+resulting simulated asymmetry ratio using the described model is plotted as the green curve in Fig. 2(b), and is in excellent agreement with the experimental measurements. Even accounting for DW expansion [red curve in Fig. 2(b)], the agreement can be obtained for a \(\sim 10\) degrees tilt angle. Although the exchange driven DW distortion is established on a very short timescale, it should last for the nanosecond timescale of the micromagnetic evolution. On the other hand, the incoherent part of the spin current shall relax at the ps timescale of the remagnetization processes, similarly to what we have measured. Interestingly, enhanced spin relaxation existing inside the DWs should speed up remagnetization, explaining that the asymmetry ratio can exceed 1, again in agreement with the experimental results.  
+
+<|ref|>text<|/ref|><|det|>[[113, 294, 884, 741]]<|/det|>
+In conclusion, we report here about the experimental investigation of the ultra- short timescale evolution of complex chiral Néel spin textures after laser induced demagnetization. Circular dichroism in x- ray resonant magnetic scattering is used to obtain information in the time domain about both the magnetic domain configuration and the magnetic chirality. Beyond the evolution of the period of the magnetic domains in magnetic multilayers with large perpendicular anisotropy, we acquire new insights into the way that the chirality of the non- collinear spin textures, and their long- range ordering, is evolving in the few ps after demagnetization by a strong optical pulse. We observe that the magnetic difference CL- CR (reflecting the DW properties) reduces faster than the diffracted sum signal (associated to domain magnetization) in the first 2 ps after the laser pulse. To explain this unexpected change of XRMS chirality signal at this short timescale, we propose that angular momentum flowing from the interior of the domains inside the DWs associated to hot electrons induces an ultrafast distortion of the DW magnetization. This transient in- plane deformation of the DWs leads to a transient mixed Bloch- Néel- Bloch DW accompanied by an increase of the DWs width and a reduction of the magnetization inside the DW. These original experimental results are reproduced by calculations, considering a magnetization reduction of \(12\%\) with a 7.5 degrees distortion of the DW. On a longer timescale, i.e., after a few ps, the DWs return to their pure chiral Néel configuration preserving the original sense of rotation (i.e., chirality) together with a recovery of their magnetization. We emphasize that our approach using dichroism in x- ray resonant scattering is applicable to any other magnetic chiral texture and should provide a better understanding of the evolution of the chirality of spin textures on the ultrafast timescale.  
+
+<|ref|>text<|/ref|><|det|>[[114, 783, 884, 912]]<|/det|>
+Acknowledgment: We acknowledge Ivaylo Nikolov, Michele Manfredda, Luca Giannessi, and Giuseppe Penco for their inestimable help to set up the FEL and the laser for our experiment. NJ would like to thanks S. Flewett for discussion on XRMS simulations. Financial supports from FLAG- ERA SographMEM (ANR- 15- GRFL- 0005), funding from the Agence Nationale de la Recherche, France, under grant agreement no. ANR- 17- CE24- 0025 (TOPSKY) and 18- CE24- 0018- 01 (SANTA), the Horizon2020 Framework Program of the European Commission under FET- Proactive Grant agreement
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[60, 80, 884, 899]]<|/det|>
+268 no. 824123 (SKYTOP). E. J. is grateful for financial support received from the CNRS- MOMENTUM. 269 O. S. L., A. V. S., and V. V. K. acknowledge funding from the Engineering and Physical Sciences 270 Research Council (EPSRC) in the United Kingdom (Grant No. EP/T016574/1). 271 272 273 References: 274 [beaurepaire96] E. Beaurepaire et al., Ultrafast Spin Dynamics in Ferromagnetic Nickel 275 Phys. Rev. Lett. 76, 4250 (1996). 276 [Melnikov11] A. Melnikov et al. Ultrafast Transport of Laser- Excited Spin- Polarized Carriers 277 in Au/Fe/MgO(001). Phys. Rev. Lett. 107, 076601 (2011). 278 [Siegrist19] F. Siegrist, Light- wave dynamic control of magnetism. Nature 571, 240 (2019). 279 [Malinowski08] G. Malinowski, et al., Control of speed and efficiency of ultrafast demagnetization by 280 direct transfer of spin angular momentum. Nat. Phys. 4, 855 (2008) 281 [Battiato10] M. Battiato et al., Superdiffusive Spin Transport as a Mechanism of Ultrafast 282 Demagnetization. Phys. Rev. Lett. 105, 027203 (2010) 283 [vodungbo16] B. Vodungbo et al., Indirect excitation of ultrafast demagnetization. Sci. Rep. 6, 18970 284 (2016). 285 [Moisan14] N. Moisan et al., Investigating the role of superdiffusive currents in laser induced 286 demagnetization of ferromagnets with nanoscale magnetic domains. Sci. Rep. 4, 4658 (2014). 287 [Pfau2012] B. Pfau et al., Ultrafast optical demagnetization manipulates nanoscale spin structure in 288 domain walls, Nat. Commun. 3, 1100 (2012). 289 [zuzin2020] D. Zusin et al., Ultrafast domain dilation induced by optical pumping in ferromagnetic 290 CoFe/Ni multilayers. https://arxiv.org/abs/2001.11719 291 [Kerber20] N. Kerber et al., Faster chiral versus collinear magnetic order recovery after optical 292 excitation revealed by femtosecond XUV scattering. Nat. Commun. 11, 6304 (2020). 293 [Hennes20b] M. Hennes et al., Laser- induced ultrafast demagnetization and perpendicular magnetic 294 anisotropy reduction in a Co88Tb12 thin film with stripe domains. Phys. Rev. B 102, 174437 (2020) 295 [Durr99] H. A. Durr et al, Chiral Magnetic Domain Structures in Ultrathin FePd Films. Science 284, 296 (1999). 296 [Chauleau2018] J.- Y. Chauleau et al., Chirality in Magnetic Multilayers Probed by the Symmetry and 298 the Amplitude of Dichroism in X- Ray Resonant Magnetic Scattering. Phys. Rev. Lett. 120, 037202 299 (2018). 300 [Fert80] A. Fert and P.M. Levy. Role of Anisotropic Exchange Interactions in Determining the 301 Properties of Spin- Glasses. Phys. Rev. Lett. 44, 1538 (1980). 302 [Fert90] A. Fert, « Magnetic and Transport Properties of Metallic Multilayers », Materials Science 303 Forum, 59- 60, 439 (1990). 304 [Zhang17] S. L. Zhang et al. Direct experimental determination of the topological winding number of 305 skyrmions in Cu2OSeO3. Nat. Commun. 8, 14619 (2017). 306 [Legrand2018] W. Legrand et al., Hybrid chiral domain walls and skyrmions in magnetic multilayers. 307 Sci. Adv. 4 : eaat0415 (2018)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 78, 880, 720]]<|/det|>
+308 [Zhang20] S. L. Zhang et al., Robust Perpendicular Skyrmions and Their Surface Confinement. 309 NanoLett. 20 1428 (2020). 310 [Thiaville12] A. Thiaville et al., Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films. 311 Euro. Phys. Lett. 100, 57002 (2012). 312 [Ruy13] K. S. Ruy et al., Chiral spin torque at magnetic domain walls. Nat. Nanotech. 8, 527 (2013). 313 [Nagoasa13] N. Nagoasa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions. 314 Nat. Nanotech. 8, 899 (2013). 315 [Fert17] A. Fert, N. Reyren, V. Cros, Magnetic skyrmions: advances in physics and potential 316 applications. Nat. Rev. Mater. 2, 17031 (2017). 317 [Yang15] S. Yang, K., Ryu, and S. Parkin, Domain-wall velocities of up to \(750\mathrm{m s^{- 1}}\) driven by 318 exchange-coupling torque in synthetic antiferromagnets. Nat. Nanotech. 10, 221 (2015). 319 [Vansteenkiste14] A. Vansteenkiste et al. The design and verification of MuMax3. AIP Adv. 4, 320 107133 (2014). 321 [Capotondi13] F. Capotondi et al., Coherent imaging using seeded free-electron laser pulses with 322 variable polarization: First results and research opportunities. Rev. Sci. Instrum. 84, 051301 (2013). 323 [Allaria12] E. Allaria et al., Highly coherent and stable pulses from the FERMI seeded free-electron 324 laser in the extreme ultraviolet. Nat. Photonics 6, 699 (2012). 325 [Allaria14] E. Allaria et al., Control of the Polarization of a Vacuum-Ultraviolet, High-Gain, Free- 326 Electron Laser. Phys. Rev. X 4, 041040 (2014). 327 [yao2020] K. Yao et al., Distinct spectral response in M-edge magnetic circular dichroism. Phys. Rev. 328 B 102, 100405 (2020). 329 [hennes20] M. Hennes et al., Time-Resolved XUV absorption spectroscopy and magnetic circular 330 dichroism at the Ni M2,3-edges. https://arxiv.org/abs/2011.14352 331 [Sacchi13] M. Sacchi et al., The SEXTANTS beamline at SOLEIL: a new facility for elastic, 332 inelastic and coherent scattering of soft X-rays. J. Phys. Conf. Ser. 425, 072018 (2013). 333 [Mathieu18] B. Mathieu et al., Probing warm dense matter using femtosecond X-ray absorption 334 spectroscopy with a laser-produced betatron source. Nat. Commun. 9, 3276 (2018). 335 [Kampfrath13] T. Kampfrath et al., Terahertz spin current pulses controlled by magnetic 336 heterostructures. Nat. Nano. 8, 256 (2013). 337 [Viret96] M. Viret et al., Spin scattering in ferromagnetic thin films. Phys. Rev. B 53, 8464 (1996). 338 [Vanhaverbeke07] A. Vanhaverbeke and M. Viret, Simple model of current-induced spin torque in 339 domain walls. Phys. Rev. B 75, 024411 (2007). 340 [Waintal04] X. Waintal, and M. Viret, Current-induced distortion of a magnetic domain wall. 341 Europhys. Lett. 65, 427 (2004).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 44, 143, 70]]<|/det|>
+## Figures  
+
+<|ref|>image<|/ref|><|det|>[[45, 97, 944, 303]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 325, 115, 345]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 367, 947, 500]]<|/det|>
+CD- XRMS experiments. (a) Experimental configuration with the incident beams of the IR pump and the x- ray probe. (b) Magnetic diffraction pattern, (CL+CR) (c) Dichroic pattern (CL- CR), displaying the typical signature of clockwise Néel domain walls. The images in panels b and c have been geometrically corrected to account for the projection related to the photon incidence angle \(\theta = 45^{\circ}\) , and the scale corresponds to the sum of the counts (500 XFEL pulse of each polarization) for (CL+CR) (b) and (CL- CR) (c).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[50, 52, 551, 775]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 802, 116, 821]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 841, 944, 932]]<|/det|>
+Evolution of the XRMS signal over the first 5 ps: (a) intensity of integrated diffraction ring (CL+CR) and dichroism (CL- CR) normalized at their values at negative time delays; (b) experimental asymmetry ratio (CL- CR)/(CL+CR) normalized by its value at \(t < 0\) in grey circles and black dots. The simulations for different models discussed in the main text appear as colored lines (see Supplementary Materials S3 for
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 928, 88]]<|/det|>
+details). (c) Full width at half maximum (FWHM) (red dots) and the position (blue circles) in reciprocal space of the magnetic dichroic peak as a function of time.  
+
+<|ref|>image<|/ref|><|det|>[[45, 92, 940, 333]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 356, 117, 376]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 398, 952, 511]]<|/det|>
+Magnetization texture modification by hot electrons. (a) Schematic representation of the torque (black arrows) imposed by the 'hot spins' flowing from the domains to the DWs resulting in transient mixed Bloch/Neel/Bloch contributions. (b) Transient DW shape. (c) Precession angles (red) and DW magnetization normalized by Domain one (blue) used in the simulations of the asymmetry ratio shown in Fig. 2(b).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 533, 311, 560]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 583, 765, 603]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 621, 317, 641]]<|/det|>
+- trXRMSSupplementary.pdf
+
+<--- Page Split --->

preprint/preprint__0040553aacfe354742b83e1386dd94b013703c55b639bcf87dcd675a88c10bf0/images_list.json

@@ -0,0 +1,40 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
+    "footnote": [],
+    "bbox": [
+      [
+        48,
+        50,
+        945,
+        450
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2",
+    "footnote": [],
+    "bbox": [
+      [
+        45,
+        45,
+        950,
+        610
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 13
+  }
+]

preprint/preprint__0040553aacfe354742b83e1386dd94b013703c55b639bcf87dcd675a88c10bf0/preprint__0040553aacfe354742b83e1386dd94b013703c55b639bcf87dcd675a88c10bf0.mmd

@@ -0,0 +1,221 @@
+
+# Rationally synthesized framework polymer membranes enable high selectivity and barrierless anion conduction  
+
+Zhengjin Yang yangz.j09@ustc.edu.cn  
+
+University of Science and Technology of China https://orcid.org/0000- 0002- 0722- 7908  
+
+Junkai Fang University of Science and Technology of China  
+
+Guozhen Zhang University of Science and Technology of China https://orcid.org/0000- 0003- 0125- 9666  
+
+Marc- Antoni Goulet Concordia University https://orcid.org/0000- 0002- 9146- 6759  
+
+Peipei Zuo University of Science and Technology of China https://orcid.org/0000- 0001- 5043- 7188  
+
+Hui Li University of Science and Technology of China  
+
+Jun Jiang University of Science and Technology of China https://orcid.org/0000- 0002- 6116- 5605  
+
+Michael Guiver Tianjin University https://orcid.org/0000- 0003- 2619- 6809  
+
+Tongwen Xu University of Science and Technology of China https://orcid.org/0000- 0002- 9221- 5126  
+
+Article  
+
+Keywords:  
+
+Posted Date: June 11th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4392718/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+
+Version of Record: A version of this preprint was published at Nature Communications on April 6th, 2025. See the published version at https://doi.org/10.1038/s41467-025-58638-0.
+
+<--- Page Split --->
+
+## Abstract  
+
+AbstractThe understanding gleaned from studying ion transport within the interaction confinement regime enables the near- frictionless transport of cations (e.g., \(\mathrm{Na^{+} / K^{+}}\) ). However, anion transport (e.g., Cl⁻) is suppressed under confinement because of the different polarization of water molecules around cations and anions, also known as the charge asymmetry effect. Here we report the rational synthesis of anion- selective framework polymer membranes having similar densities of subnanometer- sized pores with nearly identical micropore size distributions, which overcome the charge asymmetry effect and promote barrierless anion conduction. We find that anion transport within the micropore free volume elements can be dramatically accelerated by regulating the pore chemistry, which lowers the energy barrier for anion transport, leading to an almost twofold increase in Cl⁻ conductivity and barrierless F⁻ diffusion. The resultant membrane enables an aqueous organic redox flow battery that utilizes Cl⁻ ions as charge carriers to operate at extreme current densities and delivers competitive performance to counterparts where K⁺ ions are charge carriers. These results may benefit broadly electrochemical devices and inspire single- species selectivity with separation membranes that exploit controlled or chemically gated ion/molecule transport.  
+
+## Main Text  
+
+Replicating the extreme selectivity and high permeability of biological ion channels is an enduring challenge for membrane scientists (1- 3). Beyond the generally- accepted mechanisms of size exclusion and Coulombic repulsion, it is argued that the subtle interactions between ions and channel walls at atomic- scale confinement play a crucial role. These interactions were not clearly elucidated until the fabrication of angstrom- scale slits/capillaries/channels with atomic- scale precision (4, 5).  
+
+The spatial confinement of ion transport down to molecular- sized ion channels magnifies the impact of channel wall interactions and gives rise to exotic transport behavior. For example, hysteretic ion conduction occurs, resulting in an ion memory effect (6, 7), while the formation of Bjerrum ion pairs causes ionic Coulombic blockade (8). These atypical ion motions are intimately related to the dramatically enhanced material- dependent interactions between hydrated ions and the confining channel walls (e.g., electrostatic, adsorption/desorption) (9). For chemically inert and atomically smooth graphite channel walls, \(\mathrm{K^{+}}\) demonstrates a mobility close to that of the value in bulk solutions (10). By applying a voltage bias on the graphite channel, the streaming mobility of \(\mathrm{K^{+}}\) is increased by up to 20 times (11) and this may be ascribed to the electronic structure change under an external voltage bias (12). It has also been demonstrated that by introducing \(\mathrm{Li^{+}}\) - coordinating functionality within the shape- persistent free volume elements of microporous polymer membranes, \(\mathrm{Li^{+}}\) diffusivity can be greatly enhanced (13). Similar improvements to \(\mathrm{Na^{+}}\) transport have also been achieved by exploiting the synergy between micropore confinement and ion- membrane interactions (14).
+
+<--- Page Split --->
+
+Despite the considerable improvements in cation transport due to the confinement effect, it is notable that chloride \((\mathsf{Cl}^{- })\) mobility experiences significant suppression under confinement. This charge asymmetry is likely due to the slightly different hydration shell configurations between \(\mathsf{Cl}^{- }\) and \(\mathsf{K}^{+}(10)\) . The mobility of \(\mathsf{Cl}^{- }\) under confinement is three times less than that of \(\mathsf{K}^{+}\) , even though \(\mathsf{Cl}^{- }\) and \(\mathsf{K}^{+}\) have similar mobilities in bulk water \((7.58\times 10^{- 8}\mathrm{vs.}7.86\times 10^{- 8}\mathrm{m}^{2}\mathrm{V}^{- 1}\mathrm{s}^{- 1})\) and hydrated diameters \((6.64\mathring{\mathrm{A}}\mathrm{vs.}\) 6.62 Å) (15, 16). For a more extreme case, \(\mathsf{Cs}^{+}\) and \(\mathsf{Cl}^{- }\) exhibit similar ion- core sizes and hydrated diameters, but \(\mathsf{Cl}^{- }\) exhibits more than three times lower mobility under \(\mathring{\mathrm{A}}\) - scale confinement \((1.7\times 10^{- 8}\) vs. \(6.0\times 10^{- 8}\mathrm{m}^{2}\mathrm{V}^{- 1}\mathrm{s}^{- 1})\) (16). For chloride salts of high valency cations, the overall \(\mathsf{Cl}^{- }\) mobility decreases to almost zero in single- digit- sized nanopores (17). A decrease in the mobility of other anions under confinement has also been observed (16). This phenomenon is echoed by the relatively high energy barrier associated with anion exchange membranes that transport chloride ions (see Supplementary Table S1).  
+
+The transport and selectivity of anions are of critical relevance to applications such as direct seawater electrolysis (18), solid- state batteries (19) and redox flow batteries (20- 25). Understanding and overcoming the charge asymmetry effect for anion transport under confinement is therefore essential for enabling these technologies. Here we report the design and synthesis of a series of positively charged (quaternary ammonium cations) covalent triazine framework (QCTF) membranes with nearly the same density of rigid micropores with almost identical pore size distributions. The QCTF membranes exhibit Coulombic repulsion- induced anion selectivity, with a chloride transference number \(t_{- }\) of 0.95, and size exclusion- induced rejection of BTMAP- Vi (bis(3- trimethylammonio) propyl viologen tetrachloride) and FcNCl ((ferrocenylmethyl) trimethylammonium chloride), redox- active organic flow battery electrolytes. The cross- membrane BTMAP- Vi diffusion coefficient at \(3.1\times 10^{- 11}\mathrm{cm}^{2}\mathrm{s}^{- 1}\) is over 20 times lower than that of commercial membranes. We demonstrate that through on- membrane modification, the charge distribution of the pristine QCTF membrane framework can be regulated by protonation (affording P- QCTF) and methylation (affording M- QCTF), which dramatically alters the interactions between anions and the membrane framework and helps lower the energy barrier for anion transport. The cross- membrane \(\mathsf{Cl}^{- }\) conductivity increased twofold from \(13.2\mathrm{mScm}^{- 1}\) for QCTF to 25.9 \(\mathrm{mScm}^{- 1}\) for M- QCTF at \(30^{\circ}\mathrm{C}\) , and the activation energy for \(\mathsf{Cl}^{- }\) conduction decreased from \(20.6\mathrm{kJmol}^{- 1}\) to \(13.1\mathrm{kJmol}^{- 1}\) , lower than any value reported in the literature (see Supplementary Table S1). \(^{19}\mathrm{F}\) PFG- NMR revealed an increase in the \(\mathrm{F}^{- }\) diffusion coefficient from \(0.63\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for QCTF and \(0.93\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for P- QCTF, to \(1.1\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for M- QCTF which is close to the value in bulk water \((1.2\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1})\) . The greater anion conductivity can dramatically improve device performance as exemplified here in an BTMAP- Vi- and FcNCl- based aqueous organic redox flow battery (AORFB) in pH- neutral solutions. The BTMAP- Vi/FcNCl cell configured with the M- QCTF membrane exhibited a high- frequency area- specific resistance (ASR) as low as \(0.23\Omega \cdot \mathrm{cm}^{2}\) , which enabled charging and discharging of the BTMAP- Vi/FcNCl cell at an extreme current density of \(500\mathrm{mAcm}^{- 2}\) . The prolonged galvanostatic cell cycling at \(400\mathrm{mAcm}^{- 2}\) maintained a Coulombic efficiency of \(>99\%\) and a stable energy efficiency of around \(60\%\) over the course of 1000 cycles. Notably, the achieved capacity utilization and efficiency with
+
+<--- Page Split --->
+
+M- QCTF approaches similar values to those of alkaline AORFBs that leverage \(\mathsf{K}^{+}\) as charge- carrying ions, while in otherwise identical cells assembled with QCTF or P- QCTF, an almost \(20\%\) lower energy efficiency was observed. This is significant and can be attributed to a dramatic reduction in the contribution of membrane resistance to whole- cell resistance, e.g., from \(>70\%\) for the Seleminon \(^{\circledR}\) AMV membrane to \(\sim\) \(25\%\) for M- QCTF (Supplementary Tables S2 and S3). The above results imply a breakthrough in the charge asymmetry effect.  
+
+## Results and Discussion  
+
+## Covalent triazine framework membranes with tunable pore chemistry  
+
+Covalent triazine framework chemistry gives rise to a wide variety of microporous materials and offers enormous diversity in pore chemistry. We thus synthesized a stand- alone triazine framework membrane from \(4,4^{'}\) - biphenyldicarbonitrile and a derivative of 3- hydroxy- [1,1'- biphenyl]- 4,4'- dicarbonitrile bearing a quaternary ammonium moiety via a superacid- catalyzed organic sol- gel procedure (Fig. 1a and Supplementary Figures S1- S4) (26). The process yields a free- standing membrane (namely, QCTF) with a Young's modulus and tensile strength of 0.91 GPa and 32.0 MPa, respectively (Supplementary Figure S5). The skeletal triazine rings of QCTF were subsequently protonated with HCl or methylated with \(\mathrm{CH}_3\mathrm{I}\) , affording P- QCTF and M- QCTF, respectively. Overall, we constructed three covalent triazine framework polymers with similar molecular configurations and pore structures that can be processed into hydrophilic, uniform and robust ion- selective membranes via an organo- sol- gel procedure (Supplementary Figures S6- S8, Supplementary Table S4), but with slightly different and deliberately tailored pore chemistries.  
+
+Carbon dioxide \(\mathrm{CO_2}\) ) adsorption experiments and molecular simulations were conducted to probe the micropore structure of the covalent triazine framework polymers. \(\mathrm{CO_2}\) sorption isotherms measured at 273 K revealed that powder samples of QCTF, P- QCTF, and M- QCTF had similar \(\mathrm{CO_2}\) uptake capacities of 16, 15.2, and \(14.7\mathrm{cm}^3\mathrm{g}^{- 1}\) STP, respectively (Fig. 1b). Notably, QCTF, P- QCTF, and M- QCTF exhibit almost identical pore size distributions, ranging from 0.3 nm to 0.9 nm, as derived from \(\mathrm{CO_2}\) adsorption isotherms based on density functional theory (DFT) calculations (Fig. 1c). These experimental results are further supported by molecular simulations of the 3D framework structure and the computation of \(\mathrm{CO_2}\) distributions within the framework structures (Supplementary Figures S9 and S10). This again indicates that QCTF, P- QCTF, and M- QCTF have similar framework structures, interconnected micropores and pore size distributions.  
+
+The amount of charged functional groups (quaternary ammonium groups) within the pristine QCTF membrane, characterized by the ion exchange capacity (IEC, in mmol \(\mathrm{g}^{- 1}\) ), is \(1.20\mathrm{mmol}\mathrm{g}^{- 1}\) for QCTF (as- designed IEC value is \(\sim 1.00\mathrm{mmol}\mathrm{g}^{- 1}\) ). During protonation, approximately \(55\%\) of the triazine rings were protonated and the same amount of triazine rings was methylated after methylation, as revealed by
+
+<--- Page Split --->
+
+X- ray photoelectron spectroscopy (XPS, Fig. 1d). This suggests that P- QCTF and M- QCTF should have identical IEC values, which was confirmed by titration and zeta potential measurements (Supplementary Figure S11).  
+
+## Ion Transport and Selectivity  
+
+Despite the similar framework structure and almost identical pore size/size distributions, our experimental results reflect that cross- membrane ion transport is significantly affected by pore chemistry. We speculate that the difference is synergistically determined by Coulombic/steric effects and specific ion- pore wall interactions, as shown in Fig. 2a. The current- voltage (I- V) curves across the membranes, as measured in a two- compartment diffusional H- cell under a 10- fold concentration gradient KCl solution (Fig. 2b), reveal a net anion flux, indicating anion selectivity. The anion transference number (t.) calculated for QCTF is 0.940, while the values for protonated QCTF (P- QCTF) and methylated QCTF (M- QCTF) are 0.947 and 0.953, respectively (Supplementary Figure S12). These values suggest the superior anion selectivity of the QCTF membranes compared to that of commercial anion exchange membranes (AEMs). This result is reasonable considering the Coulombic repulsion of the \(< 1\) nm pore channel within the QCTF membranes.  
+
+The measured transference numbers align with the cross- membrane permeation/diffusion rates for BTMAP- Vi (a redox- active organic cation) and Cl- (Fig. 2c and 2d, Supplementary Figures S13- S15, Supplementary Tables S5- S6), which are dramatically different in size. Compared with commercial AEMs (Fig. 2c), all the QCTF membranes exhibited superior blocking capabilities toward BTMAP- Vi. The diffusion coefficients of BTMAP- Vi across the QCTF and the P- QCTF were determined to be \(4.5 \times 10^{- 11} \text{cm}^2 \text{s}^{- 1}\) and \(3.4 \times 10^{- 11} \text{cm}^2 \text{s}^{- 2}\) , respectively. These values are at least one order of magnitude smaller than those of commercial AEMs. Note that the value further decreases to \(3.1 \times 10^{- 11} \text{cm}^2 \text{s}^{- 1}\) for M- QCTF, a value that is over 20 times smaller than that of Selemon® DSV. The diffusion coefficients of Cl- through the QCTF and P- QCTF are \(1.8 \times 10^{- 7} \text{cm}^2 \text{s}^{- 1}\) and \(2.6 \times 10^{- 7} \text{cm}^2 \text{s}^{- 2}\) , respectively. By contrast, commercial anion- selective membranes demonstrated Cl- diffusion coefficients at least one order of magnitude smaller than those of QCTF membranes. Surprisingly, the Cl- diffusion coefficient measured for M- QCTF reached \(3.0 \times 10^{- 7} \text{cm}^2 \text{s}^{- 1}\) , which is nearly 2 times that for the QCTF membrane (Fig. 2d). A comparison of the Cl- diffusion coefficients and the Cl- /BTMAP- Vi selectivity for QCTF membranes, commercial AEMs and previously reported membranes implies that these framework membranes can simultaneously deliver fast ion permeation and high selectivity, overcoming the usual tradeoff observed for many ion exchange membranes (Supplementary Figure S16 and Supplementary Table S6).  
+
+The fast Cl- transport across the triazine framework membranes is further supported by the membrane conductivity measurements. Compared with commercial AEMs, triazine framework membranes show high Cl- conductivity at relatively low hydration numbers (Fig. 2e, Supplementary Figure S17 and Supplementary Tables S7- S8). The Cl- conductivity of QCTF, as measured by four- point electrochemical
+
+<--- Page Split --->
+
+impedance spectroscopy (EIS), is \(13.2 \mathrm{mS cm}^{- 1}\) at \(30.0^{\circ}\mathrm{C}\) and approaches \(42.0 \mathrm{mS cm}^{- 1}\) at \(80^{\circ}\mathrm{C}\) at low hydration numbers (3.5 at \(30^{\circ}\mathrm{C}\) , 4.4 at \(80^{\circ}\mathrm{C}\) ). In comparison, the \(\mathrm{Cl}^{- }\) conductivity of P- QCTF is \(20.0 \mathrm{mS cm}^{- 1}\) at \(30^{\circ}\mathrm{C}\) and increases to \(48.4 \mathrm{mS cm}^{- 1}\) at \(80^{\circ}\mathrm{C}\) . We find that the \(\mathrm{Cl}^{- }\) conductivity of M- QCTF is \(26.0\) at \(30.0^{\circ}\mathrm{C}\) , which is nearly twice that of QCTF, and reaches \(53.0 \mathrm{mS cm}^{- 1}\) at \(80^{\circ}\mathrm{C}\) . The activation energy \((E_{a})\) for \(\mathrm{Cl}^{- }\) conduction across the QCTF membrane is \(20.6 \mathrm{kJ mol}^{- 1}\) , as derived from the conductivities at various temperatures (Fig. 2f and Supplementary Figure S18), contrasting an \(E_{a}\) of \(12.9 \mathrm{kJ mol}^{- 1}\) for \(\mathrm{K}^{+}\) transport across an otherwise identical membrane with sulfonate functional groups (ref 14). Surprisingly, the \(E_{a}\) value for M- QCTF is as low as \(13.1 \mathrm{kJ mol}^{- 1}\) , which is nearly half that of QCTF and lower than any value reported in the literature (Fig. 2g and Supplementary Table S1). Considering the similar framework structure and almost identical pore size/size distributions, this significant result indicates that the methylation of triazine rings alters the transport energy barrier for \(\mathrm{Cl}^{- }\) ions.  
+
+Due to the aforementioned results, we conclude that electrostatic interactions alone cannot explain the differences in \(\mathrm{Cl}^{- }\) diffusion coefficients, \(\mathrm{Cl}^{- }\) conductivity or activation energy for cross- membrane \(\mathrm{Cl}^{- }\) transport. To unravel why methylation of the triazine ring promotes fast \(\mathrm{Cl}^{- }\) conduction, compared to the protonated triazine ring in P- QCTF and the charge- neutral triazine ring in QCTF, the charge distribution and the \(\mathrm{Cl}^{- }\) transport routes within the matrix of the triazine framework membranes were portrayed based on molecular simulations, and the two- dimensional free- energy landscapes were computed according to current methodology (13, 14). Our calculations show that the charge distributions of triazine framework membranes vary dramatically after protonation and methylation (Fig. 3a, Supplementary Figure S19). The most even charge distribution is observed for M- QCTF. We speculate that the variation in charge distribution alters the interactions between anions and the membrane frameworks and helps establish low- energy- barrier pathways for anion transport. This is supported by free energy calculations for \(\mathrm{Cl}^{- }\) conduction (Fig. 3b). The simulation results showed that \(\mathrm{Cl}^{- }\) can interact with quaternary ammonium (QA) groups (Fig. 3c, Supplementary Figures S20 and S21) and lower the free energy, but an energy barrier must be overcome for \(\mathrm{Cl}^{- }\) ions to approach adjacent QA groups. The energy barrier for \(\mathrm{Cl}^{- }\) conduction is the highest for QCTF (Fig. 3b, left panel) and decreases when the triazine ring is protonated (Fig. 3b, middle panel), while methylation of the triazine ring in M- QCTF improves the diffusivity of \(\mathrm{Cl}^{- }\) within the framework and creates a \(\mathrm{Cl}^{- }\) diffusion pathway with the lowest energy barrier (Fig. 3b, right panel). We suspect that the synergy of electrostatic interactions between \(\mathrm{Cl}^{- }\) and the methylated triazine ring and the change in electron density along the \(\mathrm{Cl}^{- }\) diffusion path after methylation may account for the emergence of the low- energy- barrier diffusion pathway.  
+
+Molecular simulation results are further supported by measurements of transmembrane \(\mathrm{F}^{- }\) diffusion coefficients via \(^{19}\mathrm{F}\) pulsed- field gradient- stimulated- echo nuclear magnetic resonance ( \(^{19}\mathrm{F}\) PFG- NMR; \(^{19}\mathrm{F}\) was selected owing to its higher sensitivity compared with \(^{35}\mathrm{Cl}\) ). \(^{19}\mathrm{F}\) PFG- NMR revealed two separate \(\mathrm{F}^{- }\) signals for Selenium® DSV and Selenium® AMV membranes (Fig. 3d and Supplementary Figure S22), with the upfield signal corresponding to free \(\mathrm{F}^{- }\) in water (located at the same position as that in 0.1 M KF
+
+<--- Page Split --->
+
+aqueous solution) and the downfield signal corresponding to associated \(\mathsf{F}^{- }\) within the membrane. In contrast, only the upfield signal was observed for all three triazine framework membranes (Fig. 3d), which is an indication of freely exchangeable \(\mathsf{F}^{- }\) within the membrane, with slight variations in the \(^{19}\mathsf{F}\) chemical shifts. By fitting the echo profiles with the Stejskal- Tanner equation (Supplementary Figure S23), the derived \(\mathsf{F}^{- }\) diffusion coefficients within the P- QCTF and QCTF are \(0.93\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) and \(0.63\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) , respectively (Fig. 3e). The value reaches \(1.1\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for M- QCTF, almost a twofold increase compared to that for QCTF. Notably, this value is 12.8 times that of Selemion® AMV and 10.8 times that of Selemion® DSV (Fig. 3e and Supplementary Figure S23) and approaches the measured diffusion coefficient of \(\mathsf{F}^{- }\) in water \((1.2\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) ; Supplementary Figure S23). In summary, by tailoring the pore chemistry of framework membranes, intimate ion- pore wall interactions provide a low- energy- barrier diffusion pathway for anions. Taken together with the Coulombic/steric exclusion by the charged framework micropores, the triazine framework membranes, particularly M- QCTF, will be of interest in applications demanding extremely fast and highly selective transport of anions.  
+
+## Triazine framework membrane powers fast-charging AORFBs  
+
+The extremely fast and highly selective anion (particularly chloride ions) conduction through chemically tuned triazine framework membranes is desirable in electrochemical devices, such as aqueous organic redox flow batteries. As a proof of concept, we configured pH- neutral AORFBs with BTMAP- Vi/FcNCl as the redox- active organic electrolyte couple and triazine framework membranes as the ion- conducting membranes, while \(\mathsf{Cl}^{- }\) ions were transported back and forth as charge carriers (Fig. 4a). At an electrolyte concentration of 0.1 M, EIS of the BTMAP- Vi/FcNCl cells assembled with QCTF or P- QCTF showed area- specific membrane resistances (ASRs) of \(0.63\Omega \mathrm{cm}^{2}\) and \(0.53\Omega \mathrm{cm}^{2}\) , respectively (Supplementary Figures S24- S25). An otherwise identical cell assembled with M- QCTF showed an ASR of \(0.37\Omega \mathrm{cm}^{2}\) (Supplementary Figure S26), which is almost twofold lower than that of the QCTF membrane. This finding aligns with the high conductivity of M- QCTF (Fig. 2e, 3b), which enables charging of the BTMAP- Vi/FcNCl cells at extreme current densities. For example, at \(200\mathrm{mAcm}^{- 2}\) , BTMAP- Vi/FcNCl with M- QCTF exhibited an energy efficiency (EE) of over \(60\%\) (Supplementary Figure S26). In contrast, the control BTMAP- Vi/FcNCl cells assembled with Selemion® DSV or Selemion® AMV could not operate at this current density due to the immediate voltage cutoff. At lower current densities ranging from 20 to 80 mA cm \(^{- 2}\) , the reported energy efficiency for the control cells drops from 89.4- 65.9% for Selemion® DSV or from 80.0- 26.6% for Selemion® AMV (27).  
+
+At a higher electrolyte concentration of \(0.5\mathrm{M}\) , BTMAP- Vi/FcNCl with M- QCTF demonstrated an even lower ASR of \(0.23\Omega \mathrm{cm}^{2}\) (Fig. 4b), a much lower value than that for Selemion® DSV or Selemion® AMV. The rate performance of the cell reveals an EE of \(49.7\%\) and a capacity utilization of \(58.8\%\) at an extreme current density of \(500\mathrm{mAcm}^{- 2}\) (Fig. 4c). Compared with the most recent report of an AEM (MTCP- 50 membrane, with the optimal ratio 1:1 of \(m\) - terphenyl to \(p\) - terphenyl) for pH- neutral AORFBs at \(0.5\mathrm{M}\) (21), M- QCTF achieved a much greater energy efficiency ( \(76.9\%\) vs. \(60.1\%\) ) and capacity utilization ( \(94.3\%\) vs.
+
+<--- Page Split --->
+
+\(63.7\%)\) at the same current density of \(200 \text{mA cm}^{- 2}\) . Notably, alkaline AORFBs that utilize \(\text{K}^{+}\) as charge- carrying ions assembled with a cation exchange membrane (SCTF- BP), which allows cation diffusion close to the value in bulk electrolyte, exhibit an EE of \(50.4\%\) and a capacity utilization of \(62\%\) at \(500 \text{mA cm}^{- 2}\) . The current results demonstrate a similar efficiency for \(\text{Cl}^{- }\) transport and therefore suggest a breakthrough in the charge asymmetry effect.  
+
+Robust and exceptional cell performance was observed during long- term galvanostatic cycling of over 2000 cycles at \(200 \text{mA cm}^{- 2}\) (0.1 M electrolyte concentration, Supplementary Figure S26) and over 1000 cycles at \(400 \text{mA cm}^{- 2}\) (0.5 M electrolyte concentration, Fig. 4d). Comparisons of the EE and capacity utilization against the current density shows consistently superior battery performance over multiple cell cycling experiments for the BTMAP- Vi/FcNCl cells with M- QCTF, compared to the pH- neutral AORFB with different membranes (Fig. 4e, 4f and Supplementary Table S10).  
+
+This work demonstrates that chloride and fluoride anions traverse the M- QCTF membrane with a very low energy barrier, leading to exceptional flow battery performance. This significant development can be applied more broadly to designing anion exchange membranes for other technologies such as \(\text{CO}_{2}\) electrolytes (28) and ion- capture electrodialysis (29). Although the anion diffusion constants within the developed membranes are approaching the theoretical limit of the bulk electrolyte solution, we expect further improvements in overall conductivity to be achievable by eliminating micropore tortuosity and creating perfectly aligned micropore channels with monodispersed pore size distributions.  
+
+## Declarations  
+
+## Acknowledgments  
+
+This work was funded by the National Key R&D Program of China (2021YFB4000302) and the National Natural Science Foundation of China (Grant/Award No. U20A20127, 52021002). This work was partially carried out at the Instruments Center for Physical Science, University of Science and Technology of China.  
+
+## Competing interests  
+
+The authors declare no competing interests.  
+
+## Data availability  
+
+The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials. Source data are available on reasonable request from the corresponding author.  
+
+## References
+
+<--- Page Split --->
+
+1. D. A. Doyle et al., The structure of the potassium channel: molecular basis of \(\mathsf{K}^{+}\) conduction and selectivity. Science 280, 69 (1998).  
+
+2. H. B. Park et al., Maximizing the right stuff: the trade-off between membrane permeability and selectivity. Science 356, eaab0530 (2017).  
+
+3. Y. J. Lim et al., The coming of age of water channels for separation membranes: from biological to biomimetic to synthetic. Chem. Soc. Rev. 51, 4537-4582 (2022).  
+
+4. B. Radha et al., Molecular transport through capillaries made with atomic-scale precision. Nature 538, 222-225 (2016).  
+
+5. A. Bhardwaj et al., Fabrication of angstrom-scale two-dimensional channels for mass transport. Nat. Protoc. 19, 240-280 (2023).  
+
+6. T. Xiong et al., Neuromorphic functions with a polyelectrolyte-confined fluidic memristor. Science 379, 156-161 (2023).  
+
+7. P. Robin et al., Long-term memory and synapse-like dynamics in two-dimensional nanofluidic channels. Science 379, 161-167 (2023).  
+
+8. N. Kavokine et al., Ionic Coulomb blockade as a fractional Wien effect. Nat. Nanotechnol. 14, 573-578 (2019).  
+
+9. P. Robin et al., Modeling of emergent memory and voltage spiking in ionic transport through angstrom-scale slits. Science 373, 687-691 (2021).  
+
+10. A. Esfandiar et al., Size effect in ion transport through angstrom-scale slits. Science 358, 511-513 (2017).  
+
+11. T. Mouterde et al., Molecular streaming and its voltage control in ángström-scale channels. Nature 567, 87-90 (2019).  
+
+12. F. Chen et al., Inducing electric current in graphene using Ionic flow. Nano Lett. 23, 4464-4470 (2023).  
+
+13. M. J. Baran et al., Diversity-oriented synthesis of polymer membranes with ion solvation cages. Nature 592, 225-231 (2021).  
+
+14. P. Zuo et al., Near-frictionless ion transport within triazine framework membranes. Nature 617, 299-305 (2023).  
+
+15. Y. Zhao et al., Differentiating solutes with precise nanofiltration for next generation environmental separations: a review. Environ. Sci. Technol. 55, 1359-1376 (2021).  
+
+16. S. Goutham et al., Beyond steric selectivity of ions using ángström-scale capillaries. Nat. Nanotechnol. 18, 596-601 (2023).  
+
+17. J. Ma et al., Multivalent ion transport through a nanopore. J. Phys. Chem. C 126, 14661-14668 (2022).  
+
+18. H. Xie et al., A membrane-based seawater electrolyser for hydrogen generation. Nature 612, 673-678 (2022).
+
+<--- Page Split --->
+
+19. G. Karkera et al., A structurally flexible halide solid electrolyte with high ionic conductivity and air processability. Adv. Energy Mater. 13, 2300982 (2023).  
+20. S. Pang et al., Biomimetic amino acid functionalized phenazine flow batteries with long lifetime at near-neutral pH. Angew. Chem. Int. Edit. 60, 5289-5298 (2021).  
+21. W. Song et al., Upscaled production of an ultramicroporous anion-exchange membrane enables long-term operation in electrochemical energy devices. Nat. Commun. 14, 2732 (2023).  
+22. M. E. Carrington et al., Associative pyridinium electrolytes for air-tolerant redox flow batteries. Nature 623, 949-955 (2023).  
+23. P. Xiong et al., A chemistry and microstructure perspective on ion-conducting membranes for redox flow batteries. Angew. Chem. Int. Edit. 60, 24770-24798 (2021).  
+24. B. Hu et al., Long-cycling aqueous organic redox flow battery (AORFB) toward sustainable and safe energy storage. J. Am. Chem. Soc. 139, 1207-1214 (2017).  
+25. J. Luo et al., A π-conjugation extended viologen as a two-electron storage anolyte for total organic aqueous redox flow batteries. Angew. Chem. Int. Edit. 57, 231-235 (2017).  
+26. X. Zhu et al., A superacid-catalyzed synthesis of porous membranes based on triazine frameworks for CO₂ separation. J. Am. Chem. Soc. 134, 10478-10484 (2012).  
+27. H. Li et al., Ultra-microporous anion conductive membranes for crossover-free pH-neutral aqueous organic flow batteries. J. Membr. Sci. 668, 121195 (2023).  
+28. D. A. Salvatore et al., Designing anion exchange membranes for CO₂ electrolysers. Nat. Energy 6, 339-348 (2021).  
+29. A. A. Uliana et al., Ion-capture electrodialysis using multifunctional adsorptive membranes. Science 372, 296-299 (2021).  
+
+## Figures
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+Synthesis and characterization of microporous covalent triazine framework membranes. (a) Left panel: schematic showing the 3D interconnected micropore free volume for anion transport. Right panel: Molecular structure and synthesis of the covalent triazine framework membrane QCTF and subsequent protonation or methylation of the triazine ring skeleton, affording P- QCTF and M- QCTF. Coulombic/steric exclusion and intimate ion- pore wall interactions enable selective and fast anion transport. Red and blue spheres: fixed functional groups or charged triazine rings; green spheres: counterions or charge carrier ions; lightning: ion- pore wall interactions. (b) \(\mathrm{CO_2}\) adsorption isotherms of QCTF, P- QCTF and M- QCTF at 273 K. (c) Pore size distributions of QCTF, P- QCTF and M- QCTF derived from \(\mathrm{CO_2}\) adsorption isotherms through density functional theory (DFT) calculations. (d) XPS (N1s) spectra of covalent triazine framework (CTF) membranes: QCTF (top), protonated QCTF (P- QCTF, middle), and methylated QCTF (M- QCTF, bottom).
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+Ion selectivity and conductivity of microporous covalent triazine framework membranes. (a) Schematic showing the transport of anions across rigid micropores within positively charged covalent triazine framework QCTF membranes. Coulombic/steric exclusion and intimate ion- pore wall interactions enable selective and fast anion transport. Red and blue spheres: fixed functional groups or charged triazine rings; green spheres: counterions or charge carrier ions; blue and gray spheres: positively charged ions with large or small hydrated diameters. The dashed lines indicate ion- pore wall interactions, while the arrowed lines suggest rejection or transport of ions. (b) Current- voltage \((I - V)\) curves of the M- QCTF, P- QCTF, QCTF, Selemion® DSV and Selemion® AMV membranes under a 10- fold concentration gradient in KCl solution. The intercept at \(0\mu \mathrm{A}\) correlates to the transmembrane potential as a result of selective ion transport, from which the transference number \(t\) can then be deduced. The diffusion coefficient of BTMAP- Vi (c) and Cl (d) across QCTF membranes and commercial membranes, as determined from a two- compartment diffusional H- cell. (e) Cl⁻ conductivity plotted as a function of
+
+<--- Page Split --->
+
+hydration number for the M- QCTF, P- QCTF, QCTF, Selenium® DSV and Selenium® AMV membranes. The conductivity was measured via the four- probe EIS method. Each data point represents the Cl⁻ conductivity at an individual temperature: from left to right (or from larger data points to smaller data points), 30–80 °C, with a 10 °C increment. (f) The calculated activation energy for Cl⁻ conduction (Ea) across the M- QCTF, P- QCTF, QCTF, Selenium® DSV and Selenium® AMV membranes, as derived from Arrhenius equations. (g) Comparison on activation energy for QCTF membranes, commercial membranes and those reported previously. The detailed values can be found in Supplementary Table S1.  
+
+![](images/Figure_4.jpg)
+  
+
+![PLACEHOLDER_13_1]
+
+
+<--- Page Split --->
+
+Low barrier anion transport enabled by ion- pore wall interactions under confinement. (a) Charge distributions of QCTF (left), P- QCTF (middle), and M- QCTF (right) from restrained electrostatic potential (RESP). The charge values shown can be found in Supplementary Table S9. (b) Computed free energy map for the transport of Cl- ions within the QCTF (left), P- QCTF (middle) and M- QCTF (right) membrane matrices. The black or white lines denote the Cl- ion transport pathways (1- 1 or 1- 2- 1) with the lowest free energy barrier. (c) Snapshots taken during simulation, demonstrating the interactions between Cl- and the M- QCTF membrane pore walls. Insets denote the specific interactions at positions 1 and 2. The parameters \((r_{1}\) and \(r_{2}\) ) represent the distance between the Cl- ion and the geometric center of two quaternary ammonium (QA) groups. (d) \(^{19}\mathrm{F}\) PFG- NMR spectra recorded for membrane samples of Selenium® DSV, QCTF, P- QCTF and M- QCTF immersed in 0.1 M KF solutions. (e) F- self-diffusion coefficients derived from \(^{19}\mathrm{F}\) PFG- NMR spectra ( \(^{19}\mathrm{F}\) - is used instead of \(^{35}\mathrm{Cl}\) because of its superior NMR sensitivity). Error bars are standard deviations derived from three measurements based on three separate membrane samples.
+
+<--- Page Split --->
+![PLACEHOLDER_15_0]
+
+<center>Figure 4 </center>  
+
+Fast charging of pH- neutral AORFBs enabled by the M- QCTF membrane. (a) Schematic illustration of a pH- neutral BTMAP- Vi/FcNCI AORFB assembled with an M- QCTF membrane. (b) EIS spectra measured in cells assembled with M- QCTF, Selemion® DSV and Selemion® AMV membranes. A control EIS spectrum was recorded in a cell without a membrane. (c) Coulombic efficiency (CE), energy efficiency (EE), and capacity of cells assembled with the M- QCTF membrane at various current densities. (d) Galvanostatic cycling of the BTMAP- Vi/FcNCI cell assembled with the M- QCTF membrane at \(400 \text{mA cm}^{-2}\) . The electrolyte compositions through b to d: the anolyte comprised \(5 \text{mL}\) of \(0.5 \text{M BTMAP-Vi}\) in \(2 \text{M KCl}\) , while the catholyte comprised \(10 \text{mL}\) of \(0.5 \text{M FcNCI}\) in \(2 \text{M KCl}\) . Capacity utilization (e) and energy efficiency (f) of pH- neutral AORFBs assembled with Selemion® DSV and Selemion® AMV, AME 115, PIM- TDQTB, or M- QCTF are plotted as a function of current density. Dashed lines and shades are visual guides. The detailed values can be found in Supplementary Table S10.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- 03supplementarymaterials.docx
+
+<--- Page Split --->

preprint/preprint__0040553aacfe354742b83e1386dd94b013703c55b639bcf87dcd675a88c10bf0/preprint__0040553aacfe354742b83e1386dd94b013703c55b639bcf87dcd675a88c10bf0_det.mmd

@@ -0,0 +1,286 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 919, 206]]<|/det|>
+# Rationally synthesized framework polymer membranes enable high selectivity and barrierless anion conduction  
+
+<|ref|>text<|/ref|><|det|>[[44, 228, 280, 275]]<|/det|>
+Zhengjin Yang yangz.j09@ustc.edu.cn  
+
+<|ref|>text<|/ref|><|det|>[[44, 300, 821, 323]]<|/det|>
+University of Science and Technology of China https://orcid.org/0000- 0002- 0722- 7908  
+
+<|ref|>text<|/ref|><|det|>[[44, 328, 461, 368]]<|/det|>
+Junkai Fang University of Science and Technology of China  
+
+<|ref|>text<|/ref|><|det|>[[44, 373, 821, 415]]<|/det|>
+Guozhen Zhang University of Science and Technology of China https://orcid.org/0000- 0003- 0125- 9666  
+
+<|ref|>text<|/ref|><|det|>[[44, 419, 598, 460]]<|/det|>
+Marc- Antoni Goulet Concordia University https://orcid.org/0000- 0002- 9146- 6759  
+
+<|ref|>text<|/ref|><|det|>[[44, 465, 821, 507]]<|/det|>
+Peipei Zuo University of Science and Technology of China https://orcid.org/0000- 0001- 5043- 7188  
+
+<|ref|>text<|/ref|><|det|>[[44, 512, 461, 552]]<|/det|>
+Hui Li University of Science and Technology of China  
+
+<|ref|>text<|/ref|><|det|>[[44, 558, 821, 600]]<|/det|>
+Jun Jiang University of Science and Technology of China https://orcid.org/0000- 0002- 6116- 5605  
+
+<|ref|>text<|/ref|><|det|>[[44, 604, 565, 645]]<|/det|>
+Michael Guiver Tianjin University https://orcid.org/0000- 0003- 2619- 6809  
+
+<|ref|>text<|/ref|><|det|>[[44, 650, 821, 693]]<|/det|>
+Tongwen Xu University of Science and Technology of China https://orcid.org/0000- 0002- 9221- 5126  
+
+<|ref|>text<|/ref|><|det|>[[44, 735, 102, 752]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 772, 136, 790]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 810, 303, 829]]<|/det|>
+Posted Date: June 11th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 848, 474, 867]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4392718/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 885, 914, 927]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 100, 904, 142]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on April 6th, 2025. See the published version at https://doi.org/10.1038/s41467-025-58638-0.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 158, 68]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[40, 82, 951, 409]]<|/det|>
+AbstractThe understanding gleaned from studying ion transport within the interaction confinement regime enables the near- frictionless transport of cations (e.g., \(\mathrm{Na^{+} / K^{+}}\) ). However, anion transport (e.g., Cl⁻) is suppressed under confinement because of the different polarization of water molecules around cations and anions, also known as the charge asymmetry effect. Here we report the rational synthesis of anion- selective framework polymer membranes having similar densities of subnanometer- sized pores with nearly identical micropore size distributions, which overcome the charge asymmetry effect and promote barrierless anion conduction. We find that anion transport within the micropore free volume elements can be dramatically accelerated by regulating the pore chemistry, which lowers the energy barrier for anion transport, leading to an almost twofold increase in Cl⁻ conductivity and barrierless F⁻ diffusion. The resultant membrane enables an aqueous organic redox flow battery that utilizes Cl⁻ ions as charge carriers to operate at extreme current densities and delivers competitive performance to counterparts where K⁺ ions are charge carriers. These results may benefit broadly electrochemical devices and inspire single- species selectivity with separation membranes that exploit controlled or chemically gated ion/molecule transport.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 431, 175, 456]]<|/det|>
+## Main Text  
+
+<|ref|>text<|/ref|><|det|>[[42, 470, 945, 584]]<|/det|>
+Replicating the extreme selectivity and high permeability of biological ion channels is an enduring challenge for membrane scientists (1- 3). Beyond the generally- accepted mechanisms of size exclusion and Coulombic repulsion, it is argued that the subtle interactions between ions and channel walls at atomic- scale confinement play a crucial role. These interactions were not clearly elucidated until the fabrication of angstrom- scale slits/capillaries/channels with atomic- scale precision (4, 5).  
+
+<|ref|>text<|/ref|><|det|>[[40, 598, 955, 905]]<|/det|>
+The spatial confinement of ion transport down to molecular- sized ion channels magnifies the impact of channel wall interactions and gives rise to exotic transport behavior. For example, hysteretic ion conduction occurs, resulting in an ion memory effect (6, 7), while the formation of Bjerrum ion pairs causes ionic Coulombic blockade (8). These atypical ion motions are intimately related to the dramatically enhanced material- dependent interactions between hydrated ions and the confining channel walls (e.g., electrostatic, adsorption/desorption) (9). For chemically inert and atomically smooth graphite channel walls, \(\mathrm{K^{+}}\) demonstrates a mobility close to that of the value in bulk solutions (10). By applying a voltage bias on the graphite channel, the streaming mobility of \(\mathrm{K^{+}}\) is increased by up to 20 times (11) and this may be ascribed to the electronic structure change under an external voltage bias (12). It has also been demonstrated that by introducing \(\mathrm{Li^{+}}\) - coordinating functionality within the shape- persistent free volume elements of microporous polymer membranes, \(\mathrm{Li^{+}}\) diffusivity can be greatly enhanced (13). Similar improvements to \(\mathrm{Na^{+}}\) transport have also been achieved by exploiting the synergy between micropore confinement and ion- membrane interactions (14).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 44, 953, 333]]<|/det|>
+Despite the considerable improvements in cation transport due to the confinement effect, it is notable that chloride \((\mathsf{Cl}^{- })\) mobility experiences significant suppression under confinement. This charge asymmetry is likely due to the slightly different hydration shell configurations between \(\mathsf{Cl}^{- }\) and \(\mathsf{K}^{+}(10)\) . The mobility of \(\mathsf{Cl}^{- }\) under confinement is three times less than that of \(\mathsf{K}^{+}\) , even though \(\mathsf{Cl}^{- }\) and \(\mathsf{K}^{+}\) have similar mobilities in bulk water \((7.58\times 10^{- 8}\mathrm{vs.}7.86\times 10^{- 8}\mathrm{m}^{2}\mathrm{V}^{- 1}\mathrm{s}^{- 1})\) and hydrated diameters \((6.64\mathring{\mathrm{A}}\mathrm{vs.}\) 6.62 Å) (15, 16). For a more extreme case, \(\mathsf{Cs}^{+}\) and \(\mathsf{Cl}^{- }\) exhibit similar ion- core sizes and hydrated diameters, but \(\mathsf{Cl}^{- }\) exhibits more than three times lower mobility under \(\mathring{\mathrm{A}}\) - scale confinement \((1.7\times 10^{- 8}\) vs. \(6.0\times 10^{- 8}\mathrm{m}^{2}\mathrm{V}^{- 1}\mathrm{s}^{- 1})\) (16). For chloride salts of high valency cations, the overall \(\mathsf{Cl}^{- }\) mobility decreases to almost zero in single- digit- sized nanopores (17). A decrease in the mobility of other anions under confinement has also been observed (16). This phenomenon is echoed by the relatively high energy barrier associated with anion exchange membranes that transport chloride ions (see Supplementary Table S1).  
+
+<|ref|>text<|/ref|><|det|>[[38, 344, 951, 965]]<|/det|>
+The transport and selectivity of anions are of critical relevance to applications such as direct seawater electrolysis (18), solid- state batteries (19) and redox flow batteries (20- 25). Understanding and overcoming the charge asymmetry effect for anion transport under confinement is therefore essential for enabling these technologies. Here we report the design and synthesis of a series of positively charged (quaternary ammonium cations) covalent triazine framework (QCTF) membranes with nearly the same density of rigid micropores with almost identical pore size distributions. The QCTF membranes exhibit Coulombic repulsion- induced anion selectivity, with a chloride transference number \(t_{- }\) of 0.95, and size exclusion- induced rejection of BTMAP- Vi (bis(3- trimethylammonio) propyl viologen tetrachloride) and FcNCl ((ferrocenylmethyl) trimethylammonium chloride), redox- active organic flow battery electrolytes. The cross- membrane BTMAP- Vi diffusion coefficient at \(3.1\times 10^{- 11}\mathrm{cm}^{2}\mathrm{s}^{- 1}\) is over 20 times lower than that of commercial membranes. We demonstrate that through on- membrane modification, the charge distribution of the pristine QCTF membrane framework can be regulated by protonation (affording P- QCTF) and methylation (affording M- QCTF), which dramatically alters the interactions between anions and the membrane framework and helps lower the energy barrier for anion transport. The cross- membrane \(\mathsf{Cl}^{- }\) conductivity increased twofold from \(13.2\mathrm{mScm}^{- 1}\) for QCTF to 25.9 \(\mathrm{mScm}^{- 1}\) for M- QCTF at \(30^{\circ}\mathrm{C}\) , and the activation energy for \(\mathsf{Cl}^{- }\) conduction decreased from \(20.6\mathrm{kJmol}^{- 1}\) to \(13.1\mathrm{kJmol}^{- 1}\) , lower than any value reported in the literature (see Supplementary Table S1). \(^{19}\mathrm{F}\) PFG- NMR revealed an increase in the \(\mathrm{F}^{- }\) diffusion coefficient from \(0.63\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for QCTF and \(0.93\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for P- QCTF, to \(1.1\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for M- QCTF which is close to the value in bulk water \((1.2\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1})\) . The greater anion conductivity can dramatically improve device performance as exemplified here in an BTMAP- Vi- and FcNCl- based aqueous organic redox flow battery (AORFB) in pH- neutral solutions. The BTMAP- Vi/FcNCl cell configured with the M- QCTF membrane exhibited a high- frequency area- specific resistance (ASR) as low as \(0.23\Omega \cdot \mathrm{cm}^{2}\) , which enabled charging and discharging of the BTMAP- Vi/FcNCl cell at an extreme current density of \(500\mathrm{mAcm}^{- 2}\) . The prolonged galvanostatic cell cycling at \(400\mathrm{mAcm}^{- 2}\) maintained a Coulombic efficiency of \(>99\%\) and a stable energy efficiency of around \(60\%\) over the course of 1000 cycles. Notably, the achieved capacity utilization and efficiency with
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 46, 953, 181]]<|/det|>
+M- QCTF approaches similar values to those of alkaline AORFBs that leverage \(\mathsf{K}^{+}\) as charge- carrying ions, while in otherwise identical cells assembled with QCTF or P- QCTF, an almost \(20\%\) lower energy efficiency was observed. This is significant and can be attributed to a dramatic reduction in the contribution of membrane resistance to whole- cell resistance, e.g., from \(>70\%\) for the Seleminon \(^{\circledR}\) AMV membrane to \(\sim\) \(25\%\) for M- QCTF (Supplementary Tables S2 and S3). The above results imply a breakthrough in the charge asymmetry effect.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 203, 350, 229]]<|/det|>
+## Results and Discussion  
+
+<|ref|>sub_title<|/ref|><|det|>[[43, 242, 936, 304]]<|/det|>
+## Covalent triazine framework membranes with tunable pore chemistry  
+
+<|ref|>text<|/ref|><|det|>[[40, 319, 951, 591]]<|/det|>
+Covalent triazine framework chemistry gives rise to a wide variety of microporous materials and offers enormous diversity in pore chemistry. We thus synthesized a stand- alone triazine framework membrane from \(4,4^{'}\) - biphenyldicarbonitrile and a derivative of 3- hydroxy- [1,1'- biphenyl]- 4,4'- dicarbonitrile bearing a quaternary ammonium moiety via a superacid- catalyzed organic sol- gel procedure (Fig. 1a and Supplementary Figures S1- S4) (26). The process yields a free- standing membrane (namely, QCTF) with a Young's modulus and tensile strength of 0.91 GPa and 32.0 MPa, respectively (Supplementary Figure S5). The skeletal triazine rings of QCTF were subsequently protonated with HCl or methylated with \(\mathrm{CH}_3\mathrm{I}\) , affording P- QCTF and M- QCTF, respectively. Overall, we constructed three covalent triazine framework polymers with similar molecular configurations and pore structures that can be processed into hydrophilic, uniform and robust ion- selective membranes via an organo- sol- gel procedure (Supplementary Figures S6- S8, Supplementary Table S4), but with slightly different and deliberately tailored pore chemistries.  
+
+<|ref|>text<|/ref|><|det|>[[40, 608, 953, 846]]<|/det|>
+Carbon dioxide \(\mathrm{CO_2}\) ) adsorption experiments and molecular simulations were conducted to probe the micropore structure of the covalent triazine framework polymers. \(\mathrm{CO_2}\) sorption isotherms measured at 273 K revealed that powder samples of QCTF, P- QCTF, and M- QCTF had similar \(\mathrm{CO_2}\) uptake capacities of 16, 15.2, and \(14.7\mathrm{cm}^3\mathrm{g}^{- 1}\) STP, respectively (Fig. 1b). Notably, QCTF, P- QCTF, and M- QCTF exhibit almost identical pore size distributions, ranging from 0.3 nm to 0.9 nm, as derived from \(\mathrm{CO_2}\) adsorption isotherms based on density functional theory (DFT) calculations (Fig. 1c). These experimental results are further supported by molecular simulations of the 3D framework structure and the computation of \(\mathrm{CO_2}\) distributions within the framework structures (Supplementary Figures S9 and S10). This again indicates that QCTF, P- QCTF, and M- QCTF have similar framework structures, interconnected micropores and pore size distributions.  
+
+<|ref|>text<|/ref|><|det|>[[41, 863, 951, 957]]<|/det|>
+The amount of charged functional groups (quaternary ammonium groups) within the pristine QCTF membrane, characterized by the ion exchange capacity (IEC, in mmol \(\mathrm{g}^{- 1}\) ), is \(1.20\mathrm{mmol}\mathrm{g}^{- 1}\) for QCTF (as- designed IEC value is \(\sim 1.00\mathrm{mmol}\mathrm{g}^{- 1}\) ). During protonation, approximately \(55\%\) of the triazine rings were protonated and the same amount of triazine rings was methylated after methylation, as revealed by
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 947, 112]]<|/det|>
+X- ray photoelectron spectroscopy (XPS, Fig. 1d). This suggests that P- QCTF and M- QCTF should have identical IEC values, which was confirmed by titration and zeta potential measurements (Supplementary Figure S11).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 141, 417, 168]]<|/det|>
+## Ion Transport and Selectivity  
+
+<|ref|>text<|/ref|><|det|>[[41, 183, 955, 433]]<|/det|>
+Despite the similar framework structure and almost identical pore size/size distributions, our experimental results reflect that cross- membrane ion transport is significantly affected by pore chemistry. We speculate that the difference is synergistically determined by Coulombic/steric effects and specific ion- pore wall interactions, as shown in Fig. 2a. The current- voltage (I- V) curves across the membranes, as measured in a two- compartment diffusional H- cell under a 10- fold concentration gradient KCl solution (Fig. 2b), reveal a net anion flux, indicating anion selectivity. The anion transference number (t.) calculated for QCTF is 0.940, while the values for protonated QCTF (P- QCTF) and methylated QCTF (M- QCTF) are 0.947 and 0.953, respectively (Supplementary Figure S12). These values suggest the superior anion selectivity of the QCTF membranes compared to that of commercial anion exchange membranes (AEMs). This result is reasonable considering the Coulombic repulsion of the \(< 1\) nm pore channel within the QCTF membranes.  
+
+<|ref|>text<|/ref|><|det|>[[40, 449, 949, 836]]<|/det|>
+The measured transference numbers align with the cross- membrane permeation/diffusion rates for BTMAP- Vi (a redox- active organic cation) and Cl- (Fig. 2c and 2d, Supplementary Figures S13- S15, Supplementary Tables S5- S6), which are dramatically different in size. Compared with commercial AEMs (Fig. 2c), all the QCTF membranes exhibited superior blocking capabilities toward BTMAP- Vi. The diffusion coefficients of BTMAP- Vi across the QCTF and the P- QCTF were determined to be \(4.5 \times 10^{- 11} \text{cm}^2 \text{s}^{- 1}\) and \(3.4 \times 10^{- 11} \text{cm}^2 \text{s}^{- 2}\) , respectively. These values are at least one order of magnitude smaller than those of commercial AEMs. Note that the value further decreases to \(3.1 \times 10^{- 11} \text{cm}^2 \text{s}^{- 1}\) for M- QCTF, a value that is over 20 times smaller than that of Selemon® DSV. The diffusion coefficients of Cl- through the QCTF and P- QCTF are \(1.8 \times 10^{- 7} \text{cm}^2 \text{s}^{- 1}\) and \(2.6 \times 10^{- 7} \text{cm}^2 \text{s}^{- 2}\) , respectively. By contrast, commercial anion- selective membranes demonstrated Cl- diffusion coefficients at least one order of magnitude smaller than those of QCTF membranes. Surprisingly, the Cl- diffusion coefficient measured for M- QCTF reached \(3.0 \times 10^{- 7} \text{cm}^2 \text{s}^{- 1}\) , which is nearly 2 times that for the QCTF membrane (Fig. 2d). A comparison of the Cl- diffusion coefficients and the Cl- /BTMAP- Vi selectivity for QCTF membranes, commercial AEMs and previously reported membranes implies that these framework membranes can simultaneously deliver fast ion permeation and high selectivity, overcoming the usual tradeoff observed for many ion exchange membranes (Supplementary Figure S16 and Supplementary Table S6).  
+
+<|ref|>text<|/ref|><|det|>[[42, 853, 943, 947]]<|/det|>
+The fast Cl- transport across the triazine framework membranes is further supported by the membrane conductivity measurements. Compared with commercial AEMs, triazine framework membranes show high Cl- conductivity at relatively low hydration numbers (Fig. 2e, Supplementary Figure S17 and Supplementary Tables S7- S8). The Cl- conductivity of QCTF, as measured by four- point electrochemical
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 44, 951, 317]]<|/det|>
+impedance spectroscopy (EIS), is \(13.2 \mathrm{mS cm}^{- 1}\) at \(30.0^{\circ}\mathrm{C}\) and approaches \(42.0 \mathrm{mS cm}^{- 1}\) at \(80^{\circ}\mathrm{C}\) at low hydration numbers (3.5 at \(30^{\circ}\mathrm{C}\) , 4.4 at \(80^{\circ}\mathrm{C}\) ). In comparison, the \(\mathrm{Cl}^{- }\) conductivity of P- QCTF is \(20.0 \mathrm{mS cm}^{- 1}\) at \(30^{\circ}\mathrm{C}\) and increases to \(48.4 \mathrm{mS cm}^{- 1}\) at \(80^{\circ}\mathrm{C}\) . We find that the \(\mathrm{Cl}^{- }\) conductivity of M- QCTF is \(26.0\) at \(30.0^{\circ}\mathrm{C}\) , which is nearly twice that of QCTF, and reaches \(53.0 \mathrm{mS cm}^{- 1}\) at \(80^{\circ}\mathrm{C}\) . The activation energy \((E_{a})\) for \(\mathrm{Cl}^{- }\) conduction across the QCTF membrane is \(20.6 \mathrm{kJ mol}^{- 1}\) , as derived from the conductivities at various temperatures (Fig. 2f and Supplementary Figure S18), contrasting an \(E_{a}\) of \(12.9 \mathrm{kJ mol}^{- 1}\) for \(\mathrm{K}^{+}\) transport across an otherwise identical membrane with sulfonate functional groups (ref 14). Surprisingly, the \(E_{a}\) value for M- QCTF is as low as \(13.1 \mathrm{kJ mol}^{- 1}\) , which is nearly half that of QCTF and lower than any value reported in the literature (Fig. 2g and Supplementary Table S1). Considering the similar framework structure and almost identical pore size/size distributions, this significant result indicates that the methylation of triazine rings alters the transport energy barrier for \(\mathrm{Cl}^{- }\) ions.  
+
+<|ref|>text<|/ref|><|det|>[[39, 333, 950, 808]]<|/det|>
+Due to the aforementioned results, we conclude that electrostatic interactions alone cannot explain the differences in \(\mathrm{Cl}^{- }\) diffusion coefficients, \(\mathrm{Cl}^{- }\) conductivity or activation energy for cross- membrane \(\mathrm{Cl}^{- }\) transport. To unravel why methylation of the triazine ring promotes fast \(\mathrm{Cl}^{- }\) conduction, compared to the protonated triazine ring in P- QCTF and the charge- neutral triazine ring in QCTF, the charge distribution and the \(\mathrm{Cl}^{- }\) transport routes within the matrix of the triazine framework membranes were portrayed based on molecular simulations, and the two- dimensional free- energy landscapes were computed according to current methodology (13, 14). Our calculations show that the charge distributions of triazine framework membranes vary dramatically after protonation and methylation (Fig. 3a, Supplementary Figure S19). The most even charge distribution is observed for M- QCTF. We speculate that the variation in charge distribution alters the interactions between anions and the membrane frameworks and helps establish low- energy- barrier pathways for anion transport. This is supported by free energy calculations for \(\mathrm{Cl}^{- }\) conduction (Fig. 3b). The simulation results showed that \(\mathrm{Cl}^{- }\) can interact with quaternary ammonium (QA) groups (Fig. 3c, Supplementary Figures S20 and S21) and lower the free energy, but an energy barrier must be overcome for \(\mathrm{Cl}^{- }\) ions to approach adjacent QA groups. The energy barrier for \(\mathrm{Cl}^{- }\) conduction is the highest for QCTF (Fig. 3b, left panel) and decreases when the triazine ring is protonated (Fig. 3b, middle panel), while methylation of the triazine ring in M- QCTF improves the diffusivity of \(\mathrm{Cl}^{- }\) within the framework and creates a \(\mathrm{Cl}^{- }\) diffusion pathway with the lowest energy barrier (Fig. 3b, right panel). We suspect that the synergy of electrostatic interactions between \(\mathrm{Cl}^{- }\) and the methylated triazine ring and the change in electron density along the \(\mathrm{Cl}^{- }\) diffusion path after methylation may account for the emergence of the low- energy- barrier diffusion pathway.  
+
+<|ref|>text<|/ref|><|det|>[[41, 824, 955, 943]]<|/det|>
+Molecular simulation results are further supported by measurements of transmembrane \(\mathrm{F}^{- }\) diffusion coefficients via \(^{19}\mathrm{F}\) pulsed- field gradient- stimulated- echo nuclear magnetic resonance ( \(^{19}\mathrm{F}\) PFG- NMR; \(^{19}\mathrm{F}\) was selected owing to its higher sensitivity compared with \(^{35}\mathrm{Cl}\) ). \(^{19}\mathrm{F}\) PFG- NMR revealed two separate \(\mathrm{F}^{- }\) signals for Selenium® DSV and Selenium® AMV membranes (Fig. 3d and Supplementary Figure S22), with the upfield signal corresponding to free \(\mathrm{F}^{- }\) in water (located at the same position as that in 0.1 M KF
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 46, 940, 350]]<|/det|>
+aqueous solution) and the downfield signal corresponding to associated \(\mathsf{F}^{- }\) within the membrane. In contrast, only the upfield signal was observed for all three triazine framework membranes (Fig. 3d), which is an indication of freely exchangeable \(\mathsf{F}^{- }\) within the membrane, with slight variations in the \(^{19}\mathsf{F}\) chemical shifts. By fitting the echo profiles with the Stejskal- Tanner equation (Supplementary Figure S23), the derived \(\mathsf{F}^{- }\) diffusion coefficients within the P- QCTF and QCTF are \(0.93\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) and \(0.63\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) , respectively (Fig. 3e). The value reaches \(1.1\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) for M- QCTF, almost a twofold increase compared to that for QCTF. Notably, this value is 12.8 times that of Selemion® AMV and 10.8 times that of Selemion® DSV (Fig. 3e and Supplementary Figure S23) and approaches the measured diffusion coefficient of \(\mathsf{F}^{- }\) in water \((1.2\times 10^{- 9}\mathrm{m}^{2}\mathrm{s}^{- 1}\) ; Supplementary Figure S23). In summary, by tailoring the pore chemistry of framework membranes, intimate ion- pore wall interactions provide a low- energy- barrier diffusion pathway for anions. Taken together with the Coulombic/steric exclusion by the charged framework micropores, the triazine framework membranes, particularly M- QCTF, will be of interest in applications demanding extremely fast and highly selective transport of anions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 377, 844, 408]]<|/det|>
+## Triazine framework membrane powers fast-charging AORFBs  
+
+<|ref|>text<|/ref|><|det|>[[39, 420, 951, 795]]<|/det|>
+The extremely fast and highly selective anion (particularly chloride ions) conduction through chemically tuned triazine framework membranes is desirable in electrochemical devices, such as aqueous organic redox flow batteries. As a proof of concept, we configured pH- neutral AORFBs with BTMAP- Vi/FcNCl as the redox- active organic electrolyte couple and triazine framework membranes as the ion- conducting membranes, while \(\mathsf{Cl}^{- }\) ions were transported back and forth as charge carriers (Fig. 4a). At an electrolyte concentration of 0.1 M, EIS of the BTMAP- Vi/FcNCl cells assembled with QCTF or P- QCTF showed area- specific membrane resistances (ASRs) of \(0.63\Omega \mathrm{cm}^{2}\) and \(0.53\Omega \mathrm{cm}^{2}\) , respectively (Supplementary Figures S24- S25). An otherwise identical cell assembled with M- QCTF showed an ASR of \(0.37\Omega \mathrm{cm}^{2}\) (Supplementary Figure S26), which is almost twofold lower than that of the QCTF membrane. This finding aligns with the high conductivity of M- QCTF (Fig. 2e, 3b), which enables charging of the BTMAP- Vi/FcNCl cells at extreme current densities. For example, at \(200\mathrm{mAcm}^{- 2}\) , BTMAP- Vi/FcNCl with M- QCTF exhibited an energy efficiency (EE) of over \(60\%\) (Supplementary Figure S26). In contrast, the control BTMAP- Vi/FcNCl cells assembled with Selemion® DSV or Selemion® AMV could not operate at this current density due to the immediate voltage cutoff. At lower current densities ranging from 20 to 80 mA cm \(^{- 2}\) , the reported energy efficiency for the control cells drops from 89.4- 65.9% for Selemion® DSV or from 80.0- 26.6% for Selemion® AMV (27).  
+
+<|ref|>text<|/ref|><|det|>[[41, 810, 951, 950]]<|/det|>
+At a higher electrolyte concentration of \(0.5\mathrm{M}\) , BTMAP- Vi/FcNCl with M- QCTF demonstrated an even lower ASR of \(0.23\Omega \mathrm{cm}^{2}\) (Fig. 4b), a much lower value than that for Selemion® DSV or Selemion® AMV. The rate performance of the cell reveals an EE of \(49.7\%\) and a capacity utilization of \(58.8\%\) at an extreme current density of \(500\mathrm{mAcm}^{- 2}\) (Fig. 4c). Compared with the most recent report of an AEM (MTCP- 50 membrane, with the optimal ratio 1:1 of \(m\) - terphenyl to \(p\) - terphenyl) for pH- neutral AORFBs at \(0.5\mathrm{M}\) (21), M- QCTF achieved a much greater energy efficiency ( \(76.9\%\) vs. \(60.1\%\) ) and capacity utilization ( \(94.3\%\) vs.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 46, 940, 161]]<|/det|>
+\(63.7\%)\) at the same current density of \(200 \text{mA cm}^{- 2}\) . Notably, alkaline AORFBs that utilize \(\text{K}^{+}\) as charge- carrying ions assembled with a cation exchange membrane (SCTF- BP), which allows cation diffusion close to the value in bulk electrolyte, exhibit an EE of \(50.4\%\) and a capacity utilization of \(62\%\) at \(500 \text{mA cm}^{- 2}\) . The current results demonstrate a similar efficiency for \(\text{Cl}^{- }\) transport and therefore suggest a breakthrough in the charge asymmetry effect.  
+
+<|ref|>text<|/ref|><|det|>[[42, 178, 952, 316]]<|/det|>
+Robust and exceptional cell performance was observed during long- term galvanostatic cycling of over 2000 cycles at \(200 \text{mA cm}^{- 2}\) (0.1 M electrolyte concentration, Supplementary Figure S26) and over 1000 cycles at \(400 \text{mA cm}^{- 2}\) (0.5 M electrolyte concentration, Fig. 4d). Comparisons of the EE and capacity utilization against the current density shows consistently superior battery performance over multiple cell cycling experiments for the BTMAP- Vi/FcNCl cells with M- QCTF, compared to the pH- neutral AORFB with different membranes (Fig. 4e, 4f and Supplementary Table S10).  
+
+<|ref|>text<|/ref|><|det|>[[42, 332, 950, 494]]<|/det|>
+This work demonstrates that chloride and fluoride anions traverse the M- QCTF membrane with a very low energy barrier, leading to exceptional flow battery performance. This significant development can be applied more broadly to designing anion exchange membranes for other technologies such as \(\text{CO}_{2}\) electrolytes (28) and ion- capture electrodialysis (29). Although the anion diffusion constants within the developed membranes are approaching the theoretical limit of the bulk electrolyte solution, we expect further improvements in overall conductivity to be achievable by eliminating micropore tortuosity and creating perfectly aligned micropore channels with monodispersed pore size distributions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 516, 210, 542]]<|/det|>
+## Declarations  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 556, 208, 575]]<|/det|>
+## Acknowledgments  
+
+<|ref|>text<|/ref|><|det|>[[42, 593, 943, 682]]<|/det|>
+This work was funded by the National Key R&D Program of China (2021YFB4000302) and the National Natural Science Foundation of China (Grant/Award No. U20A20127, 52021002). This work was partially carried out at the Instruments Center for Physical Science, University of Science and Technology of China.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 700, 222, 719]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[45, 738, 428, 757]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 775, 183, 794]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[44, 813, 920, 879]]<|/det|>
+The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials. Source data are available on reasonable request from the corresponding author.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 902, 193, 927]]<|/det|>
+## References
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 46, 930, 93]]<|/det|>
+1. D. A. Doyle et al., The structure of the potassium channel: molecular basis of \(\mathsf{K}^{+}\) conduction and selectivity. Science 280, 69 (1998).  
+
+<|ref|>text<|/ref|><|det|>[[56, 97, 901, 140]]<|/det|>
+2. H. B. Park et al., Maximizing the right stuff: the trade-off between membrane permeability and selectivity. Science 356, eaab0530 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[56, 146, 936, 190]]<|/det|>
+3. Y. J. Lim et al., The coming of age of water channels for separation membranes: from biological to biomimetic to synthetic. Chem. Soc. Rev. 51, 4537-4582 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[56, 195, 930, 238]]<|/det|>
+4. B. Radha et al., Molecular transport through capillaries made with atomic-scale precision. Nature 538, 222-225 (2016).  
+
+<|ref|>text<|/ref|><|det|>[[56, 244, 950, 287]]<|/det|>
+5. A. Bhardwaj et al., Fabrication of angstrom-scale two-dimensional channels for mass transport. Nat. Protoc. 19, 240-280 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[56, 293, 928, 336]]<|/det|>
+6. T. Xiong et al., Neuromorphic functions with a polyelectrolyte-confined fluidic memristor. Science 379, 156-161 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[56, 342, 890, 386]]<|/det|>
+7. P. Robin et al., Long-term memory and synapse-like dynamics in two-dimensional nanofluidic channels. Science 379, 161-167 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[56, 391, 930, 434]]<|/det|>
+8. N. Kavokine et al., Ionic Coulomb blockade as a fractional Wien effect. Nat. Nanotechnol. 14, 573-578 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[56, 440, 880, 484]]<|/det|>
+9. P. Robin et al., Modeling of emergent memory and voltage spiking in ionic transport through angstrom-scale slits. Science 373, 687-691 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[50, 489, 930, 532]]<|/det|>
+10. A. Esfandiar et al., Size effect in ion transport through angstrom-scale slits. Science 358, 511-513 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[50, 538, 936, 582]]<|/det|>
+11. T. Mouterde et al., Molecular streaming and its voltage control in ángström-scale channels. Nature 567, 87-90 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[50, 587, 896, 630]]<|/det|>
+12. F. Chen et al., Inducing electric current in graphene using Ionic flow. Nano Lett. 23, 4464-4470 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[50, 636, 907, 680]]<|/det|>
+13. M. J. Baran et al., Diversity-oriented synthesis of polymer membranes with ion solvation cages. Nature 592, 225-231 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[50, 685, 940, 729]]<|/det|>
+14. P. Zuo et al., Near-frictionless ion transport within triazine framework membranes. Nature 617, 299-305 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[50, 735, 930, 779]]<|/det|>
+15. Y. Zhao et al., Differentiating solutes with precise nanofiltration for next generation environmental separations: a review. Environ. Sci. Technol. 55, 1359-1376 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[50, 785, 852, 828]]<|/det|>
+16. S. Goutham et al., Beyond steric selectivity of ions using ángström-scale capillaries. Nat. Nanotechnol. 18, 596-601 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[50, 834, 900, 877]]<|/det|>
+17. J. Ma et al., Multivalent ion transport through a nanopore. J. Phys. Chem. C 126, 14661-14668 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[50, 883, 951, 927]]<|/det|>
+18. H. Xie et al., A membrane-based seawater electrolyser for hydrogen generation. Nature 612, 673-678 (2022).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[45, 45, 930, 590]]<|/det|>
+19. G. Karkera et al., A structurally flexible halide solid electrolyte with high ionic conductivity and air processability. Adv. Energy Mater. 13, 2300982 (2023).  
+20. S. Pang et al., Biomimetic amino acid functionalized phenazine flow batteries with long lifetime at near-neutral pH. Angew. Chem. Int. Edit. 60, 5289-5298 (2021).  
+21. W. Song et al., Upscaled production of an ultramicroporous anion-exchange membrane enables long-term operation in electrochemical energy devices. Nat. Commun. 14, 2732 (2023).  
+22. M. E. Carrington et al., Associative pyridinium electrolytes for air-tolerant redox flow batteries. Nature 623, 949-955 (2023).  
+23. P. Xiong et al., A chemistry and microstructure perspective on ion-conducting membranes for redox flow batteries. Angew. Chem. Int. Edit. 60, 24770-24798 (2021).  
+24. B. Hu et al., Long-cycling aqueous organic redox flow battery (AORFB) toward sustainable and safe energy storage. J. Am. Chem. Soc. 139, 1207-1214 (2017).  
+25. J. Luo et al., A π-conjugation extended viologen as a two-electron storage anolyte for total organic aqueous redox flow batteries. Angew. Chem. Int. Edit. 57, 231-235 (2017).  
+26. X. Zhu et al., A superacid-catalyzed synthesis of porous membranes based on triazine frameworks for CO₂ separation. J. Am. Chem. Soc. 134, 10478-10484 (2012).  
+27. H. Li et al., Ultra-microporous anion conductive membranes for crossover-free pH-neutral aqueous organic flow batteries. J. Membr. Sci. 668, 121195 (2023).  
+28. D. A. Salvatore et al., Designing anion exchange membranes for CO₂ electrolysers. Nat. Energy 6, 339-348 (2021).  
+29. A. A. Uliana et al., Ion-capture electrodialysis using multifunctional adsorptive membranes. Science 372, 296-299 (2021).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 607, 143, 633]]<|/det|>
+## Figures
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[48, 50, 945, 450]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[43, 473, 115, 492]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[39, 513, 944, 767]]<|/det|>
+Synthesis and characterization of microporous covalent triazine framework membranes. (a) Left panel: schematic showing the 3D interconnected micropore free volume for anion transport. Right panel: Molecular structure and synthesis of the covalent triazine framework membrane QCTF and subsequent protonation or methylation of the triazine ring skeleton, affording P- QCTF and M- QCTF. Coulombic/steric exclusion and intimate ion- pore wall interactions enable selective and fast anion transport. Red and blue spheres: fixed functional groups or charged triazine rings; green spheres: counterions or charge carrier ions; lightning: ion- pore wall interactions. (b) \(\mathrm{CO_2}\) adsorption isotherms of QCTF, P- QCTF and M- QCTF at 273 K. (c) Pore size distributions of QCTF, P- QCTF and M- QCTF derived from \(\mathrm{CO_2}\) adsorption isotherms through density functional theory (DFT) calculations. (d) XPS (N1s) spectra of covalent triazine framework (CTF) membranes: QCTF (top), protonated QCTF (P- QCTF, middle), and methylated QCTF (M- QCTF, bottom).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[45, 45, 950, 610]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 625, 118, 645]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[39, 666, 944, 947]]<|/det|>
+Ion selectivity and conductivity of microporous covalent triazine framework membranes. (a) Schematic showing the transport of anions across rigid micropores within positively charged covalent triazine framework QCTF membranes. Coulombic/steric exclusion and intimate ion- pore wall interactions enable selective and fast anion transport. Red and blue spheres: fixed functional groups or charged triazine rings; green spheres: counterions or charge carrier ions; blue and gray spheres: positively charged ions with large or small hydrated diameters. The dashed lines indicate ion- pore wall interactions, while the arrowed lines suggest rejection or transport of ions. (b) Current- voltage \((I - V)\) curves of the M- QCTF, P- QCTF, QCTF, Selemion® DSV and Selemion® AMV membranes under a 10- fold concentration gradient in KCl solution. The intercept at \(0\mu \mathrm{A}\) correlates to the transmembrane potential as a result of selective ion transport, from which the transference number \(t\) can then be deduced. The diffusion coefficient of BTMAP- Vi (c) and Cl (d) across QCTF membranes and commercial membranes, as determined from a two- compartment diffusional H- cell. (e) Cl⁻ conductivity plotted as a function of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 45, 949, 207]]<|/det|>
+hydration number for the M- QCTF, P- QCTF, QCTF, Selenium® DSV and Selenium® AMV membranes. The conductivity was measured via the four- probe EIS method. Each data point represents the Cl⁻ conductivity at an individual temperature: from left to right (or from larger data points to smaller data points), 30–80 °C, with a 10 °C increment. (f) The calculated activation energy for Cl⁻ conduction (Ea) across the M- QCTF, P- QCTF, QCTF, Selenium® DSV and Selenium® AMV membranes, as derived from Arrhenius equations. (g) Comparison on activation energy for QCTF membranes, commercial membranes and those reported previously. The detailed values can be found in Supplementary Table S1.  
+
+<|ref|>image<|/ref|><|det|>[[70, 214, 884, 680]]<|/det|>  
+
+<|ref|>image<|/ref|><|det|>[[70, 707, 884, 940]]<|/det|>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 85, 944, 395]]<|/det|>
+Low barrier anion transport enabled by ion- pore wall interactions under confinement. (a) Charge distributions of QCTF (left), P- QCTF (middle), and M- QCTF (right) from restrained electrostatic potential (RESP). The charge values shown can be found in Supplementary Table S9. (b) Computed free energy map for the transport of Cl- ions within the QCTF (left), P- QCTF (middle) and M- QCTF (right) membrane matrices. The black or white lines denote the Cl- ion transport pathways (1- 1 or 1- 2- 1) with the lowest free energy barrier. (c) Snapshots taken during simulation, demonstrating the interactions between Cl- and the M- QCTF membrane pore walls. Insets denote the specific interactions at positions 1 and 2. The parameters \((r_{1}\) and \(r_{2}\) ) represent the distance between the Cl- ion and the geometric center of two quaternary ammonium (QA) groups. (d) \(^{19}\mathrm{F}\) PFG- NMR spectra recorded for membrane samples of Selenium® DSV, QCTF, P- QCTF and M- QCTF immersed in 0.1 M KF solutions. (e) F- self-diffusion coefficients derived from \(^{19}\mathrm{F}\) PFG- NMR spectra ( \(^{19}\mathrm{F}\) - is used instead of \(^{35}\mathrm{Cl}\) because of its superior NMR sensitivity). Error bars are standard deviations derived from three measurements based on three separate membrane samples.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[45, 45, 953, 640]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 655, 118, 674]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[40, 695, 955, 947]]<|/det|>
+Fast charging of pH- neutral AORFBs enabled by the M- QCTF membrane. (a) Schematic illustration of a pH- neutral BTMAP- Vi/FcNCI AORFB assembled with an M- QCTF membrane. (b) EIS spectra measured in cells assembled with M- QCTF, Selemion® DSV and Selemion® AMV membranes. A control EIS spectrum was recorded in a cell without a membrane. (c) Coulombic efficiency (CE), energy efficiency (EE), and capacity of cells assembled with the M- QCTF membrane at various current densities. (d) Galvanostatic cycling of the BTMAP- Vi/FcNCI cell assembled with the M- QCTF membrane at \(400 \text{mA cm}^{-2}\) . The electrolyte compositions through b to d: the anolyte comprised \(5 \text{mL}\) of \(0.5 \text{M BTMAP-Vi}\) in \(2 \text{M KCl}\) , while the catholyte comprised \(10 \text{mL}\) of \(0.5 \text{M FcNCI}\) in \(2 \text{M KCl}\) . Capacity utilization (e) and energy efficiency (f) of pH- neutral AORFBs assembled with Selemion® DSV and Selemion® AMV, AME 115, PIM- TDQTB, or M- QCTF are plotted as a function of current density. Dashed lines and shades are visual guides. The detailed values can be found in Supplementary Table S10.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 66, 312, 93]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 116, 768, 136]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 154, 366, 173]]<|/det|>
+- 03supplementarymaterials.docx
+
+<--- Page Split --->

preprint/preprint__00aa363715f9caf53b3b56fb3500a871c4d4ad7d3f29389a4c2af752e13f7a19/images_list.json

@@ -0,0 +1,137 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Downregulation of transcripts associated with extracellular matrix-receptor interactions and upregulation of stress and inflammation pathways in Tgfbr1<sup>M318R/+</sup> LDS VSMCs. (A) Uniform manifold approximation and projection (UMAP) of aortic cells from control (Tgfbr1<sup>+/+</sup>) and LDS (Tgfbr1<sup>M318R/+</sup>) mice. (B) Dot plot of cluster defining transcripts used to identify endothelial cells, leukocytes, fibroblasts, and VSMCs. Color of the dot represents a scaled average expression while the size indicates the percentage of cells in which the transcript was detected. (C) ClueGO gene enrichment analysis network of transcripts dysregulated in LDS VSMCs relative to controls. Each node represents a term/pathway or individual genes associated with that term. The color of the node corresponds to the ClueGO group to which each node belongs. The size of the node indicates significance of the enrichment calculated by the ClueGO algorithm. (D) ClueGO network in which terms differentially enriched among transcripts downregulated in LDS VSMCs are highlighted in blue, while those enriched among transcripts upregulated in LDS VSMCs are highlighted in red. (E) Dot plot showing expression of a selection of transcripts significantly dysregulated in LDS VSMCs. (F,G) EnrichR gene over-representation analysis for the ENCODE and ChEA Consensus transcription factors (TF) databases showing the top three most significant terms associated with transcripts that are downregulated (F) or upregulated (G) in LDS VSMCs.",
+    "footnote": [],
+    "bbox": [
+      [
+        20,
+        50,
+        970,
+        777
+      ]
+    ],
+    "page_idx": 21
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. MERFISH reveals spatially heterogeneous transcriptional profiles in LDS VSMCs. MERFISH images of the proximal aorta of LDS (A) and control (B) mice, scale bar is 1 mm. The first panel displays all detected transcripts across the aortic tissue, with key anatomic landmarks indicated. Subsequent panels depict the colocalization of Myh11 and transcripts of interest. Insets note regions of the ascending aorta and aortic root that are presented at higher magnification.",
+    "footnote": [],
+    "bbox": [
+      [
+        0,
+        66,
+        985,
+        688
+      ]
+    ],
+    "page_idx": 22
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Transcriptionaly and spatially-defined VSMC subclusters with distinct responses to LDS-causing mutations can be identified in both murine and human aortas. (A) UMAP of VSMCs from control (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) mice shown split by genotype. (B) Dot plot showing enrichment of cluster-defining transcripts in VSMC1 and VSMC2. For a given transcript, the color of the dot represents a scaled average expression while the size indicates the percentage of cells in which it was detected. (C) RNA in situ hybridization showing the expression of Gata4 along the length of the murine aorta in a 16-week old control animal. (D) UMAP of control and LDS VSMCs from human patients and dot plot of cluster defining markers in this dataset split by aortic region (Pedroza et al., 2023). (E,F) UMAP overlayed with weights for CoGAPS patterns 4 and 5, in mouse and human scRNAseq datasets. (G,H) Violin plots showing the distribution of pattern 4 and 5 weights in VSMC subclusters from mouse and human scRNAseq datasets. P-values refer to Wilcoxon test. (I) EnrichR gene over-representation analysis for the ENCODE and ChEA Consensus TF databases showing the top four most significant terms associated with transcripts that define CoGAPs Patterns 4 and 5. (J) ClueGO network of terms differentially enriched in mouse and human LDS VSMC2 relative to VSMC1. Terms highlighted in blue are enriched in VSMC1, while those highlighted in red are enriched in VSMC2.",
+    "footnote": [],
+    "bbox": [
+      [
+        19,
+        14,
+        999,
+        750
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
+    "bbox": [
+      [
+        9,
+        52,
+        978,
+        496
+      ]
+    ],
+    "page_idx": 24
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5",
+    "footnote": [],
+    "bbox": [
+      [
+        44,
+        50,
+        725,
+        711
+      ]
+    ],
+    "page_idx": 25
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "B",
+    "footnote": [],
+    "bbox": [
+      [
+        20,
+        28,
+        870,
+        270
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. Smooth muscle-specific deletion of Gata4 (Gata4SMcKO) reduces aortic root size and growth and improves aortic root media architecture in LDS mice. (A) Aortic root diameter of Ctrl (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) with (Gata4SMcKO) or without (Gata4SMcKO) smooth muscle specific deletion of Gata4 as measured by echocardiography at 8 and 16 weeks of age and aortic root growth from 8-16 weeks. P-values refer to Brown-Forsythe ANOVA. (B) Representative VVG-stained aortic root sections from three independent biological replicates per genotype. Insets identify area shown at higher magnification in the subsequent panel. Scale bars 50 and 200 microns, respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        60,
+        280,
+        720,
+        833
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7",
+    "footnote": [],
+    "bbox": [
+      [
+        45,
+        50,
+        731,
+        710
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Figure 8",
+    "footnote": [],
+    "bbox": [
+      [
+        42,
+        50,
+        728,
+        707
+      ]
+    ],
+    "page_idx": 28
+  }
+]

preprint/preprint__00aa363715f9caf53b3b56fb3500a871c4d4ad7d3f29389a4c2af752e13f7a19/preprint__00aa363715f9caf53b3b56fb3500a871c4d4ad7d3f29389a4c2af752e13f7a19.mmd

@@ -0,0 +1,333 @@
+
+# Intrinsic Gata4 expression sensitizes the aortic root to dilation in a Loeys-Dietz syndrome mouse model  
+
+Emily Bramel  Johns Hopkins University School of Medicine https://orcid.org/0000- 0003- 4602- 9506  
+
+Wendy Espinoza Camejo  Johns Hopkins University School of Medicine  
+
+Tyler Creamer  Johns Hopkins University School of Medicine  
+
+Leda Restrepo  Johns Hopkins University School of Medicine  
+
+Muzna Saqib  Johns Hopkins University School of Medicine  
+
+Rustam Bagirzadeh  Johns Hopkins University School of Medicine  
+
+Anthony Zeng  Johns Hopkins University School of Medicine  
+
+Jacob Mitchell  Johns Hopkins University School of Medicine  
+
+Genevieve Stein- O'Brien  Johns Hopkins University School of Medicine  
+
+Albert Pedroza  Stanford University https://orcid.org/0000- 0001- 5291- 5980  
+
+Michael Fischbein  Stanford University  
+
+Harry Dietz  Johns Hopkins School of Medicine https://orcid.org/0000- 0002- 6856- 0165  
+
+Elena Gallo MacFarlane  egal101@jhmi.edu  
+
+Genetic Medicine, Johns Hopkins University https://orcid.org/0000- 0001- 5677- 6842  
+
+Article  
+
+Keywords:
+
+<--- Page Split --->
+
+**Posted Date:** June 5th, 2024 
+
+**DOI:** https://doi.org/10.21203/rs.3.rs-4420617/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 Cardiovascular Research on November 20th, 2024. See the published version at https://doi.org/10.1038/s44161-024-00562-5. 
+
+## EDITORIAL NOTE: 
+
+August 15, 2024. Editorial Note: In version 1 of this preprint (posted June 5, 2024) the authors have reported some unintentional errors in the x-axis labeling of figure 6A and supplemental figures 6 and 7. New figure files with corrected labeling have now been added to the version 1 preprint in the supplementary file section as follows. 
+
+**CORRECTED** Primary figure 6 for version 1 - in part A, the x axis labels have been corrected **CORRECTED** Supplemental Figures 6 and 7 for version 1 - in both supplemental figures, the x axis labels have been corrected
+
+<--- Page Split --->
+
+1 Intrinsic Gata4 expression sensitizes the aortic root to dilation in a Loeys- Dietz syndrome 2 mouse model  
+
+3 Emily E. Bramel<sup>1,2</sup>, Wendy A. Espinoza Camejo<sup>1,2</sup>, Tyler J. Creamer<sup>1</sup>, Leda Restrepo<sup>1</sup>, 4 Muzna Saqib<sup>1</sup>, Rustam Bagirzadeh<sup>1</sup>, Anthony Zeng<sup>1</sup>, Jacob T. Mitchell<sup>1,2</sup>, Genevieve L. 5 Stein- O'Brien<sup>1,4</sup>, Albert J. Pedroza<sup>5</sup>, Michael P. Fischbein<sup>5</sup>, Harry C. Dietz<sup>1</sup>, Elena Gallo 6 MacFarlane<sup>1,3\*  
+
+7 <sup>1</sup>McKusick- Nathans Department of Genetic Medicine, Johns Hopkins University School of 8 Medicine, Baltimore, Maryland, USA 9 <sup>2</sup> Predoctoral Training in Human Genetics and Genomics, Johns Hopkins University School of 10 Medicine, Baltimore, Maryland, USA 11 <sup>3</sup> Department of Surgery, Johns Hopkins University School of Medicine, Baltimore, Maryland, 12 USA 13 <sup>4</sup>Solomon H. Snyder Department of Neuroscience, Johns Hopkins University School of 14 Medicine, Baltimore, Maryland, USA 15 <sup>5</sup>Department of Cardiothoracic Surgery, Stanford University School of Medicine, Stanford, 16 California, USA  
+
+\* Correspondence:  
+
+Elena Gallo MacFarlane  
+
+egalol1@jhmi.edu  
+
+## Conflict of interest statement  
+
+The authors have declared that no conflict of interest exists.  
+
+## Abstract  
+
+Loews- Dietz syndrome (LDS) is an aneurysm disorder caused by mutations that decrease transforming growth factor- \(\beta\) (TGF- \(\beta\) ) signaling. Although aneurysms develop throughout the arterial tree, the aortic root is a site of heightened risk. To identify molecular determinants of this vulnerability, we investigated the heterogeneity of vascular smooth muscle cells (VSMCs) in the aorta of Tgfbr1<sup>M318R/+</sup> LDS mice by single cell and spatial transcriptomics. Reduced expression of components of the extracellular matrix- receptor apparatus and upregulation of stress and inflammatory pathways were observed in all LDS VSMCs. However, regardless of genotype, a subset of Gata4- expressing VSMCs predominantly located in the aortic root intrinsically displayed a less differentiated, proinflammatory profile. A similar population was also identified among aortic VSMCs in a human scRNAseq dataset. Postnatal VSMC- specific Gata4 deletion reduced aortic root dilation in LDS mice, suggesting that this factor sensitizes the aortic root to the effects of impaired TGF- \(\beta\) signaling.
+
+<--- Page Split --->
+
+Thoracic aortic aneurysms are localized vascular dilations that increase the risk of fatal dissections and/or rupture of the vessel wall'. Effective medical therapies to prevent life- threatening aortic events remain elusive?. Loeys- Dietz syndrome (LDS) is a hereditary connective tissue disorder that presents with highly penetrant aortic aneurysms3,4. LDS is caused by heterozygous, loss- of- function mutations in positive effectors of the TGF- \(\beta\) signaling pathway, including receptors (TGFBR1, TGFBR2), ligands (TGFB2, TGFB3) and intracellular signaling mediators (SMAD2, SMAD3)5- 9. All of these mutations result in reduced phosphorylation/activation of Smad2 and Smad3, leading to defective Smad- dependent transcriptional regulation. Secondary compensatory mechanisms, including upregulation of Angiotensin II Type I Receptor (AT1R) signaling, and increased expression of TGF- \(\beta\) ligands and Smad proteins, ultimately elevate levels of Smad2/Smad3 activity at diseased aortic sites, with outcomes ranging from adaptive to maladaptive depending on disease progression and cellular context5,7,10- 13. While LDS- causing mutations heighten aneurysm risk in all arteries, the aortic root is especially vulnerable to disease14- 17. Several laboratories have highlighted how the cellular composition and/or the mechanical stresses may contribute to the increased risk of disease in this location, however, the molecular determinants of this susceptibility remain unclear13,18- 22. Additionally, VSMCs are the primary cellular component of the aortic wall, but the heterogeneity of VSMCs within the aorta and its implications for aneurysm are not fully understood. In this study, we investigate the transcriptional heterogeneity of VSMCs in the normal and diseased murine aorta leveraging both scRNAseq and spatial transcriptomics. We identify Gata4 as a regional factor whose expression is intrinsically elevated in the aortic root and further upregulated in LDS samples. We also show that postnatal deletion of Gata4 in VSMCs ameliorates aortic root dilation in a murine model of LDS harboring a Tgfbr1M318R/+ genotype.  
+
+## Results  
+
+Tgfbr1M318R/+ VSMCs downregulate extracellular matrix components, focal adhesions, and integrin receptors, and upregulate transcripts related to stress and inflammatory pathways.  
+
+LDS mouse models expressing a heterozygous missense mutation in Tgfbr1 (Tgfbr1M318R/+) develop highly penetrant aortic root aneurysms11,13. To assess transcriptomic changes associated with vascular pathology in this model, we performed single cell RNA sequencing (scRNAseq) on the aortic root and ascending aorta of control (Tgfbr1+/+) and LDS mice at 16 weeks of age, resulting in the identification of all of the expected cell types according to well- established expression profiles23 (Fig. 1A, B and Supplemental Fig. 1). In consideration of the critical role of VSMCs in the pathogenesis of aortic aneurysm24,25, we focused the downstream analysis of LDS- driven transcriptional alterations on this cell type (Supplemental Table 1). Using the Cytoscape26 ClueGO27 plug- in to leverage gene set enrichment information from multiple databases, we produced a network of functionally related terms and pathways that are differentially enriched among downregulated and upregulated transcripts. (Fig. 1C, D and Supplemental Table 2). The Tgfbr1M318R/+ LDS mutation caused broad downregulation of transcripts related to the maintenance of extracellular matrix- receptor interactions, and integrity of the elastic and contractile function of the aortic wall (Fig. 1C, D, E and Supplemental Table 2). Concurrently, pathways involved in cellular stress responses, inflammation, senescence, and cell death were enriched among transcripts upregulated in Tgfbr1M318R/+ VSMCs (Fig. 1C, D, E and Supplemental Table 2). Additional analysis of transcription factor target databases
+
+<--- Page Split --->
+
+(ENCODE \(^{28}\) and Chromatin Immunoprecipitation Enrichment Analysis (ChEA) via EnrichR \(^{29 - 32}\) ) showed that LDS- downregulated transcripts were enriched in targets of NFE2L2 (nuclear factor erythroid 2- related factor 2, also known as Nrf2), a transcription factor that activates expression of cytoprotective genes and suppresses expression of proinflammatory mediators \(^{33 - 35}\) (Fig. 1F and Supplemental Table 2). Targets of the upstream stimulatory factor (USF) family, which can modulate the expression of smooth muscle specific genes were also enriched among downregulated transcripts \(^{36 - 39}\) (Fig. 1F and Supplemental Table 2). Conversely, target genes for GATA transcription factors and CCAAT enhancer binding protein delta (CEBPD), a positive transcriptional regulator of inflammatory responses mediated by interleukin- 1 (IL- 1) and IL- \(6^{40 - 43}\) , were enriched among transcripts upregulated in LDS VSMCs (Fig. 1G and Supplemental Table 2).  
+
+## Spatial transcriptomic analysis of the murine aorta reveals region- and disease-specific patterns of expression for modulators of VSMC phenotypes.  
+
+Given the regional vulnerability observed in LDS aortas, we leveraged insight gained from the literature and scRNAseq analysis of the aorta of control and \(Tgfbr1^{M318R / + }\) mice to design a custom panel for high throughput in situ hybridization using the Multiplexed error- robust fluorescence in situ hybridization (MERFISH) spatial transcriptomics platform (Supplemental Table 3). Analysis of a longitudinal section of the proximal aorta of 16- week- old control and LDS mice showed regionally defined expression of several transcripts involved in the modulation of vascular phenotypes (Fig. 2 and Supplemental Fig. 2). Transcripts more highly detected in the aortic root of LDS mice relative to the ascending aorta included \(Agtr1a\) , which codes for angiotensin II receptor type 1a, a known contributor to LDS pathogenesis, and \(Gata4\) , which codes for a transcription factor known to positively regulate \(Agtr1a\) expression in the heart \(^{44,45}\) . CCAAT enhancer binding protein beta (Cebpb), a pro- inflammatory mediator \(^{46}\) , and maternally expressed gene 3 (Meg3), a long non- coding RNA (lncRNA) that negatively regulates TGF- \(\beta\) signaling and promotes VSMC proliferation \(^{47 - 50}\) , were also enriched in this region. In contrast, expression of cardiac mesoderm enhancer- associated noncoding RNA (Carmn), a positive regulator of VSMC contractile function that is downregulated in vascular disease, and expression of \(Myh11\) , a marker of differentiated VSMCs, was enriched in the distal ascending aorta, a region that is only mildly affected in LDS mouse models \(^{49,51 - 53}\) .  
+
+## Expression of cluster-defining transcripts for the VSMC2 and VSMC1 subclusters correlates with the proximal-to-distal axis of the mouse and human aorta.  
+
+To examine if the spatial VSMC heterogeneity observed with MERFISH could be captured by scRNAseq, we increased the clustering resolution for VSMCs, thus obtaining two subclusters, VSMC1 and VSMC2. We then examined these two VSMC subclusters for expression of transcripts our laboratory has previously shown to progressively increase (i.e. Tes and Ptrpz1) and decrease (i.e. Enpep and Notch3) along the proximal- to- distal axis in the mouse ascending aorta \(^{54}\) . VSMC1 and VSMC2 showed increased expression of transcripts whose expression is intrinsically enriched in the ascending aorta and the aortic root, respectively \(^{54}\) (Fig. 3A, B and Supplemental Table 4). Gata4 was also noted among the transcripts that defined the VSMC2 subcluster and whose expression was highest in the aortic root, progressively diminishing along the proximal- to- distal axis in the ascending aorta (Fig. 3C). Considering previous work highlighting how cell lineage modulates the effect of LDS- causing mutations \(^{13,55 - 57}\) , we explored the relationship between the VSMC2 and VSMC1 subclusters to the secondary heart field
+
+<--- Page Split --->
+
+(SHF)- and cardiac neural crest (CNC)- lineage of origin (Supplemental Fig. 3). We found that VSMCs lineage- traced with a fluorescent reporter identifying CNC- derived cells were overrepresented in the VSMC1 subcluster (Supplemental Fig. 3A). However, re- analysis of a previously published dataset of SHF- and CNC- traced VSMCs (Supplemental Table 5) showed that VSMC1 and VSMC2 were not defined by lineage of origin, with VSMCs of both lineages found in either VSMC sub- cluster \(^{58}\) (Supplemental Fig. 3B). Nevertheless, as would be expected based on the known proximal- to- distal distribution of SHF- and CNC- derived VSMCs, there was overlap between VSMC2- defining and SHF- enriched transcripts (Supplemental Fig. 3B, C and Supplemental Table 4 and 5). To assess if the VSMC substructure identified in murine models was relevant in the context of human aortic disease, we also re- analyzed a recently published scRNAseq dataset of aortic tissue from LDS patients and donor aortas in which the ascending aorta and aortic root were separately sequenced (Fig. 3D and Supplemental Fig. 4) \(^{59}\) . Subpopulations of VSMCs expressing cluster- defining transcripts analogous to those found in VSMC1 and VSMC2 in mouse aortas could be identified in the human dataset (Fig. 3D and Supplemental Table 6). Although both VSMC1 and VSMC2 were present in human aortic root and ascending aorta, GATA4 expression was highest in the VSMC2 cluster from the aortic root, with no detectable expression in the ascending aorta (Fig. 3D).  
+
+## Gata4-expressing VSMC2 are intrinsically "poised" towards a less-differentiated, maladaptive proinflammatory transcriptional signature.  
+
+To examine the biological features of VSMC1 and VSMC2, and whether they were recapitulated in both murine and patient- derived LDS VSMCs, we used the Coordinated Gene Activity in Pattern Sets (CoGAPS) algorithm to identify latent patterns of coordinated gene expression in the \(Tgbr^{M318R / +}\) VSMC mouse dataset \(^{60,61}\) . Two patterns, transcriptional patterns 4 and 5, were found to be enriched in the VSMC2 and VSMC1 subclusters, respectively, in the \(Tgbr^{M318R / +}\) VSMC mouse dataset (Fig. 3E, G, Supplemental Table 4). These same patterns were then projected onto the scRNAseq data of VSMCs from the aorta of LDS patients using ProjectR \(^{62}\) , revealing a similar enrichment of pattern 4 in VSMC2 and pattern 5 in VSMC1 (Fig. 3E- H, Supplemental Table 4).  
+
+As previously observed for transcripts upregulated in \(Tgbr^{M318R / +}\) LDS VSMCs, Pattern 4- associated transcripts were enriched for transcriptional targets of GATA family members (ENCODE \(^{28}\) and ChEA dataset, analyzed with EnrichR \(^{29 - 32}\) , Fig. 3I). Differential gene set enrichment analysis using ClueGO \(^{27}\) to compare cluster- defining transcripts for VSMC1 and VSMC2 also showed that, in both mouse and human datasets, VSMC2- defining transcripts were enriched for pathways involved in inflammation, senescence, and cellular stress (Fig. 3J and Supplemental Table 7 and Table 8). In contrast, VSMC1 expressed higher levels of transcripts related to extracellular matrix- receptor interactions and contractile function (Fig. 3J, Supplemental Fig. 4 and Supplemental Table 7 and Table 8). Network visualization of molecular signatures database (MSigDB) VSMC2- enriched pathways shared by both mouse and human samples (probed with EnrichR \(^{30 - 32,63,64}\) ) (Supplemental Fig. 5A), and biological terms with shared ClueGO grouping (Fig. 3J and Supplemental Table 7 and Table 8), highlighted the biological connections between these pathways and genes over- expressed in VSMC2 relative to VSMC1 (i.e. \(Cxcl^{165 - 68}\) , Irf1 \(^{69 - 71}\) , Thbs1 \(^{72}\) , Gata4 \(^{73}\) ) (Supplemental Fig. 5B). Overall, in both mouse and human samples, the transcriptional profile of VSMC2 relative to VSMC1 resembled that of less- differentiated VSMCs and included lower expression of \(Myh11\) , Cnn1, and Tet2, and
+
+<--- Page Split --->
+
+higher expression of transcripts associated with non- contractile VSMC phenotypes, including Klf4, Olfm2, Sox9, Tcf21, Malat1, Twist1, and Dcn<sup>74- 79</sup>.  
+
+## Gata4 is upregulated in the aortic root of Tgfbr1<sup>M318R/+</sup> LDS mice.  
+
+Based on the analysis described above, and its known role in driving the upregulation of pathways previously involved in aneurysm progression<sup>44,73,80</sup>, Gata4 emerged as a potential molecular determinant of increased risk of dilation of the aortic root in LDS. Although levels of Gata4 mRNA are intrinsically higher in the aortic root relative to the ascending aorta even in control mice (Fig. 3C), its expression was further upregulated in VSMCs in the LDS aorta, as assessed both by scRNAseq (Supplemental Table 1) and RNA in situ hybridization (Fig. 4A). Given that levels of Gata4 protein are highly regulated at the post- transcriptional level through targeted degradation<sup>73,81,82</sup>, we also examined levels of Gata4 protein in control and LDS aortic samples, and found that protein levels are increased in LDS aortic root, both by immunofluorescence and immunoblot assays (Fig. 4B, C and Fig. 5).  
+
+## Postnatal deletion of Gata4 in smooth muscle cells reduces aortic root dilation in LDS mice in association with reduced levels of Agtr1a and other proinflammatory mediators.  
+
+To assess whether increased Gata4 levels in aortic root of LDS mouse models promoted dilation in this location, we crossed conditional Gata4<sup>flox/flox</sup> mice<sup>83</sup> to LDS mice also expressing a transgenic, tamoxifen- inducible Cre recombinase under the control of a VSMC specific promoter (Myh11- Cre<sup>ER</sup>)<sup>84</sup>, and administered tamoxifen at 6 weeks of age to ablate expression of Gata4 in VSMCs (Fig. 5). VSMC- specific postnatal deletion of Gata4 in LDS mice (Tgfbr1<sup>M318R/+</sup>, Gata4<sup>SMcKO</sup>) resulted in a reduced rate of aortic root dilation relative to control LDS animals (Tgfbr1<sup>M318R/+</sup>; Gata4<sup>Ctrl</sup>) (Fig. 6A), and amelioration of aortic root medial architecture relative to control LDS aortas at 16 weeks of age (Fig. 6B). No significant dilation was observed in the ascending aorta of Tgfbr1<sup>M318R/+</sup> mice at 16 weeks of age, and Gata4 deletion had no effect on the diameter of this aortic segment (Supplemental Fig. 6). Gata4 deletion in VSMCs also did not associate with changes in blood pressure (Supplemental Fig. 7).  
+
+Previous work has shown that Gata4 binds to the Agtr1a promoter inducing its expression in heart tissue<sup>44,45</sup>, and that Agtr1a is transcriptionally upregulated in the aortic root of LDS mice, resulting in up- regulation of AT1R, which exacerbates LDS vascular pathology<sup>11,13,45</sup>. Accordingly, Gata4 deletion associated with reduced expression of Agtr1a in the aortic root of LDS mice (Fig. 7). Similarly, deletion of Gata4 reduced expression of Cebpd and Cebpb (Fig. 8 and Supplemental Fig. 8), which code for proinflammatory transcription factors regulated by and/or interacting with Gata4 in other contexts<sup>43,46,85,86</sup>, which were highly expressed in VSMC2 relative to VSMC1, and further upregulated in the presence of LDS mutations (Fig. 1, Fig. 2, Supplemental Table 1, Supplemental Table 7).  
+
+## Discussion  
+
+LDS is a hereditary connective tissue disorder characterized by skeletal, craniofacial, cutaneous, immunological, and vascular manifestations, including a high risk for aggressive arterial aneurysms<sup>4</sup>. It is caused by mutations that impair the signaling output of the TGF- \(\beta\) pathway, leading to defective transcriptional regulation of its target genes<sup>5- 9</sup>. Although loss- of- signaling initiates vascular pathology, compensatory upregulation of positive modulators of the pathway results in a “paradoxical” increase in activation of TGF- \(\beta\) signaling mediators (i.e
+
+<--- Page Split --->
+
+phosphorylated Smad2 and Smad3) and increased expression of target genes in diseased aortic tissue of both LDS patients and mouse models \(^{5,7,10 - 13}\) . This secondary upregulation depends, in part, on increased activation of angiotensin II signaling via AT1R, which positively modulates the expression of TGF- \(\beta\) ligands and TGF- \(\beta\) receptors \(^{87}\) . Whereas upregulation of the TGF- \(\beta\) pathway can have both adaptive and maladaptive consequences depending on disease stage and cellular context \(^{13,54,88 - 95}\) , upregulation of AT1R signaling has consistently been shown to be detrimental to vascular health, and both pharmacological (i.e. with angiotensin receptor blockers) and genetic antagonism of this pathway ameliorates vascular pathology in LDS mouse models \(^{87,96 - 99}\) .  
+
+Even though LDS- causing mutations confer an increased risk of disease across all arterial segments, the aortic root is one of the sites that is particularly susceptible to aneurysm development \(^{14 - 17}\) . In this study, we leveraged scRNAseq in conjunction with spatial transcriptomics to investigate the heterogeneity of VSMCs in an LDS mouse model, with the ultimate goal of identifying regional mediators that may drive upregulation of pro- pathogenic signaling in this region. We identify distinct subpopulations of VSMCs characterized by expression patterns that preferentially map to the ascending aorta (VSMC1) and aortic root (VSMC2) in mouse aorta. We also show that the regional vulnerability of the aortic root depends, in part, on higher levels of Gata4 expression in a subset of VSMCs (VSMC2), which is intrinsically more vulnerable to the effect of an LDS- causing mutation.  
+
+Prior to the advent of single- cell analysis tools, which allow precise and unbiased unraveling of cellular identity, the ability to investigate VSMC heterogeneity in the proximal aorta was limited by the availability of experimental approaches to investigate known or expected diversity. In consideration of the mixed embryological origin of the aortic root and distal ascending aorta, earlier work thus focused on understanding how the effect of LDS mutations on VSMCs was modified by the SHF- and CNC lineage of origin. In both mouse models and in iPSCs- derived in vitro models, signaling defects caused by LDS mutations were found to be more pronounced in VSMC derived from SHF (or cardiac mesoderm) progenitors relative to CNC- derived VSMCs \(^{13,57}\) .  
+
+Like SHF- derived VSMCs, Gata4- expressing VSMC2 are enriched in the aortic root and are also more vulnerable to the effects of an LDS- causing mutation. They also express a transcriptional signature similar to that of SHF- derived VSMCs (Supplemental Fig. 3). Reciprocally, SHF- derived cells are over- represented in the VSMC2 cluster in our dataset (Supplemental Fig. 3). However, the identity of VSMC2 and VSMC1 is not defined by lineage- of- origin, and SHF- or CNC- derived origin is only an imperfect approximation of the VSMC heterogeneity that can now be assessed via scRNAseq.  
+
+Heterogeneity beyond that imposed by lineage- of- origin was also shown by scRNAseq analysis of the aorta of the \(Fbn^{1C1041G / +}\) Marfan syndrome (MFS) mouse model, which revealed the existence of an aneurysm- specific population of transcriptionally modified smooth muscle cells (modSMCs) at a later stage of aneurysmal disease, and which could emerge from modulation of both SHF- and non- SHF (presumably CNC)- derived progenitors \(^{58,100}\) . These cells, which could also be identified in the aneurysmal tissue derived from the aortic root of MFS patients, showed a transcriptional signature marked by a gradual upregulation of extracellular matrix genes and
+
+<--- Page Split --->
+
+downregulation of VSMC contractile genes \(^{58,100}\) . We were not able to identify this population of modSMCs in the aorta of \(Tgfbr1^{M318R / +}\) LDS mouse models, even though it was shown to exist in the aorta of LDS patients \(^{62}\) .  
+
+Similar to the early effect of Smad3- inactivation, the \(Tgfbr1^{M318R / +}\) LDS mutation caused broad downregulation of gene programs required for extracellular matrix homeostasis and those favoring a differentiated VSMC phenotype \(^{54}\) (Fig. 1); conversely, proinflammatory transcriptional repertoires, with an enrichment in pathways related to cell stress, was observed among upregulated transcripts. This latter profile likely represents a response to the initial insult caused by decreased expression of extracellular matrix components whose expression requires TGF- \(\beta\) /Smad activity \(^{98}\) .  
+
+We also noted downregulation of several components of the lysosome, whose function is required for cellular homeostasis and degradation of protein targets via selective autophagy \(^{33,73,101,102}\) (Fig. 1). Gata4 levels are regulated via p62- mediated selective autophagy \(^{73}\) and by mechanosensitive proteasome- mediated degradation \(^{82,103}\) . The aortic root would be especially vulnerable to a defect in either of these processes given increased baseline levels of Gata4 mRNA expression in VSMC2. Increased levels of Gata4 may contribute to vascular pathogenesis by several potential mechanisms. In other cellular contexts, Gata4 has been shown to promote induction of the pro- inflammatory senescence- associated secretory phenotype (SASP) as well as transcription of the lncRNA Malat1, which promotes aneurysm development in other mouse models \(^{78}\) . Gata4 is also a negative regulator of contractile gene expression in Sertoli and Leydig cells \(^{104}\) . Additionally, Gata4 binds the promoter and activates the expression of \(Agtr1a^{44}\) , which is known to drive pro- pathogenic signaling in LDS aorta \(^{45}\) . Accordingly, we find that Gata4 deletion downregulates expression of \(Agtr1a\) in the aortic media of LDS mouse models (Fig. 7).  
+
+Re- analysis of a scRNAseq dataset of human aortic samples from LDS patients, which included both the aortic root and the ascending aorta, shows that a population of Gata4- expressing VSMC similar to that found in mice can also be identified in LDS patients. Additionally, patterns of coordinated gene expression identifying VSMC1 and VSMC2, which were learned from the scRNAseq analysis of mouse aorta, could be projected onto the human dataset, suggesting that these two subsets of VSMCs are conserved across species and that the existence of a Gata4- expressing VSMC2 population may underlie increased risk in the aortic root of LDS patients as well. Assessing the effects of Gata4 deletion at additional postnatal timepoints will be important to understand the consequences of increased Gata4 and its downstream targets during later stages of disease. Although direct targeting of Gata4 for therapeutic purposes is unfeasible given its critical role in the regulation of numerous biological processes in non- vascular tissues \(^{105- 109}\) , this work highlights how the investigation of factors that increase or decrease the regional risk of aneurysm may lead to a better understanding of adaptive and maladaptive pathways activated in response to a given aneurysm- causing mutations. This knowledge may be leveraged to develop therapeutic strategies that target the vulnerabilities of specific arterial segments.
+
+<--- Page Split --->
+
+## Methods  
+
+## Animal Experiments  
+
+Study approval  
+
+Animal experiments were conducted according to protocols approved by the Johns Hopkins University School of Medicine Animal Care and Use Committee.  
+
+## Mouse models  
+
+All mice were maintained in an animal facility with unlimited access to standard chow and water unless otherwise described. \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + 11}\) (The Jackson Laboratory, strain #036511) mice, some bearing the \(E G F P - L10a^{110}\) (The Jackson Laboratory, strain #024750) conditional tracer allele and a CNC- specific CRE recombinase expressed under the control of Wnt2 promoter111 (The Jackson Laboratory, strain #003829) were used for scRNAseq as described below. All mice were maintained on a 129- background strain (Taconic, 129SVE). \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + }\) mice were bred to \(G a t a^{4l o x / l o x 83}\) (The Jackson Laboratory, strain #008194) and mice carrying the \(M y h I1 - C r e^{E R}\) transgene84 (The Jackson Laboratory, strain #019079). \(M y h I1 - C r e^{E R}\) is integrated on the Y chromosome therefore only male mice were used for this set of experiments. \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + }\) bearing \(G a t a^{4l o x / l o x}\) and \(M y h I1 - C r e^{E R}\) are referred to as \(G a t a^{4S M c K O}\) . \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + }\) bearing \(G a t a^{4 + / + }\) with or without \(M y h I1-\) \(C r e^{E R}\) or \(G a t a^{4l o x / l o x}\) or \(G a t a^{4l o x / + }\) without \(M y h I1 - C r e^{E R}\) are referred to as \(G a t a^{4C u l}\) . All \(G a t a^{4S M c K O}\) and \(G a t a^{4C u l}\) mice were injected with 2 mg/day of tamoxifen (Millipore Sigma, T5648) starting at 6 weeks of age for 5 consecutive days. Mice were genotyped by PCR using primer sequences described in the original references for these models. Serial echocardiography was performed using the Visual Sonics Vivo 2100 machine and a 30 MHz probe. As there is some variability in the onset of aortic dilation in \(T g f b r I^{M318R / + }\) mice, and starting aortic size will affect final measurements, aortic root diameter of 1.9 mm and above at baseline (8 weeks of age) was defined a priori as an exclusion criterion.  
+
+## Molecular validation techniques  
+
+Aortic Sample Preparation  
+
+All mice were euthanized by halothane inhalation at a \(4\%\) concentration, \(0.2\mathrm{ml}\) per liter of container volume (Millipore Sigma, H0150000). As we described previously \(^{11,54}\) , the heart and thoracic aorta were dissected en bloc and fixed in \(4\%\) paraformaldehyde (Electron Microscopy Sciences, 15710) in PBS at \(4^{\circ}\mathrm{C}\) overnight. Samples were subsequently incubated in \(70\%\) ethanol at \(4^{\circ}\mathrm{C}\) overnight prior to embedding in paraffin. Paraffin- embedded tissues were cut into 5 micron sections to expose a longitudinal section of the thoracic aorta. Sections were then stained with Verhoeff- van Gieson (StatLab, STVGI) to visualize elastic fiber morphology or to assess protein and RNA abundance by immunofluorescence or fluorescence in situ hybridization.  
+
+## Immunofluorescence  
+
+Immunofluorescence was performed following a protocol adapted from Cell Signaling Technology (CST) for formaldehyde- fixed tissues as previously described in detail \(^{45}\) , using a rabbit monoclonal antibody for GATA4 (Cell Signaling Technology, CST36966) and a donkey anti- rabbit secondary antibody Alexa Fluor 555 (ThermoFisher, A32794). Images were taken using a Zeiss LSM880 Airyscan FAST confocal microscope at \(20\times\) magnification and are presented as maximal intensity projection.
+
+<--- Page Split --->
+
+RNAscope Fluorescence in situ hybridization  
+
+RNA in situ hybridization was performed using the RNAscope Multiplex Fluorescent Reagent Kit v2 Assay (ACD Biosciences, 323100) according to the manufacturer's protocol with the following probes Mm- Gata4 (417881), Mm- Agtr1a (481161), Mm- Cebpd (556661), Mm- Cebpb (547471). Images were taken using a Zeiss LSM880 Airyscan FAST confocal microscope at \(20 \times\) magnification and are presented as maximal intensity projection.  
+
+## Immunoblotting  
+
+Aortic root tissue was flash- frozen immediately upon dissection and stored at \(- 80^{\circ}\mathrm{C}\) until protein extraction. Protein was extracted using Full Moon Lysis Buffer (Full Moon Biosystems, EXB1000) with added phosphatase and protease inhibitors (MilliporeSigma, 11836170001 and 4906845001) and Full Moon lysis beads (Full Moon Biosystems, LB020) using an MP Biomedicals FastPrep 24 5G automatic bead homogenizer. After homogenization, the cell debris was pelleted, and the supernatant was collected. Immunoblot was performed as previously described in detail54, using a rabbit monoclonal antibody for Gata4 (Cell Signaling Technology, 36966) and a mouse monoclonal antibody for \(\beta\) - Actin. (Cell Signaling Technology, 8H10D10).  
+
+## Transcriptomic Analyses  
+
+Single Cell RNA sequencing and analysis  
+
+Single cell RNA sequencing was performed as we previously described112. Single cell suspensions from each mouse were processed separately using the 10x Genomics \(3^{\circ}\) v3 platform and sequenced on an Illumina NovaSeq. A total of 30,704 aortic cells were sequenced from six female mice. The raw data was processed, aligned to the mouse genome (mm10), and aggregated using 10x Genomics Cell Ranger V6'13. The data were then filtered using the Seurat V5 package112 based on the following criteria: \(>1000\) transcripts detected per cell but \(< 5000\) , \(>1500\) total molecules detected per cell but \(< 25000\) , and \(< 20\%\) mitochondrial transcripts per cell. Filtering reduced this dataset from 30,704 aortic cells to 24,971 cells for further analysis. The data was then normalized using the function SCTransform v2. As samples were prepared on multiple days, the data was integrated across batches using reciprocal principal component analysis (RPCAIntegration). Principal component analysis and uniform manifold approximation and projection (UMAP) were performed followed by the FindNeighbors and FindClusters functions. We opted to cluster at a low resolution (0.25) to differentiate aortic cell types and to identify only major subpopulations of smooth muscle cells that vary by a large number of differentially expressed genes. FindMarkers was used to identify cluster- defining transcripts and differentially expression genes between control and diseased cell populations based on a Wilcoxon rank sum test.  
+
+Re- analysis of human aortic cells from Pedroza et al., 2023  
+
+For re- analysis of the ascending aorta and aortic root samples from a recently published scRNAseq dataset of the donor and LDS patient aortas59 we used the following criteria: \(>1000\) transcripts detected per cell but \(< 6000\) , \(>1500\) total molecules detected per cell \(< 30000\) , and \(< 20\%\) mitochondrial transcripts per cell. This reduces this dataset from 58,947 aortic cells to 43,349 for further analysis. We analyzed this dataset as described above with the FindClusters resolution parameter set to 0.15.
+
+<--- Page Split --->
+
+CoGAPS and ProjectR  
+
+CoGAPS and ProjectRCoGAPS<sup>60,61</sup> (v3.22), an R package that utilizes non- negative matrix factorization to uncover latent patterns of coordinated gene expression representative of shared biological functions, was used to identify transcriptional patterns associated with VSMC subpopulations, with the npatterns parameter set to 8, in scRNAseq analysis of murine aortas. ProjectR<sup>62</sup> (v1.2), an R package that enables integration and analysis of multiple scRNAseq data sets by identifying transcriptional patterns shared among datasets, was used to project these patterns into scRNAseq analysis of the human aortic root and ascending aorta.  
+
+Gene over- representation analyses  
+
+Gene over- representation analysesClueGO<sup>27</sup> was used for gene over- representation analysis and visualization of enriched functional terms for transcripts globally dysregulated in all VSMCs as well as VSMC subsets. Transcripts were filtered based on an adjusted P- value less than 0.05 and an average absolute Log2 fold change of 0.25 or greater, as well as detection in at least 20 percent of either control or LDS VSMCs. The resulting list of 502 downregulated and 200 upregulated genes was compared against five gene ontology databases (MSigDB Hallmark, KEGG, WikiPathways, Bioplanet, and Reactome). The list of transcripts and ClueGO log files are provided in supplemental material. Differentially expressed gene lists were also analyzed using the online gene list enrichment analysis tool EnrichR<sup>30- 32</sup> (https://maayanlab.cloud/Enrichr/) for pathways using the Molecular Signatures Database (MSigDB)<sup>63,64</sup> and for transcription factors target enrichment using the ENCODE<sup>28</sup> and ChEA<sup>29</sup> databases.  
+
+Multiplexed Error- Robust Fluorescence in situ Hybridization (MERFISH) Spatial Transcriptomics  
+
+MERFISH spatial transcriptomics using a custom panel was performed on 5- micron Formalin- Fixed Paraffin- Embedded (FFPE) sections of control and LDS aortas according to manufacturer's protocols (MERSCOPE FFPE Tissue Sample Preparation User Guide_Rev B, Vizgen). Slides were processed and imaged on a MERSCOPE instrument platform according to the manufacturer's protocols (MERSCOPE Instrument User Guide Rev G, Vizgen). The raw images were processed by the instrument software to generate a matrix of spatial genomics measurements and associated image files that were analyzed using the MERSCOPE visualizer software.  
+
+## Statistics  
+
+GraphPad Prism 10.0 was used for data visualization and statistical analysis. Data tested for normality using the Shapiro- Wilk test and upon verification of normal distribution, analyzed using the Brown- Forsythe ANOVA test. For echocardiographic and blood pressure measurements, data are presented as a box and whisker plot with the whiskers indicating the maximum and minimum values and a horizontal bar indicating the median. All individual data points are shown as dots. Figures indicating statistical significance include the statistical tests used in the figure caption.  
+
+## Data availability  
+
+All single- cell RNA sequencing data, both raw fastq files and aggregated matrixes, will be available in the gene expression omnibus (GEO) repository under accession number GSE267204. MERFISH spatial transcriptomics data is available upon request.
+
+<--- Page Split --->
+
+## Author contributions  
+
+EM and EB conceptualized the study, designed the experiments, interpreted data, and prepared the manuscript. EB and TJC generated and processed the single- cell RNA (scRNAseq) sequencing data. EB conducted the primary analysis of the scRNAseq data and performed a reanalysis of published scRNAseq datasets, with input from WE, TC, LR, and JM. EM conducted gene- over- representation analysis and visualization. EB, EM, WE, and LR were involved in sample preparation and processing for MERFISH. EB conducted in situ hybridization, immunofluorescence, and immunoblotting experiments. EB was responsible for echocardiography, blood pressure measurements, genotyping, and animal husbandry with support from TC, MS, WE, LR, and RB. AZ performed histological staining and imaging. GS provided support for CoGAPS analysis and MERFISH spatial transcriptomics. AP and MF provided human scRNAseq data and offered valuable insight on interpretation of the analysis. HD provided valuable input on the study design. EM and EB wrote the manuscript, all authors contributed to its revision.  
+
+## Acknowledgments  
+
+Research in this publication was supported by the National Heart, Lung, and Blood Institute of the National Institutes of Health under Award Numbers R01HL147947 to EM and F31HL163924 to EB as well as a generous gift from the Loeys- Dietz Foundation. Fluorescence Microscopy imaging was also supported by NIH award number S10OD023548 to the School of Medicine Microscope Facility. We would also like to acknowledge the Dietz and Stein- O'Brien labs for sharing resources.
+
+<--- Page Split --->
+
+505 References
+506 1 Chou, E., Pirruccello, J. P., Ellinor, P. T. & Lindsay, M. E. Genetics and mechanisms of thoracic aortic disease. Nat Rev Cardiol 20, 168- 180, doi:10.1038/s41569- 022- 00763- 0 (2023).
+510 2 Verstraeten, A., Luyckx, I. & Loeys, B. Aetiology and management of hereditary aortopathy. Nat Rev Cardiol 14, 197- 208, doi:10.1038/nrcardio.2016.211 (2017).
+511 3 Rodrigues Bento, J. et al. The Genetics and Typical Traits of Thoracic Aortic Aneurysm and Dissection. Annu Rev Genomics Hum Genet 23, 223- 253, doi:10.1146/annurev-genom- 111521- 104455 (2022).
+514 4 MacCarrick, G. et al. Loeys- Dietz syndrome: a primer for diagnosis and management. Genet Med 16, 576- 587, doi:10.1038/gim.2014.11 (2014).
+515 5 Loeys, B. L. et al. A syndrome of altered cardiovascular, craniofacial, neurocognitive and skeletal development caused by mutations in TGFBR1 or TGFBR2. Nat Genet 37, 275- 281, doi:10.1038/ng1511 (2005).
+516 6 van de Laar, I. M. et al. Mutations in SMAD3 cause a syndromic form of aortic aneurysms and dissections with early- onset osteoarthritis. Nat Genet 43, 121- 126, doi:ng.744 [pii]
+517 7 10.1038/ng.744 (2011).
+518 7 Lindsay, M. E. et al. Loss- of- function mutations in TGFB2 cause a syndromic presentation of thoracic aortic aneurysm. Nat Genet 44, 922- 927, doi:10.1038/ng.2349 (2012).
+519 8 Bertoli- Avella, A. M. et al. Mutations in a TGF- beta ligand, TGFB3, cause syndromic aortic aneurysms and dissections. J Am Coll Cardiol 65, 1324- 1336, doi:10.1016/j.jacc.2015.01.040 (2015).
+520 9 Micha, D. et al. SMAD2 Mutations Are Associated with Arterial Aneurysms and Dissections. Hum Mutat 36, 1145- 1149, doi:10.1002/humu.22854 (2015).
+521 10 van de Laar, I. M. et al. Phenotypic spectrum of the SMAD3- related aneurysms- osteoarthritis syndrome. J Med Genet 49, 47- 57, doi:10.1136/jmedgenet- 2011- 100382 (2012).
+522 11 Gallo, E. M. et al. Angiotensin II- dependent TGF- beta signaling contributes to Loeys- Dietz syndrome vascular pathogenesis. J Clin Invest 124, 448- 460, doi:69666 [pii]
+523 10.1172/JCI169666 (2014).
+524 12 Bertoli- Avella, A. M. et al. Mutations in a TGF- beta ligand, TGFB3, cause syndromic aortic aneurysms and dissections. J Am Coll Cardiol 65, 1324- 1336, doi:10.1016/j.jacc.2015.01.040 (2015).
+525 13 MacFarlane, E. G. et al. Lineage- specific events underlie aortic root aneurysm pathogenesis in Loeys- Dietz syndrome. J Clin Invest 129, 659- 675, doi:10.1172/JCI123547 (2019).
+526 14 Williams, J. A. et al. Early surgical experience with Loeys- Dietz: a new syndrome of aggressive thoracic aortic aneurysm disease. Ann Thorac Surg 83, S757- 763; discussion S785- 790, doi:10.1016/j.athoracsur.2006.10.091 (2007).
+527 15 Hughes, G. C. Aggressive aortic replacement for Loeys- Dietz syndrome. Tex Heart Inst J 38, 663- 666 (2011).
+
+<--- Page Split --->
+
+549 16 van der Linde, D. et al. Progression rate and early surgical experience in the new 550 aggressive aneurysms- osteoarthritis syndrome. Ann Thorac Surg 95, 563- 569, 551 doi:10.1016/j.athorascr.2012.07.009 (2013). 552 17 Patel, N. D. et al. Aortic Root Replacement for Children With Loeys- Dietz Syndrome. 553 Ann Thorac Surg 103, 1513- 1518, doi:10.1016/j.athorascr.2017.01.053 (2017). 554 18 Bell, V. et al. Longitudinal and circumferential strain of the proximal aorta. J Am Heart 555 Assoc 3, e001536, doi:10.1161/JAHA.114.001536 (2014). 556 19 Avril, S., Bersi, M. R., Bellini, C., Genovese, K. & Humphrey, J. D. Regional 557 identification of mechanical properties in arteries. Comput Methods Biomech Biomed 558 Engin 18 Suppl 1, 1874- 1875, doi:10.1080/10255842.2015.1070577 (2015). 559 20 Bersi, M. R., Bellini, C., Humphrey, J. D. & Avril, S. Local variations in material and 560 structural properties characterize murine thoracic aortic aneurysm mechanics. Biomech 561 Model Mechanobiol 18, 203- 218, doi:10.1007/s10237- 018- 1077- 9 (2019). 562 21 Gong, J. et al. In Vitro Lineage- Specific Differentiation of Vascular Smooth Muscle 563 Cells in Response to SMAD3 Deficiency: Implications for SMAD3- Related Thoracic 564 Aortic Aneurysm. Arterioscler Thromb Vasc Biol 40, 1651- 1663, 565 doi:10.1161/ATVBAHA.120.313033 (2020). 566 22 Sawada, H. et al. Second Heart Field- Derived Cells Contribute to Angiotensin II- 567 Mediated Ascending Aortopathies. Circulation 145, 987- 1001, 568 doi:10.1161/CIRCULATIONAHA.121.058173 (2022). 569 23 Kalluri, A. S. et al. Single- Cell Analysis of the Normal Mouse Aorta Reveals 570 Functionally Distinct Endothelial Cell Populations. Circulation 140, 147- 163, 571 doi:10.1161/CIRCULATIONAHA.118.038362 (2019). 572 24 Shen, Y. H. & LeMaire, S. A. Molecular pathogenesis of genetic and sporadic aortic 573 aneurysms and dissections. Curr Probl Surg 54, 95- 155, 574 doi:10.1067/j.cpsurg.2017.01.001 (2017). 575 25 Lu, H. et al. Vascular Smooth Muscle Cells in Aortic Aneurysm: From Genetics to 576 Mechanisms. J Am Heart Assoc 10, e023601, doi:10.1161/JAHA.121.023601 (2021). 577 26 Shannon, P. et al. Cytoscape: a software environment for integrated models of 578 biomolecular interaction networks. Genome Res 13, 2498- 2504, doi:10.1101/gr.1239303 (2003). 579 27 Bindea, G. et al. ClueGO: a Cytoscape plug- in to decipher functionally grouped gene 580 ontology and pathway annotation networks. Bioinformatics 25, 1091- 1093, 581 doi:10.1093/bioinformatics/btp101 (2009). 582 28 Luo, Y. et al. New developments on the Encyclopedia of DNA Elements (ENCODE) 583 data portal. Nucleic Acids Res 48, D882- D889, doi:10.1093/nar/gkz1062 (2020). 584 Lachmann, A. et al. ChEA: transcription factor regulation inferred from integrating 585 genome- wide ChIP- X experiments. Bioinformatics 26, 2438- 2444, 586 doi:10.1093/bioinformatics/btq466 (2010). 587 30 Chen, E. Y. et al. Enrichr: interactive and collaborative HTML5 gene list enrichment 588 analysis tool. BMC Bioinformatics 14, 128, doi:10.1186/1471- 2105- 14- 128 (2013). 589 31 Kuleshov, M. V. et al. Enrichr: a comprehensive gene set enrichment analysis web server 590 2016 update. Nucleic Acids Res 44, W90- 97, doi:10.1093/nar/gkw377 (2016). 591 32 Xie, Z. et al. Gene Set Knowledge Discovery with Enrichr. Curr Protoc 1, e90, 592 doi:10.1002/cpz1.90 (2021).
+
+<--- Page Split --->
+
+594 33 Jain, A. et al. p62/SQSTM1 is a target gene for transcription factor NRF2 and creates a 595 positive feedback loop by inducing antioxidant response element- driven gene 596 transcription. J Biol Chem 285, 22576- 22591, doi:10.1074/jbc.M110.118976 (2010). 597 34 Ashino, T., Yamamoto, M., Yoshida, T. & Numazawa, S. Redox- sensitive transcription 598 factor Nrf2 regulates vascular smooth muscle cell migration and neointimal hyperplasia. 599 Arterioscler Thromb Vasc Biol 33, 760- 768, doi:10.1161/ATVBAHA.112.300614 600 (2013). 601 35 Olagnier, D. et al. Nrf2 negatively regulates STING indicating a link between antiviral 602 sensing and metabolic reprogramming. Nat Commun 9, 3506, doi:10.1038/s41467- 018- 603 05861- 7 (2018). 604 36 Johnson, A. D. & Owens, G. K. Differential activation of the SMalphaA promoter in 605 smooth vs. skeletal muscle cells by bHLH factors. Am J Physiol 276, C1420- 1431, 606 doi:10.1152/ajpcell.1999.276.6.C1420 (1999). 607 37 Chen, Y. H., Layne, M. D., Watanabe, M., Yet, S. F. & Perrella, M. A. Upstream 608 stimulatory factors regulate aortic preferentially expressed gene- 1 expression in vascular 609 smooth muscle cells. J Biol Chem 276, 47658- 47663, doi:10.1074/jbc.M108678200 610 (2001). 611 38 Kumar, M. S. & Owens, G. K. Combinatorial control of smooth muscle- specific gene 612 expression. Arterioscler Thromb Vasc Biol 23, 737- 747, 613 doi:10.1161/01.ATV.0000065197.07635.BA (2003). 614 39 Sellak, H., Choi, C., Browner, N. & Lincoln, T. M. Upstream stimulatory factors (USF- 615 1/USF- 2) regulate human cGMP- dependent protein kinase I gene expression in vascular 616 smooth muscle cells. J Biol Chem 280, 18425- 18433, doi:10.1074/jbc.M500775200 617 (2005). 618 40 Ackers- Johnson, M. et al. Myocardin regulates vascular smooth muscle cell 619 inflammatory activation and disease. Arterioscler Thromb Vasc Biol 35, 817- 828, 620 doi:10.1161/ATVBAHA.114.305218 (2015). 621 41 Wang, Q. et al. A hierarchical and collaborative BRD4/CEBPD partnership governs 622 vascular smooth muscle cell inflammation. Mol Ther Methods Clin Dev 21, 54- 66, 623 doi:10.1016/j.omtm.2021.02.021 (2021). 624 42 Kan, M. et al. CEBPD modulates the airway smooth muscle transcriptomic response to 625 glucocorticoids. Respir Res 23, 193, doi:10.1186/s12931- 022- 02119- 1 (2022). 626 43 Ko, C. Y., Chang, W. C. & Wang, J. M. Biological roles of CCAAT/Enhancer- binding 627 protein delta during inflammation. J Biomed Sci 22, 6, doi:10.1186/s12929- 014- 0110- 2 628 (2015). 629 44 Herzig, T. C. et al. Angiotensin II type1a receptor gene expression in the heart: AP- 1 and 630 GATA- 4 participate in the response to pressure overload. Proc Natl Acad Sci U S A 94, 631 7543- 7548 (1997). 632 45 Bramel, E. E. et al. Distinct Contribution of Global and Regional Angiotensin II Type 1a 633 Receptor Inactivation to Amelioration of Aortopathy in Tgfb1 (M318R/) Mice. Front 634 Cardiovasc Med 9, 936142, doi:10.3389/fcvm.2022.936142 (2022). 635 46 Ren, Q. et al. C/EBPbeta: The structure, regulation, and its roles in inflammation- related 636 diseases. Biomed Pharmacother 169, 115938, doi:10.1016/j.biopha.2023.115938 (2023). 637 47 Mondal, T. et al. MEG3 long noncoding RNA regulates the TGF- beta pathway genes 638 through formation of RNA- DNA triplex structures. Nat Commun 6, 7743, 639 doi:10.1038/ncomms8743 (2015).
+
+<--- Page Split --->
+
+640 48 Mondal, T. et al. Author Correction: MEG3 long noncoding RNA regulates the TGF- beta pathway genes through formation of RNA- DNA triplex structures. Nat Commun 10, 5290, doi:10.1038/s41467- 019- 13200- 7 (2019). 643 49 Wang, M. et al. LncRNA MEG3- derived miR- 361- 5p regulate vascular smooth muscle cells proliferation and apoptosis by targeting ABCA1. Am J Transl Res 11, 3600- 3609 (2019). 646 50 Zhou, Y., Li, X., Zhao, D., Li, X. & Dai, J. Long noncoding RNA MEG3 knockdown alleviates hypoxiainduced injury in rat cardiomyocytes via the miR3253p/TRPV4 axis. Mol Med Rep 23, doi:10.3892/mmr.2020.11656 (2021). 649 51 Dong, K. et al. CARMN Is an Evolutionarily Conserved Smooth Muscle Cell- Specific LncRNA That Maintains Contractile Phenotype by Binding Myocardin. Circulation 144, 1856- 1875, doi:10.1161/CIRCULATIONAHA.121.055949 (2021). 652 52 Lu, B. H. et al. Long non- coding RNAs: Modulators of phenotypic transformation in vascular smooth muscle cells. Front Cardiovasc Med 9, 959955, doi:10.3389/fcvm.2022.959955 (2022). 653 53 Liu, S. et al. LncRNA CARMN inhibits abdominal aortic aneurysm formation and vascular smooth muscle cell phenotypic transformation by interacting with SRF. Cell Mol Life Sci 81, 175, doi:10.1007/s00018- 024- 05193- 4 (2024). 654 54 Bramel, E. E. et al. Postnatal Smad3 Inactivation in Murine Smooth Muscle Cells Elicits a Temporally and Regionally Distinct Transcriptional Response. Front Cardiovasc Med 9, 826495, doi:10.3389/fcvm.2022.826495 (2022). 655 55 Sawada, H., Rateri, D. L., Moorleghen, J. J., Majesky, M. W. & Daugherty, A. Smooth Muscle Cells Derived From Second Heart Field and Cardiac Neural Crest Reside in Spatially Distinct Domains in the Media of the Ascending Aorta- Brief Report. Arterioscler Thromb Vasc Biol 37, 1722- 1726, doi:10.1161/ATVBAHA.117.309599 (2017). 656 56 Sawada, H. et al. Heterogeneity of Aortic Smooth Muscle Cells: A Determinant for Regional Characteristics of Thoracic Aortic Aneurysms? J Transl Int Med 6, 93- 96, doi:10.2478/jtim- 2018- 0023 (2018). 657 57 Zhou, D. et al. hiPSC Modeling of Lineage- Specific Smooth Muscle Cell Defects Caused by TGFBR1(A230T) Variant, and Its Therapeutic Implications for Loeys- Dietz Syndrome. Circulation 144, 1145- 1159, doi:10.1161/CIRCULATIONAHA.121.054744 (2021). 658 58 Pedroza, A. J. et al. Embryologic Origin Influences Smooth Muscle Cell Phenotypic Modulation Signatures in Murine Marfan Syndrome Aortic Aneurysm. Arterioscler Thromb Vasc Biol 42, 1154- 1168, doi:10.1161/ATVBAHA.122.317381 (2022). 659 59 Pedroza, A. J. et al. Early clinical outcomes and molecular smooth muscle cell phenotyping using a prophylactic aortic arch replacement strategy in Loeys- Dietz syndrome. J Thorac Cardiovasc Surg 166, e332- e376, doi:10.1016/j.jtcvs.2023.07.023 (2023). 660 60 Sherman, T. D., Gao, T. & Fertig, E. J. CoGAPS 3: Bayesian non- negative matrix factorization for single- cell analysis with asynchronous updates and sparse data structures. BMC Bioinformatics 21, 453, doi:10.1186/s12859- 020- 03796- 9 (2020). 661 61 Johnson, J. A. I., Tsang, A., Mitchell, J. T., Davis- Marcisak, E. F., Sherman, T., Liefeld, T., Stein- O'Brien, G. L. . Inferring cellular and molecular processes in single- cell data
+
+<--- Page Split --->
+
+685 with non- negative matrix factorization using Python, R, and GenePattern Notebook 686 implementations of CoGAPS. BioRxiv. (2022). 687 Sharma, G., Colantuoni, C., Goff, L. A., Fertig, E. J. & Stein- O'Brien, G. projectR: an 688 R/Bioconductor package for transfer learning via PCA, NMF, correlation and clustering. 689 Bioinformatics 36, 3592- 3593, doi:10.1093/bioinformatics/btaa183 (2020). 690 Liberzon, A. et al. The Molecular Signatures Database (MSigDB) hallmark gene set 691 collection. Cell Syst 1, 417- 425, doi:10.1016/j.cels.2015.12.004 (2015). 692 Castanza, A. S. et al. Extending support for mouse data in the Molecular Signatures 693 Database (MSigDB). Nat Methods 20, 1619- 1620, doi:10.1038/s41592- 023- 02014- 7 694 (2023). 695 Anisowicz, A., Messineo, M., Lee, S. W. & Sager, R. An NF- kappa B- like transcription 696 factor mediates IL- 1/TNF- alpha induction of gro in human fibroblasts. J Immunol 147, 520- 527 (1991). 697 Issa, R. et al. GRO- alpha regulation in airway smooth muscle by IL- 1beta and TNF- 698 alpha: role of NF- kappaB and MAP kinases. Am J Physiol Lung Cell Mol Physiol 291, 700 L66- 74, doi:10.1152/ajplung.00384.2005 (2006). 701 Wang, L. et al. Genetic and Pharmacologic Inhibition of the Chemokine Receptor 702 CXCR2 Prevents Experimental Hypertension and Vascular Dysfunction. Circulation 134, 703 1353- 1368, doi:10.1161/CIRCULATIONAHA.115.020754 (2016). 704 Korbecki, J., Maruszewska, A., Bosiacki, M., Chlubek, D. & Baranowska- Bosiacka, I. 705 The Potential Importance of CXCL1 in the Physiological State and in Noncancer 706 Diseases of the Cardiovascular System, Respiratory System and Skin. Int J Mol Sci 24, 707 doi:10.3390/ijms24010205 (2022). 708 Tliba, O. et al. Tumor necrosis factor alpha modulates airway smooth muscle function via 709 the autocrine action of interferon beta. J Biol Chem 278, 50615- 50623, 710 doi:10.1074/jbc.M303680200 (2003). 711 Dagia, N. M. et al. Phenyl methimazole inhibits TNF- alpha- induced VCAM- 1 expression 712 in an IFN regulatory factor- 1- dependent manner and reduces monocytic cell adhesion to 713 endothelial cells. J Immunol 173, 2041- 2049, doi:10.4049/jimmunol.173.3.2041 (2004). 714 Shen, Y. et al. IRF- 1 contributes to the pathological phenotype of VSMCs during 715 atherogenesis by increasing CCL19 transcription. Aging (Albany NY) 13, 933- 943, 716 doi:10.18632/aging.202204 (2020). 717 Liu, Z. et al. Thrombospondin- 1 (TSP1) contributes to the development of vascular 718 inflammation by regulating monocytic cell motility in mouse models of abdominal aortic 719 aneurysm. Circ Res 117, 129- 141, doi:10.1161/CIRCRESAHA.117.305262 (2015). 720 Kang, C. et al. The DNA damage response induces inflammation and senescence by 721 inhibiting autophagy of GATA4. Science 349, aaa5612, doi:10.1126/science.aaa5612 722 (2015). 723 Birsoy, K., Chen, Z. & Friedman, J. Transcriptional regulation of adipogenesis by KLF4. 724 Cell Metab 7, 339- 347, doi:10.1016/j.cmet.2008.02.001 (2008). 725 Liu, R. et al. Ten- eleven translocation- 2 (TET2) is a master regulator of smooth muscle 726 cell plasticity. Circulation 128, 2047- 2057, 727 doi:10.1161/CIRCULATIONAHA.113.002887 (2013). 728 Shi, N., Li, C. X., Cui, X. B., Tomarev, S. I. & Chen, S. Y. Olfactomedin 2 Regulates 729 Smooth Muscle Phenotypic Modulation and Vascular Remodeling Through Mediating
+
+<--- Page Split --->
+
+730 Runt- Related Transcription Factor 2 Binding to Serum Response Factor. Arterioscler 731 Thromb Vasc Biol 37, 446- 454, doi:10.1161/ATVBAHA.116.308606 (2017). 732 77 Iyer, D. et al. Coronary artery disease genes SMAD3 and TCF21 promote opposing 733 interactive genetic programs that regulate smooth muscle cell differentiation and disease 734 risk. PLoS Genet 14, e1007681, doi:10.1371/journal.pgen.1007681 (2018). 735 78 Lino Cardenas, C. L. et al. An HDAC9- MALAT1- BRG1 complex mediates smooth 736 muscle dysfunction in thoracic aortic aneurysm. Nat Commun 9, 1009, 737 doi:10.1038/s41467- 018- 03394- 7 (2018). 738 79 Yap, C., Mieremet, A., de Vries, C. J. M., Micha, D. & de Waard, V. Six Shades of 739 Vascular Smooth Muscle Cells Illuminated by KLF4 (Kruppel- Like Factor 4). 740 Arterioscler Thromb Vasc Biol 41, 2693- 2707, doi:10.1161/ATVBAHA.121.316600 741 (2021). 742 80 Huang, X., Jie, S., Li, W. & Liu, C. GATA4- activated lncRNA MALAT1 promotes 743 osteogenic differentiation through inhibiting NEDD4- mediated RUNX1 degradation. Cell 744 Death Discov 9, 150, doi:10.1038/s41420- 023- 01422- 0 (2023). 745 81 Grootaert, M. O. et al. Defective autophagy in vascular smooth muscle cells accelerates 746 senescence and promotes neointima formation and atherogenesis. Autophagy 11, 2014- 747 2032, doi:10.1080/15548627.2015.1096485 (2015). 748 82 Jeong, K. et al. Nuclear Focal Adhesion Kinase Controls Vascular Smooth Muscle Cell 749 Proliferation and Neointimal Hyperplasia Through GATA4- Mediated Cyclin D1 750 Transcription. Circ Res 125, 152- 166, doi:10.1161/CIRCRESAHA.118.314344 (2019). 751 83 Watt, A. J., Battle, M. A., Li, J. & Duncan, S. A. GATA4 is essential for formation of the 752 proepicardium and regulates cardiogenesis. Proc Natl Acad Sci U S A 101, 12573- 12578, 753 doi:10.1073/pnas.0400752101 (2004). 754 84 Wirth, A. et al. G12- G13- LARG- mediated signaling in vascular smooth muscle is 755 required for salt- induced hypertension. Nat Med 14, 64- 68, doi:10.1038/nm1666 (2008). 756 85 Bostrom, P. et al. C/EBPbeta controls exercise- induced cardiac growth and protects 757 against pathological cardiac remodeling. Cell 143, 1072- 1083, 758 doi:10.1016/j.cell.2010.11.036 (2010). 759 86 Chang, L. H. et al. Role of macrophage CCAAT/enhancer binding protein delta in the 760 pathogenesis of rheumatoid arthritis in collagen- induced arthritic mice. PLoS One 7, 761 e45378, doi:10.1371/journal.pone.0045378 (2012). 762 87 van Dorst, D. C. H. et al. Transforming Growth Factor- beta and the Renin- Angiotensin 763 System in Syndromic Thoracic Aortic Aneurysms: Implications for Treatment. 764 Cardiovasc Drugs Ther, doi:10.1007/s10557- 020- 07116- 4 (2020). 765 88 Gillis, E., Van Laer, L. & Loeys, B. L. Genetics of thoracic aortic aneurysm: at the 766 crossroad of transforming growth factor- beta signaling and vascular smooth muscle cell 767 contractility. Circ Res 113, 327- 340, doi:10.1161/CIRCRESAHA.113.300675 (2013). 768 89 Li, W. et al. Tgfrb2 disruption in postnatal smooth muscle impairs aortic wall 769 homeostasis. J Clin Invest 124, 755- 767, doi:69942 [pii] 770 10.1172/JCI69942 (2014). 771 90 Hu, J. H. et al. Postnatal Deletion of the Type II Transforming Growth Factor- beta 772 Receptor in Smooth Muscle Cells Causes Severe Aortopathy in Mice. Arterioscler 773 Thromb Vasc Biol 35, 2647- 2656, doi:10.1161/ATVBAHA.115.306573 (2015). 774 91 Angelov, S. N. et al. TGF- beta (Transforming Growth Factor- beta) Signaling Protects the 775 Thoracic and Abdominal Aorta From Angiotensin II- Induced Pathology by Distinct
+
+<--- Page Split --->
+
+776 Mechanisms. Arterioscler Thromb Vasc Biol 37, 2102- 2113, 777 doi:10.1161/ATVBAHA.117.309401 (2017). 778 92 Wei, H. et al. Aortopathy in a Mouse Model of Marfan Syndrome Is Not Mediated by 779 Altered Transforming Growth Factor beta Signaling. J Am Heart Assoc 6, e004968, 780 doi:10.1161/JAHA.116.004968 (2017). 781 93 Chen, P. Y. et al. Endothelial TGF- beta signalling drives vascular inflammation and 782 atherosclerosis. Nat Metab 1, 912- 926, doi:10.1038/s42255- 019- 0102- 3 (2019). 783 94 Chen, P. Y. et al. Smooth Muscle Cell Reprogramming in Aortic Aneurysms. Cell Stem 784 Cell 26, 542- 557 e511, doi:10.1016/j.stem.2020.02.013 (2020). 785 95 Creamer, T. J., Bramel, E. E. & MacFarlane, E. G. Insights on the Pathogenesis of 786 Aneurysm through the Study of Hereditary Aortopathies. Genes (Basel) 12, 787 doi:10.3390/genes12020183 (2021). 788 96 Eguchi, S. et al. Recent Advances in Understanding the Molecular Pathophysiology of 789 Angiotensin II Receptors: Lessons From Cell- Selective Receptor Deletion in Mice. Can J 790 Cardiol 39, 1795- 1807, doi:10.1016/j.cjca.2023.06.421 (2023). 791 97 Daugherty, A., Sawada, H., Sheppard, M. B. & Lu, H. S. Angiotensinogen as a 792 Therapeutic Target for Cardiovascular and Metabolic Diseases. Arterioscler Thromb 793 Vasc Biol 44, 1021- 1030, doi:10.1161/ATVBAHA.124.318374 (2024). 794 98 Michel, J. B., Jondeau, G. & Milewicz, D. M. From genetics to response to injury: 795 vascular smooth muscle cells in aneurysms and dissections of the ascending aorta. 796 Cardiovasc Res 114, 578- 589, doi:10.1093/cvr/cvy006 (2018). 797 99 Karimi, A. & Milewicz, D. M. Structure of the Elastin- Contractile Units in the Thoracic 798 Aorta and How Genes That Cause Thoracic Aortic Aneurysms and Dissections Disrupt 799 This Structure. Can J Cardiol 32, 26- 34, doi:10.1016/j.cjca.2015.11.004 (2016). 800 100 Pedroza, A. J. et al. Single- Cell Transcriptomic Profiling of Vascular Smooth Muscle 801 Cell Phenotype Modulation in Marfan Syndrome Aortic Aneurysm. Arterioscler Thromb 802 Vasc Biol, ATVBAHA120314670, doi:10.1161/ATVBAHA.120.314670 (2020). 803 101 Salabei, J. K. & Hill, B. G. Autophagic regulation of smooth muscle cell biology. Redox 804 Biol 4, 97- 103, doi:10.1016/j.redox.2014.12.007 (2015). 805 102 Clement, M. et al. Vascular Smooth Muscle Cell Plasticity and Autophagy in Dissecting 806 Aortic Aneurysms. Arterioscler Thromb Vasc Biol 39, 1149- 1159, 807 doi:10.1161/ATVBAHA.118.311727 (2019). 808 103 Pikkarainen, S. et al. GATA- 4 is a nuclear mediator of mechanical stretch- activated 809 hypertrophic program. J Biol Chem 278, 23807- 23816, doi:10.1074/jbc.M302719200 810 (2003). 811 104 Wang, Y. Q., Batool, A., Chen, S. R. & Liu, Y. X. GATA4 is a negative regulator of 812 contractility in mouse testicular peritubular myoid cells. Reproduction 156, 343- 351, 813 doi:10.1530/REP- 18- 0148 (2018). 814 105 Oka, T. et al. Cardiac- specific deletion of Gata4 reveals its requirement for hypertrophy, 815 compensation, and myocyte viability. Circ Res 98, 837- 845, 816 doi:10.1161/01.RES.0000215985.18538.c4 (2006). 817 106 Garg, V. et al. GATA4 mutations cause human congenital heart defects and reveal an 818 interaction with TBX5. Nature 424, 443- 447, doi:10.1038/nature01827 (2003). 819 107 Kuo, C. T. et al. GATA4 transcription factor is required for ventral morphogenesis and 820 heart tube formation. Genes Dev 11, 1048- 1060 (1997).
+
+<--- Page Split --->
+
+821 108 Liang, Q. et al. The transcription factors GATA4 and GATA6 regulate cardiomyocyte 822 hypertrophy in vitro and in vivo. J Biol Chem 276, 30245- 30253, 823 doi:10.1074/jbc.M102174200 (2001). 824 109 Lepage, D. et al. Gata4 is critical to maintain gut barrier function and mucosal integrity 825 following epithelial injury. Sci Rep 6, 36776, doi:10.1038/srep36776 (2016). 826 110 Liu, J. et al. Cell- specific translational profiling in acute kidney injury. J Clin Invest 124, 827 1242- 1254, doi:10.1172/JCI72126 (2014). 828 111 Lewis, A. E., Vasudevan, H. N., O'Neill, A. K., Soriano, P. & Bush, J. O. The widely 829 used Wnt1- Cre transgene causes developmental phenotypes by ectopic activation of Wnt 830 signaling. Dev Biol 379, 229- 234, doi:10.1016/j.ydbio.2013.04.026 (2013). 831 112 Hao, Y. et al. Dictionary learning for integrative, multimodal and scalable single- cell 832 analysis. Nat Biotechnol 42, 293- 304, doi:10.1038/s41587- 023- 01767- y (2024). 833 113 Zheng, G. X. et al. Massively parallel digital transcriptional profiling of single cells. Nat 834 Commun 8, 14049, doi:10.1038/ncomms14049 (2017). 835 836
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Downregulation of transcripts associated with extracellular matrix-receptor interactions and upregulation of stress and inflammation pathways in Tgfbr1<sup>M318R/+</sup> LDS VSMCs. (A) Uniform manifold approximation and projection (UMAP) of aortic cells from control (Tgfbr1<sup>+/+</sup>) and LDS (Tgfbr1<sup>M318R/+</sup>) mice. (B) Dot plot of cluster defining transcripts used to identify endothelial cells, leukocytes, fibroblasts, and VSMCs. Color of the dot represents a scaled average expression while the size indicates the percentage of cells in which the transcript was detected. (C) ClueGO gene enrichment analysis network of transcripts dysregulated in LDS VSMCs relative to controls. Each node represents a term/pathway or individual genes associated with that term. The color of the node corresponds to the ClueGO group to which each node belongs. The size of the node indicates significance of the enrichment calculated by the ClueGO algorithm. (D) ClueGO network in which terms differentially enriched among transcripts downregulated in LDS VSMCs are highlighted in blue, while those enriched among transcripts upregulated in LDS VSMCs are highlighted in red. (E) Dot plot showing expression of a selection of transcripts significantly dysregulated in LDS VSMCs. (F,G) EnrichR gene over-representation analysis for the ENCODE and ChEA Consensus transcription factors (TF) databases showing the top three most significant terms associated with transcripts that are downregulated (F) or upregulated (G) in LDS VSMCs. </center>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. MERFISH reveals spatially heterogeneous transcriptional profiles in LDS VSMCs. MERFISH images of the proximal aorta of LDS (A) and control (B) mice, scale bar is 1 mm. The first panel displays all detected transcripts across the aortic tissue, with key anatomic landmarks indicated. Subsequent panels depict the colocalization of Myh11 and transcripts of interest. Insets note regions of the ascending aorta and aortic root that are presented at higher magnification. </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. Transcriptionaly and spatially-defined VSMC subclusters with distinct responses to LDS-causing mutations can be identified in both murine and human aortas. (A) UMAP of VSMCs from control (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) mice shown split by genotype. (B) Dot plot showing enrichment of cluster-defining transcripts in VSMC1 and VSMC2. For a given transcript, the color of the dot represents a scaled average expression while the size indicates the percentage of cells in which it was detected. (C) RNA in situ hybridization showing the expression of Gata4 along the length of the murine aorta in a 16-week old control animal. (D) UMAP of control and LDS VSMCs from human patients and dot plot of cluster defining markers in this dataset split by aortic region (Pedroza et al., 2023). (E,F) UMAP overlayed with weights for CoGAPS patterns 4 and 5, in mouse and human scRNAseq datasets. (G,H) Violin plots showing the distribution of pattern 4 and 5 weights in VSMC subclusters from mouse and human scRNAseq datasets. P-values refer to Wilcoxon test. (I) EnrichR gene over-representation analysis for the ENCODE and ChEA Consensus TF databases showing the top four most significant terms associated with transcripts that define CoGAPs Patterns 4 and 5. (J) ClueGO network of terms differentially enriched in mouse and human LDS VSMC2 relative to VSMC1. Terms highlighted in blue are enriched in VSMC1, while those highlighted in red are enriched in VSMC2. </center>
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4 </center>  
+
+Figure 4. Gata4 mRNA and protein are upregulated in the aortic root of LDS mice. (A) Representative images of RNA in situ hybridization for Gata4 in the aortic root and ascending aorta of control and LDS (Tgfbr1M318R/+) mice. Insets identify the location shown at higher magnification in the subsequent panel. Scale bars 50 and 200 microns, respectively. (B) Representative images of immunofluorescence for GATA4in the aortic root and ascending aorta of control and LDS mice. Insets identify the location shown at higher magnification in the subsequent panel. Scale bars 50 and 200 microns, respectively. (C) Immunoblot for Gata4 expression relative to \(\beta\) - actin in aortic root lysates of control \((n = 3)\) and LDS mice \((n = 3)\) , and related quantification of immunoblot, P- value refers to two- tailed Student's t- test.
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5 </center>  
+
+Figure 5. Gata4 protein is upregulated in LDS aortic root of Gata4<sup>Ctrl</sup> and effectively ablated in Gata4<sup>SMckO</sup> mice. Representative images of immunofluorescence for GATA4 at 16 weeks of age. Three independent biological replicates are shown per genotype abbreviated as follows Control (Tgfbr1<sup>+/+</sup>) and LDS (Tgfbr1<sup>M318R/+</sup>) with (Gata4<sup>SMckO</sup>) or without (Gata4<sup>Ctrl</sup>) smooth muscle specific deletion of Gata4 Insets identify location shown at higher magnification in subsequent panels. Images were acquired at 20x magnification. Scale bars 50 and 200 microns, respectively.
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+<center>B </center>  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6. Smooth muscle-specific deletion of Gata4 (Gata4SMcKO) reduces aortic root size and growth and improves aortic root media architecture in LDS mice. (A) Aortic root diameter of Ctrl (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) with (Gata4SMcKO) or without (Gata4SMcKO) smooth muscle specific deletion of Gata4 as measured by echocardiography at 8 and 16 weeks of age and aortic root growth from 8-16 weeks. P-values refer to Brown-Forsythe ANOVA. (B) Representative VVG-stained aortic root sections from three independent biological replicates per genotype. Insets identify area shown at higher magnification in the subsequent panel. Scale bars 50 and 200 microns, respectively. </center>
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Figure 7 </center>  
+
+Figure 7. Smooth muscle-specific deletion of Gata4 results in reduced expression of Agtr1a. Representative images of RNA in situ hybridization for Agtr1a in the aortic root of mice at 16 weeks of age. Three independent biological replicates are shown per genotype abbreviated as follows Control (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) with (Gata4SmKo) or without (Gata4Ctl) smooth muscle specific deletion of Gata4. Insets identify location shown at higher magnification in subsequent panels. Images were acquired at 20x magnification. Scale bars 50 and 200 microns, respectively.
+
+<--- Page Split --->
+![](images/Figure_8.jpg)
+
+<center>Figure 8 </center>  
+
+Figure 8. Smooth muscle-specific deletion of Gata4 results in reduced expression of Cebpb. Representative images of RNA in situ hybridization for Cebpb in the aortic root of mice of indicated genotype at 16 weeks of age. Three independent biological replicates are shown per genotype abbreviated as follows Control (Tgfbr1<sup>+/+</sup>) and LDS (Tgfbr1<sup>M318R/+</sup>) with (Gata4<sup>SMckO</sup>) or without (Gata4<sup>Ctrl</sup>) smooth muscle specific deletion of Gata4. Insets identify location shown at higher magnification in subsequent panels. Images were acquired at 20x magnification. Scale bars 50 and 200 microns, respectively.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryTables.zip  - SupplementalFigures.zip  - CORRECTEDPrimaryfigure6forversion1. pdf  - CORRECTEDSupplementalFigures6and7forversion1. pdf
+
+<--- Page Split --->

preprint/preprint__00aa363715f9caf53b3b56fb3500a871c4d4ad7d3f29389a4c2af752e13f7a19/preprint__00aa363715f9caf53b3b56fb3500a871c4d4ad7d3f29389a4c2af752e13f7a19_det.mmd

@@ -0,0 +1,425 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 940, 175]]<|/det|>
+# Intrinsic Gata4 expression sensitizes the aortic root to dilation in a Loeys-Dietz syndrome mouse model  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 810, 240]]<|/det|>
+Emily Bramel  Johns Hopkins University School of Medicine https://orcid.org/0000- 0003- 4602- 9506  
+
+<|ref|>text<|/ref|><|det|>[[44, 244, 450, 285]]<|/det|>
+Wendy Espinoza Camejo  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 291, 450, 332]]<|/det|>
+Tyler Creamer  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 338, 450, 378]]<|/det|>
+Leda Restrepo  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 383, 450, 424]]<|/det|>
+Muzna Saqib  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 430, 450, 470]]<|/det|>
+Rustam Bagirzadeh  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 476, 450, 516]]<|/det|>
+Anthony Zeng  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 521, 450, 562]]<|/det|>
+Jacob Mitchell  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 567, 450, 608]]<|/det|>
+Genevieve Stein- O'Brien  Johns Hopkins University School of Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 613, 582, 654]]<|/det|>
+Albert Pedroza  Stanford University https://orcid.org/0000- 0001- 5291- 5980  
+
+<|ref|>text<|/ref|><|det|>[[44, 659, 225, 700]]<|/det|>
+Michael Fischbein  Stanford University  
+
+<|ref|>text<|/ref|><|det|>[[44, 706, 720, 747]]<|/det|>
+Harry Dietz  Johns Hopkins School of Medicine https://orcid.org/0000- 0002- 6856- 0165  
+
+<|ref|>text<|/ref|><|det|>[[44, 752, 250, 793]]<|/det|>
+Elena Gallo MacFarlane  egal101@jhmi.edu  
+
+<|ref|>text<|/ref|><|det|>[[52, 824, 799, 844]]<|/det|>
+Genetic Medicine, Johns Hopkins University https://orcid.org/0000- 0001- 5677- 6842  
+
+<|ref|>text<|/ref|><|det|>[[44, 885, 102, 902]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 923, 136, 941]]<|/det|>
+Keywords:
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[43, 45, 291, 64]]<|/det|>
+**Posted Date:** June 5th, 2024 
+
+<|ref|>text<|/ref|><|det|>[[43, 84, 476, 102]]<|/det|>
+**DOI:** https://doi.org/10.21203/rs.3.rs-4420617/v1 
+
+<|ref|>text<|/ref|><|det|>[[43, 121, 914, 163]]<|/det|>
+**License:** © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License 
+
+<|ref|>text<|/ref|><|det|>[[43, 183, 536, 201]]<|/det|>
+**Additional Declarations:** There is **NO** Competing Interest. 
+
+<|ref|>text<|/ref|><|det|>[[43, 239, 890, 280]]<|/det|>
+**Version of Record:** A version of this preprint was published at Nature Cardiovascular Research on November 20th, 2024. See the published version at https://doi.org/10.1038/s44161-024-00562-5. 
+
+<|ref|>sub_title<|/ref|><|det|>[[65, 322, 303, 345]]<|/det|>
+## EDITORIAL NOTE: 
+
+<|ref|>text<|/ref|><|det|>[[65, 373, 930, 460]]<|/det|>
+August 15, 2024. Editorial Note: In version 1 of this preprint (posted June 5, 2024) the authors have reported some unintentional errors in the x-axis labeling of figure 6A and supplemental figures 6 and 7. New figure files with corrected labeling have now been added to the version 1 preprint in the supplementary file section as follows. 
+
+<|ref|>text<|/ref|><|det|>[[65, 464, 912, 528]]<|/det|>
+**CORRECTED** Primary figure 6 for version 1 - in part A, the x axis labels have been corrected **CORRECTED** Supplemental Figures 6 and 7 for version 1 - in both supplemental figures, the x axis labels have been corrected
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[75, 89, 861, 125]]<|/det|>
+1 Intrinsic Gata4 expression sensitizes the aortic root to dilation in a Loeys- Dietz syndrome 2 mouse model  
+
+<|ref|>text<|/ref|><|det|>[[112, 138, 857, 210]]<|/det|>
+3 Emily E. Bramel<sup>1,2</sup>, Wendy A. Espinoza Camejo<sup>1,2</sup>, Tyler J. Creamer<sup>1</sup>, Leda Restrepo<sup>1</sup>, 4 Muzna Saqib<sup>1</sup>, Rustam Bagirzadeh<sup>1</sup>, Anthony Zeng<sup>1</sup>, Jacob T. Mitchell<sup>1,2</sup>, Genevieve L. 5 Stein- O'Brien<sup>1,4</sup>, Albert J. Pedroza<sup>5</sup>, Michael P. Fischbein<sup>5</sup>, Harry C. Dietz<sup>1</sup>, Elena Gallo 6 MacFarlane<sup>1,3\*  
+
+<|ref|>text<|/ref|><|det|>[[112, 225, 861, 396]]<|/det|>
+7 <sup>1</sup>McKusick- Nathans Department of Genetic Medicine, Johns Hopkins University School of 8 Medicine, Baltimore, Maryland, USA 9 <sup>2</sup> Predoctoral Training in Human Genetics and Genomics, Johns Hopkins University School of 10 Medicine, Baltimore, Maryland, USA 11 <sup>3</sup> Department of Surgery, Johns Hopkins University School of Medicine, Baltimore, Maryland, 12 USA 13 <sup>4</sup>Solomon H. Snyder Department of Neuroscience, Johns Hopkins University School of 14 Medicine, Baltimore, Maryland, USA 15 <sup>5</sup>Department of Cardiothoracic Surgery, Stanford University School of Medicine, Stanford, 16 California, USA  
+
+<|ref|>text<|/ref|><|det|>[[115, 416, 310, 432]]<|/det|>
+\* Correspondence:  
+
+<|ref|>text<|/ref|><|det|>[[115, 434, 310, 450]]<|/det|>
+Elena Gallo MacFarlane  
+
+<|ref|>text<|/ref|><|det|>[[115, 452, 262, 468]]<|/det|>
+egalol1@jhmi.edu  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 486, 361, 503]]<|/det|>
+## Conflict of interest statement  
+
+<|ref|>text<|/ref|><|det|>[[115, 504, 584, 520]]<|/det|>
+The authors have declared that no conflict of interest exists.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 538, 192, 553]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[113, 555, 877, 764]]<|/det|>
+Loews- Dietz syndrome (LDS) is an aneurysm disorder caused by mutations that decrease transforming growth factor- \(\beta\) (TGF- \(\beta\) ) signaling. Although aneurysms develop throughout the arterial tree, the aortic root is a site of heightened risk. To identify molecular determinants of this vulnerability, we investigated the heterogeneity of vascular smooth muscle cells (VSMCs) in the aorta of Tgfbr1<sup>M318R/+</sup> LDS mice by single cell and spatial transcriptomics. Reduced expression of components of the extracellular matrix- receptor apparatus and upregulation of stress and inflammatory pathways were observed in all LDS VSMCs. However, regardless of genotype, a subset of Gata4- expressing VSMCs predominantly located in the aortic root intrinsically displayed a less differentiated, proinflammatory profile. A similar population was also identified among aortic VSMCs in a human scRNAseq dataset. Postnatal VSMC- specific Gata4 deletion reduced aortic root dilation in LDS mice, suggesting that this factor sensitizes the aortic root to the effects of impaired TGF- \(\beta\) signaling.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 90, 875, 508]]<|/det|>
+Thoracic aortic aneurysms are localized vascular dilations that increase the risk of fatal dissections and/or rupture of the vessel wall'. Effective medical therapies to prevent life- threatening aortic events remain elusive?. Loeys- Dietz syndrome (LDS) is a hereditary connective tissue disorder that presents with highly penetrant aortic aneurysms3,4. LDS is caused by heterozygous, loss- of- function mutations in positive effectors of the TGF- \(\beta\) signaling pathway, including receptors (TGFBR1, TGFBR2), ligands (TGFB2, TGFB3) and intracellular signaling mediators (SMAD2, SMAD3)5- 9. All of these mutations result in reduced phosphorylation/activation of Smad2 and Smad3, leading to defective Smad- dependent transcriptional regulation. Secondary compensatory mechanisms, including upregulation of Angiotensin II Type I Receptor (AT1R) signaling, and increased expression of TGF- \(\beta\) ligands and Smad proteins, ultimately elevate levels of Smad2/Smad3 activity at diseased aortic sites, with outcomes ranging from adaptive to maladaptive depending on disease progression and cellular context5,7,10- 13. While LDS- causing mutations heighten aneurysm risk in all arteries, the aortic root is especially vulnerable to disease14- 17. Several laboratories have highlighted how the cellular composition and/or the mechanical stresses may contribute to the increased risk of disease in this location, however, the molecular determinants of this susceptibility remain unclear13,18- 22. Additionally, VSMCs are the primary cellular component of the aortic wall, but the heterogeneity of VSMCs within the aorta and its implications for aneurysm are not fully understood. In this study, we investigate the transcriptional heterogeneity of VSMCs in the normal and diseased murine aorta leveraging both scRNAseq and spatial transcriptomics. We identify Gata4 as a regional factor whose expression is intrinsically elevated in the aortic root and further upregulated in LDS samples. We also show that postnatal deletion of Gata4 in VSMCs ameliorates aortic root dilation in a murine model of LDS harboring a Tgfbr1M318R/+ genotype.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 525, 182, 540]]<|/det|>
+## Results  
+
+<|ref|>text<|/ref|><|det|>[[115, 541, 870, 595]]<|/det|>
+Tgfbr1M318R/+ VSMCs downregulate extracellular matrix components, focal adhesions, and integrin receptors, and upregulate transcripts related to stress and inflammatory pathways.  
+
+<|ref|>text<|/ref|><|det|>[[111, 595, 880, 892]]<|/det|>
+LDS mouse models expressing a heterozygous missense mutation in Tgfbr1 (Tgfbr1M318R/+) develop highly penetrant aortic root aneurysms11,13. To assess transcriptomic changes associated with vascular pathology in this model, we performed single cell RNA sequencing (scRNAseq) on the aortic root and ascending aorta of control (Tgfbr1+/+) and LDS mice at 16 weeks of age, resulting in the identification of all of the expected cell types according to well- established expression profiles23 (Fig. 1A, B and Supplemental Fig. 1). In consideration of the critical role of VSMCs in the pathogenesis of aortic aneurysm24,25, we focused the downstream analysis of LDS- driven transcriptional alterations on this cell type (Supplemental Table 1). Using the Cytoscape26 ClueGO27 plug- in to leverage gene set enrichment information from multiple databases, we produced a network of functionally related terms and pathways that are differentially enriched among downregulated and upregulated transcripts. (Fig. 1C, D and Supplemental Table 2). The Tgfbr1M318R/+ LDS mutation caused broad downregulation of transcripts related to the maintenance of extracellular matrix- receptor interactions, and integrity of the elastic and contractile function of the aortic wall (Fig. 1C, D, E and Supplemental Table 2). Concurrently, pathways involved in cellular stress responses, inflammation, senescence, and cell death were enriched among transcripts upregulated in Tgfbr1M318R/+ VSMCs (Fig. 1C, D, E and Supplemental Table 2). Additional analysis of transcription factor target databases
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 878, 281]]<|/det|>
+(ENCODE \(^{28}\) and Chromatin Immunoprecipitation Enrichment Analysis (ChEA) via EnrichR \(^{29 - 32}\) ) showed that LDS- downregulated transcripts were enriched in targets of NFE2L2 (nuclear factor erythroid 2- related factor 2, also known as Nrf2), a transcription factor that activates expression of cytoprotective genes and suppresses expression of proinflammatory mediators \(^{33 - 35}\) (Fig. 1F and Supplemental Table 2). Targets of the upstream stimulatory factor (USF) family, which can modulate the expression of smooth muscle specific genes were also enriched among downregulated transcripts \(^{36 - 39}\) (Fig. 1F and Supplemental Table 2). Conversely, target genes for GATA transcription factors and CCAAT enhancer binding protein delta (CEBPD), a positive transcriptional regulator of inflammatory responses mediated by interleukin- 1 (IL- 1) and IL- \(6^{40 - 43}\) , were enriched among transcripts upregulated in LDS VSMCs (Fig. 1G and Supplemental Table 2).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 298, 842, 334]]<|/det|>
+## Spatial transcriptomic analysis of the murine aorta reveals region- and disease-specific patterns of expression for modulators of VSMC phenotypes.  
+
+<|ref|>text<|/ref|><|det|>[[112, 333, 880, 630]]<|/det|>
+Given the regional vulnerability observed in LDS aortas, we leveraged insight gained from the literature and scRNAseq analysis of the aorta of control and \(Tgfbr1^{M318R / + }\) mice to design a custom panel for high throughput in situ hybridization using the Multiplexed error- robust fluorescence in situ hybridization (MERFISH) spatial transcriptomics platform (Supplemental Table 3). Analysis of a longitudinal section of the proximal aorta of 16- week- old control and LDS mice showed regionally defined expression of several transcripts involved in the modulation of vascular phenotypes (Fig. 2 and Supplemental Fig. 2). Transcripts more highly detected in the aortic root of LDS mice relative to the ascending aorta included \(Agtr1a\) , which codes for angiotensin II receptor type 1a, a known contributor to LDS pathogenesis, and \(Gata4\) , which codes for a transcription factor known to positively regulate \(Agtr1a\) expression in the heart \(^{44,45}\) . CCAAT enhancer binding protein beta (Cebpb), a pro- inflammatory mediator \(^{46}\) , and maternally expressed gene 3 (Meg3), a long non- coding RNA (lncRNA) that negatively regulates TGF- \(\beta\) signaling and promotes VSMC proliferation \(^{47 - 50}\) , were also enriched in this region. In contrast, expression of cardiac mesoderm enhancer- associated noncoding RNA (Carmn), a positive regulator of VSMC contractile function that is downregulated in vascular disease, and expression of \(Myh11\) , a marker of differentiated VSMCs, was enriched in the distal ascending aorta, a region that is only mildly affected in LDS mouse models \(^{49,51 - 53}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 647, 805, 682]]<|/det|>
+## Expression of cluster-defining transcripts for the VSMC2 and VSMC1 subclusters correlates with the proximal-to-distal axis of the mouse and human aorta.  
+
+<|ref|>text<|/ref|><|det|>[[112, 682, 875, 891]]<|/det|>
+To examine if the spatial VSMC heterogeneity observed with MERFISH could be captured by scRNAseq, we increased the clustering resolution for VSMCs, thus obtaining two subclusters, VSMC1 and VSMC2. We then examined these two VSMC subclusters for expression of transcripts our laboratory has previously shown to progressively increase (i.e. Tes and Ptrpz1) and decrease (i.e. Enpep and Notch3) along the proximal- to- distal axis in the mouse ascending aorta \(^{54}\) . VSMC1 and VSMC2 showed increased expression of transcripts whose expression is intrinsically enriched in the ascending aorta and the aortic root, respectively \(^{54}\) (Fig. 3A, B and Supplemental Table 4). Gata4 was also noted among the transcripts that defined the VSMC2 subcluster and whose expression was highest in the aortic root, progressively diminishing along the proximal- to- distal axis in the ascending aorta (Fig. 3C). Considering previous work highlighting how cell lineage modulates the effect of LDS- causing mutations \(^{13,55 - 57}\) , we explored the relationship between the VSMC2 and VSMC1 subclusters to the secondary heart field
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 880, 386]]<|/det|>
+(SHF)- and cardiac neural crest (CNC)- lineage of origin (Supplemental Fig. 3). We found that VSMCs lineage- traced with a fluorescent reporter identifying CNC- derived cells were overrepresented in the VSMC1 subcluster (Supplemental Fig. 3A). However, re- analysis of a previously published dataset of SHF- and CNC- traced VSMCs (Supplemental Table 5) showed that VSMC1 and VSMC2 were not defined by lineage of origin, with VSMCs of both lineages found in either VSMC sub- cluster \(^{58}\) (Supplemental Fig. 3B). Nevertheless, as would be expected based on the known proximal- to- distal distribution of SHF- and CNC- derived VSMCs, there was overlap between VSMC2- defining and SHF- enriched transcripts (Supplemental Fig. 3B, C and Supplemental Table 4 and 5). To assess if the VSMC substructure identified in murine models was relevant in the context of human aortic disease, we also re- analyzed a recently published scRNAseq dataset of aortic tissue from LDS patients and donor aortas in which the ascending aorta and aortic root were separately sequenced (Fig. 3D and Supplemental Fig. 4) \(^{59}\) . Subpopulations of VSMCs expressing cluster- defining transcripts analogous to those found in VSMC1 and VSMC2 in mouse aortas could be identified in the human dataset (Fig. 3D and Supplemental Table 6). Although both VSMC1 and VSMC2 were present in human aortic root and ascending aorta, GATA4 expression was highest in the VSMC2 cluster from the aortic root, with no detectable expression in the ascending aorta (Fig. 3D).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 401, 797, 437]]<|/det|>
+## Gata4-expressing VSMC2 are intrinsically "poised" towards a less-differentiated, maladaptive proinflammatory transcriptional signature.  
+
+<|ref|>text<|/ref|><|det|>[[112, 436, 880, 595]]<|/det|>
+To examine the biological features of VSMC1 and VSMC2, and whether they were recapitulated in both murine and patient- derived LDS VSMCs, we used the Coordinated Gene Activity in Pattern Sets (CoGAPS) algorithm to identify latent patterns of coordinated gene expression in the \(Tgbr^{M318R / +}\) VSMC mouse dataset \(^{60,61}\) . Two patterns, transcriptional patterns 4 and 5, were found to be enriched in the VSMC2 and VSMC1 subclusters, respectively, in the \(Tgbr^{M318R / +}\) VSMC mouse dataset (Fig. 3E, G, Supplemental Table 4). These same patterns were then projected onto the scRNAseq data of VSMCs from the aorta of LDS patients using ProjectR \(^{62}\) , revealing a similar enrichment of pattern 4 in VSMC2 and pattern 5 in VSMC1 (Fig. 3E- H, Supplemental Table 4).  
+
+<|ref|>text<|/ref|><|det|>[[111, 610, 880, 891]]<|/det|>
+As previously observed for transcripts upregulated in \(Tgbr^{M318R / +}\) LDS VSMCs, Pattern 4- associated transcripts were enriched for transcriptional targets of GATA family members (ENCODE \(^{28}\) and ChEA dataset, analyzed with EnrichR \(^{29 - 32}\) , Fig. 3I). Differential gene set enrichment analysis using ClueGO \(^{27}\) to compare cluster- defining transcripts for VSMC1 and VSMC2 also showed that, in both mouse and human datasets, VSMC2- defining transcripts were enriched for pathways involved in inflammation, senescence, and cellular stress (Fig. 3J and Supplemental Table 7 and Table 8). In contrast, VSMC1 expressed higher levels of transcripts related to extracellular matrix- receptor interactions and contractile function (Fig. 3J, Supplemental Fig. 4 and Supplemental Table 7 and Table 8). Network visualization of molecular signatures database (MSigDB) VSMC2- enriched pathways shared by both mouse and human samples (probed with EnrichR \(^{30 - 32,63,64}\) ) (Supplemental Fig. 5A), and biological terms with shared ClueGO grouping (Fig. 3J and Supplemental Table 7 and Table 8), highlighted the biological connections between these pathways and genes over- expressed in VSMC2 relative to VSMC1 (i.e. \(Cxcl^{165 - 68}\) , Irf1 \(^{69 - 71}\) , Thbs1 \(^{72}\) , Gata4 \(^{73}\) ) (Supplemental Fig. 5B). Overall, in both mouse and human samples, the transcriptional profile of VSMC2 relative to VSMC1 resembled that of less- differentiated VSMCs and included lower expression of \(Myh11\) , Cnn1, and Tet2, and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 90, 855, 126]]<|/det|>
+higher expression of transcripts associated with non- contractile VSMC phenotypes, including Klf4, Olfm2, Sox9, Tcf21, Malat1, Twist1, and Dcn<sup>74- 79</sup>.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 142, 660, 161]]<|/det|>
+## Gata4 is upregulated in the aortic root of Tgfbr1<sup>M318R/+</sup> LDS mice.  
+
+<|ref|>text<|/ref|><|det|>[[113, 161, 870, 334]]<|/det|>
+Based on the analysis described above, and its known role in driving the upregulation of pathways previously involved in aneurysm progression<sup>44,73,80</sup>, Gata4 emerged as a potential molecular determinant of increased risk of dilation of the aortic root in LDS. Although levels of Gata4 mRNA are intrinsically higher in the aortic root relative to the ascending aorta even in control mice (Fig. 3C), its expression was further upregulated in VSMCs in the LDS aorta, as assessed both by scRNAseq (Supplemental Table 1) and RNA in situ hybridization (Fig. 4A). Given that levels of Gata4 protein are highly regulated at the post- transcriptional level through targeted degradation<sup>73,81,82</sup>, we also examined levels of Gata4 protein in control and LDS aortic samples, and found that protein levels are increased in LDS aortic root, both by immunofluorescence and immunoblot assays (Fig. 4B, C and Fig. 5).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 350, 872, 386]]<|/det|>
+## Postnatal deletion of Gata4 in smooth muscle cells reduces aortic root dilation in LDS mice in association with reduced levels of Agtr1a and other proinflammatory mediators.  
+
+<|ref|>text<|/ref|><|det|>[[113, 386, 881, 578]]<|/det|>
+To assess whether increased Gata4 levels in aortic root of LDS mouse models promoted dilation in this location, we crossed conditional Gata4<sup>flox/flox</sup> mice<sup>83</sup> to LDS mice also expressing a transgenic, tamoxifen- inducible Cre recombinase under the control of a VSMC specific promoter (Myh11- Cre<sup>ER</sup>)<sup>84</sup>, and administered tamoxifen at 6 weeks of age to ablate expression of Gata4 in VSMCs (Fig. 5). VSMC- specific postnatal deletion of Gata4 in LDS mice (Tgfbr1<sup>M318R/+</sup>, Gata4<sup>SMcKO</sup>) resulted in a reduced rate of aortic root dilation relative to control LDS animals (Tgfbr1<sup>M318R/+</sup>; Gata4<sup>Ctrl</sup>) (Fig. 6A), and amelioration of aortic root medial architecture relative to control LDS aortas at 16 weeks of age (Fig. 6B). No significant dilation was observed in the ascending aorta of Tgfbr1<sup>M318R/+</sup> mice at 16 weeks of age, and Gata4 deletion had no effect on the diameter of this aortic segment (Supplemental Fig. 6). Gata4 deletion in VSMCs also did not associate with changes in blood pressure (Supplemental Fig. 7).  
+
+<|ref|>text<|/ref|><|det|>[[113, 594, 874, 750]]<|/det|>
+Previous work has shown that Gata4 binds to the Agtr1a promoter inducing its expression in heart tissue<sup>44,45</sup>, and that Agtr1a is transcriptionally upregulated in the aortic root of LDS mice, resulting in up- regulation of AT1R, which exacerbates LDS vascular pathology<sup>11,13,45</sup>. Accordingly, Gata4 deletion associated with reduced expression of Agtr1a in the aortic root of LDS mice (Fig. 7). Similarly, deletion of Gata4 reduced expression of Cebpd and Cebpb (Fig. 8 and Supplemental Fig. 8), which code for proinflammatory transcription factors regulated by and/or interacting with Gata4 in other contexts<sup>43,46,85,86</sup>, which were highly expressed in VSMC2 relative to VSMC1, and further upregulated in the presence of LDS mutations (Fig. 1, Fig. 2, Supplemental Table 1, Supplemental Table 7).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 768, 205, 784]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[115, 785, 872, 891]]<|/det|>
+LDS is a hereditary connective tissue disorder characterized by skeletal, craniofacial, cutaneous, immunological, and vascular manifestations, including a high risk for aggressive arterial aneurysms<sup>4</sup>. It is caused by mutations that impair the signaling output of the TGF- \(\beta\) pathway, leading to defective transcriptional regulation of its target genes<sup>5- 9</sup>. Although loss- of- signaling initiates vascular pathology, compensatory upregulation of positive modulators of the pathway results in a “paradoxical” increase in activation of TGF- \(\beta\) signaling mediators (i.e
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 880, 247]]<|/det|>
+phosphorylated Smad2 and Smad3) and increased expression of target genes in diseased aortic tissue of both LDS patients and mouse models \(^{5,7,10 - 13}\) . This secondary upregulation depends, in part, on increased activation of angiotensin II signaling via AT1R, which positively modulates the expression of TGF- \(\beta\) ligands and TGF- \(\beta\) receptors \(^{87}\) . Whereas upregulation of the TGF- \(\beta\) pathway can have both adaptive and maladaptive consequences depending on disease stage and cellular context \(^{13,54,88 - 95}\) , upregulation of AT1R signaling has consistently been shown to be detrimental to vascular health, and both pharmacological (i.e. with angiotensin receptor blockers) and genetic antagonism of this pathway ameliorates vascular pathology in LDS mouse models \(^{87,96 - 99}\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 262, 880, 439]]<|/det|>
+Even though LDS- causing mutations confer an increased risk of disease across all arterial segments, the aortic root is one of the sites that is particularly susceptible to aneurysm development \(^{14 - 17}\) . In this study, we leveraged scRNAseq in conjunction with spatial transcriptomics to investigate the heterogeneity of VSMCs in an LDS mouse model, with the ultimate goal of identifying regional mediators that may drive upregulation of pro- pathogenic signaling in this region. We identify distinct subpopulations of VSMCs characterized by expression patterns that preferentially map to the ascending aorta (VSMC1) and aortic root (VSMC2) in mouse aorta. We also show that the regional vulnerability of the aortic root depends, in part, on higher levels of Gata4 expression in a subset of VSMCs (VSMC2), which is intrinsically more vulnerable to the effect of an LDS- causing mutation.  
+
+<|ref|>text<|/ref|><|det|>[[113, 454, 880, 612]]<|/det|>
+Prior to the advent of single- cell analysis tools, which allow precise and unbiased unraveling of cellular identity, the ability to investigate VSMC heterogeneity in the proximal aorta was limited by the availability of experimental approaches to investigate known or expected diversity. In consideration of the mixed embryological origin of the aortic root and distal ascending aorta, earlier work thus focused on understanding how the effect of LDS mutations on VSMCs was modified by the SHF- and CNC lineage of origin. In both mouse models and in iPSCs- derived in vitro models, signaling defects caused by LDS mutations were found to be more pronounced in VSMC derived from SHF (or cardiac mesoderm) progenitors relative to CNC- derived VSMCs \(^{13,57}\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 627, 881, 752]]<|/det|>
+Like SHF- derived VSMCs, Gata4- expressing VSMC2 are enriched in the aortic root and are also more vulnerable to the effects of an LDS- causing mutation. They also express a transcriptional signature similar to that of SHF- derived VSMCs (Supplemental Fig. 3). Reciprocally, SHF- derived cells are over- represented in the VSMC2 cluster in our dataset (Supplemental Fig. 3). However, the identity of VSMC2 and VSMC1 is not defined by lineage- of- origin, and SHF- or CNC- derived origin is only an imperfect approximation of the VSMC heterogeneity that can now be assessed via scRNAseq.  
+
+<|ref|>text<|/ref|><|det|>[[113, 767, 875, 891]]<|/det|>
+Heterogeneity beyond that imposed by lineage- of- origin was also shown by scRNAseq analysis of the aorta of the \(Fbn^{1C1041G / +}\) Marfan syndrome (MFS) mouse model, which revealed the existence of an aneurysm- specific population of transcriptionally modified smooth muscle cells (modSMCs) at a later stage of aneurysmal disease, and which could emerge from modulation of both SHF- and non- SHF (presumably CNC)- derived progenitors \(^{58,100}\) . These cells, which could also be identified in the aneurysmal tissue derived from the aortic root of MFS patients, showed a transcriptional signature marked by a gradual upregulation of extracellular matrix genes and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 880, 143]]<|/det|>
+downregulation of VSMC contractile genes \(^{58,100}\) . We were not able to identify this population of modSMCs in the aorta of \(Tgfbr1^{M318R / +}\) LDS mouse models, even though it was shown to exist in the aorta of LDS patients \(^{62}\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 158, 872, 283]]<|/det|>
+Similar to the early effect of Smad3- inactivation, the \(Tgfbr1^{M318R / +}\) LDS mutation caused broad downregulation of gene programs required for extracellular matrix homeostasis and those favoring a differentiated VSMC phenotype \(^{54}\) (Fig. 1); conversely, proinflammatory transcriptional repertoires, with an enrichment in pathways related to cell stress, was observed among upregulated transcripts. This latter profile likely represents a response to the initial insult caused by decreased expression of extracellular matrix components whose expression requires TGF- \(\beta\) /Smad activity \(^{98}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 298, 872, 544]]<|/det|>
+We also noted downregulation of several components of the lysosome, whose function is required for cellular homeostasis and degradation of protein targets via selective autophagy \(^{33,73,101,102}\) (Fig. 1). Gata4 levels are regulated via p62- mediated selective autophagy \(^{73}\) and by mechanosensitive proteasome- mediated degradation \(^{82,103}\) . The aortic root would be especially vulnerable to a defect in either of these processes given increased baseline levels of Gata4 mRNA expression in VSMC2. Increased levels of Gata4 may contribute to vascular pathogenesis by several potential mechanisms. In other cellular contexts, Gata4 has been shown to promote induction of the pro- inflammatory senescence- associated secretory phenotype (SASP) as well as transcription of the lncRNA Malat1, which promotes aneurysm development in other mouse models \(^{78}\) . Gata4 is also a negative regulator of contractile gene expression in Sertoli and Leydig cells \(^{104}\) . Additionally, Gata4 binds the promoter and activates the expression of \(Agtr1a^{44}\) , which is known to drive pro- pathogenic signaling in LDS aorta \(^{45}\) . Accordingly, we find that Gata4 deletion downregulates expression of \(Agtr1a\) in the aortic media of LDS mouse models (Fig. 7).  
+
+<|ref|>text<|/ref|><|det|>[[112, 558, 880, 821]]<|/det|>
+Re- analysis of a scRNAseq dataset of human aortic samples from LDS patients, which included both the aortic root and the ascending aorta, shows that a population of Gata4- expressing VSMC similar to that found in mice can also be identified in LDS patients. Additionally, patterns of coordinated gene expression identifying VSMC1 and VSMC2, which were learned from the scRNAseq analysis of mouse aorta, could be projected onto the human dataset, suggesting that these two subsets of VSMCs are conserved across species and that the existence of a Gata4- expressing VSMC2 population may underlie increased risk in the aortic root of LDS patients as well. Assessing the effects of Gata4 deletion at additional postnatal timepoints will be important to understand the consequences of increased Gata4 and its downstream targets during later stages of disease. Although direct targeting of Gata4 for therapeutic purposes is unfeasible given its critical role in the regulation of numerous biological processes in non- vascular tissues \(^{105- 109}\) , this work highlights how the investigation of factors that increase or decrease the regional risk of aneurysm may lead to a better understanding of adaptive and maladaptive pathways activated in response to a given aneurysm- causing mutations. This knowledge may be leveraged to develop therapeutic strategies that target the vulnerabilities of specific arterial segments.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 191, 106]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 125, 291, 142]]<|/det|>
+## Animal Experiments  
+
+<|ref|>text<|/ref|><|det|>[[115, 144, 233, 160]]<|/det|>
+Study approval  
+
+<|ref|>text<|/ref|><|det|>[[115, 160, 839, 195]]<|/det|>
+Animal experiments were conducted according to protocols approved by the Johns Hopkins University School of Medicine Animal Care and Use Committee.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 213, 230, 228]]<|/det|>
+## Mouse models  
+
+<|ref|>text<|/ref|><|det|>[[111, 230, 882, 560]]<|/det|>
+All mice were maintained in an animal facility with unlimited access to standard chow and water unless otherwise described. \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + 11}\) (The Jackson Laboratory, strain #036511) mice, some bearing the \(E G F P - L10a^{110}\) (The Jackson Laboratory, strain #024750) conditional tracer allele and a CNC- specific CRE recombinase expressed under the control of Wnt2 promoter111 (The Jackson Laboratory, strain #003829) were used for scRNAseq as described below. All mice were maintained on a 129- background strain (Taconic, 129SVE). \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + }\) mice were bred to \(G a t a^{4l o x / l o x 83}\) (The Jackson Laboratory, strain #008194) and mice carrying the \(M y h I1 - C r e^{E R}\) transgene84 (The Jackson Laboratory, strain #019079). \(M y h I1 - C r e^{E R}\) is integrated on the Y chromosome therefore only male mice were used for this set of experiments. \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + }\) bearing \(G a t a^{4l o x / l o x}\) and \(M y h I1 - C r e^{E R}\) are referred to as \(G a t a^{4S M c K O}\) . \(T g f b r I^{+ / + }\) and \(T g f b r I^{M318R / + }\) bearing \(G a t a^{4 + / + }\) with or without \(M y h I1-\) \(C r e^{E R}\) or \(G a t a^{4l o x / l o x}\) or \(G a t a^{4l o x / + }\) without \(M y h I1 - C r e^{E R}\) are referred to as \(G a t a^{4C u l}\) . All \(G a t a^{4S M c K O}\) and \(G a t a^{4C u l}\) mice were injected with 2 mg/day of tamoxifen (Millipore Sigma, T5648) starting at 6 weeks of age for 5 consecutive days. Mice were genotyped by PCR using primer sequences described in the original references for these models. Serial echocardiography was performed using the Visual Sonics Vivo 2100 machine and a 30 MHz probe. As there is some variability in the onset of aortic dilation in \(T g f b r I^{M318R / + }\) mice, and starting aortic size will affect final measurements, aortic root diameter of 1.9 mm and above at baseline (8 weeks of age) was defined a priori as an exclusion criterion.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 578, 386, 595]]<|/det|>
+## Molecular validation techniques  
+
+<|ref|>text<|/ref|><|det|>[[115, 597, 330, 612]]<|/det|>
+Aortic Sample Preparation  
+
+<|ref|>text<|/ref|><|det|>[[115, 613, 875, 752]]<|/det|>
+All mice were euthanized by halothane inhalation at a \(4\%\) concentration, \(0.2\mathrm{ml}\) per liter of container volume (Millipore Sigma, H0150000). As we described previously \(^{11,54}\) , the heart and thoracic aorta were dissected en bloc and fixed in \(4\%\) paraformaldehyde (Electron Microscopy Sciences, 15710) in PBS at \(4^{\circ}\mathrm{C}\) overnight. Samples were subsequently incubated in \(70\%\) ethanol at \(4^{\circ}\mathrm{C}\) overnight prior to embedding in paraffin. Paraffin- embedded tissues were cut into 5 micron sections to expose a longitudinal section of the thoracic aorta. Sections were then stained with Verhoeff- van Gieson (StatLab, STVGI) to visualize elastic fiber morphology or to assess protein and RNA abundance by immunofluorescence or fluorescence in situ hybridization.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 770, 281, 785]]<|/det|>
+## Immunofluorescence  
+
+<|ref|>text<|/ref|><|det|>[[115, 786, 866, 892]]<|/det|>
+Immunofluorescence was performed following a protocol adapted from Cell Signaling Technology (CST) for formaldehyde- fixed tissues as previously described in detail \(^{45}\) , using a rabbit monoclonal antibody for GATA4 (Cell Signaling Technology, CST36966) and a donkey anti- rabbit secondary antibody Alexa Fluor 555 (ThermoFisher, A32794). Images were taken using a Zeiss LSM880 Airyscan FAST confocal microscope at \(20\times\) magnification and are presented as maximal intensity projection.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 108, 474, 125]]<|/det|>
+RNAscope Fluorescence in situ hybridization  
+
+<|ref|>text<|/ref|><|det|>[[113, 126, 877, 213]]<|/det|>
+RNA in situ hybridization was performed using the RNAscope Multiplex Fluorescent Reagent Kit v2 Assay (ACD Biosciences, 323100) according to the manufacturer's protocol with the following probes Mm- Gata4 (417881), Mm- Agtr1a (481161), Mm- Cebpd (556661), Mm- Cebpb (547471). Images were taken using a Zeiss LSM880 Airyscan FAST confocal microscope at \(20 \times\) magnification and are presented as maximal intensity projection.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 230, 245, 246]]<|/det|>
+## Immunoblotting  
+
+<|ref|>text<|/ref|><|det|>[[113, 246, 877, 386]]<|/det|>
+Aortic root tissue was flash- frozen immediately upon dissection and stored at \(- 80^{\circ}\mathrm{C}\) until protein extraction. Protein was extracted using Full Moon Lysis Buffer (Full Moon Biosystems, EXB1000) with added phosphatase and protease inhibitors (MilliporeSigma, 11836170001 and 4906845001) and Full Moon lysis beads (Full Moon Biosystems, LB020) using an MP Biomedicals FastPrep 24 5G automatic bead homogenizer. After homogenization, the cell debris was pelleted, and the supernatant was collected. Immunoblot was performed as previously described in detail54, using a rabbit monoclonal antibody for Gata4 (Cell Signaling Technology, 36966) and a mouse monoclonal antibody for \(\beta\) - Actin. (Cell Signaling Technology, 8H10D10).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 403, 328, 420]]<|/det|>
+## Transcriptomic Analyses  
+
+<|ref|>text<|/ref|><|det|>[[115, 420, 444, 437]]<|/det|>
+Single Cell RNA sequencing and analysis  
+
+<|ref|>text<|/ref|><|det|>[[112, 437, 880, 732]]<|/det|>
+Single cell RNA sequencing was performed as we previously described112. Single cell suspensions from each mouse were processed separately using the 10x Genomics \(3^{\circ}\) v3 platform and sequenced on an Illumina NovaSeq. A total of 30,704 aortic cells were sequenced from six female mice. The raw data was processed, aligned to the mouse genome (mm10), and aggregated using 10x Genomics Cell Ranger V6'13. The data were then filtered using the Seurat V5 package112 based on the following criteria: \(>1000\) transcripts detected per cell but \(< 5000\) , \(>1500\) total molecules detected per cell but \(< 25000\) , and \(< 20\%\) mitochondrial transcripts per cell. Filtering reduced this dataset from 30,704 aortic cells to 24,971 cells for further analysis. The data was then normalized using the function SCTransform v2. As samples were prepared on multiple days, the data was integrated across batches using reciprocal principal component analysis (RPCAIntegration). Principal component analysis and uniform manifold approximation and projection (UMAP) were performed followed by the FindNeighbors and FindClusters functions. We opted to cluster at a low resolution (0.25) to differentiate aortic cell types and to identify only major subpopulations of smooth muscle cells that vary by a large number of differentially expressed genes. FindMarkers was used to identify cluster- defining transcripts and differentially expression genes between control and diseased cell populations based on a Wilcoxon rank sum test.  
+
+<|ref|>text<|/ref|><|det|>[[115, 750, 585, 768]]<|/det|>
+Re- analysis of human aortic cells from Pedroza et al., 2023  
+
+<|ref|>text<|/ref|><|det|>[[115, 768, 866, 872]]<|/det|>
+For re- analysis of the ascending aorta and aortic root samples from a recently published scRNAseq dataset of the donor and LDS patient aortas59 we used the following criteria: \(>1000\) transcripts detected per cell but \(< 6000\) , \(>1500\) total molecules detected per cell \(< 30000\) , and \(< 20\%\) mitochondrial transcripts per cell. This reduces this dataset from 58,947 aortic cells to 43,349 for further analysis. We analyzed this dataset as described above with the FindClusters resolution parameter set to 0.15.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 90, 298, 107]]<|/det|>
+CoGAPS and ProjectR  
+
+<|ref|>text<|/ref|><|det|>[[112, 107, 876, 230]]<|/det|>
+CoGAPS and ProjectRCoGAPS<sup>60,61</sup> (v3.22), an R package that utilizes non- negative matrix factorization to uncover latent patterns of coordinated gene expression representative of shared biological functions, was used to identify transcriptional patterns associated with VSMC subpopulations, with the npatterns parameter set to 8, in scRNAseq analysis of murine aortas. ProjectR<sup>62</sup> (v1.2), an R package that enables integration and analysis of multiple scRNAseq data sets by identifying transcriptional patterns shared among datasets, was used to project these patterns into scRNAseq analysis of the human aortic root and ascending aorta.  
+
+<|ref|>text<|/ref|><|det|>[[115, 247, 392, 264]]<|/det|>
+Gene over- representation analyses  
+
+<|ref|>text<|/ref|><|det|>[[112, 264, 881, 455]]<|/det|>
+Gene over- representation analysesClueGO<sup>27</sup> was used for gene over- representation analysis and visualization of enriched functional terms for transcripts globally dysregulated in all VSMCs as well as VSMC subsets. Transcripts were filtered based on an adjusted P- value less than 0.05 and an average absolute Log2 fold change of 0.25 or greater, as well as detection in at least 20 percent of either control or LDS VSMCs. The resulting list of 502 downregulated and 200 upregulated genes was compared against five gene ontology databases (MSigDB Hallmark, KEGG, WikiPathways, Bioplanet, and Reactome). The list of transcripts and ClueGO log files are provided in supplemental material. Differentially expressed gene lists were also analyzed using the online gene list enrichment analysis tool EnrichR<sup>30- 32</sup> (https://maayanlab.cloud/Enrichr/) for pathways using the Molecular Signatures Database (MSigDB)<sup>63,64</sup> and for transcription factors target enrichment using the ENCODE<sup>28</sup> and ChEA<sup>29</sup> databases.  
+
+<|ref|>text<|/ref|><|det|>[[113, 472, 761, 508]]<|/det|>
+Multiplexed Error- Robust Fluorescence in situ Hybridization (MERFISH) Spatial Transcriptomics  
+
+<|ref|>text<|/ref|><|det|>[[112, 508, 866, 649]]<|/det|>
+MERFISH spatial transcriptomics using a custom panel was performed on 5- micron Formalin- Fixed Paraffin- Embedded (FFPE) sections of control and LDS aortas according to manufacturer's protocols (MERSCOPE FFPE Tissue Sample Preparation User Guide_Rev B, Vizgen). Slides were processed and imaged on a MERSCOPE instrument platform according to the manufacturer's protocols (MERSCOPE Instrument User Guide Rev G, Vizgen). The raw images were processed by the instrument software to generate a matrix of spatial genomics measurements and associated image files that were analyzed using the MERSCOPE visualizer software.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 666, 193, 682]]<|/det|>
+## Statistics  
+
+<|ref|>text<|/ref|><|det|>[[113, 682, 860, 805]]<|/det|>
+GraphPad Prism 10.0 was used for data visualization and statistical analysis. Data tested for normality using the Shapiro- Wilk test and upon verification of normal distribution, analyzed using the Brown- Forsythe ANOVA test. For echocardiographic and blood pressure measurements, data are presented as a box and whisker plot with the whiskers indicating the maximum and minimum values and a horizontal bar indicating the median. All individual data points are shown as dots. Figures indicating statistical significance include the statistical tests used in the figure caption.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 821, 256, 838]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[113, 839, 829, 892]]<|/det|>
+All single- cell RNA sequencing data, both raw fastq files and aggregated matrixes, will be available in the gene expression omnibus (GEO) repository under accession number GSE267204. MERFISH spatial transcriptomics data is available upon request.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 91, 296, 106]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[111, 106, 870, 336]]<|/det|>
+EM and EB conceptualized the study, designed the experiments, interpreted data, and prepared the manuscript. EB and TJC generated and processed the single- cell RNA (scRNAseq) sequencing data. EB conducted the primary analysis of the scRNAseq data and performed a reanalysis of published scRNAseq datasets, with input from WE, TC, LR, and JM. EM conducted gene- over- representation analysis and visualization. EB, EM, WE, and LR were involved in sample preparation and processing for MERFISH. EB conducted in situ hybridization, immunofluorescence, and immunoblotting experiments. EB was responsible for echocardiography, blood pressure measurements, genotyping, and animal husbandry with support from TC, MS, WE, LR, and RB. AZ performed histological staining and imaging. GS provided support for CoGAPS analysis and MERFISH spatial transcriptomics. AP and MF provided human scRNAseq data and offered valuable insight on interpretation of the analysis. HD provided valuable input on the study design. EM and EB wrote the manuscript, all authors contributed to its revision.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 353, 270, 368]]<|/det|>
+## Acknowledgments  
+
+<|ref|>text<|/ref|><|det|>[[115, 369, 870, 473]]<|/det|>
+Research in this publication was supported by the National Heart, Lung, and Blood Institute of the National Institutes of Health under Award Numbers R01HL147947 to EM and F31HL163924 to EB as well as a generous gift from the Loeys- Dietz Foundation. Fluorescence Microscopy imaging was also supported by NIH award number S10OD023548 to the School of Medicine Microscope Facility. We would also like to acknowledge the Dietz and Stein- O'Brien labs for sharing resources.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 90, 884, 860]]<|/det|>
+505 References
+506 1 Chou, E., Pirruccello, J. P., Ellinor, P. T. & Lindsay, M. E. Genetics and mechanisms of thoracic aortic disease. Nat Rev Cardiol 20, 168- 180, doi:10.1038/s41569- 022- 00763- 0 (2023).
+510 2 Verstraeten, A., Luyckx, I. & Loeys, B. Aetiology and management of hereditary aortopathy. Nat Rev Cardiol 14, 197- 208, doi:10.1038/nrcardio.2016.211 (2017).
+511 3 Rodrigues Bento, J. et al. The Genetics and Typical Traits of Thoracic Aortic Aneurysm and Dissection. Annu Rev Genomics Hum Genet 23, 223- 253, doi:10.1146/annurev-genom- 111521- 104455 (2022).
+514 4 MacCarrick, G. et al. Loeys- Dietz syndrome: a primer for diagnosis and management. Genet Med 16, 576- 587, doi:10.1038/gim.2014.11 (2014).
+515 5 Loeys, B. L. et al. A syndrome of altered cardiovascular, craniofacial, neurocognitive and skeletal development caused by mutations in TGFBR1 or TGFBR2. Nat Genet 37, 275- 281, doi:10.1038/ng1511 (2005).
+516 6 van de Laar, I. M. et al. Mutations in SMAD3 cause a syndromic form of aortic aneurysms and dissections with early- onset osteoarthritis. Nat Genet 43, 121- 126, doi:ng.744 [pii]
+517 7 10.1038/ng.744 (2011).
+518 7 Lindsay, M. E. et al. Loss- of- function mutations in TGFB2 cause a syndromic presentation of thoracic aortic aneurysm. Nat Genet 44, 922- 927, doi:10.1038/ng.2349 (2012).
+519 8 Bertoli- Avella, A. M. et al. Mutations in a TGF- beta ligand, TGFB3, cause syndromic aortic aneurysms and dissections. J Am Coll Cardiol 65, 1324- 1336, doi:10.1016/j.jacc.2015.01.040 (2015).
+520 9 Micha, D. et al. SMAD2 Mutations Are Associated with Arterial Aneurysms and Dissections. Hum Mutat 36, 1145- 1149, doi:10.1002/humu.22854 (2015).
+521 10 van de Laar, I. M. et al. Phenotypic spectrum of the SMAD3- related aneurysms- osteoarthritis syndrome. J Med Genet 49, 47- 57, doi:10.1136/jmedgenet- 2011- 100382 (2012).
+522 11 Gallo, E. M. et al. Angiotensin II- dependent TGF- beta signaling contributes to Loeys- Dietz syndrome vascular pathogenesis. J Clin Invest 124, 448- 460, doi:69666 [pii]
+523 10.1172/JCI169666 (2014).
+524 12 Bertoli- Avella, A. M. et al. Mutations in a TGF- beta ligand, TGFB3, cause syndromic aortic aneurysms and dissections. J Am Coll Cardiol 65, 1324- 1336, doi:10.1016/j.jacc.2015.01.040 (2015).
+525 13 MacFarlane, E. G. et al. Lineage- specific events underlie aortic root aneurysm pathogenesis in Loeys- Dietz syndrome. J Clin Invest 129, 659- 675, doi:10.1172/JCI123547 (2019).
+526 14 Williams, J. A. et al. Early surgical experience with Loeys- Dietz: a new syndrome of aggressive thoracic aortic aneurysm disease. Ann Thorac Surg 83, S757- 763; discussion S785- 790, doi:10.1016/j.athoracsur.2006.10.091 (2007).
+527 15 Hughes, G. C. Aggressive aortic replacement for Loeys- Dietz syndrome. Tex Heart Inst J 38, 663- 666 (2011).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 90, 875, 875]]<|/det|>
+549 16 van der Linde, D. et al. Progression rate and early surgical experience in the new 550 aggressive aneurysms- osteoarthritis syndrome. Ann Thorac Surg 95, 563- 569, 551 doi:10.1016/j.athorascr.2012.07.009 (2013). 552 17 Patel, N. D. et al. Aortic Root Replacement for Children With Loeys- Dietz Syndrome. 553 Ann Thorac Surg 103, 1513- 1518, doi:10.1016/j.athorascr.2017.01.053 (2017). 554 18 Bell, V. et al. Longitudinal and circumferential strain of the proximal aorta. J Am Heart 555 Assoc 3, e001536, doi:10.1161/JAHA.114.001536 (2014). 556 19 Avril, S., Bersi, M. R., Bellini, C., Genovese, K. & Humphrey, J. D. Regional 557 identification of mechanical properties in arteries. Comput Methods Biomech Biomed 558 Engin 18 Suppl 1, 1874- 1875, doi:10.1080/10255842.2015.1070577 (2015). 559 20 Bersi, M. R., Bellini, C., Humphrey, J. D. & Avril, S. Local variations in material and 560 structural properties characterize murine thoracic aortic aneurysm mechanics. Biomech 561 Model Mechanobiol 18, 203- 218, doi:10.1007/s10237- 018- 1077- 9 (2019). 562 21 Gong, J. et al. In Vitro Lineage- Specific Differentiation of Vascular Smooth Muscle 563 Cells in Response to SMAD3 Deficiency: Implications for SMAD3- Related Thoracic 564 Aortic Aneurysm. Arterioscler Thromb Vasc Biol 40, 1651- 1663, 565 doi:10.1161/ATVBAHA.120.313033 (2020). 566 22 Sawada, H. et al. Second Heart Field- Derived Cells Contribute to Angiotensin II- 567 Mediated Ascending Aortopathies. Circulation 145, 987- 1001, 568 doi:10.1161/CIRCULATIONAHA.121.058173 (2022). 569 23 Kalluri, A. S. et al. Single- Cell Analysis of the Normal Mouse Aorta Reveals 570 Functionally Distinct Endothelial Cell Populations. Circulation 140, 147- 163, 571 doi:10.1161/CIRCULATIONAHA.118.038362 (2019). 572 24 Shen, Y. H. & LeMaire, S. A. Molecular pathogenesis of genetic and sporadic aortic 573 aneurysms and dissections. Curr Probl Surg 54, 95- 155, 574 doi:10.1067/j.cpsurg.2017.01.001 (2017). 575 25 Lu, H. et al. Vascular Smooth Muscle Cells in Aortic Aneurysm: From Genetics to 576 Mechanisms. J Am Heart Assoc 10, e023601, doi:10.1161/JAHA.121.023601 (2021). 577 26 Shannon, P. et al. Cytoscape: a software environment for integrated models of 578 biomolecular interaction networks. Genome Res 13, 2498- 2504, doi:10.1101/gr.1239303 (2003). 579 27 Bindea, G. et al. ClueGO: a Cytoscape plug- in to decipher functionally grouped gene 580 ontology and pathway annotation networks. Bioinformatics 25, 1091- 1093, 581 doi:10.1093/bioinformatics/btp101 (2009). 582 28 Luo, Y. et al. New developments on the Encyclopedia of DNA Elements (ENCODE) 583 data portal. Nucleic Acids Res 48, D882- D889, doi:10.1093/nar/gkz1062 (2020). 584 Lachmann, A. et al. ChEA: transcription factor regulation inferred from integrating 585 genome- wide ChIP- X experiments. Bioinformatics 26, 2438- 2444, 586 doi:10.1093/bioinformatics/btq466 (2010). 587 30 Chen, E. Y. et al. Enrichr: interactive and collaborative HTML5 gene list enrichment 588 analysis tool. BMC Bioinformatics 14, 128, doi:10.1186/1471- 2105- 14- 128 (2013). 589 31 Kuleshov, M. V. et al. Enrichr: a comprehensive gene set enrichment analysis web server 590 2016 update. Nucleic Acids Res 44, W90- 97, doi:10.1093/nar/gkw377 (2016). 591 32 Xie, Z. et al. Gene Set Knowledge Discovery with Enrichr. Curr Protoc 1, e90, 592 doi:10.1002/cpz1.90 (2021).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 90, 875, 895]]<|/det|>
+594 33 Jain, A. et al. p62/SQSTM1 is a target gene for transcription factor NRF2 and creates a 595 positive feedback loop by inducing antioxidant response element- driven gene 596 transcription. J Biol Chem 285, 22576- 22591, doi:10.1074/jbc.M110.118976 (2010). 597 34 Ashino, T., Yamamoto, M., Yoshida, T. & Numazawa, S. Redox- sensitive transcription 598 factor Nrf2 regulates vascular smooth muscle cell migration and neointimal hyperplasia. 599 Arterioscler Thromb Vasc Biol 33, 760- 768, doi:10.1161/ATVBAHA.112.300614 600 (2013). 601 35 Olagnier, D. et al. Nrf2 negatively regulates STING indicating a link between antiviral 602 sensing and metabolic reprogramming. Nat Commun 9, 3506, doi:10.1038/s41467- 018- 603 05861- 7 (2018). 604 36 Johnson, A. D. & Owens, G. K. Differential activation of the SMalphaA promoter in 605 smooth vs. skeletal muscle cells by bHLH factors. Am J Physiol 276, C1420- 1431, 606 doi:10.1152/ajpcell.1999.276.6.C1420 (1999). 607 37 Chen, Y. H., Layne, M. D., Watanabe, M., Yet, S. F. & Perrella, M. A. Upstream 608 stimulatory factors regulate aortic preferentially expressed gene- 1 expression in vascular 609 smooth muscle cells. J Biol Chem 276, 47658- 47663, doi:10.1074/jbc.M108678200 610 (2001). 611 38 Kumar, M. S. & Owens, G. K. Combinatorial control of smooth muscle- specific gene 612 expression. Arterioscler Thromb Vasc Biol 23, 737- 747, 613 doi:10.1161/01.ATV.0000065197.07635.BA (2003). 614 39 Sellak, H., Choi, C., Browner, N. & Lincoln, T. M. Upstream stimulatory factors (USF- 615 1/USF- 2) regulate human cGMP- dependent protein kinase I gene expression in vascular 616 smooth muscle cells. J Biol Chem 280, 18425- 18433, doi:10.1074/jbc.M500775200 617 (2005). 618 40 Ackers- Johnson, M. et al. Myocardin regulates vascular smooth muscle cell 619 inflammatory activation and disease. Arterioscler Thromb Vasc Biol 35, 817- 828, 620 doi:10.1161/ATVBAHA.114.305218 (2015). 621 41 Wang, Q. et al. A hierarchical and collaborative BRD4/CEBPD partnership governs 622 vascular smooth muscle cell inflammation. Mol Ther Methods Clin Dev 21, 54- 66, 623 doi:10.1016/j.omtm.2021.02.021 (2021). 624 42 Kan, M. et al. CEBPD modulates the airway smooth muscle transcriptomic response to 625 glucocorticoids. Respir Res 23, 193, doi:10.1186/s12931- 022- 02119- 1 (2022). 626 43 Ko, C. Y., Chang, W. C. & Wang, J. M. Biological roles of CCAAT/Enhancer- binding 627 protein delta during inflammation. J Biomed Sci 22, 6, doi:10.1186/s12929- 014- 0110- 2 628 (2015). 629 44 Herzig, T. C. et al. Angiotensin II type1a receptor gene expression in the heart: AP- 1 and 630 GATA- 4 participate in the response to pressure overload. Proc Natl Acad Sci U S A 94, 631 7543- 7548 (1997). 632 45 Bramel, E. E. et al. Distinct Contribution of Global and Regional Angiotensin II Type 1a 633 Receptor Inactivation to Amelioration of Aortopathy in Tgfb1 (M318R/) Mice. Front 634 Cardiovasc Med 9, 936142, doi:10.3389/fcvm.2022.936142 (2022). 635 46 Ren, Q. et al. C/EBPbeta: The structure, regulation, and its roles in inflammation- related 636 diseases. Biomed Pharmacother 169, 115938, doi:10.1016/j.biopha.2023.115938 (2023). 637 47 Mondal, T. et al. MEG3 long noncoding RNA regulates the TGF- beta pathway genes 638 through formation of RNA- DNA triplex structures. Nat Commun 6, 7743, 639 doi:10.1038/ncomms8743 (2015).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[56, 90, 884, 875]]<|/det|>
+640 48 Mondal, T. et al. Author Correction: MEG3 long noncoding RNA regulates the TGF- beta pathway genes through formation of RNA- DNA triplex structures. Nat Commun 10, 5290, doi:10.1038/s41467- 019- 13200- 7 (2019). 643 49 Wang, M. et al. LncRNA MEG3- derived miR- 361- 5p regulate vascular smooth muscle cells proliferation and apoptosis by targeting ABCA1. Am J Transl Res 11, 3600- 3609 (2019). 646 50 Zhou, Y., Li, X., Zhao, D., Li, X. & Dai, J. Long noncoding RNA MEG3 knockdown alleviates hypoxiainduced injury in rat cardiomyocytes via the miR3253p/TRPV4 axis. Mol Med Rep 23, doi:10.3892/mmr.2020.11656 (2021). 649 51 Dong, K. et al. CARMN Is an Evolutionarily Conserved Smooth Muscle Cell- Specific LncRNA That Maintains Contractile Phenotype by Binding Myocardin. Circulation 144, 1856- 1875, doi:10.1161/CIRCULATIONAHA.121.055949 (2021). 652 52 Lu, B. H. et al. Long non- coding RNAs: Modulators of phenotypic transformation in vascular smooth muscle cells. Front Cardiovasc Med 9, 959955, doi:10.3389/fcvm.2022.959955 (2022). 653 53 Liu, S. et al. LncRNA CARMN inhibits abdominal aortic aneurysm formation and vascular smooth muscle cell phenotypic transformation by interacting with SRF. Cell Mol Life Sci 81, 175, doi:10.1007/s00018- 024- 05193- 4 (2024). 654 54 Bramel, E. E. et al. Postnatal Smad3 Inactivation in Murine Smooth Muscle Cells Elicits a Temporally and Regionally Distinct Transcriptional Response. Front Cardiovasc Med 9, 826495, doi:10.3389/fcvm.2022.826495 (2022). 655 55 Sawada, H., Rateri, D. L., Moorleghen, J. J., Majesky, M. W. & Daugherty, A. Smooth Muscle Cells Derived From Second Heart Field and Cardiac Neural Crest Reside in Spatially Distinct Domains in the Media of the Ascending Aorta- Brief Report. Arterioscler Thromb Vasc Biol 37, 1722- 1726, doi:10.1161/ATVBAHA.117.309599 (2017). 656 56 Sawada, H. et al. Heterogeneity of Aortic Smooth Muscle Cells: A Determinant for Regional Characteristics of Thoracic Aortic Aneurysms? J Transl Int Med 6, 93- 96, doi:10.2478/jtim- 2018- 0023 (2018). 657 57 Zhou, D. et al. hiPSC Modeling of Lineage- Specific Smooth Muscle Cell Defects Caused by TGFBR1(A230T) Variant, and Its Therapeutic Implications for Loeys- Dietz Syndrome. Circulation 144, 1145- 1159, doi:10.1161/CIRCULATIONAHA.121.054744 (2021). 658 58 Pedroza, A. J. et al. Embryologic Origin Influences Smooth Muscle Cell Phenotypic Modulation Signatures in Murine Marfan Syndrome Aortic Aneurysm. Arterioscler Thromb Vasc Biol 42, 1154- 1168, doi:10.1161/ATVBAHA.122.317381 (2022). 659 59 Pedroza, A. J. et al. Early clinical outcomes and molecular smooth muscle cell phenotyping using a prophylactic aortic arch replacement strategy in Loeys- Dietz syndrome. J Thorac Cardiovasc Surg 166, e332- e376, doi:10.1016/j.jtcvs.2023.07.023 (2023). 660 60 Sherman, T. D., Gao, T. & Fertig, E. J. CoGAPS 3: Bayesian non- negative matrix factorization for single- cell analysis with asynchronous updates and sparse data structures. BMC Bioinformatics 21, 453, doi:10.1186/s12859- 020- 03796- 9 (2020). 661 61 Johnson, J. A. I., Tsang, A., Mitchell, J. T., Davis- Marcisak, E. F., Sherman, T., Liefeld, T., Stein- O'Brien, G. L. . Inferring cellular and molecular processes in single- cell data
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 90, 884, 877]]<|/det|>
+685 with non- negative matrix factorization using Python, R, and GenePattern Notebook 686 implementations of CoGAPS. BioRxiv. (2022). 687 Sharma, G., Colantuoni, C., Goff, L. A., Fertig, E. J. & Stein- O'Brien, G. projectR: an 688 R/Bioconductor package for transfer learning via PCA, NMF, correlation and clustering. 689 Bioinformatics 36, 3592- 3593, doi:10.1093/bioinformatics/btaa183 (2020). 690 Liberzon, A. et al. The Molecular Signatures Database (MSigDB) hallmark gene set 691 collection. Cell Syst 1, 417- 425, doi:10.1016/j.cels.2015.12.004 (2015). 692 Castanza, A. S. et al. Extending support for mouse data in the Molecular Signatures 693 Database (MSigDB). Nat Methods 20, 1619- 1620, doi:10.1038/s41592- 023- 02014- 7 694 (2023). 695 Anisowicz, A., Messineo, M., Lee, S. W. & Sager, R. An NF- kappa B- like transcription 696 factor mediates IL- 1/TNF- alpha induction of gro in human fibroblasts. J Immunol 147, 520- 527 (1991). 697 Issa, R. et al. GRO- alpha regulation in airway smooth muscle by IL- 1beta and TNF- 698 alpha: role of NF- kappaB and MAP kinases. Am J Physiol Lung Cell Mol Physiol 291, 700 L66- 74, doi:10.1152/ajplung.00384.2005 (2006). 701 Wang, L. et al. Genetic and Pharmacologic Inhibition of the Chemokine Receptor 702 CXCR2 Prevents Experimental Hypertension and Vascular Dysfunction. Circulation 134, 703 1353- 1368, doi:10.1161/CIRCULATIONAHA.115.020754 (2016). 704 Korbecki, J., Maruszewska, A., Bosiacki, M., Chlubek, D. & Baranowska- Bosiacka, I. 705 The Potential Importance of CXCL1 in the Physiological State and in Noncancer 706 Diseases of the Cardiovascular System, Respiratory System and Skin. Int J Mol Sci 24, 707 doi:10.3390/ijms24010205 (2022). 708 Tliba, O. et al. Tumor necrosis factor alpha modulates airway smooth muscle function via 709 the autocrine action of interferon beta. J Biol Chem 278, 50615- 50623, 710 doi:10.1074/jbc.M303680200 (2003). 711 Dagia, N. M. et al. Phenyl methimazole inhibits TNF- alpha- induced VCAM- 1 expression 712 in an IFN regulatory factor- 1- dependent manner and reduces monocytic cell adhesion to 713 endothelial cells. J Immunol 173, 2041- 2049, doi:10.4049/jimmunol.173.3.2041 (2004). 714 Shen, Y. et al. IRF- 1 contributes to the pathological phenotype of VSMCs during 715 atherogenesis by increasing CCL19 transcription. Aging (Albany NY) 13, 933- 943, 716 doi:10.18632/aging.202204 (2020). 717 Liu, Z. et al. Thrombospondin- 1 (TSP1) contributes to the development of vascular 718 inflammation by regulating monocytic cell motility in mouse models of abdominal aortic 719 aneurysm. Circ Res 117, 129- 141, doi:10.1161/CIRCRESAHA.117.305262 (2015). 720 Kang, C. et al. The DNA damage response induces inflammation and senescence by 721 inhibiting autophagy of GATA4. Science 349, aaa5612, doi:10.1126/science.aaa5612 722 (2015). 723 Birsoy, K., Chen, Z. & Friedman, J. Transcriptional regulation of adipogenesis by KLF4. 724 Cell Metab 7, 339- 347, doi:10.1016/j.cmet.2008.02.001 (2008). 725 Liu, R. et al. Ten- eleven translocation- 2 (TET2) is a master regulator of smooth muscle 726 cell plasticity. Circulation 128, 2047- 2057, 727 doi:10.1161/CIRCULATIONAHA.113.002887 (2013). 728 Shi, N., Li, C. X., Cui, X. B., Tomarev, S. I. & Chen, S. Y. Olfactomedin 2 Regulates 729 Smooth Muscle Phenotypic Modulation and Vascular Remodeling Through Mediating
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 90, 884, 895]]<|/det|>
+730 Runt- Related Transcription Factor 2 Binding to Serum Response Factor. Arterioscler 731 Thromb Vasc Biol 37, 446- 454, doi:10.1161/ATVBAHA.116.308606 (2017). 732 77 Iyer, D. et al. Coronary artery disease genes SMAD3 and TCF21 promote opposing 733 interactive genetic programs that regulate smooth muscle cell differentiation and disease 734 risk. PLoS Genet 14, e1007681, doi:10.1371/journal.pgen.1007681 (2018). 735 78 Lino Cardenas, C. L. et al. An HDAC9- MALAT1- BRG1 complex mediates smooth 736 muscle dysfunction in thoracic aortic aneurysm. Nat Commun 9, 1009, 737 doi:10.1038/s41467- 018- 03394- 7 (2018). 738 79 Yap, C., Mieremet, A., de Vries, C. J. M., Micha, D. & de Waard, V. Six Shades of 739 Vascular Smooth Muscle Cells Illuminated by KLF4 (Kruppel- Like Factor 4). 740 Arterioscler Thromb Vasc Biol 41, 2693- 2707, doi:10.1161/ATVBAHA.121.316600 741 (2021). 742 80 Huang, X., Jie, S., Li, W. & Liu, C. GATA4- activated lncRNA MALAT1 promotes 743 osteogenic differentiation through inhibiting NEDD4- mediated RUNX1 degradation. Cell 744 Death Discov 9, 150, doi:10.1038/s41420- 023- 01422- 0 (2023). 745 81 Grootaert, M. O. et al. Defective autophagy in vascular smooth muscle cells accelerates 746 senescence and promotes neointima formation and atherogenesis. Autophagy 11, 2014- 747 2032, doi:10.1080/15548627.2015.1096485 (2015). 748 82 Jeong, K. et al. Nuclear Focal Adhesion Kinase Controls Vascular Smooth Muscle Cell 749 Proliferation and Neointimal Hyperplasia Through GATA4- Mediated Cyclin D1 750 Transcription. Circ Res 125, 152- 166, doi:10.1161/CIRCRESAHA.118.314344 (2019). 751 83 Watt, A. J., Battle, M. A., Li, J. & Duncan, S. A. GATA4 is essential for formation of the 752 proepicardium and regulates cardiogenesis. Proc Natl Acad Sci U S A 101, 12573- 12578, 753 doi:10.1073/pnas.0400752101 (2004). 754 84 Wirth, A. et al. G12- G13- LARG- mediated signaling in vascular smooth muscle is 755 required for salt- induced hypertension. Nat Med 14, 64- 68, doi:10.1038/nm1666 (2008). 756 85 Bostrom, P. et al. C/EBPbeta controls exercise- induced cardiac growth and protects 757 against pathological cardiac remodeling. Cell 143, 1072- 1083, 758 doi:10.1016/j.cell.2010.11.036 (2010). 759 86 Chang, L. H. et al. Role of macrophage CCAAT/enhancer binding protein delta in the 760 pathogenesis of rheumatoid arthritis in collagen- induced arthritic mice. PLoS One 7, 761 e45378, doi:10.1371/journal.pone.0045378 (2012). 762 87 van Dorst, D. C. H. et al. Transforming Growth Factor- beta and the Renin- Angiotensin 763 System in Syndromic Thoracic Aortic Aneurysms: Implications for Treatment. 764 Cardiovasc Drugs Ther, doi:10.1007/s10557- 020- 07116- 4 (2020). 765 88 Gillis, E., Van Laer, L. & Loeys, B. L. Genetics of thoracic aortic aneurysm: at the 766 crossroad of transforming growth factor- beta signaling and vascular smooth muscle cell 767 contractility. Circ Res 113, 327- 340, doi:10.1161/CIRCRESAHA.113.300675 (2013). 768 89 Li, W. et al. Tgfrb2 disruption in postnatal smooth muscle impairs aortic wall 769 homeostasis. J Clin Invest 124, 755- 767, doi:69942 [pii] 770 10.1172/JCI69942 (2014). 771 90 Hu, J. H. et al. Postnatal Deletion of the Type II Transforming Growth Factor- beta 772 Receptor in Smooth Muscle Cells Causes Severe Aortopathy in Mice. Arterioscler 773 Thromb Vasc Biol 35, 2647- 2656, doi:10.1161/ATVBAHA.115.306573 (2015). 774 91 Angelov, S. N. et al. TGF- beta (Transforming Growth Factor- beta) Signaling Protects the 775 Thoracic and Abdominal Aorta From Angiotensin II- Induced Pathology by Distinct
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[56, 90, 881, 875]]<|/det|>
+776 Mechanisms. Arterioscler Thromb Vasc Biol 37, 2102- 2113, 777 doi:10.1161/ATVBAHA.117.309401 (2017). 778 92 Wei, H. et al. Aortopathy in a Mouse Model of Marfan Syndrome Is Not Mediated by 779 Altered Transforming Growth Factor beta Signaling. J Am Heart Assoc 6, e004968, 780 doi:10.1161/JAHA.116.004968 (2017). 781 93 Chen, P. Y. et al. Endothelial TGF- beta signalling drives vascular inflammation and 782 atherosclerosis. Nat Metab 1, 912- 926, doi:10.1038/s42255- 019- 0102- 3 (2019). 783 94 Chen, P. Y. et al. Smooth Muscle Cell Reprogramming in Aortic Aneurysms. Cell Stem 784 Cell 26, 542- 557 e511, doi:10.1016/j.stem.2020.02.013 (2020). 785 95 Creamer, T. J., Bramel, E. E. & MacFarlane, E. G. Insights on the Pathogenesis of 786 Aneurysm through the Study of Hereditary Aortopathies. Genes (Basel) 12, 787 doi:10.3390/genes12020183 (2021). 788 96 Eguchi, S. et al. Recent Advances in Understanding the Molecular Pathophysiology of 789 Angiotensin II Receptors: Lessons From Cell- Selective Receptor Deletion in Mice. Can J 790 Cardiol 39, 1795- 1807, doi:10.1016/j.cjca.2023.06.421 (2023). 791 97 Daugherty, A., Sawada, H., Sheppard, M. B. & Lu, H. S. Angiotensinogen as a 792 Therapeutic Target for Cardiovascular and Metabolic Diseases. Arterioscler Thromb 793 Vasc Biol 44, 1021- 1030, doi:10.1161/ATVBAHA.124.318374 (2024). 794 98 Michel, J. B., Jondeau, G. & Milewicz, D. M. From genetics to response to injury: 795 vascular smooth muscle cells in aneurysms and dissections of the ascending aorta. 796 Cardiovasc Res 114, 578- 589, doi:10.1093/cvr/cvy006 (2018). 797 99 Karimi, A. & Milewicz, D. M. Structure of the Elastin- Contractile Units in the Thoracic 798 Aorta and How Genes That Cause Thoracic Aortic Aneurysms and Dissections Disrupt 799 This Structure. Can J Cardiol 32, 26- 34, doi:10.1016/j.cjca.2015.11.004 (2016). 800 100 Pedroza, A. J. et al. Single- Cell Transcriptomic Profiling of Vascular Smooth Muscle 801 Cell Phenotype Modulation in Marfan Syndrome Aortic Aneurysm. Arterioscler Thromb 802 Vasc Biol, ATVBAHA120314670, doi:10.1161/ATVBAHA.120.314670 (2020). 803 101 Salabei, J. K. & Hill, B. G. Autophagic regulation of smooth muscle cell biology. Redox 804 Biol 4, 97- 103, doi:10.1016/j.redox.2014.12.007 (2015). 805 102 Clement, M. et al. Vascular Smooth Muscle Cell Plasticity and Autophagy in Dissecting 806 Aortic Aneurysms. Arterioscler Thromb Vasc Biol 39, 1149- 1159, 807 doi:10.1161/ATVBAHA.118.311727 (2019). 808 103 Pikkarainen, S. et al. GATA- 4 is a nuclear mediator of mechanical stretch- activated 809 hypertrophic program. J Biol Chem 278, 23807- 23816, doi:10.1074/jbc.M302719200 810 (2003). 811 104 Wang, Y. Q., Batool, A., Chen, S. R. & Liu, Y. X. GATA4 is a negative regulator of 812 contractility in mouse testicular peritubular myoid cells. Reproduction 156, 343- 351, 813 doi:10.1530/REP- 18- 0148 (2018). 814 105 Oka, T. et al. Cardiac- specific deletion of Gata4 reveals its requirement for hypertrophy, 815 compensation, and myocyte viability. Circ Res 98, 837- 845, 816 doi:10.1161/01.RES.0000215985.18538.c4 (2006). 817 106 Garg, V. et al. GATA4 mutations cause human congenital heart defects and reveal an 818 interaction with TBX5. Nature 424, 443- 447, doi:10.1038/nature01827 (2003). 819 107 Kuo, C. T. et al. GATA4 transcription factor is required for ventral morphogenesis and 820 heart tube formation. Genes Dev 11, 1048- 1060 (1997).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[52, 88, 876, 360]]<|/det|>
+821 108 Liang, Q. et al. The transcription factors GATA4 and GATA6 regulate cardiomyocyte 822 hypertrophy in vitro and in vivo. J Biol Chem 276, 30245- 30253, 823 doi:10.1074/jbc.M102174200 (2001). 824 109 Lepage, D. et al. Gata4 is critical to maintain gut barrier function and mucosal integrity 825 following epithelial injury. Sci Rep 6, 36776, doi:10.1038/srep36776 (2016). 826 110 Liu, J. et al. Cell- specific translational profiling in acute kidney injury. J Clin Invest 124, 827 1242- 1254, doi:10.1172/JCI72126 (2014). 828 111 Lewis, A. E., Vasudevan, H. N., O'Neill, A. K., Soriano, P. & Bush, J. O. The widely 829 used Wnt1- Cre transgene causes developmental phenotypes by ectopic activation of Wnt 830 signaling. Dev Biol 379, 229- 234, doi:10.1016/j.ydbio.2013.04.026 (2013). 831 112 Hao, Y. et al. Dictionary learning for integrative, multimodal and scalable single- cell 832 analysis. Nat Biotechnol 42, 293- 304, doi:10.1038/s41587- 023- 01767- y (2024). 833 113 Zheng, G. X. et al. Massively parallel digital transcriptional profiling of single cells. Nat 834 Commun 8, 14049, doi:10.1038/ncomms14049 (2017). 835 836
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[20, 50, 970, 777]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[20, 784, 978, 961]]<|/det|>
+<center>Figure 1. Downregulation of transcripts associated with extracellular matrix-receptor interactions and upregulation of stress and inflammation pathways in Tgfbr1<sup>M318R/+</sup> LDS VSMCs. (A) Uniform manifold approximation and projection (UMAP) of aortic cells from control (Tgfbr1<sup>+/+</sup>) and LDS (Tgfbr1<sup>M318R/+</sup>) mice. (B) Dot plot of cluster defining transcripts used to identify endothelial cells, leukocytes, fibroblasts, and VSMCs. Color of the dot represents a scaled average expression while the size indicates the percentage of cells in which the transcript was detected. (C) ClueGO gene enrichment analysis network of transcripts dysregulated in LDS VSMCs relative to controls. Each node represents a term/pathway or individual genes associated with that term. The color of the node corresponds to the ClueGO group to which each node belongs. The size of the node indicates significance of the enrichment calculated by the ClueGO algorithm. (D) ClueGO network in which terms differentially enriched among transcripts downregulated in LDS VSMCs are highlighted in blue, while those enriched among transcripts upregulated in LDS VSMCs are highlighted in red. (E) Dot plot showing expression of a selection of transcripts significantly dysregulated in LDS VSMCs. (F,G) EnrichR gene over-representation analysis for the ENCODE and ChEA Consensus transcription factors (TF) databases showing the top three most significant terms associated with transcripts that are downregulated (F) or upregulated (G) in LDS VSMCs. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[0, 66, 985, 688]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 694, 944, 789]]<|/det|>
+<center>Figure 2. MERFISH reveals spatially heterogeneous transcriptional profiles in LDS VSMCs. MERFISH images of the proximal aorta of LDS (A) and control (B) mice, scale bar is 1 mm. The first panel displays all detected transcripts across the aortic tissue, with key anatomic landmarks indicated. Subsequent panels depict the colocalization of Myh11 and transcripts of interest. Insets note regions of the ascending aorta and aortic root that are presented at higher magnification. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[19, 14, 999, 750]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[4, 777, 980, 972]]<|/det|>
+<center>Figure 3. Transcriptionaly and spatially-defined VSMC subclusters with distinct responses to LDS-causing mutations can be identified in both murine and human aortas. (A) UMAP of VSMCs from control (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) mice shown split by genotype. (B) Dot plot showing enrichment of cluster-defining transcripts in VSMC1 and VSMC2. For a given transcript, the color of the dot represents a scaled average expression while the size indicates the percentage of cells in which it was detected. (C) RNA in situ hybridization showing the expression of Gata4 along the length of the murine aorta in a 16-week old control animal. (D) UMAP of control and LDS VSMCs from human patients and dot plot of cluster defining markers in this dataset split by aortic region (Pedroza et al., 2023). (E,F) UMAP overlayed with weights for CoGAPS patterns 4 and 5, in mouse and human scRNAseq datasets. (G,H) Violin plots showing the distribution of pattern 4 and 5 weights in VSMC subclusters from mouse and human scRNAseq datasets. P-values refer to Wilcoxon test. (I) EnrichR gene over-representation analysis for the ENCODE and ChEA Consensus TF databases showing the top four most significant terms associated with transcripts that define CoGAPs Patterns 4 and 5. (J) ClueGO network of terms differentially enriched in mouse and human LDS VSMC2 relative to VSMC1. Terms highlighted in blue are enriched in VSMC1, while those highlighted in red are enriched in VSMC2. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[9, 52, 978, 496]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[870, 15, 955, 35]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[33, 523, 928, 691]]<|/det|>
+Figure 4. Gata4 mRNA and protein are upregulated in the aortic root of LDS mice. (A) Representative images of RNA in situ hybridization for Gata4 in the aortic root and ascending aorta of control and LDS (Tgfbr1M318R/+) mice. Insets identify the location shown at higher magnification in the subsequent panel. Scale bars 50 and 200 microns, respectively. (B) Representative images of immunofluorescence for GATA4in the aortic root and ascending aorta of control and LDS mice. Insets identify the location shown at higher magnification in the subsequent panel. Scale bars 50 and 200 microns, respectively. (C) Immunoblot for Gata4 expression relative to \(\beta\) - actin in aortic root lysates of control \((n = 3)\) and LDS mice \((n = 3)\) , and related quantification of immunoblot, P- value refers to two- tailed Student's t- test.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[44, 50, 725, 711]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[871, 16, 961, 37]]<|/det|>
+<center>Figure 5 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 716, 872, 848]]<|/det|>
+Figure 5. Gata4 protein is upregulated in LDS aortic root of Gata4<sup>Ctrl</sup> and effectively ablated in Gata4<sup>SMckO</sup> mice. Representative images of immunofluorescence for GATA4 at 16 weeks of age. Three independent biological replicates are shown per genotype abbreviated as follows Control (Tgfbr1<sup>+/+</sup>) and LDS (Tgfbr1<sup>M318R/+</sup>) with (Gata4<sup>SMckO</sup>) or without (Gata4<sup>Ctrl</sup>) smooth muscle specific deletion of Gata4 Insets identify location shown at higher magnification in subsequent panels. Images were acquired at 20x magnification. Scale bars 50 and 200 microns, respectively.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[20, 28, 870, 270]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[20, 280, 40, 295]]<|/det|>
+<center>B </center>  
+
+<|ref|>image<|/ref|><|det|>[[60, 280, 720, 833]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[15, 845, 965, 957]]<|/det|>
+<center>Figure 6. Smooth muscle-specific deletion of Gata4 (Gata4SMcKO) reduces aortic root size and growth and improves aortic root media architecture in LDS mice. (A) Aortic root diameter of Ctrl (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) with (Gata4SMcKO) or without (Gata4SMcKO) smooth muscle specific deletion of Gata4 as measured by echocardiography at 8 and 16 weeks of age and aortic root growth from 8-16 weeks. P-values refer to Brown-Forsythe ANOVA. (B) Representative VVG-stained aortic root sections from three independent biological replicates per genotype. Insets identify area shown at higher magnification in the subsequent panel. Scale bars 50 and 200 microns, respectively. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[45, 50, 731, 710]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[870, 15, 961, 36]]<|/det|>
+<center>Figure 7 </center>  
+
+<|ref|>text<|/ref|><|det|>[[46, 719, 933, 833]]<|/det|>
+Figure 7. Smooth muscle-specific deletion of Gata4 results in reduced expression of Agtr1a. Representative images of RNA in situ hybridization for Agtr1a in the aortic root of mice at 16 weeks of age. Three independent biological replicates are shown per genotype abbreviated as follows Control (Tgfbr1+/+) and LDS (Tgfbr1M318R/+) with (Gata4SmKo) or without (Gata4Ctl) smooth muscle specific deletion of Gata4. Insets identify location shown at higher magnification in subsequent panels. Images were acquired at 20x magnification. Scale bars 50 and 200 microns, respectively.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[42, 50, 728, 707]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[872, 17, 961, 37]]<|/det|>
+<center>Figure 8 </center>  
+
+<|ref|>text<|/ref|><|det|>[[35, 714, 880, 844]]<|/det|>
+Figure 8. Smooth muscle-specific deletion of Gata4 results in reduced expression of Cebpb. Representative images of RNA in situ hybridization for Cebpb in the aortic root of mice of indicated genotype at 16 weeks of age. Three independent biological replicates are shown per genotype abbreviated as follows Control (Tgfbr1<sup>+/+</sup>) and LDS (Tgfbr1<sup>M318R/+</sup>) with (Gata4<sup>SMckO</sup>) or without (Gata4<sup>Ctrl</sup>) smooth muscle specific deletion of Gata4. Insets identify location shown at higher magnification in subsequent panels. Images were acquired at 20x magnification. Scale bars 50 and 200 microns, respectively.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 43, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[59, 131, 568, 231]]<|/det|>
+SupplementaryTables.zip  - SupplementalFigures.zip  - CORRECTEDPrimaryfigure6forversion1. pdf  - CORRECTEDSupplementalFigures6and7forversion1. pdf
+
+<--- Page Split --->

preprint/preprint__00b9c52ff18ddf879d531bb5dd46e2c462d8c5a2f0fc667773ff3a23635e2342/images_list.json

@@ -0,0 +1,47 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "e. Ultrametricity: sample tree shapes among sequence-defined families (OMA families)",
+    "footnote": [],
+    "bbox": [
+      [
+        147,
+        110,
+        850,
+        450
+      ]
+    ],
+    "page_idx": 7
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1 a) Trees using the Foldtree metric exhibit higher taxonomic congruence than sequence trees on average (protein families defined from sequences); by contrast, structure trees from LDDT and TM underperform sequence trees; b) After filtering the input dataset for structural quality (families with average pLDDT structure scores \\(>40\\) ), the proportion of Foldtree trees which have a greater normalized congruence than sequence-based trees increased from \\(48\\%\\) to \\(53\\%\\) ; c) the Foldtree metric on the CATH dataset of structurally defined families using experimental structures",
+    "footnote": [],
+    "bbox": [
+      [
+        190,
+        476,
+        848,
+        757
+      ]
+    ],
+    "page_idx": 7
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Phylogeny of cytosolic receptors from the RRNPPA family paired with a communication proppetide. a) Functional diversity of the RRNPPA family. The MAD root separates paralogs of Anoxybacter fermentans with a singular architecture from the other canonical RRNPPA systems.",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
+        85,
+        875,
+        860
+      ]
+    ],
+    "page_idx": 10
+  }
+]

preprint/preprint__00b9c52ff18ddf879d531bb5dd46e2c462d8c5a2f0fc667773ff3a23635e2342/preprint__00b9c52ff18ddf879d531bb5dd46e2c462d8c5a2f0fc667773ff3a23635e2342.mmd

@@ -0,0 +1,446 @@
+
+# Structural phylogenetics unravels the evolutionary diversification of communication systems in gram-positive bacteria and their viruses  
+
+David Moi dmoi@uni1.ch  
+
+University of Lausanne https://orcid.org/0000- 0002- 2664- 7385  
+
+Charles Bernard UNIL DBC  
+
+Yannis Never UNIL DBC  
+
+Martin Stenegger Artificial Intelligence Institute, Seoul National University  
+
+Mauricio Langleib Universidad de la Republica  
+
+Christophe Dessimoz University of Lausanne https://orcid.org/0000- 0002- 2170- 853X  
+
+Biological Sciences - Article  
+
+Keywords:  
+
+Posted Date: October 4th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3368849/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 Structural & Molecular Biology on October 10th, 2025. See the published version at https://doi.org/10.1038/s41594- 025- 01649- 8.
+
+<--- Page Split --->
+
+Structural phylogenetics unravels the evolutionary diversification of communication systems in gram-positive bacteria and their viruses  
+
+David Moi \(^{1,2,\#}\) , Charles Bernard \(^{1,2}\) , Martin Steinegger \(^{3,4,5}\) , Yannis Nevers \(^{1,2}\) , Mauricio Langleib \(^{6,7}\) , Christophe Dessimoz \(^{1,2,\#}\)  
+
+\(^{1}\) Department of Computational Biology, University of Lausanne, Lausanne, Switzerland \(^{2}\) Swiss Institute of Bioinformatics, Lausanne, Switzerland \(^{3}\) School of Biological Sciences, Seoul National University, Seoul, South Korea \(^{4}\) Artificial Intelligence Institute, Seoul National University, Seoul, South Korea \(^{5}\) Institute of Molecular Biology and Genetics, Seoul National University, Seoul, South Korea \(^{6}\) Unidad de Bioinformática, Institut Pasteur de Montevideo, Montevideo, Uruguay \(^{7}\) Unidad de Genómica Evolutiva, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay  
+
+\(^{4}\) Correspondence and requests for materials should be addressed to D.M. or C.D.  
+
+## Abstract  
+
+Recent advances in AI- based protein structure modeling have yielded remarkable progress in predicting protein structures. Since structures are constrained by their biological function, their geometry tends to evolve more slowly than the underlying amino acids sequences. This feature of structures could in principle be used to reconstruct phylogenetic trees over longer evolutionary timescales than sequence- based approaches, but until now a reliable structure- based tree building method has been elusive. Here, we demonstrate that the use of structure- based
+
+<--- Page Split --->
+
+phylogenies can outperform sequence- based ones not only for distantly related proteins but also, remarkably, for more closely related ones. This is achieved by inferring trees from protein structures using a local structural alphabet, an approach robust to conformational changes that confound traditional structural distance measures. As an illustration, we used structures to decipher the evolutionary diversification of a particularly challenging family: the fast- evolving RRNPPA quorum sensing receptors enabling gram- positive bacteria, plasmids and bacteriophages to communicate and coordinate key behaviors such as sporulation, virulence, antibiotic resistance, conjugation or phage lysis/lysogeny decision. The advent of high- accuracy structural phylogenetics enables myriad of applications across biology, such as uncovering deeper evolutionary relationships, elucidating unknown protein functions, or refining the design of bioengineered molecules.  
+
+## Introduction  
+
+Since Darwin, phylogenetic trees have depicted evolutionary relationships among organisms, viruses, genes, and other evolving entities, enabling an understanding of shared ancestry and tracing the events that led to the observable extant diversity. Trees based on molecular data are typically reconstructed from nucleotide or amino- acid sequences, by aligning homologous sequences and inferring the tree topology and branch lengths under a model of character substitution \(^{1 - 3}\) . However, over long evolutionary time scales, multiple substitutions occurring at the same site cause uncertainty in alignment and tree building. The problem is particularly acute when dealing with fast evolving sequences, such as viral or immune- related ones, or when attempting to resolve distant relationships, such as at the origins of animals \(^{4 - 6}\) or beyond.  
+
+In contrast, the fold of proteins is often conserved well past sequence signal saturation. Furthermore, because 3D structure determines function, protein structures have long been studied to gain insight into their biological role within the cell whether it be catalyzing reactions, interacting with other proteins to form complexes or regulating the expression of genes among a myriad of other functions.
+
+<--- Page Split --->
+
+Until recently, protein structures had to be obtained through labor intensive crystallography, with modeling efforts often falling short of the level of accuracy required to describe a fold for the many tasks crystal structures were used for. Due to these limitations, structural biology and phylogenetics have developed as largely separate disciplines and each field has created models describing evolutionary or molecular phenomena suited to the availability of computational power and experimental data.  
+
+Now, the widespread availability of accurate structural models \(^{7,8}\) opens up the prospect of reconstructing trees from structures. However, there are pitfalls to avoid in order to derive evolutionary distances between homologous protein structures. Geometric distances between rigid body representations of structures, such as root mean square deviation (RMSD) distance or template modeling (TM) score \(^{9}\) , are confounded by spatial variations caused by conformational changes \(^{10,11}\) . More local structural similarity measures have been proposed in the context of protein classification \(^{10}\) , but due to the relative paucity of available structures until recently, little is known about the accuracy of structure- based phylogenetic reconstruction beyond a few isolated case studies \(^{12,13}\) .  
+
+Here, we report on a comprehensive evaluation of phylogenetic trees reconstructed from the structures of thousands of protein families across the tree of life, using multiple kinds of distance measures. We built trees from structural divergence measures obtained using Foldseek \(^{14}\) , which outputs scores from rigid body alignment, local superposition- free alignment and structural alphabet based sequence alignments. The performance of these measures has been previously assessed on the task of detecting whether folds are homologous and belong to the same family \(^{14 - 16}\) , but have never been benchmarked with regards to how well they perform as evolutionary distances. Remarkably, we found that the structural alphabet- based measure outperforms phylogenies from sequence alone even at relatively short evolutionary distances. To demonstrate the capabilities of structural phylogenetics, we employ our methodology, released as open- source software named Foldtree, to resolve the difficult phylogeny of a fast- evolving protein family of high relevance: the RRNPPA (Rap, Rgg, NprR, PlcR, PrgX and AimR) receptors of
+
+<--- Page Split --->
+
+communication peptides. These proteins allow gram- positive bacteria, their plasmids and their viruses to assess their population density and regulate key biological processes accordingly. These communication systems have been shown to regulate virulence, biofilm formation, sporulation, competence, solventogenesis, antibiotic resistance or antimicrobial production in bacteria \(^{17 - 21}\) , conjugation in conjugative elements, lysis/lysogeny decision in bacteriophages \(^{22}\) and host manipulation by mobile genetic elements (MGEs) \(^{19,23}\) . Accordingly, the RRNPPA family has a substantial impact on human societies as it connects to the virulence and transmissibility of pathogenic bacteria and the spread of antimicrobial resistance genes through horizontal gene transfers. We analyze and discuss the parsimonious characteristics of the phylogeny of this family, highlighting the contrasts with the sequence- based tree.  
+
+## Results  
+
+## Structural trees outperform sequence based trees at both short and long evolutionary divergence times  
+
+To find a structural distance metric with high informative phylogenetic signal, we investigated the use of local superposition- free comparison (local distance difference test; LDDT \(^{16}\) ), rigid body alignment (TM score \(^{9}\) ) and a distance derived from similarity over a structural alphabet (Fident) \(^{14}\) . These measures were used to compute distance trees using neighbor joining, after being aligned in an all- vs- all comparison using the Foldseek structural alphabet (Methods).  
+
+Assessing the accuracy of trees reconstructed from empirical data is notoriously difficult. We used two complementary indicators. The first one, taxonomic congruence score (TCS) (Methods and Supplementary Figures 1- 2), assesses the congruence of reconstructed protein trees with the known taxonomy \(^{24}\) . Among several potential tree topologies reconstructed from the same set of input proteins, the better topologies can be expected to have higher TCS on average.  
+
+For trees reconstructed from closely related protein families using standard sequence alignments, both local structure LDDT and global structure TM measures
+
+<--- Page Split --->
+
+showed poorer taxonomic congruence than sequence- based trees on average (Figure 1a). By contrast, trees derived from the Fident distance (henceforth referred to as the Foldtree measure) outperformed those based on sequence. The difference was even larger if we excluded families for which the Alphafold2- inferred structures are of low confidence (Figure 1b). This trend was observed consistently across various protein family subsets, taken from clades with different divergence levels (Supplementary Figure 8). We also experimented with statistical corrections and other parameter variations, but they did not lead to further improvements (Supplementary Figures 4- 9).  
+
+We then assessed the Foldtree measure's performance against sequence- based trees over larger evolutionary distances, using structure- informed homologous families from the CATH database<sup>25</sup>. This database classifies proteins hierarchically, grouping them based on Class, Architecture, Topology and Homology of experimentally determined protein structures. We examined both proteins from the same homology set as well as proteins within the same topology sets (Methods). Efforts were made to correct structures with discontinuities or other defects before treebuilding (Methods) since these adversely affect structural comparisons. With this more divergent CATH dataset, structure- based methods performed better overall. Foldtree outperformed the sequence- based method even more (Figure 1c). Results for LDDT versus sequence flipped in favour of LDDT, while results for the global TM measure remained inferior to sequence (Supplementary Figure 9).  
+
+To delve deeper into the reasons for these performance differences, we applied a gradient- boosted decision tree regressor<sup>26</sup> on features derived from the input structures and taxonomic lineages of the input protein sets, aiming to predict the TCS difference (Supp Methods Table 1). We found that features measuring the confidence of the AlphaFold structure prediction (predicted LDDT or pLDDT) emerged as significant factors in the analysis (Supplementary Figure 3). This suggests that advancements in structural prediction might further benefit structural trees in the future.
+
+<--- Page Split --->
+
+To validate our findings using an entirely different indicator of tree quality, we assessed the “ultrametricity” of trees—how uniform a tree’s root- to- tip lengths are for all its tips, akin to following a molecular clock. Although strict adherence to a molecular clock is unlikely in general, it is reasonable to assume that distance measures resulting in more ultrametric trees on average (i.e., with reduced root- to- tip variance, see Methods) are more accurate<sup>27</sup>. We found that in the sequence- based family dataset, Foldtree trees had by far the lowest root- to- tip variance of all approaches (Figure 1d). The difference was so pronounced that it is evident in visual comparison of tree shapes for several randomly chosen families (Figure 1e). Foldtree performed the best of all metrics and sequence- based trees the worst.
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+<center>e. Ultrametricity: sample tree shapes among sequence-defined families (OMA families) </center>  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1 a) Trees using the Foldtree metric exhibit higher taxonomic congruence than sequence trees on average (protein families defined from sequences); by contrast, structure trees from LDDT and TM underperform sequence trees; b) After filtering the input dataset for structural quality (families with average pLDDT structure scores \(>40\) ), the proportion of Foldtree trees which have a greater normalized congruence than sequence-based trees increased from \(48\%\) to \(53\%\) ; c) the Foldtree metric on the CATH dataset of structurally defined families using experimental structures </center>
+
+<--- Page Split --->
+
+outperforms sequence trees to an even greater proportion; d) The variance of normalized root- to- tip distances were compiled for all trees within the OMA dataset for all tree structural tree methods and sequence trees. Foldtree has a lower variance than other methods. The median of each distribution is shown with a vertical red line. Distributions are truncated to values between 0 and 0.2; e) A random sample of trees is shown where each column is from from equivalent protein input sets and each row of trees is derived using a distinct tree building method.  
+
+Both of the orthogonal metrics of ultrametricity and species tree discordance indicate that Foldtree produces trees with desirable characteristics that are ideal for constructing phylogenies with sets of highly divergent homologs.  
+
+## Foldtree reveals the evolutionary diversification of RRNPPA communication systems  
+
+To illustrate the potential of structural phylogenies, we reconstructed the intricate evolutionary history of the RRNPPA family of intracellular quorum sensing receptors in gram- positive Bacillota bacteria, their conjugative elements and temperate bacteriophages<sup>17,21,28</sup>. These receptors, vital for microbial communication and decision- making, are paired with a small secreted communication peptide that accumulates extracellularly as the encoding population replicates. Once a quorum of cells, plasmids or viruses is met, communication peptides get frequently internalized within cells and binds to the tetratricopeptide repeats (TPRs) of cognate intracellular receptors, leading to gene or protein activation or inhibition, facilitating a coordinated response beneficial for a dense population. The density- dependent regulations of RRNPPA systems control behaviors like bacterial virulence, biofilm formation, sporulation, competence, conjugation and bacteriophage lysis/lysogeny decisions<sup>17- 21</sup>. Although these receptors were identified in the early 1990s<sup>29,30</sup>, their evolutionary history is unclear due to frequent mutations and transfers, making sequence comparisons challenging<sup>28,31,32</sup>. This is reflected by the nomenclature of the family: RRNPPA is an acronym for Rap, Rgg, NprR, PlcR, PrgX and AimR, which were historically described as six different families of intracellular receptors, and of which only structural comparisons allowed to establish the actual consensus on their common evolutionary origin<sup>28,33,34</sup>. Recently, a pioneer work combining
+
+<--- Page Split --->
+
+structural comparisons among folds and sequence- based phylogenetics have provided insights among some of these families<sup>28</sup>, but a comprehensive reconstruction of the evolutionary history of this family that includes all described subfamilies<sup>19</sup> remains elusive.  
+
+The Foldtree structure- based phylogeny illuminates key evolutionary features of the diversification of RRNPPA communication systems that could not be resolved based on sequences (Figure 2). The evolutionary trajectory it implies is more parsimonious in terms of subfamily classification, taxonomy, functions, and protein architectures than a phylogeny obtained with a state- of- the- art sequence- based method (details in Supplementary Figure 9). In particular, the structure- based phylogeny implies that folds composed of 9 tetratricopeptide repeats (TPRs) and folds composed of 5 TPRs emerged only once while the sequence- based tree implies a less plausible scenario of convergent evolution of two clades toward 5- TPR protein architectures.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Phylogeny of cytosolic receptors from the RRNPPA family paired with a communication proppetide. a) Functional diversity of the RRNPPA family. The MAD root separates paralogs of Anoxybacter fermentans with a singular architecture from the other canonical RRNPPA systems. </center>
+
+<--- Page Split --->
+
+Subfamilies with experimental validation of at least one member are highlighted in color. Other subfamilies correspond to high- confidence candidate subfamilies detected with RRNPP_ detector in \(^{19}\) . Biological processes experimentally shown to be regulated in a density- dependent manner by a QS system are displayed for each validated subfamily. Subfamilies in gray correspond to novel, high- confidence candidate RRNPPA subfamilies from \(^{19}\) . A star mapped to a leaf indicates a predicted regulation of an adjacent biosynthetic gene cluster by the corresponding QS system. b) Main implied events of the tree, with normalized branch length for visualization purposes (the events that are implied from alternate roots are shown in Supplementary Figure 10). c) Distribution and prevalence of the different members of each RRNPPA subfamily into the different taxonomic families. d) Genomic orientation and encoding element of the receptor - adjacent propeptide pairs. e) The first colostrip indicates the domain architecture of each receptor. A representative fold for each domain architecture is displayed in the legend (AlphaFold models of subfamily 27, NprR, Rap and PlcR, respectively) with an indication of the implied events from panel a) at the origin of each fold/architecture. The second colostrip gives the degeneration score of TPR sequences of each receptor (given as 1 - TprPred_likelihood, as in \(^{33}\) ). The histogram shows the length (in amino-acids) of each receptor.  
+
+The minimal ancestor deviation (MAD) method placed the root right next to receptors encoded by Anoxybacter fermentans DY22613, a piezophilic and thermophilic endospore- forming bacterium from the Clostridia class isolated from a deep- sea hydrothermal vent. These proteins exhibit a unique domain architecture lacking the DNA- binding HTH domain and harboring 7 TPRs (Table S1). Their singular architecture, and the proximity to the MAD root lead us to infer Anoxybacter's receptors as the outgroup of all other RRNPPA systems (Figure 2a- b). This suggests that the early history of canonical RRNPPA systems could have been linked to extremophile endospore- forming Bacillota and may have started with a gain of a N- terminal HTH DNA binding domain, enabling to coupling quorum sensing with transcriptional regulation (Figure 2e). We considered alternative rooting scenarios (Supplementary Figure 11) but only the MAD rooting implies a unique origin of receptors with non- degenerated TPR sequences that predates the last common ancestor of each clade of receptors with degenerated TPRs (Figure 2e), in line with Declerck et al.'s conjecture \(^{33}\) .  
+
+The widespread distribution of sporulation- regulation on the tree (Figure 2a) suggests that the early history of the 9 TPRs group may have been linked to the regulation of the costly differentiation into a resistant endospore in extremophile spore- forming taxa from the Clostridia (Biomaibacter acetigenes, Sulfobacillus thermotolerans, Thermoanaerobacter italicus) and Bacilli (Alicyclobacillaceae and
+
+<--- Page Split --->
+
+Thermoactinomycetaceae families) classes (Table S1). Consistently, the NprR subfamily is suggested to have diversified first in extremophile spore- forming Bacillusaceae (Psychrobacilli, Halobacilli, Anoxybacilli etc.) and Planococcaceae (Sporosarcina, Planococcus antarticus, halotolerans, glaciei etc.) (Table S1). The Rap clade, exclusively found in Bacillus and Alkalihalobacillus genera, is nested within NprR, and is inferred to have diverged from the same ancestral gene as that of NprR receptors found in Halobacilli, Geobacilli, Virgibacilli, Oceanobacilli and Bacilli from the Bacillus cereus group (Table S1). This indicates that the absence of the N- terminal HTH domain observed in Rap receptors originates from a loss of the ancestral domain (Figure 2e), as previously reported by Felipe- Ruiz et al<sup>28</sup>. However, many Rap receptors have retained the ability to regulate sporulation, but only through protein inhibition of the Spo0F- P and ComA regulators, rather than through transcriptional regulation<sup>35</sup>. The Rap clade is characterized by a wide occurrence in MGEs, consistent with the high rate of horizontal gene transfers described for this subfamily<sup>32</sup>. The MGE distribution in the Rap clade is polyphyletic, suggesting frequent exchanges of these communication systems between the host genome, phages and conjugative elements (Figure 2d). The QssR validated clade is specific to solventogenic Clostridiaceae (Figure 2a- c) while its sister clade (subfamily 09) is specific to pathogenic Clostridium such as C. perfringens and C. botulinum, which may indicate a novel link between quorum sensing and pathogenesis in these taxa of medical relevance that may warrant further investigation.  
+
+AloR and AimR members appear to be the most diverged representatives of the HTH- 9TPRs architectural organization. Consistently, their TPR sequences harbor signs of degeneration, which is especially true in the AimR clade, consistent with its specificity to Bacillus phages, since viruses evolve at higher evolutionary rates (Figure 2f). The AimR receptors supporting phage- phage communication are adjacent to non- viral communication systems from subfamily 21, found in the chromosome of Alkalihalobacillus clausii or lehensis. For the first time, the structural phylogeny reveals that the AimR- subfamily 21 clade is evolutionary close from Paenibacillaceae receptors from the AloR subfamily prevalent in the Paenibacillus
+
+<--- Page Split --->
+
+genus and the candidate subfamily 08 predominantly found in the Brevibacillus genus (Figure 2). Subfamily 08, AloR and AimR are suggested to form a monophyletic group with a presumable Paenibacillaceae ancestry. This is supported by systems from Paenibacillus xylanexedens and Brevibacillus formosus position in the outgroup, close to the QssR subfamily (Figure 2a, Table S1). Remarkably, the cognate communication peptides of AimR receptors from the Bacillus cereus group are highly similar to that of subfamily 08, with the presence of the DPG amino- acid motif in the C- terminal (Table S1). Our results therefore suggest that a QSS similar to the ancestor of the AloR- subfam08 clade was co- opted by a temperate phage to regulate the lysis/lysogeny decision. This successful functional association has spread in Bacillus phages and led to the AimR clade. The numerous phage- and prophage- encoded systems from the subfamily 08 support this hypothesis<sup>19</sup>.  
+
+The proteins composed of 5 TPRs are suggested to have emerged from the loss of 4 TPRs in the C- terminus, drastically shortening their length (Figure 2b, Figure 2e), although other evolutionary scenarios that do not imply such loss exist as well<sup>28</sup> (Supplementary Figure 10). The 5 TPRs group is divided in two sister clades: one with a wide taxonomic range composed of PlcR, TprA and their outgroup (Figure 2a and Figure 2c), the second including PrgX, TraA, ComR and Rgg validated subfamilies, specific to non- spore forming Lactobactillales. The emergence of the 5TPRs clade is associated with fundamental functional shifts. First, receptor- propeptide orientations are highly diversified compared to the HTH- 9TPRs group (Figure 9d). These heterogeneous orientations correlate with functional changes as receptors divergently transcribed from their propeptide tend to repress target genes while co- directional receptors tend to activate them<sup>36</sup>. Second, the diversification of the PrgX- ComR- Rgg clade was accompanied with an important diversification of propeptide secretion modes: their cognate propeptides are exported through the alternative PptAB translocon rather than through the SEC translocon<sup>17,28</sup> and it has even been shown that a paralog of Rgg in S. pyogenes is paired with a functional leaderless communication peptide that lacks a signal sequence for an export system, highlighting that another secretory process of
+
+<--- Page Split --->
+
+communication peptides emerged in the clade<sup>37</sup>. Last, the biological processes controlled by these communication systems are not linked to cellular dormancy or viral latency, but rather to the production of virulence factors and antimicrobials<sup>21</sup>. This is mirrored by the substantial number of syntenic biosynthetic gene clusters (BGCs) predicted to be regulated by TprA and Rgg members (Figure 2a)<sup>19</sup>. Consistently, the primary role of members of the HTH- 5TPRs clade may be to assess the threshold population density at which a collective production of biomolecules starts to be ecologically impactful and becomes the most evolutionary advantageous strategy, with a few exceptions such as the regulation of competence by ComR or conjugation by PrgX.  
+
+## Discussion  
+
+As early as 1975, Eventoff and Rossmann employed the number of structurally dissimilar residues between pairs of proteins to infer phylogenetic relationships by means of a distance method<sup>38</sup>. This approach has been revisited to infer deep phylogenetic trees and networks using different combinations of dissimilarity measures (e.g., RMSD, \(\mathrm{Q}_{\mathrm{score}}\) , Z- score) and inference algorithms<sup>12,39- 43</sup>. Conformational sampling has been proposed to assess tree confidence when using this approach<sup>11</sup>. Some models have been developed that mathematically describe the molecular clock in structural evolution<sup>44</sup> or integrate sequence data with structural information to inform the likelihood of certain substitutions<sup>45</sup>. Other studies have modeled structural evolution as a diffusion process in order to infer evolutionary distances<sup>46</sup>, or incorporating it into a joint sequence- structure model to infer multiple alignments and trees by means of bayesian phylogenetic analysis<sup>47,48</sup>. To date, the quality of structure- based phylogenetics, especially compared to conventional sequence- based phylogenetics, has remained largely unknown, limiting its use to niche applications.  
+
+The extensive empirical assessment reported here, using two orthogonal indicators of tree quality, demonstrates the high potential of structure- based phylogenetics. The taxonomic congruence score (TCS) measures agreement with
+
+<--- Page Split --->
+
+the established classification. Individual gene trees can be expected to deviate substantially from the underlying species tree due to gene duplication, lateral transfer, incomplete lineage sorting, or other phenomena. However, the evolutionary history of the underlying species will still be reflected in many parts of the tree—which is quantified by the TCS. All else being equal, tree inference approaches which tend to result in higher TCS over many protein families can be expected to be more accurate. On this metric, we obtained the best trees using Foldtree, which is based on Foldseek's structural alphabet, and an alignment procedure combining structural and sequence information. Furthermore, after filtering lower quality structures out of the tree building process, tree quality improved further when compared to sequence- based trees (Figure 1. b), indicating that higher confidence models with accurate structural information provide better phylogenetic signal.  
+
+When considering the ultrametricity through the root- to- tip variances of the trees, the Foldtree trees adhered more closely to a molecular clock than other structural or sequence trees. We acknowledge that in and of itself, adherence to a molecular clock is only a weak indicator of tree accuracy. Nevertheless, considering the clear, consistent differences obtained, and the agreement with the TCS criterion, the ultrametricity appears to reflect meaningful performance difference among the tree inference methods.  
+
+Folds evolve at a slower rate than the underlying sequence mutations<sup>49,50</sup>. Structural distances are therefore less likely to saturate over time, making it possible to recover the correct topology deeper in the tree with greater certainty. This could be observed in our results on the distant, structurally defined CATH families. Interestingly, however, Foldtree distinguished itself even at divergence times when homology is identifiable using sequence to sequence comparison. It is thus both fine grained enough to account for small differences between input proteins at shorter divergence times, overcoming the often mentioned shortcoming of structural phylogenetics, and more robust than sequence comparison at longer evolutionary distances.
+
+<--- Page Split --->
+
+As the projection of each residue onto a structural character is locally influenced by its neighboring residues rather than global steric changes, Foldseek's representations of 3D structures are well suited to capture phylogenetic signals when comparing homologous proteins. In contrast, global structural similarity measures are confounded by conformational fluctuations which involve steric changes that are much larger in magnitude than the local changes observed between functionally constrained residues during evolution. Moreover, since Foldseek represents 3D structures as strings, the computational speed- ups and techniques associated with string comparisons implemented in MMseqs<sup>51</sup> can be applied to structural homology searches and comparisons making the Foldtree pipeline extremely fast and efficient.  
+
+Viral evolution, quickly evolving extracellular proteins and protein families with histories stretching back to the first self replicating cells are among the many cases that can be revisited with these new techniques. In our first study of a family using Foldtree, we present just one such case, with the fast evolving RRNPPA family of cytosolic communication receptors encoded by Firmicutes bacteria, their conjugative elements and their viruses. The phylogeny reconstructed by Foldtree includes, for the first time, all described RRNPPA subfamilies<sup>19</sup>. Remarkably, despite their significant divergence, the underlying diversifying history is parsimonious in terms of taxonomy, functions, and protein architectures (Supplementary Figure 10). The MAD rooting method flags a previously undescribed candidate outgroup with a singular architecture of 7 TPRs and no DNA- binding domain in Anoxybacter fermentans, which supports Declerck et al. speculation that the ancestral receptor at the origin of the RRNPPA clade lacked the DNA- binding domain, and that the latter was gained subsequently in the evolutionary history of the family. Declerck et al. also speculated that the level of TPR degeneracy in receptors is a marker of divergence from the last common ancestor of the family<sup>33</sup>. In this respect, root to tips lengths are remarkably uniform throughout the entire RRNPPA structural tree with slight differences being meaningful, as the longest branches correspond to receptors with degenerated TPR sequences (Figure 2e). Last, this rooting implies that receptors with non- degenerated TPRs sequences emerged only once, and
+
+<--- Page Split --->
+
+systematically involves a late emergence of clades with degenerated TPRs as a derived state of an ancestor harboring non- degenerated TPRs (Figure 2e). Although rooting is easier when a tree is more clock- like, there remains uncertainty regarding the precise placement of the root. Our interpretation of MAD rooting and domain architecture led us to infer an origin of the RRNPPA family linked to the regulation of sporulation in extreme environments, implying also that 9 TPRs folds predate 5 TPRs folds. Yet, alternative rootings of the structural phylogeny cannot be ruled out, with a root either within the HTH- 5TPRs group as in \(^{28}\) or within the AloR- AimR- subfamily08 group (hypotheses displayed in Supplementary Figure 11). Additional, yet- to- be- discovered members of RRNPPA homologs could help resolve the root with higher confidence.  
+
+Recently the fold universe has been revealed using AlphaFold on the entirety of the sequences in UniProt and the ESM model \(^{8}\) on the sequences in MGNIFY \(^{52}\) to reach a total of nearly one billion structures. The UniProt structures inferred by AlphaFold have recently been systematically organized into sequence- and structure- based clusters, shedding light on novel fold families and their possible functions \(^{14,53}\) . In future work it may be desirable to add an evolutionary layer of information to this exploration of the fold space using structural phylogenetics to further refine our understanding of how this extant diversity of folds emerged.  
+
+In conclusion, this work shows the potential of structural methods as a powerful tool for inferring evolutionary relationships among proteins. For relatively close proteins, structured- based tree inference rivals sequence- based inference, and the choice of approach should be tailored to the specific question at hand and the available data. For more distant proteins, structural phylogenetics opens new inroads into studying evolution beyond the "twilight" zone \(^{54}\) . We believe that there remains much room for improvement in refining phylogenetic methods using the tertiary representation of proteins and hope that this work serves as a starting point for further exploration of deep phylogenies in this new era of Al- generated protein structures.
+
+<--- Page Split --->
+
+## Methods  
+
+No statistical methods were used to predetermine sample size.  
+
+## OMA HOG selection for large scale benchmark  
+
+The OMA set of protein families consists of "root hierarchical orthologous groups" (root HOGs) which are derived from all- vs- all sequence comparisons<sup>55</sup>. The quest for orthologs benchmarking dataset<sup>56</sup> consists of 78 proteomes. The 2020 release of this dataset was used as input into the OMA orthology prediction pipeline<sup>55</sup> (version 2.4.1). A random selection of at most 500 orthologous groups with at least 10 proteins were compiled for each group of HOGs that were inferred to have emerged in different ancestral taxa (Bacteria, Bilateria, Chordata, Dikarya, Eukaryota, Eumetazoa, Euteleostomi, Fungi, LUCA, Opisthokonta and Tetrapoda). The UniProt identifiers of the proteins within each group were used as input to the Foldtree pipeline.  
+
+## CATH family selection for large scale benchmark  
+
+CATH structural superfamilies are constructed using structural comparisons and classification<sup>25</sup>. Each level of classification designates a different resolution of structural similarity. These are delineated as Class, Architecture, Topology and Homology. We chose to investigate tree quality using input sets within the same homology classification as well as sets within the same topology. We selected a random subsample of at most 250 proteins (or the number of proteins within the family if there were less) from each family for 635 CATH families and 500 CAT families. The Topology- based dataset is designated as CAT and the Homology- based dataset is designated as CATH. Each CAT or CATH family contains the PDB identifiers and chains of the structures they correspond to.  
+
+The PDB files were programmatically obtained from the PDB database. 3D structures of monomers corresponding to the chain identified in the CATH classification for each fold were extracted from PDB crystal structures using Biopython. PDBfizer from the OpenMM<sup>57</sup> package was used to fix crystal structures with discontinuities, non- standard residues or missing atoms before tree building since these adversely affect structural comparisons.
+
+<--- Page Split --->
+
+## Structure tree construction  
+
+Sets of homologous structures were downloaded from the AFDB or PDB and prepared according to the OMA and CATH dataset sections above. Foldseek<sup>14</sup> is then used to perform an all vs all comparison of the structures.  
+
+Structural distances between all pairs are compiled into a distance matrix which is used as input to quicktree<sup>58</sup> to create minimum evolution trees. These trees are then rooted using the MAD method<sup>59</sup>. Foldseek (Version: 30fdcac78217579fa25d59bc271bd4f3767d3ebb) has two alignment modes where character based structural alignments are performed and are scored using the 3Di substitution matrix or a combination of 3Di and amino- acid substitution matrices. A third mode, using TMalign to perform the initial alignment was not used. It is then possible to output the fraction of identical amino acids from the 3Di and amino acid based alignment (Fident), the LDDT (locally derived using Foldseek's implementation) score and the TM score (normalized by alignment length). This results in a total of 6 structural comparison methods. We then either directly used the raw score or applied a correction to the scores to transform them to the distance matrices so that pairwise distances would be linearly proportional to time (Supplementary methods). This resulted in a total of 12 possible structure trees for each set of input proteins. To compile these results, Foldseek was used with alignment type 0 and alignment type 2 flags in two separate runs with the '--exhaustive- search' flag. The output was formatted to include Iddt and alntmscore columns. The pipeline of comparing structure- and sequence- based trees is outlined in Supplementary Figure 1.  
+
+Before starting the all vs all comparison of the structures we also implemented an optional filtering step to remove poor AlphaFold models with low pLDDT values. If the user activates this option, the pipeline removes structures (and the corresponding sequences) with an average pLDDT score below 40, before establishing the final protein set and running structure and sequence tree building pipelines. We performed similar benchmarking experiments on filtered and unfiltered
+
+<--- Page Split --->
+
+versions of the OMA dataset to observe the effect of including only high quality models in the analysis.  
+
+## Sequence based tree construction  
+
+Sets of sequences and their taxonomic lineage information were downloaded using the UniProt API. Clustal Omega (version 1.2.4)60 or Muscle5 (version 5.0)61 was then used to generate a multiple sequence alignment on default parameters. This alignment was then used with either FastTree(version 2.1)62 on default parameters or IQ- TREE (version 1.6.12 using the flags LG+1) to generate a phylogenetic tree. Finally, this tree was rooted using the MAD (version 1775932) method on default parameters.  
+
+## Taxonomic congruence metric for phylogenetic trees  
+
+Taxonomic lineages were retrieved for each sequence and structure of each protein family via the UniProt API. It is assumed that the vast majority of genes will follow an evolutionary trajectory that mirrors the species tree with occasional loss or duplication events. The original development and justification for this score to measure tree quality in an unbiased way can be found in the following work 24. In this version of the metric we reward longer lineage sets towards the root by calculating a score for each leaf from the root to the tip.  
+
+The agreement of the tree with the established taxonomy (from UniProt) can be calculated recursively in a bottom up fashion when traversing the tree using equation 1. Leaves of trees were labeled with sets representing the taxonomic lineages of each sequence before calculating taxonomic congruence.
+
+<--- Page Split --->
+
+\[C(tree) = \sum_{s}^{Leaves}C(leaf)\]  
+
+\[C(x) = \left\{ \begin{array}{ll}|s(x)| & \mathrm{if~x~is~root}\\ |s(x)| + |s(x.ancestor)| & \mathrm{if~x~is~an~internal~node}\\ & \mathrm{where}\\ \end{array} \right.\]  
+
+\[s(x) = \left\{ \begin{array}{ll}L(x), & \mathrm{if~x~is~a~leaf}\\ s(x.Left)\cap s(x.Right)) & \mathrm{if~x~is~an~internal~node} \end{array} \right.\]  
+
+Equation 1- taxonomic congruence metric. This score is used to measure the agreement of binary tree topologies with the known species tree. \(\mathsf{s}(\mathsf{x})\) denotes the set of lineages found in the tree node x. \(\mathrm{C(x)}\) denotes the congruence score of node x based on its two child nodes. \(\mathsf{L}(\mathsf{x})\) denotes the labels of leaves. The total score of a tree is defined as the sum of the leaf scores. The code to calculate this metric is available on the git repository.  
+
+Both structure and sequence trees were rooted using the MAD method to make TCS comparisons between the methods equivalent. To compare large collections of trees with varying input set sizes, we normalized the congruence scores of trees by the number of the proteins in the tree.  
+
+## Ultrametricity quantification  
+
+Ultrametricity<sup>63</sup> describes the consistency of tip to root lengths of a given phylogenetic tree. If a tree building approach has an accurate molecular clock on all branches, the amount of inferred evolutionary time elapsed between the root and all of the extant species should be equivalent and proportional to real time. This would imply that the sums of branch length along a lineage from the root to any tip of the tree should be equivalent since the amount of clock time elapsed from the common ancestor until the sequencing of species in the present day is the same.
+
+<--- Page Split --->
+
+\[E(\text{rootdist}) = \sum_{i = 1}^{n_{\text{leaves}}} \text{dist}(l_i, \text{root}) / n_{\text{leaves}} \\ S_{\text{norm}}(\text{rootdist}) = \sum_{i = 1}^{n_{\text{leaves}}} (\text{dist}(l_i, \text{root}) / E(\text{rootdist}) - 1)^2 / (n_{\text{leaves}} - 1)\]
+
+**Equation 2** - To derive a unified metric for ultrametricity that could easily be applied to the trees generated by different methods, we normalized the branch lengths to center the distribution of root to tip lengths at 1. We then measured the variance of these normalized root to tip lengths. \(E(.)\) represents the average root to tip length for a given tree. \(S_{\text{norm}}(.)\) represents the variance of these normalized root to tip distances. \(\text{dist}(l_i, \text{root})\) denotes the length of the tip \((l_i)\) to root. 
+
+To describe the ultrametricity of the different methods of structural tree derivation, we measured the length of root-to-tip distances of a given tree (equation 2). We then normalized this collection of distances by their mean and calculated their variance. We compiled this variance measurement for collections of trees with corresponding input protein sets for all methods used to derive trees and compared their distributions. **Supplementary Figure 2** shows a visual representation of how this score is calculated. 
+
+## RRNPPA phylogeny 
+
+The metadata of "strict" known and candidate RRNPPA QSSs described in the RRNPP_detector paper were fetched from TableS2 in the corresponding supplementary materials¹⁹. The predicted regulations by QSSs of adjacent BGCs were fetched from TableS5. The propeptide sequences were downloaded from the following Github repository: 
+
+https://github.com/TeamAIRE/RRNPP_candidate_propeptides_exploration_dataset.
+The 11,939 receptors listed in TableS2 were downloaded from the NCBI Genbank database, and redundancy was removed by clustering at 95% identity with CD-HIT⁶⁴, yielding 1,418 protein clusters. The Genbank identifiers of the 11,939 receptors were used as queries in the UniProt Retrieve/ID mapping research engine (https://www.uniprot.org/id-mapping) to retrieve corresponding UniProt/AlphaFoldDB identifiers. 768 protein clusters successfully mapped to at least one UniProt/AlphaFoldDB identifier. The 768 predicted protein structures were downloaded and Foldseek was used to perform an all vs all comparison. Based on
+
+<--- Page Split --->
+
+our benchmarking results we used the Fident scores from a comparison using amino- acid and 3Di alphabet alignment scoring (alignment mode 1 in Foldseek). Since this family had undergone domain architecture modifications, we decided to extract the structural region between the first and last positions of each fold where \(80\%\) of all of the other structures in the set mapped. With these core structures we performed a second all vs all comparison. We again used the Fident scores (alignment mode 1) and no statistical correction to construct a distance matrix between the core structures. This matrix was then used with FastME \(^{65}\) to create a distance based tree. The resulting tree was annotated with ITOL \(^{66}\) , using the metadata available in Table S1. To derive the sequence- based phylogeny, we built a multiple sequence alignment (MSA) of receptors, using mafft \(^{67}\) with the parameters - maxiterate 1000 - localpair for high accuracy. The MSA was then trimmed with trimAl \(^{68}\) under the - automated 1 mode optimized for maximum likelihood reconstruction. The trimmed alignment of 304 sites was given as input to IQ- TREE \(^{2}\) to infer a maximum likelihood phylogenetic under the LG+G model with 1000 ultrafast bootstraps.  
+
+## Acknowledgements  
+
+We thank the Dessimoz lab members for thoughtful discussions on the topic of structural evolution and their encouragement and input on this work. We especially thank Clement Train for his brilliant work on the tree visualization tool accompanying this work. We also gratefully acknowledge helpful suggestions by Pedro Beltrao.  
+
+The work was supported by SNSF grant 216623 to C.D.. M. L. is a recipient of a doctoral scholarship from Agencia Nacional de Investigación e Innovación (ANII), Uruguay.  
+
+## Author contributions  
+
+David Moi designed and wrote the treebuilding pipeline and analysis pipelines, collected benchmarking data for CATH structural families, carried out large scale analysis for benchmarking, generated trees for protein families, and drafted the manuscript. Charles Bernard collected data relevant to the bacterial signaling case
+
+<--- Page Split --->
+
+study, analyzed and annotated the case study in light of the existing literature and wrote the corresponding sections of the paper. Martin Steinegger contributed advice and feedback on the structural distance measures evaluated in this paper. Yannis Nevers collected HOG benchmarking data and curated examples of protein families to test the pipeline. Mauricio Langlieb wrote the documentation and collected benchmarking data and curated examples of protein families. Christophe Dessimoz supervised the project and contributed to the conception of the study, the interpretation of results, and the manuscript writing.  
+
+Correspondence and requests for materials should be addressed to D.M.  
+
+## Competing interests  
+
+The authors declare no competing interests.  
+
+## Supplementary Information Guide  
+
+1. Supplementary data  
+
+The homologue list of RRNPPA sequences and their metadata is available in the RRNPPAlist.xls file. In the text it is referred to as Table S1.  
+
+2. Supplementary methods, results and discussion are found in the SI section pdf  
+
+## Code and Data availability  
+
+All UniProt identifiers necessary to replicate the experimental results are available on Zenodo: https://doi.org/10.5281/zenodo.8346286  
+
+The Foldtree pipeline is available on github: https://github.com/DessimozLab/fold_tree
+
+<--- Page Split --->
+
+All metadata used to annotate the RRNPPA phylogeny are available in the supplementary data file or on the Zenodo archive.  
+
+## References  
+
+1. Kozlov, A. M., Darriba, D., Flouri, T., Morel, B. & Stamatakis, A. RAxML-NG: a fast, scalable and user-friendly tool for maximum likelihood phylogenetic inference. Bioinformatics 35, 4453-4455 (2019).  
+2. Minh, B. Q., Trifinopoulos, J., Schrempf, D., Schmidt, H. A. & Lanfear, R. IQ-TREE version 2.0: tutorials and Manual Phylogenomic software by maximum likelihood. URL http://www. iqtree. org (2019).  
+3. Bouckaert, R. et al. BEAST 2.5: An advanced software platform for Bayesian evolutionary analysis. PLoS Comput. Biol. 15, e1006650 (2019).  
+4. Laumer, C. E. et al. Revisiting metazoan phylogeny with genomic sampling of all phyla. Proc. Biol. Sci. 286, 20190831 (2019).  
+5. Li, Y., Shen, X.-X., Evans, B., Dunn, C. W. & Rokas, A. Rooting the Animal Tree of Life. Mol. Biol. Evol. 38, 4322-4333 (2021).  
+6. Schultz, D. T. et al. Ancient gene linkages support ctenophores as sister to other animals. Nature 618, 110-117 (2023).  
+7. Tunyasuvunakool, K. et al. Highly accurate protein structure prediction for the human proteome. Nature 596, 590-596 (2021).  
+8. Lin, Z. et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 379, 1123-1130 (2023).  
+9. Zhang, Y. & Skolnick, J. TM-align: a protein structure alignment algorithm based on the TM-score. Nucleic Acids Res. 33, 2302-2309 (2005).  
+10. Le, Q., Pollastri, G. & Koehl, P. Structural alphabets for protein structure classification: a
+
+<--- Page Split --->
+
+comparison study. J. Mol. Biol. 387, 431- 450 (2009).  
+
+11. Malik, A. J., Poole, A. M. & Allison, J. R. Structural Phylogenetics with Confidence. Mol. Biol. Evol. 37, 2711-2726 (2020).  
+
+12. Bujnicki, J. M. Phylogeny of the restriction endonuclease-like superfamily inferred from comparison of protein structures. J. Mol. Evol. 50, 39-44 (2000).  
+
+13. Balaji, S. & Srinivasan, N. Use of a database of structural alignments and phylogenetic trees in investigating the relationship between sequence and structural variability among homologous proteins. Protein Eng. 14, 219-226 (2001).  
+
+14. van Kempen, M. et al. Fast and accurate protein structure search with Foldseek. Nat. Biotechnol. (2023) doi:10.1038/s41587-023-01773-0.  
+
+15. Xu, J. & Zhang, Y. How significant is a protein structure similarity with TM-score = 0.5? Bioinformatics 26, 889-895 (2010).  
+
+16. Mariani, V., Biasini, M., Barbato, A. & Schwede, T. IDDT: a local superposition-free score for comparing protein structures and models using distance difference tests. Bioinformatics 29, 2722-2728 (2013).  
+
+17. Neiditch, M. B., Capodagli, G. C., Prehna, G. & Federle, M. J. Genetic and Structural Analyses of RRNPP Intercellular Peptide Signaling of Gram-Positive Bacteria. Annu. Rev. Genet. 51, 311-333 (2017).  
+
+18. Fleuchot, B. et al. Rgg proteins associated with internalized small hydrophobic peptides: a new quorum-sensing mechanism in streptococci. Mol. Microbiol. 80, 1102-1119 (2011).  
+
+19. Bernard, C., Li, Y., Lopez, P. & Bapteste, E. Large-Scale Identification of Known and Novel RRNPP Quorum-Sensing Systems by RRNPP_Detector Captures Novel Features of Bacterial, Plasmidic, and Viral Coevolution. Mol. Biol. Evol. 40, (2023).  
+
+20. Kotte, A.-K. et al. RRNPP-type quorum sensing affects solvent formation and
+
+<--- Page Split --->
+
+sporulation in Clostridium acetobutylicum. Microbiology 166, 579- 592 (2020).  
+
+21. Perez-Pascual, D., Monnet, V. & Gardan, R. Bacterial Cell-Cell Communication in the Host via RRNPP Peptide-Binding Regulators. Front. Microbiol. 7, 706 (2016).  
+
+22. Stokar-Avihail, A., Tal, N., Erez, Z., Lopatina, A. & Sorek, R. Widespread Utilization of Peptide Communication in Phages Infecting Soil and Pathogenic Bacteria. Cell Host Microbe 25, 746-755. e5 (2019).  
+
+23. Cardoso, P. et al. Rap-Phr Systems from Plasmids pAW63 and pHT8-1 Act Together To Regulate Sporulation in the Bacillus thuringiensis Serovar kurstaki HD73 Strain. Appl. Environ. Microbiol. 86, (2020).  
+
+24. Tan, G., Gil, M., Löytynoja, A. P., Goldman, N. & Dessimoz, C. Simple chained guide trees give poorer multiple sequence alignments than inferred trees in simulation and phylogenetic benchmarks. Proceedings of the National Academy of Sciences of the United States of America vol. 112 E99-100 (2015).  
+
+25. Knudsen, M. & Wiuf, C. The CATH database. Hum. Genomics 4, 207-212 (2010).  
+
+26. Friedman, J. H. Greedy function approximation: A gradient boosting machine. aos 29, 1189-1232 (2001).  
+
+27. Bereg, S. & Zhang, Y. Phylogenetic networks based on the molecular clock hypothesis. in Fifth IEEE Symposium on Bioinformatics and Bioengineering (BIBE'05) 320-323 (2005).  
+
+28. Felipe-Ruiz, A., Marina, A. & Rocha, E. P. C. Structural and Genomic Evolution of RRNPPA Systems and Their Pheromone Signaling. MBio 13, e0251422 (2022).  
+
+29. Clewell, D. B. & Weaver, K. E. Sex pheromones and plasmid transfer in Enterococcus faecalis. Plasmid 21, 175-184 (1989).  
+
+30. Rudner, D. Z., LeDeaux, J. R., Ireton, K. & Grossman, A. D. The spo0K locus of Bacillus subtilis is homologous to the oligopeptide permease locus and is required for
+
+<--- Page Split --->
+
+sporulation and competence. J. Bacteriol. 173, 1388- 1398 (1991).  
+
+31. Kalamara, M., Spacapan, M., Mandic-Mulec, I. & Stanley-Wall, N. R. Social behaviours by Bacillus subtilis: quorum sensing, kin discrimination and beyond. Mol. Microbiol. 110, 863-878 (2018).  
+
+32. Even-Tov, E., Omer Bendori, S., Pollak, S. & Eldar, A. Transient Duplication-Dependent Divergence and Horizontal Transfer Underlie the Evolutionary Dynamics of Bacterial Cell-Cell Signaling. PLoS Biol. 14, e2000330 (2016).  
+
+33. Declerck, N. et al. Structure of PlcR: Insights into virulence regulation and evolution of quorum sensing in Gram-positive bacteria. Proc. Natl. Acad. Sci. U. S. A. 104, 18490-18495 (2007).  
+
+34. Gallego Del Sol, F., Penadés, J. R. & Marina, A. Deciphering the Molecular Mechanism Underpinning Phage Arbitrium Communication Systems. Mol. Cell 74, 59-72.e3 (2019).  
+
+35. Schultz, D., Wolynes, P. G., Ben Jacob, E. & Onuchic, J. N. Deciding fate in adverse times: sporulation and competence in Bacillus subtilis. Proc. Natl. Acad. Sci. U. S. A. 106, 21027-21034 (2009).  
+
+36. Monnet, V. & Gardan, R. Quorum-sensing regulators in Gram-positive bacteria: 'cherchez le peptide'. Molecular microbiology vol. 97 181-184 (2015).  
+
+37. Do, H. et al. Leaderless secreted peptide signaling molecule alters global gene expression and increases virulence of a human bacterial pathogen. Proc. Natl. Acad. Sci. U. S. A. 114, E8498-E8507 (2017).  
+
+38. Eventoff, W. & Rossmann, M. G. The evolution of dehydrogenases and kinases. CRC Crit. Rev. Biochem. 3, 111-140 (1975).  
+
+39. Johnson, M. S., Sali, A. & Blundell, T. L. Phylogenetic relationships from three-dimensional protein structures. Methods Enzymol. 183, 670-690 (1990).  
+
+40. Garau, G., Di Guilmi, A. M. & Hall, B. G. Structure-based phylogeny of the
+
+<--- Page Split --->
+
+metallo- beta- lactamases. Antimicrob. Agents Chemother. 49, 2778- 2784 (2005).  
+
+41. Lundin, D., Berggren, G., Logan, D. T. & Sjöberg, B.-M. The origin and evolution of ribonucleotide reduction. Life 5, 604-636 (2015).  
+
+42. Moi, D. et al. Discovery of archaeal fuseins homologous to eukaryotic HAP2/GCS1 gamete fusion proteins. Nat. Commun. 13, 3880 (2022).  
+
+43. Lakshmi, B., Mishra, M., Srinivasan, N. & Archunan, G. Structure-Based Phylogenetic Analysis of the Lipocalin Superfamily. PLoS One 10, e0135507 (2015).  
+
+44. Pascual-García, A., Arenas, M. & Bastolla, U. The Molecular Clock in the Evolution of Protein Structures. Syst. Biol. 68, 987-1002 (2019).  
+
+45. Arenas, M., Sánchez-Cobos, A. & Bastolla, U. Maximum-Likelihood Phylogenetic Inference with Selection on Protein Folding Stability. Mol. Biol. Evol. 32, 2195-2207 (2015).  
+
+46. Grishin, N. V. Estimation of evolutionary distances from protein spatial structures. J. Mol. Evol. 45, 359-369 (1997).  
+
+47. Challis, C. J. & Schmidler, S. C. A stochastic evolutionary model for protein structure alignment and phylogeny. Mol. Biol. Evol. 29, 3575-3587 (2012).  
+
+48. Herman, J. L., Challis, C. J., Novák, Á., Hein, J. & Schmidler, S. C. Simultaneous Bayesian estimation of alignment and phylogeny under a joint model of protein sequence and structure. Mol. Biol. Evol. 31, 2251-2266 (2014).  
+
+49. Illergård, K., Ardell, D. H. & Elofsson, A. Structure is three to ten times more conserved than sequence--a study of structural response in protein cores. Proteins 77, 499-508 (2009).  
+
+50. Chothia, C. & Lesk, A. M. The relation between the divergence of sequence and structure in proteins. EMBO J. 5, 823-826 (1986).  
+
+51. Steinegger, M. & Söding, J. MMseqs2 enables sensitive protein sequence searching for
+
+<--- Page Split --->
+
+the analysis of massive data sets. Nat. Biotechnol. 35, 1026- 1028 (2017).  
+
+52. Richardson, L. et al. MGNify: the microbiome sequence data analysis resource in 2023. Nucleic Acids Res. 51, D753-D759 (2023).  
+
+53. Durairaj, J. et al. Uncovering new families and folds in the natural protein universe. Nature (2023) doi:10.1038/s41586-023-06622-3.  
+
+54. Rost, B. Twilight zone of protein sequence alignments. Protein Eng. 12, 85-94 (1999).  
+
+55. Altenhoff, A. M. et al. OMA standalone: orthology inference among public and custom genomes and transcriptomes. Genome Res. 29, 1152-1163 (2019).  
+
+56. Altenhoff, A. M. et al. The Quest for Orthologs benchmark service and consensus calls in 2020. Nucleic Acids Res. 48, W538-W545 (2020).  
+
+57. Eastman, P. et al. OpenMM 7: Rapid development of high performance algorithms for molecular dynamics. PLoS Comput. Biol. 13, e1005659 (2017).  
+
+58. Howe, K., Bateman, A. & Durbin, R. QuickTree: building huge Neighbour-Joining trees of protein sequences. Bioinformatics 18, 1546-1547 (2002).  
+
+59. Tria, F. D. K., Landan, G. & Dagan, T. Phylogenetic rooting using minimal ancestor deviation. Nat Ecol Evol 1, 193 (2017).  
+
+60. Sievers, F. & Higgins, D. G. Clustal Omega, accurate alignment of very large numbers of sequences. Methods Mol. Biol. 1079, 105-116 (2014).  
+
+61. Edgar, R. C. MUSCLE: multiple sequence alignment with high accuracy and high throughput. Nucleic Acids Res. 32, 1792-1797 (2004).  
+
+62. Price, M. N., Dehal, P. S. & Arkin, A. P. FastTree: Computing Large Minimum Evolution Trees with Profiles instead of a Distance Matrix. Mol. Biol. Evol. 26, 1641-1650 (2009).  
+
+63. Moore, N. C. A. & Prosser, P. The Ultrametric Constraint and its Application to Phylogenetics. arXiv [cs.AI] (2014).  
+
+64. Li, W. & Godzik, A. Cd-hit: a fast program for clustering and comparing large sets of
+
+<--- Page Split --->
+
+protein or nucleotide sequences. Bioinformatics 22, 1658- 1659 (2006).  
+
+65. Lefort, V., Desper, R. & Gascuel, O. FastME 2.0: A Comprehensive, Accurate, and Fast Distance-Based Phylogeny Inference Program. Mol. Biol. Evol. 32, 2798-2800 (2015).  
+
+66. Letunic, I. & Bork, P. Interactive Tree Of Life (iTOL) v5: an online tool for phylogenetic tree display and annotation. Nucleic Acids Res. 49, W293-W296 (2021).  
+
+67. Katoh, K. & Standley, D. M. MAFFT multiple sequence alignment software version 7: improvements in performance and usability. Mol. Biol. Evol. 30, 772-780 (2013).  
+
+68. Capella-Gutierrez, S., Silla-Martinez, J. M. & Gabaldon, T. trimAl: a tool for automated alignment trimming in large-scale phylogenetic analyses. Bioinformatics vol. 25 1972-1973 Preprint at https://doi.org/10.1093/bioinformatics/btp348 (2009).
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- SupTableRRNPPAmetadata.xls- FoldtreeS1.pdf
+
+<--- Page Split --->

preprint/preprint__00b9c52ff18ddf879d531bb5dd46e2c462d8c5a2f0fc667773ff3a23635e2342/preprint__00b9c52ff18ddf879d531bb5dd46e2c462d8c5a2f0fc667773ff3a23635e2342_det.mmd

@@ -0,0 +1,595 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 928, 208]]<|/det|>
+# Structural phylogenetics unravels the evolutionary diversification of communication systems in gram-positive bacteria and their viruses  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 191, 275]]<|/det|>
+David Moi dmoi@uni1.ch  
+
+<|ref|>text<|/ref|><|det|>[[50, 303, 616, 323]]<|/det|>
+University of Lausanne https://orcid.org/0000- 0002- 2664- 7385  
+
+<|ref|>text<|/ref|><|det|>[[44, 328, 175, 366]]<|/det|>
+Charles Bernard UNIL DBC  
+
+<|ref|>text<|/ref|><|det|>[[44, 373, 170, 412]]<|/det|>
+Yannis Never UNIL DBC  
+
+<|ref|>text<|/ref|><|det|>[[44, 419, 536, 460]]<|/det|>
+Martin Stenegger Artificial Intelligence Institute, Seoul National University  
+
+<|ref|>text<|/ref|><|det|>[[44, 465, 297, 505]]<|/det|>
+Mauricio Langleib Universidad de la Republica  
+
+<|ref|>text<|/ref|><|det|>[[44, 512, 617, 554]]<|/det|>
+Christophe Dessimoz University of Lausanne https://orcid.org/0000- 0002- 2170- 853X  
+
+<|ref|>text<|/ref|><|det|>[[44, 594, 288, 614]]<|/det|>
+Biological Sciences - Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 633, 137, 652]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 670, 317, 690]]<|/det|>
+Posted Date: October 4th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 709, 475, 728]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3368849/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 745, 916, 789]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 806, 535, 826]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 862, 936, 905]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Structural & Molecular Biology on October 10th, 2025. See the published version at https://doi.org/10.1038/s41594- 025- 01649- 8.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[125, 86, 870, 290]]<|/det|>
+Structural phylogenetics unravels the evolutionary diversification of communication systems in gram-positive bacteria and their viruses  
+
+<|ref|>text<|/ref|><|det|>[[118, 333, 878, 381]]<|/det|>
+David Moi \(^{1,2,\#}\) , Charles Bernard \(^{1,2}\) , Martin Steinegger \(^{3,4,5}\) , Yannis Nevers \(^{1,2}\) , Mauricio Langleib \(^{6,7}\) , Christophe Dessimoz \(^{1,2,\#}\)  
+
+<|ref|>text<|/ref|><|det|>[[116, 414, 879, 592]]<|/det|>
+\(^{1}\) Department of Computational Biology, University of Lausanne, Lausanne, Switzerland \(^{2}\) Swiss Institute of Bioinformatics, Lausanne, Switzerland \(^{3}\) School of Biological Sciences, Seoul National University, Seoul, South Korea \(^{4}\) Artificial Intelligence Institute, Seoul National University, Seoul, South Korea \(^{5}\) Institute of Molecular Biology and Genetics, Seoul National University, Seoul, South Korea \(^{6}\) Unidad de Bioinformática, Institut Pasteur de Montevideo, Montevideo, Uruguay \(^{7}\) Unidad de Genómica Evolutiva, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay  
+
+<|ref|>text<|/ref|><|det|>[[118, 621, 850, 641]]<|/det|>
+\(^{4}\) Correspondence and requests for materials should be addressed to D.M. or C.D.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 677, 216, 696]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[116, 730, 881, 912]]<|/det|>
+Recent advances in AI- based protein structure modeling have yielded remarkable progress in predicting protein structures. Since structures are constrained by their biological function, their geometry tends to evolve more slowly than the underlying amino acids sequences. This feature of structures could in principle be used to reconstruct phylogenetic trees over longer evolutionary timescales than sequence- based approaches, but until now a reliable structure- based tree building method has been elusive. Here, we demonstrate that the use of structure- based
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[116, 82, 882, 400]]<|/det|>
+phylogenies can outperform sequence- based ones not only for distantly related proteins but also, remarkably, for more closely related ones. This is achieved by inferring trees from protein structures using a local structural alphabet, an approach robust to conformational changes that confound traditional structural distance measures. As an illustration, we used structures to decipher the evolutionary diversification of a particularly challenging family: the fast- evolving RRNPPA quorum sensing receptors enabling gram- positive bacteria, plasmids and bacteriophages to communicate and coordinate key behaviors such as sporulation, virulence, antibiotic resistance, conjugation or phage lysis/lysogeny decision. The advent of high- accuracy structural phylogenetics enables myriad of applications across biology, such as uncovering deeper evolutionary relationships, elucidating unknown protein functions, or refining the design of bioengineered molecules.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 434, 257, 454]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[116, 488, 882, 779]]<|/det|>
+Since Darwin, phylogenetic trees have depicted evolutionary relationships among organisms, viruses, genes, and other evolving entities, enabling an understanding of shared ancestry and tracing the events that led to the observable extant diversity. Trees based on molecular data are typically reconstructed from nucleotide or amino- acid sequences, by aligning homologous sequences and inferring the tree topology and branch lengths under a model of character substitution \(^{1 - 3}\) . However, over long evolutionary time scales, multiple substitutions occurring at the same site cause uncertainty in alignment and tree building. The problem is particularly acute when dealing with fast evolving sequences, such as viral or immune- related ones, or when attempting to resolve distant relationships, such as at the origins of animals \(^{4 - 6}\) or beyond.  
+
+<|ref|>text<|/ref|><|det|>[[116, 785, 881, 912]]<|/det|>
+In contrast, the fold of proteins is often conserved well past sequence signal saturation. Furthermore, because 3D structure determines function, protein structures have long been studied to gain insight into their biological role within the cell whether it be catalyzing reactions, interacting with other proteins to form complexes or regulating the expression of genes among a myriad of other functions.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 82, 881, 265]]<|/det|>
+Until recently, protein structures had to be obtained through labor intensive crystallography, with modeling efforts often falling short of the level of accuracy required to describe a fold for the many tasks crystal structures were used for. Due to these limitations, structural biology and phylogenetics have developed as largely separate disciplines and each field has created models describing evolutionary or molecular phenomena suited to the availability of computational power and experimental data.  
+
+<|ref|>text<|/ref|><|det|>[[116, 272, 881, 533]]<|/det|>
+Now, the widespread availability of accurate structural models \(^{7,8}\) opens up the prospect of reconstructing trees from structures. However, there are pitfalls to avoid in order to derive evolutionary distances between homologous protein structures. Geometric distances between rigid body representations of structures, such as root mean square deviation (RMSD) distance or template modeling (TM) score \(^{9}\) , are confounded by spatial variations caused by conformational changes \(^{10,11}\) . More local structural similarity measures have been proposed in the context of protein classification \(^{10}\) , but due to the relative paucity of available structures until recently, little is known about the accuracy of structure- based phylogenetic reconstruction beyond a few isolated case studies \(^{12,13}\) .  
+
+<|ref|>text<|/ref|><|det|>[[116, 541, 881, 911]]<|/det|>
+Here, we report on a comprehensive evaluation of phylogenetic trees reconstructed from the structures of thousands of protein families across the tree of life, using multiple kinds of distance measures. We built trees from structural divergence measures obtained using Foldseek \(^{14}\) , which outputs scores from rigid body alignment, local superposition- free alignment and structural alphabet based sequence alignments. The performance of these measures has been previously assessed on the task of detecting whether folds are homologous and belong to the same family \(^{14 - 16}\) , but have never been benchmarked with regards to how well they perform as evolutionary distances. Remarkably, we found that the structural alphabet- based measure outperforms phylogenies from sequence alone even at relatively short evolutionary distances. To demonstrate the capabilities of structural phylogenetics, we employ our methodology, released as open- source software named Foldtree, to resolve the difficult phylogeny of a fast- evolving protein family of high relevance: the RRNPPA (Rap, Rgg, NprR, PlcR, PrgX and AimR) receptors of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[116, 82, 881, 400]]<|/det|>
+communication peptides. These proteins allow gram- positive bacteria, their plasmids and their viruses to assess their population density and regulate key biological processes accordingly. These communication systems have been shown to regulate virulence, biofilm formation, sporulation, competence, solventogenesis, antibiotic resistance or antimicrobial production in bacteria \(^{17 - 21}\) , conjugation in conjugative elements, lysis/lysogeny decision in bacteriophages \(^{22}\) and host manipulation by mobile genetic elements (MGEs) \(^{19,23}\) . Accordingly, the RRNPPA family has a substantial impact on human societies as it connects to the virulence and transmissibility of pathogenic bacteria and the spread of antimicrobial resistance genes through horizontal gene transfers. We analyze and discuss the parsimonious characteristics of the phylogeny of this family, highlighting the contrasts with the sequence- based tree.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 434, 205, 454]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 489, 877, 533]]<|/det|>
+## Structural trees outperform sequence based trees at both short and long evolutionary divergence times  
+
+<|ref|>text<|/ref|><|det|>[[116, 538, 881, 693]]<|/det|>
+To find a structural distance metric with high informative phylogenetic signal, we investigated the use of local superposition- free comparison (local distance difference test; LDDT \(^{16}\) ), rigid body alignment (TM score \(^{9}\) ) and a distance derived from similarity over a structural alphabet (Fident) \(^{14}\) . These measures were used to compute distance trees using neighbor joining, after being aligned in an all- vs- all comparison using the Foldseek structural alphabet (Methods).  
+
+<|ref|>text<|/ref|><|det|>[[116, 700, 881, 855]]<|/det|>
+Assessing the accuracy of trees reconstructed from empirical data is notoriously difficult. We used two complementary indicators. The first one, taxonomic congruence score (TCS) (Methods and Supplementary Figures 1- 2), assesses the congruence of reconstructed protein trees with the known taxonomy \(^{24}\) . Among several potential tree topologies reconstructed from the same set of input proteins, the better topologies can be expected to have higher TCS on average.  
+
+<|ref|>text<|/ref|><|det|>[[118, 862, 880, 908]]<|/det|>
+For trees reconstructed from closely related protein families using standard sequence alignments, both local structure LDDT and global structure TM measures
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 882, 319]]<|/det|>
+showed poorer taxonomic congruence than sequence- based trees on average (Figure 1a). By contrast, trees derived from the Fident distance (henceforth referred to as the Foldtree measure) outperformed those based on sequence. The difference was even larger if we excluded families for which the Alphafold2- inferred structures are of low confidence (Figure 1b). This trend was observed consistently across various protein family subsets, taken from clades with different divergence levels (Supplementary Figure 8). We also experimented with statistical corrections and other parameter variations, but they did not lead to further improvements (Supplementary Figures 4- 9).  
+
+<|ref|>text<|/ref|><|det|>[[115, 326, 882, 667]]<|/det|>
+We then assessed the Foldtree measure's performance against sequence- based trees over larger evolutionary distances, using structure- informed homologous families from the CATH database<sup>25</sup>. This database classifies proteins hierarchically, grouping them based on Class, Architecture, Topology and Homology of experimentally determined protein structures. We examined both proteins from the same homology set as well as proteins within the same topology sets (Methods). Efforts were made to correct structures with discontinuities or other defects before treebuilding (Methods) since these adversely affect structural comparisons. With this more divergent CATH dataset, structure- based methods performed better overall. Foldtree outperformed the sequence- based method even more (Figure 1c). Results for LDDT versus sequence flipped in favour of LDDT, while results for the global TM measure remained inferior to sequence (Supplementary Figure 9).  
+
+<|ref|>text<|/ref|><|det|>[[115, 675, 882, 885]]<|/det|>
+To delve deeper into the reasons for these performance differences, we applied a gradient- boosted decision tree regressor<sup>26</sup> on features derived from the input structures and taxonomic lineages of the input protein sets, aiming to predict the TCS difference (Supp Methods Table 1). We found that features measuring the confidence of the AlphaFold structure prediction (predicted LDDT or pLDDT) emerged as significant factors in the analysis (Supplementary Figure 3). This suggests that advancements in structural prediction might further benefit structural trees in the future.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 883, 373]]<|/det|>
+To validate our findings using an entirely different indicator of tree quality, we assessed the “ultrametricity” of trees—how uniform a tree’s root- to- tip lengths are for all its tips, akin to following a molecular clock. Although strict adherence to a molecular clock is unlikely in general, it is reasonable to assume that distance measures resulting in more ultrametric trees on average (i.e., with reduced root- to- tip variance, see Methods) are more accurate<sup>27</sup>. We found that in the sequence- based family dataset, Foldtree trees had by far the lowest root- to- tip variance of all approaches (Figure 1d). The difference was so pronounced that it is evident in visual comparison of tree shapes for several randomly chosen families (Figure 1e). Foldtree performed the best of all metrics and sequence- based trees the worst.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[147, 110, 850, 450]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[157, 461, 644, 475]]<|/det|>
+<center>e. Ultrametricity: sample tree shapes among sequence-defined families (OMA families) </center>  
+
+<|ref|>image<|/ref|><|det|>[[190, 476, 848, 757]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[123, 787, 870, 893]]<|/det|>
+<center>Figure 1 a) Trees using the Foldtree metric exhibit higher taxonomic congruence than sequence trees on average (protein families defined from sequences); by contrast, structure trees from LDDT and TM underperform sequence trees; b) After filtering the input dataset for structural quality (families with average pLDDT structure scores \(>40\) ), the proportion of Foldtree trees which have a greater normalized congruence than sequence-based trees increased from \(48\%\) to \(53\%\) ; c) the Foldtree metric on the CATH dataset of structurally defined families using experimental structures </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[125, 88, 866, 194]]<|/det|>
+outperforms sequence trees to an even greater proportion; d) The variance of normalized root- to- tip distances were compiled for all trees within the OMA dataset for all tree structural tree methods and sequence trees. Foldtree has a lower variance than other methods. The median of each distribution is shown with a vertical red line. Distributions are truncated to values between 0 and 0.2; e) A random sample of trees is shown where each column is from from equivalent protein input sets and each row of trees is derived using a distinct tree building method.  
+
+<|ref|>text<|/ref|><|det|>[[117, 227, 880, 302]]<|/det|>
+Both of the orthogonal metrics of ultrametricity and species tree discordance indicate that Foldtree produces trees with desirable characteristics that are ideal for constructing phylogenies with sets of highly divergent homologs.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 338, 877, 383]]<|/det|>
+## Foldtree reveals the evolutionary diversification of RRNPPA communication systems  
+
+<|ref|>text<|/ref|><|det|>[[115, 389, 881, 900]]<|/det|>
+To illustrate the potential of structural phylogenies, we reconstructed the intricate evolutionary history of the RRNPPA family of intracellular quorum sensing receptors in gram- positive Bacillota bacteria, their conjugative elements and temperate bacteriophages<sup>17,21,28</sup>. These receptors, vital for microbial communication and decision- making, are paired with a small secreted communication peptide that accumulates extracellularly as the encoding population replicates. Once a quorum of cells, plasmids or viruses is met, communication peptides get frequently internalized within cells and binds to the tetratricopeptide repeats (TPRs) of cognate intracellular receptors, leading to gene or protein activation or inhibition, facilitating a coordinated response beneficial for a dense population. The density- dependent regulations of RRNPPA systems control behaviors like bacterial virulence, biofilm formation, sporulation, competence, conjugation and bacteriophage lysis/lysogeny decisions<sup>17- 21</sup>. Although these receptors were identified in the early 1990s<sup>29,30</sup>, their evolutionary history is unclear due to frequent mutations and transfers, making sequence comparisons challenging<sup>28,31,32</sup>. This is reflected by the nomenclature of the family: RRNPPA is an acronym for Rap, Rgg, NprR, PlcR, PrgX and AimR, which were historically described as six different families of intracellular receptors, and of which only structural comparisons allowed to establish the actual consensus on their common evolutionary origin<sup>28,33,34</sup>. Recently, a pioneer work combining
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 82, 880, 184]]<|/det|>
+structural comparisons among folds and sequence- based phylogenetics have provided insights among some of these families<sup>28</sup>, but a comprehensive reconstruction of the evolutionary history of this family that includes all described subfamilies<sup>19</sup> remains elusive.  
+
+<|ref|>text<|/ref|><|det|>[[115, 194, 881, 457]]<|/det|>
+The Foldtree structure- based phylogeny illuminates key evolutionary features of the diversification of RRNPPA communication systems that could not be resolved based on sequences (Figure 2). The evolutionary trajectory it implies is more parsimonious in terms of subfamily classification, taxonomy, functions, and protein architectures than a phylogeny obtained with a state- of- the- art sequence- based method (details in Supplementary Figure 9). In particular, the structure- based phylogeny implies that folds composed of 9 tetratricopeptide repeats (TPRs) and folds composed of 5 TPRs emerged only once while the sequence- based tree implies a less plausible scenario of convergent evolution of two clades toward 5- TPR protein architectures.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[123, 85, 875, 860]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[123, 858, 870, 906]]<|/det|>
+<center>Figure 2. Phylogeny of cytosolic receptors from the RRNPPA family paired with a communication proppetide. a) Functional diversity of the RRNPPA family. The MAD root separates paralogs of Anoxybacter fermentans with a singular architecture from the other canonical RRNPPA systems. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[125, 88, 872, 333]]<|/det|>
+Subfamilies with experimental validation of at least one member are highlighted in color. Other subfamilies correspond to high- confidence candidate subfamilies detected with RRNPP_ detector in \(^{19}\) . Biological processes experimentally shown to be regulated in a density- dependent manner by a QS system are displayed for each validated subfamily. Subfamilies in gray correspond to novel, high- confidence candidate RRNPPA subfamilies from \(^{19}\) . A star mapped to a leaf indicates a predicted regulation of an adjacent biosynthetic gene cluster by the corresponding QS system. b) Main implied events of the tree, with normalized branch length for visualization purposes (the events that are implied from alternate roots are shown in Supplementary Figure 10). c) Distribution and prevalence of the different members of each RRNPPA subfamily into the different taxonomic families. d) Genomic orientation and encoding element of the receptor - adjacent propeptide pairs. e) The first colostrip indicates the domain architecture of each receptor. A representative fold for each domain architecture is displayed in the legend (AlphaFold models of subfamily 27, NprR, Rap and PlcR, respectively) with an indication of the implied events from panel a) at the origin of each fold/architecture. The second colostrip gives the degeneration score of TPR sequences of each receptor (given as 1 - TprPred_likelihood, as in \(^{33}\) ). The histogram shows the length (in amino-acids) of each receptor.  
+
+<|ref|>text<|/ref|><|det|>[[115, 370, 881, 768]]<|/det|>
+The minimal ancestor deviation (MAD) method placed the root right next to receptors encoded by Anoxybacter fermentans DY22613, a piezophilic and thermophilic endospore- forming bacterium from the Clostridia class isolated from a deep- sea hydrothermal vent. These proteins exhibit a unique domain architecture lacking the DNA- binding HTH domain and harboring 7 TPRs (Table S1). Their singular architecture, and the proximity to the MAD root lead us to infer Anoxybacter's receptors as the outgroup of all other RRNPPA systems (Figure 2a- b). This suggests that the early history of canonical RRNPPA systems could have been linked to extremophile endospore- forming Bacillota and may have started with a gain of a N- terminal HTH DNA binding domain, enabling to coupling quorum sensing with transcriptional regulation (Figure 2e). We considered alternative rooting scenarios (Supplementary Figure 11) but only the MAD rooting implies a unique origin of receptors with non- degenerated TPR sequences that predates the last common ancestor of each clade of receptors with degenerated TPRs (Figure 2e), in line with Declerck et al.'s conjecture \(^{33}\) .  
+
+<|ref|>text<|/ref|><|det|>[[116, 779, 880, 907]]<|/det|>
+The widespread distribution of sporulation- regulation on the tree (Figure 2a) suggests that the early history of the 9 TPRs group may have been linked to the regulation of the costly differentiation into a resistant endospore in extremophile spore- forming taxa from the Clostridia (Biomaibacter acetigenes, Sulfobacillus thermotolerans, Thermoanaerobacter italicus) and Bacilli (Alicyclobacillaceae and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 78, 882, 644]]<|/det|>
+Thermoactinomycetaceae families) classes (Table S1). Consistently, the NprR subfamily is suggested to have diversified first in extremophile spore- forming Bacillusaceae (Psychrobacilli, Halobacilli, Anoxybacilli etc.) and Planococcaceae (Sporosarcina, Planococcus antarticus, halotolerans, glaciei etc.) (Table S1). The Rap clade, exclusively found in Bacillus and Alkalihalobacillus genera, is nested within NprR, and is inferred to have diverged from the same ancestral gene as that of NprR receptors found in Halobacilli, Geobacilli, Virgibacilli, Oceanobacilli and Bacilli from the Bacillus cereus group (Table S1). This indicates that the absence of the N- terminal HTH domain observed in Rap receptors originates from a loss of the ancestral domain (Figure 2e), as previously reported by Felipe- Ruiz et al<sup>28</sup>. However, many Rap receptors have retained the ability to regulate sporulation, but only through protein inhibition of the Spo0F- P and ComA regulators, rather than through transcriptional regulation<sup>35</sup>. The Rap clade is characterized by a wide occurrence in MGEs, consistent with the high rate of horizontal gene transfers described for this subfamily<sup>32</sup>. The MGE distribution in the Rap clade is polyphyletic, suggesting frequent exchanges of these communication systems between the host genome, phages and conjugative elements (Figure 2d). The QssR validated clade is specific to solventogenic Clostridiaceae (Figure 2a- c) while its sister clade (subfamily 09) is specific to pathogenic Clostridium such as C. perfringens and C. botulinum, which may indicate a novel link between quorum sensing and pathogenesis in these taxa of medical relevance that may warrant further investigation.  
+
+<|ref|>text<|/ref|><|det|>[[116, 652, 882, 888]]<|/det|>
+AloR and AimR members appear to be the most diverged representatives of the HTH- 9TPRs architectural organization. Consistently, their TPR sequences harbor signs of degeneration, which is especially true in the AimR clade, consistent with its specificity to Bacillus phages, since viruses evolve at higher evolutionary rates (Figure 2f). The AimR receptors supporting phage- phage communication are adjacent to non- viral communication systems from subfamily 21, found in the chromosome of Alkalihalobacillus clausii or lehensis. For the first time, the structural phylogeny reveals that the AimR- subfamily 21 clade is evolutionary close from Paenibacillaceae receptors from the AloR subfamily prevalent in the Paenibacillus
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 400]]<|/det|>
+genus and the candidate subfamily 08 predominantly found in the Brevibacillus genus (Figure 2). Subfamily 08, AloR and AimR are suggested to form a monophyletic group with a presumable Paenibacillaceae ancestry. This is supported by systems from Paenibacillus xylanexedens and Brevibacillus formosus position in the outgroup, close to the QssR subfamily (Figure 2a, Table S1). Remarkably, the cognate communication peptides of AimR receptors from the Bacillus cereus group are highly similar to that of subfamily 08, with the presence of the DPG amino- acid motif in the C- terminal (Table S1). Our results therefore suggest that a QSS similar to the ancestor of the AloR- subfam08 clade was co- opted by a temperate phage to regulate the lysis/lysogeny decision. This successful functional association has spread in Bacillus phages and led to the AimR clade. The numerous phage- and prophage- encoded systems from the subfamily 08 support this hypothesis<sup>19</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 409, 881, 889]]<|/det|>
+The proteins composed of 5 TPRs are suggested to have emerged from the loss of 4 TPRs in the C- terminus, drastically shortening their length (Figure 2b, Figure 2e), although other evolutionary scenarios that do not imply such loss exist as well<sup>28</sup> (Supplementary Figure 10). The 5 TPRs group is divided in two sister clades: one with a wide taxonomic range composed of PlcR, TprA and their outgroup (Figure 2a and Figure 2c), the second including PrgX, TraA, ComR and Rgg validated subfamilies, specific to non- spore forming Lactobactillales. The emergence of the 5TPRs clade is associated with fundamental functional shifts. First, receptor- propeptide orientations are highly diversified compared to the HTH- 9TPRs group (Figure 9d). These heterogeneous orientations correlate with functional changes as receptors divergently transcribed from their propeptide tend to repress target genes while co- directional receptors tend to activate them<sup>36</sup>. Second, the diversification of the PrgX- ComR- Rgg clade was accompanied with an important diversification of propeptide secretion modes: their cognate propeptides are exported through the alternative PptAB translocon rather than through the SEC translocon<sup>17,28</sup> and it has even been shown that a paralog of Rgg in S. pyogenes is paired with a functional leaderless communication peptide that lacks a signal sequence for an export system, highlighting that another secretory process of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[116, 82, 882, 347]]<|/det|>
+communication peptides emerged in the clade<sup>37</sup>. Last, the biological processes controlled by these communication systems are not linked to cellular dormancy or viral latency, but rather to the production of virulence factors and antimicrobials<sup>21</sup>. This is mirrored by the substantial number of syntenic biosynthetic gene clusters (BGCs) predicted to be regulated by TprA and Rgg members (Figure 2a)<sup>19</sup>. Consistently, the primary role of members of the HTH- 5TPRs clade may be to assess the threshold population density at which a collective production of biomolecules starts to be ecologically impactful and becomes the most evolutionary advantageous strategy, with a few exceptions such as the regulation of competence by ComR or conjugation by PrgX.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 384, 246, 404]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[115, 411, 882, 809]]<|/det|>
+As early as 1975, Eventoff and Rossmann employed the number of structurally dissimilar residues between pairs of proteins to infer phylogenetic relationships by means of a distance method<sup>38</sup>. This approach has been revisited to infer deep phylogenetic trees and networks using different combinations of dissimilarity measures (e.g., RMSD, \(\mathrm{Q}_{\mathrm{score}}\) , Z- score) and inference algorithms<sup>12,39- 43</sup>. Conformational sampling has been proposed to assess tree confidence when using this approach<sup>11</sup>. Some models have been developed that mathematically describe the molecular clock in structural evolution<sup>44</sup> or integrate sequence data with structural information to inform the likelihood of certain substitutions<sup>45</sup>. Other studies have modeled structural evolution as a diffusion process in order to infer evolutionary distances<sup>46</sup>, or incorporating it into a joint sequence- structure model to infer multiple alignments and trees by means of bayesian phylogenetic analysis<sup>47,48</sup>. To date, the quality of structure- based phylogenetics, especially compared to conventional sequence- based phylogenetics, has remained largely unknown, limiting its use to niche applications.  
+
+<|ref|>text<|/ref|><|det|>[[117, 816, 880, 890]]<|/det|>
+The extensive empirical assessment reported here, using two orthogonal indicators of tree quality, demonstrates the high potential of structure- based phylogenetics. The taxonomic congruence score (TCS) measures agreement with
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 882, 427]]<|/det|>
+the established classification. Individual gene trees can be expected to deviate substantially from the underlying species tree due to gene duplication, lateral transfer, incomplete lineage sorting, or other phenomena. However, the evolutionary history of the underlying species will still be reflected in many parts of the tree—which is quantified by the TCS. All else being equal, tree inference approaches which tend to result in higher TCS over many protein families can be expected to be more accurate. On this metric, we obtained the best trees using Foldtree, which is based on Foldseek's structural alphabet, and an alignment procedure combining structural and sequence information. Furthermore, after filtering lower quality structures out of the tree building process, tree quality improved further when compared to sequence- based trees (Figure 1. b), indicating that higher confidence models with accurate structural information provide better phylogenetic signal.  
+
+<|ref|>text<|/ref|><|det|>[[115, 433, 882, 614]]<|/det|>
+When considering the ultrametricity through the root- to- tip variances of the trees, the Foldtree trees adhered more closely to a molecular clock than other structural or sequence trees. We acknowledge that in and of itself, adherence to a molecular clock is only a weak indicator of tree accuracy. Nevertheless, considering the clear, consistent differences obtained, and the agreement with the TCS criterion, the ultrametricity appears to reflect meaningful performance difference among the tree inference methods.  
+
+<|ref|>text<|/ref|><|det|>[[115, 621, 882, 884]]<|/det|>
+Folds evolve at a slower rate than the underlying sequence mutations<sup>49,50</sup>. Structural distances are therefore less likely to saturate over time, making it possible to recover the correct topology deeper in the tree with greater certainty. This could be observed in our results on the distant, structurally defined CATH families. Interestingly, however, Foldtree distinguished itself even at divergence times when homology is identifiable using sequence to sequence comparison. It is thus both fine grained enough to account for small differences between input proteins at shorter divergence times, overcoming the often mentioned shortcoming of structural phylogenetics, and more robust than sequence comparison at longer evolutionary distances.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[116, 82, 882, 373]]<|/det|>
+As the projection of each residue onto a structural character is locally influenced by its neighboring residues rather than global steric changes, Foldseek's representations of 3D structures are well suited to capture phylogenetic signals when comparing homologous proteins. In contrast, global structural similarity measures are confounded by conformational fluctuations which involve steric changes that are much larger in magnitude than the local changes observed between functionally constrained residues during evolution. Moreover, since Foldseek represents 3D structures as strings, the computational speed- ups and techniques associated with string comparisons implemented in MMseqs<sup>51</sup> can be applied to structural homology searches and comparisons making the Foldtree pipeline extremely fast and efficient.  
+
+<|ref|>text<|/ref|><|det|>[[115, 377, 881, 912]]<|/det|>
+Viral evolution, quickly evolving extracellular proteins and protein families with histories stretching back to the first self replicating cells are among the many cases that can be revisited with these new techniques. In our first study of a family using Foldtree, we present just one such case, with the fast evolving RRNPPA family of cytosolic communication receptors encoded by Firmicutes bacteria, their conjugative elements and their viruses. The phylogeny reconstructed by Foldtree includes, for the first time, all described RRNPPA subfamilies<sup>19</sup>. Remarkably, despite their significant divergence, the underlying diversifying history is parsimonious in terms of taxonomy, functions, and protein architectures (Supplementary Figure 10). The MAD rooting method flags a previously undescribed candidate outgroup with a singular architecture of 7 TPRs and no DNA- binding domain in Anoxybacter fermentans, which supports Declerck et al. speculation that the ancestral receptor at the origin of the RRNPPA clade lacked the DNA- binding domain, and that the latter was gained subsequently in the evolutionary history of the family. Declerck et al. also speculated that the level of TPR degeneracy in receptors is a marker of divergence from the last common ancestor of the family<sup>33</sup>. In this respect, root to tips lengths are remarkably uniform throughout the entire RRNPPA structural tree with slight differences being meaningful, as the longest branches correspond to receptors with degenerated TPR sequences (Figure 2e). Last, this rooting implies that receptors with non- degenerated TPRs sequences emerged only once, and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 882, 373]]<|/det|>
+systematically involves a late emergence of clades with degenerated TPRs as a derived state of an ancestor harboring non- degenerated TPRs (Figure 2e). Although rooting is easier when a tree is more clock- like, there remains uncertainty regarding the precise placement of the root. Our interpretation of MAD rooting and domain architecture led us to infer an origin of the RRNPPA family linked to the regulation of sporulation in extreme environments, implying also that 9 TPRs folds predate 5 TPRs folds. Yet, alternative rootings of the structural phylogeny cannot be ruled out, with a root either within the HTH- 5TPRs group as in \(^{28}\) or within the AloR- AimR- subfamily08 group (hypotheses displayed in Supplementary Figure 11). Additional, yet- to- be- discovered members of RRNPPA homologs could help resolve the root with higher confidence.  
+
+<|ref|>text<|/ref|><|det|>[[115, 382, 882, 591]]<|/det|>
+Recently the fold universe has been revealed using AlphaFold on the entirety of the sequences in UniProt and the ESM model \(^{8}\) on the sequences in MGNIFY \(^{52}\) to reach a total of nearly one billion structures. The UniProt structures inferred by AlphaFold have recently been systematically organized into sequence- and structure- based clusters, shedding light on novel fold families and their possible functions \(^{14,53}\) . In future work it may be desirable to add an evolutionary layer of information to this exploration of the fold space using structural phylogenetics to further refine our understanding of how this extant diversity of folds emerged.  
+
+<|ref|>text<|/ref|><|det|>[[115, 601, 882, 864]]<|/det|>
+In conclusion, this work shows the potential of structural methods as a powerful tool for inferring evolutionary relationships among proteins. For relatively close proteins, structured- based tree inference rivals sequence- based inference, and the choice of approach should be tailored to the specific question at hand and the available data. For more distant proteins, structural phylogenetics opens new inroads into studying evolution beyond the "twilight" zone \(^{54}\) . We believe that there remains much room for improvement in refining phylogenetic methods using the tertiary representation of proteins and hope that this work serves as a starting point for further exploration of deep phylogenies in this new era of Al- generated protein structures.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 217, 103]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[118, 113, 684, 131]]<|/det|>
+No statistical methods were used to predetermine sample size.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 165, 568, 185]]<|/det|>
+## OMA HOG selection for large scale benchmark  
+
+<|ref|>text<|/ref|><|det|>[[115, 190, 882, 454]]<|/det|>
+The OMA set of protein families consists of "root hierarchical orthologous groups" (root HOGs) which are derived from all- vs- all sequence comparisons<sup>55</sup>. The quest for orthologs benchmarking dataset<sup>56</sup> consists of 78 proteomes. The 2020 release of this dataset was used as input into the OMA orthology prediction pipeline<sup>55</sup> (version 2.4.1). A random selection of at most 500 orthologous groups with at least 10 proteins were compiled for each group of HOGs that were inferred to have emerged in different ancestral taxa (Bacteria, Bilateria, Chordata, Dikarya, Eukaryota, Eumetazoa, Euteleostomi, Fungi, LUCA, Opisthokonta and Tetrapoda). The UniProt identifiers of the proteins within each group were used as input to the Foldtree pipeline.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 487, 587, 506]]<|/det|>
+## CATH family selection for large scale benchmark  
+
+<|ref|>text<|/ref|><|det|>[[116, 510, 882, 751]]<|/det|>
+CATH structural superfamilies are constructed using structural comparisons and classification<sup>25</sup>. Each level of classification designates a different resolution of structural similarity. These are delineated as Class, Architecture, Topology and Homology. We chose to investigate tree quality using input sets within the same homology classification as well as sets within the same topology. We selected a random subsample of at most 250 proteins (or the number of proteins within the family if there were less) from each family for 635 CATH families and 500 CAT families. The Topology- based dataset is designated as CAT and the Homology- based dataset is designated as CATH. Each CAT or CATH family contains the PDB identifiers and chains of the structures they correspond to.  
+
+<|ref|>text<|/ref|><|det|>[[116, 756, 882, 911]]<|/det|>
+The PDB files were programmatically obtained from the PDB database. 3D structures of monomers corresponding to the chain identified in the CATH classification for each fold were extracted from PDB crystal structures using Biopython. PDBfizer from the OpenMM<sup>57</sup> package was used to fix crystal structures with discontinuities, non- standard residues or missing atoms before tree building since these adversely affect structural comparisons.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[119, 110, 380, 128]]<|/det|>
+## Structure tree construction  
+
+<|ref|>text<|/ref|><|det|>[[118, 134, 880, 208]]<|/det|>
+Sets of homologous structures were downloaded from the AFDB or PDB and prepared according to the OMA and CATH dataset sections above. Foldseek<sup>14</sup> is then used to perform an all vs all comparison of the structures.  
+
+<|ref|>text<|/ref|><|det|>[[115, 214, 881, 723]]<|/det|>
+Structural distances between all pairs are compiled into a distance matrix which is used as input to quicktree<sup>58</sup> to create minimum evolution trees. These trees are then rooted using the MAD method<sup>59</sup>. Foldseek (Version: 30fdcac78217579fa25d59bc271bd4f3767d3ebb) has two alignment modes where character based structural alignments are performed and are scored using the 3Di substitution matrix or a combination of 3Di and amino- acid substitution matrices. A third mode, using TMalign to perform the initial alignment was not used. It is then possible to output the fraction of identical amino acids from the 3Di and amino acid based alignment (Fident), the LDDT (locally derived using Foldseek's implementation) score and the TM score (normalized by alignment length). This results in a total of 6 structural comparison methods. We then either directly used the raw score or applied a correction to the scores to transform them to the distance matrices so that pairwise distances would be linearly proportional to time (Supplementary methods). This resulted in a total of 12 possible structure trees for each set of input proteins. To compile these results, Foldseek was used with alignment type 0 and alignment type 2 flags in two separate runs with the '--exhaustive- search' flag. The output was formatted to include Iddt and alntmscore columns. The pipeline of comparing structure- and sequence- based trees is outlined in Supplementary Figure 1.  
+
+<|ref|>text<|/ref|><|det|>[[116, 727, 881, 882]]<|/det|>
+Before starting the all vs all comparison of the structures we also implemented an optional filtering step to remove poor AlphaFold models with low pLDDT values. If the user activates this option, the pipeline removes structures (and the corresponding sequences) with an average pLDDT score below 40, before establishing the final protein set and running structure and sequence tree building pipelines. We performed similar benchmarking experiments on filtered and unfiltered
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[118, 83, 879, 130]]<|/det|>
+versions of the OMA dataset to observe the effect of including only high quality models in the analysis.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 164, 450, 183]]<|/det|>
+## Sequence based tree construction  
+
+<|ref|>text<|/ref|><|det|>[[116, 188, 882, 370]]<|/det|>
+Sets of sequences and their taxonomic lineage information were downloaded using the UniProt API. Clustal Omega (version 1.2.4)60 or Muscle5 (version 5.0)61 was then used to generate a multiple sequence alignment on default parameters. This alignment was then used with either FastTree(version 2.1)62 on default parameters or IQ- TREE (version 1.6.12 using the flags LG+1) to generate a phylogenetic tree. Finally, this tree was rooted using the MAD (version 1775932) method on default parameters.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 404, 627, 423]]<|/det|>
+## Taxonomic congruence metric for phylogenetic trees  
+
+<|ref|>text<|/ref|><|det|>[[116, 428, 881, 609]]<|/det|>
+Taxonomic lineages were retrieved for each sequence and structure of each protein family via the UniProt API. It is assumed that the vast majority of genes will follow an evolutionary trajectory that mirrors the species tree with occasional loss or duplication events. The original development and justification for this score to measure tree quality in an unbiased way can be found in the following work 24. In this version of the metric we reward longer lineage sets towards the root by calculating a score for each leaf from the root to the tip.  
+
+<|ref|>text<|/ref|><|det|>[[116, 617, 881, 718]]<|/det|>
+The agreement of the tree with the established taxonomy (from UniProt) can be calculated recursively in a bottom up fashion when traversing the tree using equation 1. Leaves of trees were labeled with sets representing the taxonomic lineages of each sequence before calculating taxonomic congruence.
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[370, 100, 597, 135]]<|/det|>
+\[C(tree) = \sum_{s}^{Leaves}C(leaf)\]  
+
+<|ref|>equation<|/ref|><|det|>[[215, 147, 755, 216]]<|/det|>
+\[C(x) = \left\{ \begin{array}{ll}|s(x)| & \mathrm{if~x~is~root}\\ |s(x)| + |s(x.ancestor)| & \mathrm{if~x~is~an~internal~node}\\ & \mathrm{where}\\ \end{array} \right.\]  
+
+<|ref|>equation<|/ref|><|det|>[[214, 216, 755, 255]]<|/det|>
+\[s(x) = \left\{ \begin{array}{ll}L(x), & \mathrm{if~x~is~a~leaf}\\ s(x.Left)\cap s(x.Right)) & \mathrm{if~x~is~an~internal~node} \end{array} \right.\]  
+
+<|ref|>text<|/ref|><|det|>[[124, 300, 872, 410]]<|/det|>
+Equation 1- taxonomic congruence metric. This score is used to measure the agreement of binary tree topologies with the known species tree. \(\mathsf{s}(\mathsf{x})\) denotes the set of lineages found in the tree node x. \(\mathrm{C(x)}\) denotes the congruence score of node x based on its two child nodes. \(\mathsf{L}(\mathsf{x})\) denotes the labels of leaves. The total score of a tree is defined as the sum of the leaf scores. The code to calculate this metric is available on the git repository.  
+
+<|ref|>text<|/ref|><|det|>[[116, 442, 880, 549]]<|/det|>
+Both structure and sequence trees were rooted using the MAD method to make TCS comparisons between the methods equivalent. To compare large collections of trees with varying input set sizes, we normalized the congruence scores of trees by the number of the proteins in the tree.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 580, 388, 599]]<|/det|>
+## Ultrametricity quantification  
+
+<|ref|>text<|/ref|><|det|>[[116, 603, 881, 773]]<|/det|>
+Ultrametricity<sup>63</sup> describes the consistency of tip to root lengths of a given phylogenetic tree. If a tree building approach has an accurate molecular clock on all branches, the amount of inferred evolutionary time elapsed between the root and all of the extant species should be equivalent and proportional to real time. This would imply that the sums of branch length along a lineage from the root to any tip of the tree should be equivalent since the amount of clock time elapsed from the common ancestor until the sequencing of species in the present day is the same.
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[185, 99, 775, 194]]<|/det|>
+\[E(\text{rootdist}) = \sum_{i = 1}^{n_{\text{leaves}}} \text{dist}(l_i, \text{root}) / n_{\text{leaves}} \\ S_{\text{norm}}(\text{rootdist}) = \sum_{i = 1}^{n_{\text{leaves}}} (\text{dist}(l_i, \text{root}) / E(\text{rootdist}) - 1)^2 / (n_{\text{leaves}} - 1)\]
+
+<|ref|>text<|/ref|><|det|>[[125, 220, 870, 321]]<|/det|>
+**Equation 2** - To derive a unified metric for ultrametricity that could easily be applied to the trees generated by different methods, we normalized the branch lengths to center the distribution of root to tip lengths at 1. We then measured the variance of these normalized root to tip lengths. \(E(.)\) represents the average root to tip length for a given tree. \(S_{\text{norm}}(.)\) represents the variance of these normalized root to tip distances. \(\text{dist}(l_i, \text{root})\) denotes the length of the tip \((l_i)\) to root. 
+
+<|ref|>text<|/ref|><|det|>[[116, 351, 880, 515]]<|/det|>
+To describe the ultrametricity of the different methods of structural tree derivation, we measured the length of root-to-tip distances of a given tree (equation 2). We then normalized this collection of distances by their mean and calculated their variance. We compiled this variance measurement for collections of trees with corresponding input protein sets for all methods used to derive trees and compared their distributions. **Supplementary Figure 2** shows a visual representation of how this score is calculated. 
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 548, 314, 565]]<|/det|>
+## RRNPPA phylogeny 
+
+<|ref|>text<|/ref|><|det|>[[116, 572, 880, 686]]<|/det|>
+The metadata of "strict" known and candidate RRNPPA QSSs described in the RRNPP_detector paper were fetched from TableS2 in the corresponding supplementary materials¹⁹. The predicted regulations by QSSs of adjacent BGCs were fetched from TableS5. The propeptide sequences were downloaded from the following Github repository: 
+
+<|ref|>text<|/ref|><|det|>[[116, 694, 870, 911]]<|/det|>
+https://github.com/TeamAIRE/RRNPP_candidate_propeptides_exploration_dataset.
+The 11,939 receptors listed in TableS2 were downloaded from the NCBI Genbank database, and redundancy was removed by clustering at 95% identity with CD-HIT⁶⁴, yielding 1,418 protein clusters. The Genbank identifiers of the 11,939 receptors were used as queries in the UniProt Retrieve/ID mapping research engine (https://www.uniprot.org/id-mapping) to retrieve corresponding UniProt/AlphaFoldDB identifiers. 768 protein clusters successfully mapped to at least one UniProt/AlphaFoldDB identifier. The 768 predicted protein structures were downloaded and Foldseek was used to perform an all vs all comparison. Based on
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 472]]<|/det|>
+our benchmarking results we used the Fident scores from a comparison using amino- acid and 3Di alphabet alignment scoring (alignment mode 1 in Foldseek). Since this family had undergone domain architecture modifications, we decided to extract the structural region between the first and last positions of each fold where \(80\%\) of all of the other structures in the set mapped. With these core structures we performed a second all vs all comparison. We again used the Fident scores (alignment mode 1) and no statistical correction to construct a distance matrix between the core structures. This matrix was then used with FastME \(^{65}\) to create a distance based tree. The resulting tree was annotated with ITOL \(^{66}\) , using the metadata available in Table S1. To derive the sequence- based phylogeny, we built a multiple sequence alignment (MSA) of receptors, using mafft \(^{67}\) with the parameters - maxiterate 1000 - localpair for high accuracy. The MSA was then trimmed with trimAl \(^{68}\) under the - automated 1 mode optimized for maximum likelihood reconstruction. The trimmed alignment of 304 sites was given as input to IQ- TREE \(^{2}\) to infer a maximum likelihood phylogenetic under the LG+G model with 1000 ultrafast bootstraps.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 496, 340, 516]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[116, 524, 881, 625]]<|/det|>
+We thank the Dessimoz lab members for thoughtful discussions on the topic of structural evolution and their encouragement and input on this work. We especially thank Clement Train for his brilliant work on the tree visualization tool accompanying this work. We also gratefully acknowledge helpful suggestions by Pedro Beltrao.  
+
+<|ref|>text<|/ref|><|det|>[[117, 658, 880, 732]]<|/det|>
+The work was supported by SNSF grant 216623 to C.D.. M. L. is a recipient of a doctoral scholarship from Agencia Nacional de Investigación e Innovación (ANII), Uruguay.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 767, 354, 787]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[116, 794, 881, 895]]<|/det|>
+David Moi designed and wrote the treebuilding pipeline and analysis pipelines, collected benchmarking data for CATH structural families, carried out large scale analysis for benchmarking, generated trees for protein families, and drafted the manuscript. Charles Bernard collected data relevant to the bacterial signaling case
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[116, 82, 882, 293]]<|/det|>
+study, analyzed and annotated the case study in light of the existing literature and wrote the corresponding sections of the paper. Martin Steinegger contributed advice and feedback on the structural distance measures evaluated in this paper. Yannis Nevers collected HOG benchmarking data and curated examples of protein families to test the pipeline. Mauricio Langlieb wrote the documentation and collected benchmarking data and curated examples of protein families. Christophe Dessimoz supervised the project and contributed to the conception of the study, the interpretation of results, and the manuscript writing.  
+
+<|ref|>text<|/ref|><|det|>[[116, 326, 776, 346]]<|/det|>
+Correspondence and requests for materials should be addressed to D.M.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 380, 348, 400]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[118, 409, 516, 427]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 463, 500, 484]]<|/det|>
+## Supplementary Information Guide  
+
+<|ref|>text<|/ref|><|det|>[[149, 495, 365, 512]]<|/det|>
+1. Supplementary data  
+
+<|ref|>text<|/ref|><|det|>[[116, 521, 880, 567]]<|/det|>
+The homologue list of RRNPPA sequences and their metadata is available in the RRNPPAlist.xls file. In the text it is referred to as Table S1.  
+
+<|ref|>text<|/ref|><|det|>[[146, 575, 880, 621]]<|/det|>
+2. Supplementary methods, results and discussion are found in the SI section pdf  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 657, 412, 677]]<|/det|>
+## Code and Data availability  
+
+<|ref|>text<|/ref|><|det|>[[116, 714, 880, 760]]<|/det|>
+All UniProt identifiers necessary to replicate the experimental results are available on Zenodo: https://doi.org/10.5281/zenodo.8346286  
+
+<|ref|>text<|/ref|><|det|>[[116, 794, 880, 841]]<|/det|>
+The Foldtree pipeline is available on github: https://github.com/DessimozLab/fold_tree
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 83, 880, 131]]<|/det|>
+All metadata used to annotate the RRNPPA phylogeny are available in the supplementary data file or on the Zenodo archive.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 165, 240, 185]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[115, 204, 880, 884]]<|/det|>
+1. Kozlov, A. M., Darriba, D., Flouri, T., Morel, B. & Stamatakis, A. RAxML-NG: a fast, scalable and user-friendly tool for maximum likelihood phylogenetic inference. Bioinformatics 35, 4453-4455 (2019).  
+2. Minh, B. Q., Trifinopoulos, J., Schrempf, D., Schmidt, H. A. & Lanfear, R. IQ-TREE version 2.0: tutorials and Manual Phylogenomic software by maximum likelihood. URL http://www. iqtree. org (2019).  
+3. Bouckaert, R. et al. BEAST 2.5: An advanced software platform for Bayesian evolutionary analysis. PLoS Comput. Biol. 15, e1006650 (2019).  
+4. Laumer, C. E. et al. Revisiting metazoan phylogeny with genomic sampling of all phyla. Proc. Biol. Sci. 286, 20190831 (2019).  
+5. Li, Y., Shen, X.-X., Evans, B., Dunn, C. W. & Rokas, A. Rooting the Animal Tree of Life. Mol. Biol. Evol. 38, 4322-4333 (2021).  
+6. Schultz, D. T. et al. Ancient gene linkages support ctenophores as sister to other animals. Nature 618, 110-117 (2023).  
+7. Tunyasuvunakool, K. et al. Highly accurate protein structure prediction for the human proteome. Nature 596, 590-596 (2021).  
+8. Lin, Z. et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 379, 1123-1130 (2023).  
+9. Zhang, Y. & Skolnick, J. TM-align: a protein structure alignment algorithm based on the TM-score. Nucleic Acids Res. 33, 2302-2309 (2005).  
+10. Le, Q., Pollastri, G. & Koehl, P. Structural alphabets for protein structure classification: a
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[152, 83, 590, 101]]<|/det|>
+comparison study. J. Mol. Biol. 387, 431- 450 (2009).  
+
+<|ref|>text<|/ref|><|det|>[[118, 116, 872, 168]]<|/det|>
+11. Malik, A. J., Poole, A. M. & Allison, J. R. Structural Phylogenetics with Confidence. Mol. Biol. Evol. 37, 2711-2726 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[118, 182, 871, 234]]<|/det|>
+12. Bujnicki, J. M. Phylogeny of the restriction endonuclease-like superfamily inferred from comparison of protein structures. J. Mol. Evol. 50, 39-44 (2000).  
+
+<|ref|>text<|/ref|><|det|>[[118, 248, 869, 333]]<|/det|>
+13. Balaji, S. & Srinivasan, N. Use of a database of structural alignments and phylogenetic trees in investigating the relationship between sequence and structural variability among homologous proteins. Protein Eng. 14, 219-226 (2001).  
+
+<|ref|>text<|/ref|><|det|>[[118, 346, 852, 398]]<|/det|>
+14. van Kempen, M. et al. Fast and accurate protein structure search with Foldseek. Nat. Biotechnol. (2023) doi:10.1038/s41587-023-01773-0.  
+
+<|ref|>text<|/ref|><|det|>[[118, 412, 869, 464]]<|/det|>
+15. Xu, J. & Zhang, Y. How significant is a protein structure similarity with TM-score = 0.5? Bioinformatics 26, 889-895 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[118, 478, 836, 562]]<|/det|>
+16. Mariani, V., Biasini, M., Barbato, A. & Schwede, T. IDDT: a local superposition-free score for comparing protein structures and models using distance difference tests. Bioinformatics 29, 2722-2728 (2013).  
+
+<|ref|>text<|/ref|><|det|>[[118, 576, 850, 660]]<|/det|>
+17. Neiditch, M. B., Capodagli, G. C., Prehna, G. & Federle, M. J. Genetic and Structural Analyses of RRNPP Intercellular Peptide Signaling of Gram-Positive Bacteria. Annu. Rev. Genet. 51, 311-333 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[118, 675, 820, 760]]<|/det|>
+18. Fleuchot, B. et al. Rgg proteins associated with internalized small hydrophobic peptides: a new quorum-sensing mechanism in streptococci. Mol. Microbiol. 80, 1102-1119 (2011).  
+
+<|ref|>text<|/ref|><|det|>[[118, 774, 876, 858]]<|/det|>
+19. Bernard, C., Li, Y., Lopez, P. & Bapteste, E. Large-Scale Identification of Known and Novel RRNPP Quorum-Sensing Systems by RRNPP_Detector Captures Novel Features of Bacterial, Plasmidic, and Viral Coevolution. Mol. Biol. Evol. 40, (2023).  
+
+<|ref|>text<|/ref|><|det|>[[115, 872, 792, 891]]<|/det|>
+20. Kotte, A.-K. et al. RRNPP-type quorum sensing affects solvent formation and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[150, 82, 794, 101]]<|/det|>
+sporulation in Clostridium acetobutylicum. Microbiology 166, 579- 592 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[115, 115, 854, 168]]<|/det|>
+21. Perez-Pascual, D., Monnet, V. & Gardan, R. Bacterial Cell-Cell Communication in the Host via RRNPP Peptide-Binding Regulators. Front. Microbiol. 7, 706 (2016).  
+
+<|ref|>text<|/ref|><|det|>[[115, 182, 855, 266]]<|/det|>
+22. Stokar-Avihail, A., Tal, N., Erez, Z., Lopatina, A. & Sorek, R. Widespread Utilization of Peptide Communication in Phages Infecting Soil and Pathogenic Bacteria. Cell Host Microbe 25, 746-755. e5 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[115, 280, 875, 365]]<|/det|>
+23. Cardoso, P. et al. Rap-Phr Systems from Plasmids pAW63 and pHT8-1 Act Together To Regulate Sporulation in the Bacillus thuringiensis Serovar kurstaki HD73 Strain. Appl. Environ. Microbiol. 86, (2020).  
+
+<|ref|>text<|/ref|><|det|>[[115, 378, 850, 496]]<|/det|>
+24. Tan, G., Gil, M., Löytynoja, A. P., Goldman, N. & Dessimoz, C. Simple chained guide trees give poorer multiple sequence alignments than inferred trees in simulation and phylogenetic benchmarks. Proceedings of the National Academy of Sciences of the United States of America vol. 112 E99-100 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[115, 510, 820, 530]]<|/det|>
+25. Knudsen, M. & Wiuf, C. The CATH database. Hum. Genomics 4, 207-212 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[115, 544, 861, 596]]<|/det|>
+26. Friedman, J. H. Greedy function approximation: A gradient boosting machine. aos 29, 1189-1232 (2001).  
+
+<|ref|>text<|/ref|><|det|>[[115, 610, 874, 694]]<|/det|>
+27. Bereg, S. & Zhang, Y. Phylogenetic networks based on the molecular clock hypothesis. in Fifth IEEE Symposium on Bioinformatics and Bioengineering (BIBE'05) 320-323 (2005).  
+
+<|ref|>text<|/ref|><|det|>[[115, 708, 822, 760]]<|/det|>
+28. Felipe-Ruiz, A., Marina, A. & Rocha, E. P. C. Structural and Genomic Evolution of RRNPPA Systems and Their Pheromone Signaling. MBio 13, e0251422 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[115, 774, 860, 826]]<|/det|>
+29. Clewell, D. B. & Weaver, K. E. Sex pheromones and plasmid transfer in Enterococcus faecalis. Plasmid 21, 175-184 (1989).  
+
+<|ref|>text<|/ref|><|det|>[[115, 840, 873, 892]]<|/det|>
+30. Rudner, D. Z., LeDeaux, J. R., Ireton, K. & Grossman, A. D. The spo0K locus of Bacillus subtilis is homologous to the oligopeptide permease locus and is required for
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[150, 83, 700, 101]]<|/det|>
+sporulation and competence. J. Bacteriol. 173, 1388- 1398 (1991).  
+
+<|ref|>text<|/ref|><|det|>[[117, 115, 870, 200]]<|/det|>
+31. Kalamara, M., Spacapan, M., Mandic-Mulec, I. & Stanley-Wall, N. R. Social behaviours by Bacillus subtilis: quorum sensing, kin discrimination and beyond. Mol. Microbiol. 110, 863-878 (2018).  
+
+<|ref|>text<|/ref|><|det|>[[117, 214, 866, 300]]<|/det|>
+32. Even-Tov, E., Omer Bendori, S., Pollak, S. & Eldar, A. Transient Duplication-Dependent Divergence and Horizontal Transfer Underlie the Evolutionary Dynamics of Bacterial Cell-Cell Signaling. PLoS Biol. 14, e2000330 (2016).  
+
+<|ref|>text<|/ref|><|det|>[[117, 313, 866, 397]]<|/det|>
+33. Declerck, N. et al. Structure of PlcR: Insights into virulence regulation and evolution of quorum sensing in Gram-positive bacteria. Proc. Natl. Acad. Sci. U. S. A. 104, 18490-18495 (2007).  
+
+<|ref|>text<|/ref|><|det|>[[117, 411, 872, 465]]<|/det|>
+34. Gallego Del Sol, F., Penadés, J. R. & Marina, A. Deciphering the Molecular Mechanism Underpinning Phage Arbitrium Communication Systems. Mol. Cell 74, 59-72.e3 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[117, 478, 856, 563]]<|/det|>
+35. Schultz, D., Wolynes, P. G., Ben Jacob, E. & Onuchic, J. N. Deciding fate in adverse times: sporulation and competence in Bacillus subtilis. Proc. Natl. Acad. Sci. U. S. A. 106, 21027-21034 (2009).  
+
+<|ref|>text<|/ref|><|det|>[[117, 577, 805, 629]]<|/det|>
+36. Monnet, V. & Gardan, R. Quorum-sensing regulators in Gram-positive bacteria: 'cherchez le peptide'. Molecular microbiology vol. 97 181-184 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[117, 643, 852, 728]]<|/det|>
+37. Do, H. et al. Leaderless secreted peptide signaling molecule alters global gene expression and increases virulence of a human bacterial pathogen. Proc. Natl. Acad. Sci. U. S. A. 114, E8498-E8507 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[117, 741, 855, 794]]<|/det|>
+38. Eventoff, W. & Rossmann, M. G. The evolution of dehydrogenases and kinases. CRC Crit. Rev. Biochem. 3, 111-140 (1975).  
+
+<|ref|>text<|/ref|><|det|>[[117, 808, 795, 860]]<|/det|>
+39. Johnson, M. S., Sali, A. & Blundell, T. L. Phylogenetic relationships from three-dimensional protein structures. Methods Enzymol. 183, 670-690 (1990).  
+
+<|ref|>text<|/ref|><|det|>[[117, 873, 763, 893]]<|/det|>
+40. Garau, G., Di Guilmi, A. M. & Hall, B. G. Structure-based phylogeny of the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[150, 83, 820, 101]]<|/det|>
+metallo- beta- lactamases. Antimicrob. Agents Chemother. 49, 2778- 2784 (2005).  
+
+<|ref|>text<|/ref|><|det|>[[117, 116, 835, 167]]<|/det|>
+41. Lundin, D., Berggren, G., Logan, D. T. & Sjöberg, B.-M. The origin and evolution of ribonucleotide reduction. Life 5, 604-636 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[117, 182, 844, 234]]<|/det|>
+42. Moi, D. et al. Discovery of archaeal fuseins homologous to eukaryotic HAP2/GCS1 gamete fusion proteins. Nat. Commun. 13, 3880 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[117, 248, 858, 300]]<|/det|>
+43. Lakshmi, B., Mishra, M., Srinivasan, N. & Archunan, G. Structure-Based Phylogenetic Analysis of the Lipocalin Superfamily. PLoS One 10, e0135507 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[117, 314, 857, 365]]<|/det|>
+44. Pascual-García, A., Arenas, M. & Bastolla, U. The Molecular Clock in the Evolution of Protein Structures. Syst. Biol. 68, 987-1002 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[117, 379, 841, 465]]<|/det|>
+45. Arenas, M., Sánchez-Cobos, A. & Bastolla, U. Maximum-Likelihood Phylogenetic Inference with Selection on Protein Folding Stability. Mol. Biol. Evol. 32, 2195-2207 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[117, 479, 844, 530]]<|/det|>
+46. Grishin, N. V. Estimation of evolutionary distances from protein spatial structures. J. Mol. Evol. 45, 359-369 (1997).  
+
+<|ref|>text<|/ref|><|det|>[[117, 544, 855, 596]]<|/det|>
+47. Challis, C. J. & Schmidler, S. C. A stochastic evolutionary model for protein structure alignment and phylogeny. Mol. Biol. Evol. 29, 3575-3587 (2012).  
+
+<|ref|>text<|/ref|><|det|>[[117, 610, 820, 694]]<|/det|>
+48. Herman, J. L., Challis, C. J., Novák, Á., Hein, J. & Schmidler, S. C. Simultaneous Bayesian estimation of alignment and phylogeny under a joint model of protein sequence and structure. Mol. Biol. Evol. 31, 2251-2266 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[117, 708, 867, 793]]<|/det|>
+49. Illergård, K., Ardell, D. H. & Elofsson, A. Structure is three to ten times more conserved than sequence--a study of structural response in protein cores. Proteins 77, 499-508 (2009).  
+
+<|ref|>text<|/ref|><|det|>[[117, 807, 814, 859]]<|/det|>
+50. Chothia, C. & Lesk, A. M. The relation between the divergence of sequence and structure in proteins. EMBO J. 5, 823-826 (1986).  
+
+<|ref|>text<|/ref|><|det|>[[115, 873, 875, 893]]<|/det|>
+51. Steinegger, M. & Söding, J. MMseqs2 enables sensitive protein sequence searching for
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[150, 83, 760, 101]]<|/det|>
+the analysis of massive data sets. Nat. Biotechnol. 35, 1026- 1028 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[117, 116, 870, 168]]<|/det|>
+52. Richardson, L. et al. MGNify: the microbiome sequence data analysis resource in 2023. Nucleic Acids Res. 51, D753-D759 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[117, 182, 832, 234]]<|/det|>
+53. Durairaj, J. et al. Uncovering new families and folds in the natural protein universe. Nature (2023) doi:10.1038/s41586-023-06622-3.  
+
+<|ref|>text<|/ref|><|det|>[[117, 248, 860, 269]]<|/det|>
+54. Rost, B. Twilight zone of protein sequence alignments. Protein Eng. 12, 85-94 (1999).  
+
+<|ref|>text<|/ref|><|det|>[[117, 281, 864, 334]]<|/det|>
+55. Altenhoff, A. M. et al. OMA standalone: orthology inference among public and custom genomes and transcriptomes. Genome Res. 29, 1152-1163 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[117, 347, 868, 399]]<|/det|>
+56. Altenhoff, A. M. et al. The Quest for Orthologs benchmark service and consensus calls in 2020. Nucleic Acids Res. 48, W538-W545 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[117, 412, 861, 465]]<|/det|>
+57. Eastman, P. et al. OpenMM 7: Rapid development of high performance algorithms for molecular dynamics. PLoS Comput. Biol. 13, e1005659 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[117, 479, 864, 531]]<|/det|>
+58. Howe, K., Bateman, A. & Durbin, R. QuickTree: building huge Neighbour-Joining trees of protein sequences. Bioinformatics 18, 1546-1547 (2002).  
+
+<|ref|>text<|/ref|><|det|>[[117, 544, 830, 596]]<|/det|>
+59. Tria, F. D. K., Landan, G. & Dagan, T. Phylogenetic rooting using minimal ancestor deviation. Nat Ecol Evol 1, 193 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[117, 610, 878, 662]]<|/det|>
+60. Sievers, F. & Higgins, D. G. Clustal Omega, accurate alignment of very large numbers of sequences. Methods Mol. Biol. 1079, 105-116 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[117, 676, 823, 728]]<|/det|>
+61. Edgar, R. C. MUSCLE: multiple sequence alignment with high accuracy and high throughput. Nucleic Acids Res. 32, 1792-1797 (2004).  
+
+<|ref|>text<|/ref|><|det|>[[117, 741, 864, 794]]<|/det|>
+62. Price, M. N., Dehal, P. S. & Arkin, A. P. FastTree: Computing Large Minimum Evolution Trees with Profiles instead of a Distance Matrix. Mol. Biol. Evol. 26, 1641-1650 (2009).  
+
+<|ref|>text<|/ref|><|det|>[[117, 808, 797, 860]]<|/det|>
+63. Moore, N. C. A. & Prosser, P. The Ultrametric Constraint and its Application to Phylogenetics. arXiv [cs.AI] (2014).  
+
+<|ref|>text<|/ref|><|det|>[[115, 873, 848, 894]]<|/det|>
+64. Li, W. & Godzik, A. Cd-hit: a fast program for clustering and comparing large sets of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[150, 82, 738, 101]]<|/det|>
+protein or nucleotide sequences. Bioinformatics 22, 1658- 1659 (2006).  
+
+<|ref|>text<|/ref|><|det|>[[115, 115, 866, 168]]<|/det|>
+65. Lefort, V., Desper, R. & Gascuel, O. FastME 2.0: A Comprehensive, Accurate, and Fast Distance-Based Phylogeny Inference Program. Mol. Biol. Evol. 32, 2798-2800 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[115, 182, 853, 235]]<|/det|>
+66. Letunic, I. & Bork, P. Interactive Tree Of Life (iTOL) v5: an online tool for phylogenetic tree display and annotation. Nucleic Acids Res. 49, W293-W296 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[115, 248, 852, 301]]<|/det|>
+67. Katoh, K. & Standley, D. M. MAFFT multiple sequence alignment software version 7: improvements in performance and usability. Mol. Biol. Evol. 30, 772-780 (2013).  
+
+<|ref|>text<|/ref|><|det|>[[115, 314, 860, 400]]<|/det|>
+68. Capella-Gutierrez, S., Silla-Martinez, J. M. & Gabaldon, T. trimAl: a tool for automated alignment trimming in large-scale phylogenetic analyses. Bioinformatics vol. 25 1972-1973 Preprint at https://doi.org/10.1093/bioinformatics/btp348 (2009).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 355, 177]]<|/det|>
+- SupTableRRNPPAmetadata.xls- FoldtreeS1.pdf
+
+<--- Page Split --->

preprint/preprint__00c089bc5362865e32d087a7de2c59c85939f78a3756c6991e0e05e515c9142f/images_list.json

@@ -0,0 +1,62 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 | Crystal structure, MCD measurements of trilayer \\(\\mathrm{NiI}_2\\) at room temperature. a, Schematic of trilayer \\(\\mathrm{NiI}_2\\) sandwiched between graphene and hBN. b, View of the in-plane and out-of-plane atomic lattice. The magnetic \\(\\mathrm{Ni}^{2 + }\\) ions are surrounded by the octahedron of \\(\\mathrm{I}^{-}\\) ions, and three \\(\\mathrm{NiI}_2\\) layers as a repeating unit stack in a staggered fashion along the c axis. c, Atomic-resolution ADF-STEM image showing signature hexagonal patterns of rhombohedral stacking in few-layer \\(\\mathrm{NiI}_2\\) crystals. The inset shows the corresponding FFT image. d, Circular polarization resolved Raman spectra of a trilayer \\(\\mathrm{NiI}_2\\) device (Fig. 1a) at room temperature, excited by \\(532\\mathrm{nm}\\) laser. “SM” indicates the interlayer shear mode of trilayer \\(\\mathrm{NiI}_2\\) . e, The MCD spectra of trilayer \\(\\mathrm{NiI}_2\\) at \\(+3\\mathrm{T}\\) , \\(0\\mathrm{T}\\) and -3T. MCD signals are sensitive to spin electronic transitions and magnetic moments in the electronic states. The MCD features are spin-sign dependent and reverse as magnetic field switch. The zero remanent MCD signals at \\(\\sim 2.3\\mathrm{eV}\\) at \\(0\\mathrm{T}\\) suggest antiferromagnetic orders.",
+    "footnote": [],
+    "bbox": [
+      [
+        177,
+        88,
+        840,
+        504
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 | Non-collinear antiferromagnetism in trilayer NiI₂ device. a, Polar RMCD maps upon a 2.33 eV laser with diffraction-limited spatial resolution (see Methods), collected at room temperature and selected magnetic field. b, Schematic of the spin textures of bimerons-like domains and corresponding zoom-in RMCD images (white dashed-line box in Fig. 2a). c, The polar RMCD signals along with the line sections of RMCD map (b). d, The RMCD curves sweeping between \\(+3\\mathrm{T}\\) and \\(-3\\mathrm{T}\\) at \\(10\\mathrm{K}\\) , suggesting a non-collinear antiferromagnetism.",
+    "footnote": [],
+    "bbox": [
+      [
+        160,
+        87,
+        833,
+        298
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 | Existence of ferroelectric and anti-ferroelectric orders in trilayer NiI2 device. a, b, \\(P - E\\) and \\(I - E\\) loops at various frequencies from device 1 (D1). c, Corresponding \\(I - E\\) loops from Fig. 3b subtracted the current background. Two pairs of current peaks (FE-AFE and AFE-FE switching peaks) were obtained by Lorentz fitting. An evolution from FE to AFE was observed. d, Schematic of the spin spiral configurations with in-plane (x-y plane) spin cycloid in monolayer NiI2, showing a periodicity of \\(7\\times 1\\) unit cells. e, Extreme case where the in-plane (x-y plane) cycloidal configuration tilts to x-z plane caused by interlayer exchange interactions, resulting in an out-of-plane ferroelectric polarization. f, Schematic of the spin spiral configurations with opposite \\(\\mathbf{q}\\) in trilayer NiI2, showing the coexistence of ferroelectric and antiferroelectric.",
+    "footnote": [],
+    "bbox": [
+      [
+        186,
+        78,
+        816,
+        675
+      ]
+    ],
+    "page_idx": 16
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 | Magnetic control of ferroelectricity in trilayer NiI2 device. a-c, The \\(P_r\\) extracted from the \\(P\\) - \\(E\\) hysteresis loop is plotted as a function of out-of-plane magnetic field at different frequencies. The error bars are standard deviations of \\(P_r\\) . d, The magnetic control ratio \\((P_r - P_{r0}) / P_{r0}\\) are frequency dependent, where \\(P_r\\) and \\(P_{r0}\\) is remanent polarization in a magnetic field and without magnetic field, respectively. e, The \\(I\\) - \\(E\\) curves at different magnetic field. The decrease in the current peak accompanied by an increase in the coercive field due to the increased magnetic field is unambiguously observed. f, g, Fitting by KAI model for different magnetic field at 10 K, giving the switching time \\(\\tau\\) . h, The \\((\\tau - \\tau_0) / \\tau_0\\) as a function of magnetic field at 10 K, indicating a degree of magnetic control of switching time, where \\(\\tau\\) and \\(\\tau_0\\) is switching time in a magnetic field and without magnetic field, respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        161,
+        81,
+        828,
+        505
+      ]
+    ],
+    "page_idx": 17
+  }
+]

preprint/preprint__00c089bc5362865e32d087a7de2c59c85939f78a3756c6991e0e05e515c9142f/preprint__00c089bc5362865e32d087a7de2c59c85939f78a3756c6991e0e05e515c9142f.mmd

@@ -0,0 +1,228 @@
+
+# Coexistence of ferroelectricity and antiferroelectricity in 2D van der Waals multiferroic  
+
+Bo Peng bo_peng@uestc.edu.cn  
+
+University of Electronic Science and Technology of China https://orcid.org/0000- 0001- 9411- 716X  
+
+Yangliu Wu 1450683589@qq.com  
+
+Haipeng Lu University of Electronic Science and Technology of China  
+
+Xiaocang Han Peking University  
+
+Chendi Yang Laboratory of Advanced Materials, Department of Materials Science and Shanghai Key Lab of Molecular Catalysis and Innovative Materials, Fudan University  
+
+Nanshu Liu Renmin University of China  
+
+Xiaoxu Zhao Peking University https://orcid.org/0000- 0001- 9746- 3770  
+
+Liang Qiao School of Physics, University of Electronic Science and Technology of China https://orcid.org/0000- 0003- 2400- 2986  
+
+Wei Ji Renmin University of China https://orcid.org/0000- 0001- 5249- 6624  
+
+Renchao Che Fudan University https://orcid.org/0000- 0002- 6583- 7114  
+
+Longjiang Deng University of Electronic Science and Technology of China https://orcid.org/0000- 0002- 8137- 6151  
+
+Article  
+
+Keywords:  
+
+Posted Date: April 16th, 2024
+
+<--- Page Split --->
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4229313/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on October 4th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 53019- 5.
+
+<--- Page Split --->
+
+# Coexistence of ferroelectricity and antiferroelectricity in 2D van der Waals multiferroic  
+
+Yangliu Wu \(^{1}\) , Haipeng Lu \(^{1}\) , Xiaocang Han \(^{2}\) , Chendi Yang \(^{3}\) , Nanshu Liu \(^{5}\) , Xiaoxu Zhao \(^{2}\) , Liang Qiao \(^{4}\) , Wei Ji \(^{5}\) , Renchao Che \(^{3}\) , Longjiang Deng \(^{1*}\) and Bo Peng \(^{1*}\)  
+
+\(^{1}\) National Engineering Research Center of Electromagnetic Radiation Control Materials, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China \(^{2}\) School of Materials Science and Engineering, Peking University, Beijing 100871, China \(^{3}\) Laboratory of Advanced Materials, Department of Materials Science, Collaborative Innovation Center of Chemistry for Energy Materials(iChEM), Fudan University, Shanghai 200433, China \(^{4}\) School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China \(^{5}\) Beijing Key Laboratory of Optoelectronic Functional Materials & Micro- Nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China \(^{*}\) To whom correspondence should be addressed. Email address: bo_peng@uestc.edu.cn; denglj@uestc.edu.cn  
+
+## Abstract  
+
+Multiferroic materials with a coexistence of ferroelectric and magnetic order have been intensively pursued to achieve the mutual control of electric and magnetic properties toward energy- efficient memory and logic devices. The breakthrough progress of 2D van der Waals magnet and ferroelectric encourages the exploration of low dimensional multiferroics, which holds the promise to understand inscrutable magnetoelectric coupling and invent advanced spintronic devices. However, confirming ferroelectricity with optical techniques is challenging on 2D materials, particularly in conjunction with antiferromagnetic orders in a single- layer multiferroic. The prerequisite of ferroelectric is the electrically switchable spontaneous electric polarizations, which must be proven through reliable and direct electrical measurements. Here we report the discovery of 2D vdW multiferroic with out- of- plane ferroelectric polarization in trilayer NiI₂ device, as revealed by scanning reflective magnetic circular dichroism microscopy and ferroelectric hysteresis loop. The evolutions of between ferroelectric and antiferroelectric phase have been unambiguously observed. Moreover, the magnetoelectric interaction is directly probed by external electromagnetic field control of the multiferroic domains switching. This work opens up opportunities for exploring new multiferroic orders and multiferroic physics at the limit of single or few atomic layers, and for creating advanced magnetoelectronic devices.
+
+<--- Page Split --->
+
+Multiferroic materials with a coexistence of ferroelectric and magnetic orders has been diligently sought after for a long time to achieve the mutual control of electric and magnetic properties toward the energy- efficient memory and logic devices \(^{1 - 3}\) . But the two contrasting order parameters tend to be mutually exclusive in a single material \(^{4}\) . Nondisplacive mechanisms introduce a paradigm for constructing multiferroics beyond the traditional limits of mutual obstruction of the ferroelectric and magnetic orders \(^{5,6}\) . To date, the type I multiferroic BiFeO \(_3\) is the only known room- temperature single- phase multiferroic material. Alternatively, the helical magnetic orders break the spatial inversion symmetry and simultaneously lead to electric orders \(^{7,8}\) , giving rise to type- II multiferroics. The quest for a new single- phase multiferroic remains an open challenge.  
+
+The emergence of 2D vdW magnets and ferroelectrics has opened new avenues for exploring low- dimensional physics on magnetoelectric coupling \(^{9,10}\) . Diverse isolated vdW ferromagnets \(^{11 - 13}\) and ferroelectrics \(^{14,15}\) have enabled tantalizing opportunities to create 2D vdW spintronic devices with unprecedented performances at the limit of single or few atomic layers. Few of bulk crystals of transition- metal dihalides with a trigonal layered structure have been shown that the helical spin textures break inversion symmetries and induce an orthogonal ferroelectric polarization \(^{16,17}\) , but and definitive multiferroicity remains elusive at the limit of few atomic layers.  
+
+A recent work shows the possibility of discovery of type- II monolayer \(\mathrm{NiI_2}\) multiferroics using the optical measurements of second- harmonic- generation (SHG) and linear dichroism (LD) \(^{18}\) . Our work has pointed that all- optical characterizations are not sufficient to make a judgement of a few- and single- layer multiferroic at the presence of non- collinear and antiferromagnetic orders \(^{19}\) . The observed SHG and LD signals in few- layer \(\mathrm{NiI_2}\) originate from the magnetic- order- induced breaking of spatial- inversion \(^{19,20}\) . The prerequisite of ferroelectric polarization is the non- vanishing spontaneous electric polarizations, which must be proven through reliable and direct electrical measurements, such as polarization- and current- electric field (P- E and I- E) hysteresis loops. To date, 2D vdW multiferroic has not been directly uncovered at the limit of few layers. Here, we report fascinating vdW multiferroic with coexistence of ferroelectricity and antiferroelectricity in few layer \(\mathrm{NiI_2}\) based on magneto- optical- electric joint- measurements. In this 2D vdW multiferroics, an unprecedented magnetic control of switching dynamics of ferroelectric domain has been observed.  
+
+## Non-collinear antiferromagnetism in trilayer \(\mathrm{NiI_2}\)  
+
+Due to the high reactivity of \(\mathrm{NiI_2}\) flakes, \(\mathrm{NiI_2}\) exfoliation and encapsulation by graphene and hexagonal boron nitride (hBN) flakes were carried out in a glove box (Fig. 1a and Supplementary Fig. 1). \(\mathrm{NiI_2}\) crystal shows rhombohedral structure with a repeating stack of three (I- Ni- I) layers, where Ni and I ions form a triangular lattice in each layer (Fig. 1b). The rhombohedral stacking has been atomically identified (Fig. 1c). The atom
+
+<--- Page Split --->
+
+arrangements of rhombohedral phase demonstrate signature hexagon- shaped periodic bright spots with equal contrast, validating the overlapping stack of I and Ni atoms along the \(c\) axis. The ADF- STEM and fast Fourier transform (FFT) show an interplanar spacing of \(1.9 \mathring{\mathrm{A}}\) , consistent with the (110) lattice plane of rhombohedral \(\mathrm{NiI}_2\) crystal. Circularly polarized Raman spectra in the parallel \((\sigma + / \sigma +\) and \(\sigma - / \sigma -\) ) configuration show only two distinct peaks in the \(\mathrm{NiI}_2\) device (Fig. 1d). The peak at \(\sim 124.7 \mathrm{cm}^{- 1}\) is assigned to the \(\mathrm{A_g}\) phonon modes \(^{22}\) , and this polarization behavior is consistent with Raman tensor analysis for the rhombohedral structure of \(\mathrm{NiI}_2^{23}\) . The Raman feature at \(\sim 20 \mathrm{cm}^{- 1}\) is assigned to the interlayer shear mode (SM), which suggests that the \(\mathrm{NiI}_2\) is trilayer \(^{20}\) .  
+
+For optimal optical response and sensitivity to probe the magnetic properties, the photon energy should be chosen near the absorption edge \(^{11,24}\) . Therefore, we first studied white- light magnetic circular dichroism (MCD) spectra of a trilayer \(\mathrm{NiI}_2\) device as a function of magnetic field perpendicular to the sample plane at \(10 \mathrm{K}\) (see Methods for details) \(^{25}\) . There is a strong peak near \(2.3 \mathrm{eV}\) along with two weak features around \(1.85 \mathrm{eV}\) and \(1.6 \mathrm{eV}\) (Fig. 1e). By means of ligand- field theory, the peaks are attributed to the absorption transitions of \(p\) - \(d\) exciton states \(^{26}\) . A pair of opposite MCD peaks with magnetic field manifestly appears at \(2.3 \mathrm{eV}\) , suggesting strong magneto- optical resonance. When the magnetic field is switched, MCD features is consistently reversed, and zero remanent MCD signal at \(\sim 2.3 \mathrm{eV}\) is distinctly observed at \(0 \mathrm{T}\) , indicating antiferromagnetic orders at \(10 \mathrm{K}\) .  
+
+To further validate the magnetic order, the scanning RMCD microscope was used to image and measure the magnetic domains of the as- exfoliated trilayer \(\mathrm{NiI}_2\) . The polar RMCD imaging is a reliable and powerful tool to unveil the 2D magnetism in the micro scale, and the RMCD intensity is proportional to the out- of- plane magnetization \(^{24}\) . All magneto- optical measurements were carried out using a \(2.33 \mathrm{eV}\) laser with optimal detection sensitivity (see Methods for details). Figure 2a shows RMCD maps of a trilayer \(\mathrm{NiI}_2\) sweeping between - 0.75 T and +0.75 T at \(10 \mathrm{K}\) . Remarkably, many micrometer- sized bimeron- like domains are observed in trilayer and another few- layer \(\mathrm{NiI}_2\) across the entire range of sweeping magnetic field \(^{27}\) . The spin- up and spin- down domains exist in pairs (Fig. 2a and Supplementary Fig. 2). One typical bimeron- like domains in trilayer \(\mathrm{NiI}_2\) at \(0 \mathrm{T}\) and \(10 \mathrm{K}\) are shown in Fig. 2b. The RMCD signals in each bimeron- like domain display opposite sign and nearly equal intensities. The magnetic moments point upwards or downwards in the core region and gradually decrease away from the core, and approaches zero near the perimeter (Fig. 2c). This magnetic moment distribution possibly indicates a pair of topological spin meron and antimeron with opposite chirality in a cycloid ground state \(^{28,29}\) . The bimeron- like magnetization textures remain robust in all magnetic field, indicating the bimeron- like domains are robust. The high stability of the bimeron- like magnetic domains probably
+
+<--- Page Split --->
+
+originate from the topological protection, which also contributes to the preservation of magnetization even if upon a reversal magnetic field of 0.75 T. The formation of bimeron- like magnetic domains may be related to the localized stress at the interface. But further deep studies must be done to reveal the exact physical mechanism.  
+
+Fig. 2d shows the RMCD loops of the trilayer \(\mathrm{NiI}_2\) sweeping between \(+3\mathrm{T}\) and \(- 3\mathrm{T}\) at \(10\mathrm{K}\) . The RMCD loops show a highly nonlinear behavior with magnetic field and plateau behaviors for the out- of- plane magnetization. The RMCD intensity near \(0\mathrm{T}\) is suppressed and approaches zero, suggesting the vanishing remnant magnetization, which indicates a compensation of the out- of- plane magnetization and non- collinear AFM orders in the trilayer \(\mathrm{NiI}_2^{30}\) . And the gradual increases of the RMCD signal are observed with increasing magnetic field between \(\pm 1.2\) and \(\pm 2.6\mathrm{T}\) , suggesting a spin- flop process. The spin- flop behaviors of the magnetization curve imply that the interlayer antiferromagnetic coupling of the non- collinear spins is complicated. Similar magnetic hysteresis loops have been demonstrated in another few- layer \(\mathrm{NiI}_2\) , which show definite non- collinear AFM orders in the few- layer \(\mathrm{NiI}_2\) (Supplementary Fig. 2b).  
+
+## Ferroelectricity in trilayer \(\mathrm{NiI}_2\) device  
+
+To determine ferroelectricity in few- layer \(\mathrm{NiI}_2\) device, we performed the frequency- dependent measurement of electric polarization via \(I\) - \(E\) and \(P\) - \(E\) hysteresis loops, which allows an accurate estimation of the electric polarization. We fabricated two heterostructure devices of graphene/hBN/ \(\mathrm{NiI}_2\) /graphene/hBN (Fig. 1a and Supplementary Fig. 1). The hBN flake was used as an excellent insulating layer to prevent large leakage current and guarantee the detections of ferroelectric (FE) features \(^{31,32}\) (Supplementary Fig. 3). The hBN insulator shows a linear \(P\) - \(E\) behavior and a rectangle- shaped \(I\) - \(E\) loops (Supplementary Fig. 4), indicating excellent insulativity for ferroelectric hysteresis measurements (see Methods for details) \(^{33,34}\) . The frequency- dependent \(I\) - \(E\) and \(P\) - \(E\) loops at \(10\mathrm{K}\) are shown in Fig. 3, and the forward and backward scans of the electric polarization as a function of electric field show characteristic ferroelectric \(I\) - \(E\) and \(P\) - \(E\) hysteresis. Strikingly, a characteristic double- hysteresis loop of antiferroelectric (AFE) polarization emerges accompanied with decreasing remanent polarization \((P_r)\) . More importantly, a pair of opposite single peaks of switching current \((I)\) are observed when sweeping voltage at \(6.7\mathrm{Hz}\) , which is attribute to charge displacement and implies two stable states with inverse polarity (Fig. 3b and c). Whereas two pair of opposite bimodal peaks are observed when sweeping voltage at \(1.3\mathrm{Hz}\) , which is attribute to AFE- FE and FE- AFE transitions under electric field sweeping (Fig. 3c) \(^{35}\) . This suggests an evolution from FE to AFE polarization with frequency is observed \(^{36,37}\) , exhibiting the decisive evidence for coexistence of ferroelectric and antiferroelectric \(^{38,39}\) . This comprehensive frequency- dependent evolution behaviors also confirm the coexistence of FE and AFE in another a few layers
+
+<--- Page Split --->
+
+\(\mathrm{NiI}_2\) (Supplementary Fig. 5).  
+
+The type- II multiferroicity has been demonstrated in the bulk \(\mathrm{NiI}_2\) . However, the multiferroic identification for few- layer \(\mathrm{NiI}_2\) remains challenging and elusive. All- optical methods are unreliable to make a judgement of a few- and single- layer multiferroic at the presence of non- collinear and antiferromagnetic orders<sup>19</sup>. The bulk \(\mathrm{NiI}_2\) displays a helimagnetic state below critical temperature<sup>16,17</sup>. From symmetry considerations and a Ginzburg- Landau perspective<sup>40,41</sup>, the helimagnetic state allows for the emergence of a ferroelectric polarization associated to the form:  
+
+\[\mathbf{P} = \gamma \mathbf{e}\times \mathbf{q} \quad (1)\]  
+
+where \(\mathbf{P}\) is the electric polarization, \(\mathbf{e}\) is the spin rotation axis, \(\mathbf{q}\) is the spin propagation vector of the spin spiral, and \(\gamma\) is a scalar parameter dependence with spin- orbit coupling. For monolayer \(\mathrm{NiI}_2\) , the helimagnetic order can be modeled with a 7axa supercell and an in- plane (x- y plane) spin cycloid, and the spin propagation vector \(\mathbf{q}\) is displayed along the [210] direction (in lattice vector units)<sup>42</sup>, as shown in in Fig. 3d. Thus, the in- plane (x- y plane) spin cycloid induces the in- plane electric polarization along the [010] direction (Fig. 3d). Actually, theoretical calculations have determined that the \(\mathbf{q}\) - vector in multi- layer and bulk \(\mathrm{NiI}_2\) is a consequence of the competition between magnetic exchange interactions between magnetic atoms<sup>42,43</sup>. In particular, intralayer ferromagnetic first- neighbor, intralayer antiferromagnetic third neighbor, and interlayer antiferromagnetic second- neighbor magnetic exchange interactions are the most relevant. In the monolayer limit, there are no interlayer interactions, hence the \(\mathbf{q}\) - vector is in- plane and determined by the competition between intralayer exchange interactions. For a trilayer \(\mathrm{NiI}_2\) , the \(\mathbf{q}\) - vector is modulated not only by intralayer exchange interactions but also by interlayer exchange interactions. Assuming that interlayer exchange interactions cause the tilting out- of- plane cycloidal spin configuration from in- plane (x- y plane) configuration (Fig. 3d), the \(\mathbf{e}\) - vector is no longer parallel to the z- axis, leading to an out- of- plane ferroelectric polarization component. Figure 3e illustrates the extreme case where the in- plane (x- y plane) cycloidal configuration tilts to x- z plane, resulting in an out- of- plane ferroelectric polarization. This scenario suggests the observed out- of- plane ferroelectric polarization in the trilayer \(\mathrm{NiI}_2\) device, but the precise mechanism remains to be further studied in the future. In particular, equation (1) shows that two spin spiral configurations with \(\mathbf{q}_1 = \mathbf{q}\) and \(\mathbf{q}_2 = -\mathbf{q}\) will give rise to opposite electric polarizations \(\mathbf{P} = -\mathbf{P}\) . The first principles calculations in spin configuration with both \(\mathbf{q}\) and \(-\mathbf{q}\) are energetically equivalent, and therefore show same energies with and without spin- orbit coupling<sup>42</sup>. Thus, the emergence of opposite electric dipoles can be directly observed in the total electronic density of the system. The energy of spin cycloidal configurations with positive and negative \(\mathbf{q}\) - vectors (positive and negative ferroelectric polarization \(\mathbf{P}\) ) is degenerate, which approve the coexistence of ferroelectric and antiferroelectric (Fig. 3f), consistent with the observed
+
+<--- Page Split --->
+
+coexistence of ferroelectric and antiferroelectric in trilayer \(\mathrm{NiI_2}\) .  
+
+## Magnetic control of ferroelectricity  
+
+To reveal the magnetoelectric coupling effect, we studied the magnetic control of ferroelectric properties in the trilayer \(\mathrm{NiI_2}\) device, as shown in Fig. 4. The \(P_r\) extracted from the \(P\) - \(E\) hysteresis loop is plotted as a function of out- of- plane magnetic field at different frequencies (Fig. 4a- c). The magnetic field causes a decrease in residual polarization at different frequencies (Fig. 4a- c and Supplementary Fig. 6), and the magnetic control of \(P_r\) shows frequency dependence of applied electric field (Fig. 4d). The magnetic control ratio reaches to \(\sim 7\%\) by detuning the frequency (24.5 Hz) at 7 T, which is remarkable feature of multiferroic. To better understand the magnetic control behavior, we briefly discuss the possible mechanism that leads to the decrease in \(P_r\) caused by the magnetic field from a microscopic perspective. We only discuss ferroelectric polarization flops in the model of spiral magnets<sup>40</sup>. In zero fields spins rotate in the easy x- z plane, so that the spin rotation axis \(\mathbf{e}\) is parallel to the y axis, and for \(\mathbf{q} / / \mathbf{x}\) - y plane, \(\mathbf{P} / / \mathbf{z}\) (Supplementary Fig. 7a and 7b). However, magnetic field in the z direction favors the rotation of spins in the x- y plane (Supplementary Fig. 7c and 7d), so that the spin rotation axis \(\mathbf{e}\) is parallel to the z axis, in which case, \(\mathbf{P} / / \mathbf{x}\) - y plane<sup>40</sup>. In short, applying a magnetic field parallel to the z- axis causes the spin rotation plane to tilt from the x- z plane to the x- y plane, and the corresponding ferroelectric polarization flops from the out- of- plane direction to the in- plane direction. Therefore, an out- of- plane magnetic field leads to a decrease of ferroelectric polarization in the out- of- plane direction, which is consistent with the observed decrease in \(P_r\) with increasing magnetic field. Furthermore, the decrease in the current peak accompanied by an increase in the coercive electric field due to the increased magnetic field is unambiguously observed (Fig. 4e and Supplementary Fig. 8). This is because the out- of- plane magnetic field causes the spin rotation plane to tilt from the x- z plane to the x- y plane, and the corresponding easy axis of ferroelectric polarization flops from the out- of- plane direction to the in- plane direction. The shifts of current peaks induced by ferroelectric switching vary with the magnetic field, but the background current remains constant, excluding the magnetoresistance effects (Fig. 4e and Supplementary Fig. 8). Finally, the switching time of ferroelectric domain under different magnetic fields at 10 K is calculated by KAI model<sup>44</sup> (Fig. 4f and 4g; Part A and B). The switching time \(\tau\) increase as magnetic field increase, which signifies an even symmetry with magnetic field (Fig. 4h), consistent with the above mechanisms. At 10 K, the switching time \(\tau\) , leading to a maximum enhancement of switching time by 20% (-7 T). This observation of robust control of ferroelectric properties by magnetic field, pointing to the potential use of few- layer \(\mathrm{NiI_2}\) as a research platform for studying the magneto- electric coupling physics in the two- dimensional limit and for fabricating advanced nano-
+
+<--- Page Split --->
+
+magnetoelectric devices.  
+
+In summary, we report a 2D vdW single- phase multiferroic \(\mathrm{NiI_2}\) few- layer crystal. We observed strong evidences for the coexistence of ferroelectric and non- collinear antiferromagnetism order via RMCD, \(P\) - \(E\) and \(I\) - \(E\) hysteresis loop. hysteresis loop. We achieve unprecedented magnetic control of ferroelectric properties in the \(\mathrm{NiI_2}\) trilayer. We envision that the 2D vdW single- phase multiferroic \(\mathrm{NiI_2}\) will provide numerous opportunities for exploring fundamental low- dimensional physics, and will introduce a paradigm shift for engineering new ultra- compact magnetoelectric devices.  
+
+## Methods  
+
+## Sample fabrication  
+
+\(\mathrm{NiI_2}\) flakes were mechanically exfoliated from bulk crystals via PDMS films in a glovebox, which were synthesized by chemical vapor transport method from elemental precursors with molar ratio \(\mathrm{Ni:I} = 1:2\) . All exfoliated hBN, \(\mathrm{NiI_2}\) and graphene flakes were transferred onto pre- patterned Au electrodes on \(\mathrm{SiO_2 / Si}\) substrates one by one to create heterostructure in glovebox, which were further in- situ loaded into a microscopy optical cryostat for magneto- optical- electric joint- measurement. The whole process of \(\mathrm{NiI_2}\) sample fabrications and magneto- optical- electric measurements were kept out of atmosphere.  
+
+## Magneto-optical-electric joint-measurement  
+
+The polar RMCD, white- light MCD, Raman measurements and ferroelectric \(P\) - \(E\) and \(I\) - \(E\) measurements were performed on a powerful magneto- optical- electric joint- measurement scanning imaging system (MOEJSI) \(^{19}\) , with a spatial resolution reaching diffraction limit. The MOEJSI system was built based on a Witec Alpha 300R Plus low- wavenumber confocal Raman microscope, integrated with a closed cycle superconducting magnet (7 T) with a room temperature bore and a closed cycle cryogen- free microscopy optical cryostat (10 K) with a specially designed snout sample mount and electronic transport measurement assemblies.  
+
+The Raman signals were recorded by the Witec Alpha 300R Plus low- wavenumber confocal Raman microscope system, including a spectrometer (150, 600 and 1800/mm) and a TE- cooling Andor CCD. A 532 nm laser of \(\sim 0.2 \mathrm{mW}\) is parallel to the X- axis \((0^{\circ})\) and focused onto samples by a long working distance \(50 \times\) objective \((\mathrm{NA} = 0.55, \mathrm{Zeiss})\) after passing through a quarter- wave plate \((1 / 4 \lambda)\) . The circular polarization resolved Raman signals passed through the same \(1 / 4 \lambda\) waveplate and a linear polarizer, obtained by the spectrometer \((1800 / \mathrm{mm})\) and the CCD.  
+
+For white- light MCD measurements, white light with Kohler illumination from Witec Alpha 300R Plus microscope was linearly polarized at 0o by a visible wire grid
+
+<--- Page Split --->
+
+polarizer, passed through an achromatic quarter- wave \((1 / 4\lambda)\) plate and focused onto samples by a long working distance \(50\times\) objective (Zeiss, \(\mathrm{NA} = 0.55\) ). The right- handed and left- handed circularly polarized white light was obtained by rotating \(1 / 4\lambda\) waveplate at \(+45^{\circ}\) and \(- 45^{\circ}\) . The white- light spectra were recorded by the Witec Alpha 300R Plus confocal Raman microscope system (spectrometer, \(150\mathrm{mm}\) ). The absorption spectra of right- handed and left- handed circularly polarized light in different magnetic field can be obtained as the previous work \(^{25}\) , giving corresponding MCD spectra.  
+
+For polar RMCD measurements, a free- space \(532\mathrm{nm}\) laser \((2.33\mathrm{eV})\) of \(\sim 2\mu \mathrm{W}\) modulated by photoelastic modulator (PEM, \(50\mathrm{KHz}\) ) was reflected by a non- polarizing beamsplitter cube \(\mathrm{(R / T = 30 / 70)}\) and then directly focused onto samples by a long working distance \(50\times\) objective \(\mathrm{(NA = 0.55}\) , Zeiss), with a diffraction limit spatial resolution of \(\sim 590\mathrm{nm}\) . The reflected beam which was collected by the same objective passed through the same non- polarizing beamsplitter cube and was detected by a photomultiplier (PMT), which was coupled with lock- in amplifier, Witec scanning imaging system, superconducting magnet, voltage source meter and ferroelectric tester. Ferroelectric \(P - E\) and \(I - E\) hysteresis loop of a \(\mathrm{NiI}_2\) device of \(\mathrm{Gr / hBN / NiI_2 / Gr}\) were measured by classical ferroelectric measurements and directly recorded by ferroelectric tester (Precision Premier II: Hysteresis measurement), which were contacted with the top and bottom graphene electrodes by patterned Au electrodes (Fig. 1a) through the electronic assemblies of the microscopy optical cryostat. The mechanism of ferroelectric measurement has been given by previous work \(^{45}\) . The detected signals include two components: a ferroelectric term of \(\mathrm{NiI}_2\) (2PrA) and a linear non- ferroelectric term of hBN insulator \((\sigma \mathrm{EAt})\) , \(\mathrm{Q} = \mathrm{QNiI} + \mathrm{QBN} = 2\mathrm{PrA} + \sigma \mathrm{EAt}\) . If only hBN insulator, a linear P- E loop take place, consistent with our experimental results of hBN flake (Supplementary Fig. 4). The linear hBN background have no effect on the ferroelectric features, and hBN flakes as excellent insulator suppress and overcome the leakage current, which for guarantee the detections of \(\mathrm{NiI}_2\) ferroelectric features \(^{31 - 34}\) .  
+
+## STEM Imaging, Processing, and Simulation  
+
+Atomic- resolution ADF- STEM imaging was performed on an aberration- corrected JEOL ARM 200F microscope equipped with a cold field- emission gun operating at 80 kV. The convergence semiangle of the probe was around 30 mrad. Image simulations were performed with the Prismatic package, assuming an aberration- free probe with a probe size of approximately \(1\mathrm{\AA}\) . The convergence semiangle and accelerating voltage were in line with the experiments. The collection angle for ADF imaging was between 81 and 228 mrad. ADF- STEM images were filtered by Gaussian filters, and the positions of atomic columns were located by finding the local maxima of the filtered series.
+
+<--- Page Split --->
+
+## Data availability  
+
+The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.  
+
+## References  
+
+1 Fiebig, M., Lottermoser, T., Meier, D. & Trassin, M. The evolution of multiferroics. Nat. Rev. Mater. 1, 16046, (2016).  2 Chu, Y.- H. et al. Electric- field control of local ferromagnetism using a magnetoelectric multiferroic. Nat. Mater. 7, 478- 482, (2008).  3 Ponet, L. et al. Topologically protected magnetoelectric switching in a multiferroic. Nature 607, 81- 85, (2022).  4 Cheong, S.- W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13- 20, (2007).  5 Wang, J. et al. Epitaxial BiFeO₃ multiferroic thin film heterostructures. Science 299, 1719- 1722, (2003).  6 Guo, R. et al. Continuously controllable photoconductance in freestanding BiFeO₃ by the macroscopic flexoelectric effect. Nat. Commun. 11, 2571, (2020).  7 Kimura, T. et al. Magnetic control of ferroelectric polarization. Nature 426, 55- 58, (2003).  8 Hur, N. et al. Electric polarization reversal and memory in a multiferroic material induced by magnetic fields. Nature 429, 392- 395, (2004).  9 Rogée, L. et al. Ferroelectricity in untwisted heterobilayers of transition metal dichalcogenides. Science 376, 973- 978, (2022).  10 Yang, Q. et al. Ferroelectricity in layered bismuth oxide down to 1 nanometer. Science 379, 1218- 1224, (2023).  11 Huang, B. et al. Layer- dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270- 273, (2017).  12 Gong, C. et al. Discovery of intrinsic ferromagnetism in two- dimensional van der Waals crystals. Nature 546, 265- 269, (2017).  13 Deng, Y. et al. Gate- tunable room- temperature ferromagnetism in two- dimensional Fe₃GeTe₂. Nature 563, 94- 99, (2018).  14 Yuan, S. et al. Room- temperature ferroelectricity in MoTe₂ down to the atomic monolayer limit. Nat. Commun. 10, 1775, (2019).  15 Liu, F. et al. Room- temperature ferroelectricity in CuInP₂S₆ ultrathin flakes. Nat. Commun. 7, 12357, (2016).  16 Kurumaji, T. et al. Magnetoelectric responses induced by domain rearrangement and spin structural change in triangular- lattice helimagnets NiI₂ and CoI₂. Phys. Rev. B
+
+<--- Page Split --->
+
+87, 014429, (2013).17 Zhao, L. et al. \(\mathrm{CuBr_2}\) – a new multiferroic material with high critical temperature. Adv. Mater. 24, 2469- 2473, (2012).18 Song, Q. et al. Evidence for a single-layer van der Waals multiferroic. Nature 602, 601- 605, (2022).19 Jiang, Y. et al. Dilemma in optical identification of single-layer multiferroics. Nature 619, E40- E43, (2023).20 Wu, S. et al. Layer thickness crossover of type- II multiferroic magnetism in \(\mathrm{NiI_2}\) . arXiv:2307.10686 (2023).21 Sun, Z. et al. Giant nonreciprocal second- harmonic generation from antiferromagnetic bilayer \(\mathrm{CrI_3}\) . Nature 572, 497- 501, (2019).22 Liu, H. et al. Vapor deposition of magnetic van der Waals \(\mathrm{NiI_2}\) crystals. ACS Nano 14, 10544- 10551, (2020).23 Guo, K. et al. Layer dependence of stacking order in nonencapsulated few- layer \(\mathrm{CrI_3}\) . Sci. China. Mater. 63, 413- 420, (2020).24 Wang, X. et al. Light- induced ferromagnetism in moiré superlattices. Nature 604, 468- 473, (2022).25 Mak, K. F. et al. Measurement of the optical conductivity of graphene. Phys. Rev. Lett. 101, 196405 (2008).26 Pollini, I., Thomas, J. & Lenselink, A. Optical properties of layered transition- metal iodides. Phys. Rev. B 30, 2140- 2148, (1984).27 Wu, X. et al. Topology- induced chiral photon emission from a large- scale meron lattice. Nat. Electron. 6, 516- 524, (2023).28 Wintz, S. et al. Topology and origin of effective spin meron pairs in ferromagnetic multilayer elements. Phys. Rev. Lett. 110, 177201, (2013).29 Xu, C. et al. Electric- field switching of magnetic topological charge in type- I multiferroics. Phys. Rev. Lett. 125, 037203, (2020).30 Xie, H. et al. Evidence of non- collinear spin texture in magnetic moiré superlattices. Nature Physics 19, 1150- 1155, (2023).31 Knobloch, T. et al. The performance limits of hexagonal boron nitride as an insulator for scaled CMOS devices based on two- dimensional materials. Nat. Electron. 4, 98- 108, (2021).32 Yang, T. H. et al. Ferroelectric transistors based on shear- transformation- mediated rhombohedral- stacked molybdenum disulfide. Nat. Electron. 7, 29- 38 (2024).33 Park, J. Y. et al. Revival of Ferroelectric Memories Based on Emerging Fluorite- Structured Ferroelectrics. Adv. Mater. 35, 2204904, (2023).34 Kim, Y., Min, K. K., Yu, J., Kwon, D. & Park, B.- G. Lamination method for improved polarization- leakage current relation in \(\mathrm{HfO_2}\) - based metal/ferroelectric/insulator/semiconductor structure. Semicond. Sci. Technol. 37,
+
+<--- Page Split --->
+
+045001, (2022).  
+
+35 Wu, Z. et al. Discovery of an above- room- temperature antiferroelectric in twodimensional hybrid perovskite. J. Am. Chem. Soc. 141, 3812- 3816, (2019).  
+
+36 Park, M. H. et al. Ferroelectricity and antiferroelectricity of doped thin \(\mathrm{HfO_2}\) - based films. Adv. Mater. 27, 1811- 1831, (2015).  
+
+37 Müller, J. et al. Ferroelectricity in Simple Binary \(\mathrm{ZrO_2}\) and \(\mathrm{HfO_2}\) . Nano Lett. 12, 4318- 4323, (2012).  
+
+38 Ko, K. et al. Operando electron microscopy investigation of polar domain dynamics in twisted van der Waals homobilayers. Nat. Mater. 22, 992- 998 (2023).  
+
+39 Xu, B., Paillard, C., Dkhil, B. & Bellaiche, L. Pinched hysteresis loop in defect- free ferroelectric materials. Phys. Rev. B 94, 140101 (2016).  
+
+40 Mostovoy, M. Ferroelectricity in spiral magnets. Phys. Rev. Lett. 96, 067601, (2006).  
+
+41 Hohenberg, P. C. et al. An introduction to the Ginzburg- Landau theory of phase transitions and nonequilibrium patterns Phys. Rep. 572, 1- 42, (2015).  
+
+42 Fumega, A. O. et al. Microscopic origin of multiferroic order in monolayer \(\mathrm{NiI_2}\) . 2D Mater. 9, 025010, (2022).  
+
+43 Riedl, K. et al. Microscopic origin of magnetism in monolayer \(3d\) transition metal dihalides. Phys. Rev. B 106, 035156, (2022).  
+
+44 Zhao, D., Katsouras, I., Asadi, K., Blom, P. W. M. & de Leeuw, D. M. Switching dynamics in ferroelectric P(VDF- TrFE) thin films. Phys. Rev. B 92, 214115, (2015).  
+
+45 Scott, J. F. et al. Ferroelectrics go bananas. J. Phys.: Condens. Matter 20, 021001, (2008).  
+
+46 Golla, D. et al. Optical thickness determination of hexagonal boron nitride flakes. Appl. Phys. Lett. 102, 161906, (2013).  
+
+## Acknowledgments  
+
+B.P. and L.D. acknowledge support from National Science Foundation of China (52021001). B.P. acknowledge support from National Science Foundation of China (62250073). R.C.C. acknowledge support from National Science Foundation of China (52231007). H.L. acknowledge support from National Science Foundation of China (51972046). L.D. acknowledge support from Sichuan Provincial Science and Technology Department (Grant No. 99203070). L.D. acknowledge support from Sichuan Provincial Science and Technology Department (Grant No. 9920 3070). L.Q. acknowledge support from National Science Foundation of China (520720591 and 11774044). J.W. thanks the National Natural Science Foundation of China (Grant No. 11974422), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB30000000).
+
+<--- Page Split --->
+
+## Author contributions  
+
+B.P conceived the project. Y.W. prepared the samples and performed the magneto- optical- electric joint- measurements and Raman measurements assisted by B.P., and performed the ferroelectric measurements assisted by L.Q., and analyzed and interpreted the results assisted by H.L., N. L., W.J., L.D. and B.P.. C. Y, R.C, X.X. and X.H. performed the STEM measurements. Y.W. and B.P. wrote the paper with input from all authors. All authors discussed the results.  
+
+## Competing interests  
+
+The authors declare no competing interests.  
+
+## Additional information  
+
+Supplementary information is available for this paper at xxx (will be provided).  
+
+Correspondence and requests for materials should be addressed to B.P.  
+
+Reprints and permission information is available online at http://www.nature.com/reprints.  
+
+Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 | Crystal structure, MCD measurements of trilayer \(\mathrm{NiI}_2\) at room temperature. a, Schematic of trilayer \(\mathrm{NiI}_2\) sandwiched between graphene and hBN. b, View of the in-plane and out-of-plane atomic lattice. The magnetic \(\mathrm{Ni}^{2 + }\) ions are surrounded by the octahedron of \(\mathrm{I}^{-}\) ions, and three \(\mathrm{NiI}_2\) layers as a repeating unit stack in a staggered fashion along the c axis. c, Atomic-resolution ADF-STEM image showing signature hexagonal patterns of rhombohedral stacking in few-layer \(\mathrm{NiI}_2\) crystals. The inset shows the corresponding FFT image. d, Circular polarization resolved Raman spectra of a trilayer \(\mathrm{NiI}_2\) device (Fig. 1a) at room temperature, excited by \(532\mathrm{nm}\) laser. “SM” indicates the interlayer shear mode of trilayer \(\mathrm{NiI}_2\) . e, The MCD spectra of trilayer \(\mathrm{NiI}_2\) at \(+3\mathrm{T}\) , \(0\mathrm{T}\) and -3T. MCD signals are sensitive to spin electronic transitions and magnetic moments in the electronic states. The MCD features are spin-sign dependent and reverse as magnetic field switch. The zero remanent MCD signals at \(\sim 2.3\mathrm{eV}\) at \(0\mathrm{T}\) suggest antiferromagnetic orders. </center>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 | Non-collinear antiferromagnetism in trilayer NiI₂ device. a, Polar RMCD maps upon a 2.33 eV laser with diffraction-limited spatial resolution (see Methods), collected at room temperature and selected magnetic field. b, Schematic of the spin textures of bimerons-like domains and corresponding zoom-in RMCD images (white dashed-line box in Fig. 2a). c, The polar RMCD signals along with the line sections of RMCD map (b). d, The RMCD curves sweeping between \(+3\mathrm{T}\) and \(-3\mathrm{T}\) at \(10\mathrm{K}\) , suggesting a non-collinear antiferromagnetism. </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 | Existence of ferroelectric and anti-ferroelectric orders in trilayer NiI2 device. a, b, \(P - E\) and \(I - E\) loops at various frequencies from device 1 (D1). c, Corresponding \(I - E\) loops from Fig. 3b subtracted the current background. Two pairs of current peaks (FE-AFE and AFE-FE switching peaks) were obtained by Lorentz fitting. An evolution from FE to AFE was observed. d, Schematic of the spin spiral configurations with in-plane (x-y plane) spin cycloid in monolayer NiI2, showing a periodicity of \(7\times 1\) unit cells. e, Extreme case where the in-plane (x-y plane) cycloidal configuration tilts to x-z plane caused by interlayer exchange interactions, resulting in an out-of-plane ferroelectric polarization. f, Schematic of the spin spiral configurations with opposite \(\mathbf{q}\) in trilayer NiI2, showing the coexistence of ferroelectric and antiferroelectric. </center>
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 | Magnetic control of ferroelectricity in trilayer NiI2 device. a-c, The \(P_r\) extracted from the \(P\) - \(E\) hysteresis loop is plotted as a function of out-of-plane magnetic field at different frequencies. The error bars are standard deviations of \(P_r\) . d, The magnetic control ratio \((P_r - P_{r0}) / P_{r0}\) are frequency dependent, where \(P_r\) and \(P_{r0}\) is remanent polarization in a magnetic field and without magnetic field, respectively. e, The \(I\) - \(E\) curves at different magnetic field. The decrease in the current peak accompanied by an increase in the coercive field due to the increased magnetic field is unambiguously observed. f, g, Fitting by KAI model for different magnetic field at 10 K, giving the switching time \(\tau\) . h, The \((\tau - \tau_0) / \tau_0\) as a function of magnetic field at 10 K, indicating a degree of magnetic control of switching time, where \(\tau\) and \(\tau_0\) is switching time in a magnetic field and without magnetic field, respectively. </center>
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- Sl.pdf
+
+<--- Page Split --->

preprint/preprint__00c089bc5362865e32d087a7de2c59c85939f78a3756c6991e0e05e515c9142f/preprint__00c089bc5362865e32d087a7de2c59c85939f78a3756c6991e0e05e515c9142f_det.mmd

@@ -0,0 +1,302 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 925, 175]]<|/det|>
+# Coexistence of ferroelectricity and antiferroelectricity in 2D van der Waals multiferroic  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 280, 240]]<|/det|>
+Bo Peng bo_peng@uestc.edu.cn  
+
+<|ref|>text<|/ref|><|det|>[[44, 268, 912, 288]]<|/det|>
+University of Electronic Science and Technology of China https://orcid.org/0000- 0001- 9411- 716X  
+
+<|ref|>text<|/ref|><|det|>[[44, 293, 252, 334]]<|/det|>
+Yangliu Wu 1450683589@qq.com  
+
+<|ref|>text<|/ref|><|det|>[[44, 340, 551, 382]]<|/det|>
+Haipeng Lu University of Electronic Science and Technology of China  
+
+<|ref|>text<|/ref|><|det|>[[44, 387, 208, 427]]<|/det|>
+Xiaocang Han Peking University  
+
+<|ref|>text<|/ref|><|det|>[[44, 432, 868, 497]]<|/det|>
+Chendi Yang Laboratory of Advanced Materials, Department of Materials Science and Shanghai Key Lab of Molecular Catalysis and Innovative Materials, Fudan University  
+
+<|ref|>text<|/ref|><|det|>[[44, 502, 293, 542]]<|/det|>
+Nanshu Liu Renmin University of China  
+
+<|ref|>text<|/ref|><|det|>[[44, 548, 567, 589]]<|/det|>
+Xiaoxu Zhao Peking University https://orcid.org/0000- 0001- 9746- 3770  
+
+<|ref|>text<|/ref|><|det|>[[44, 594, 931, 657]]<|/det|>
+Liang Qiao School of Physics, University of Electronic Science and Technology of China https://orcid.org/0000- 0003- 2400- 2986  
+
+<|ref|>text<|/ref|><|det|>[[44, 664, 652, 705]]<|/det|>
+Wei Ji Renmin University of China https://orcid.org/0000- 0001- 5249- 6624  
+
+<|ref|>text<|/ref|><|det|>[[44, 710, 562, 751]]<|/det|>
+Renchao Che Fudan University https://orcid.org/0000- 0002- 6583- 7114  
+
+<|ref|>text<|/ref|><|det|>[[44, 756, 908, 799]]<|/det|>
+Longjiang Deng University of Electronic Science and Technology of China https://orcid.org/0000- 0002- 8137- 6151  
+
+<|ref|>text<|/ref|><|det|>[[44, 838, 103, 856]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 876, 135, 894]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 914, 300, 933]]<|/det|>
+Posted Date: April 16th, 2024
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 475, 64]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4229313/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 82, 916, 125]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 143, 535, 163]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 199, 932, 242]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on October 4th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 53019- 5.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[148, 92, 848, 150]]<|/det|>
+# Coexistence of ferroelectricity and antiferroelectricity in 2D van der Waals multiferroic  
+
+<|ref|>text<|/ref|><|det|>[[148, 158, 848, 200]]<|/det|>
+Yangliu Wu \(^{1}\) , Haipeng Lu \(^{1}\) , Xiaocang Han \(^{2}\) , Chendi Yang \(^{3}\) , Nanshu Liu \(^{5}\) , Xiaoxu Zhao \(^{2}\) , Liang Qiao \(^{4}\) , Wei Ji \(^{5}\) , Renchao Che \(^{3}\) , Longjiang Deng \(^{1*}\) and Bo Peng \(^{1*}\)  
+
+<|ref|>text<|/ref|><|det|>[[147, 225, 852, 456]]<|/det|>
+\(^{1}\) National Engineering Research Center of Electromagnetic Radiation Control Materials, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China \(^{2}\) School of Materials Science and Engineering, Peking University, Beijing 100871, China \(^{3}\) Laboratory of Advanced Materials, Department of Materials Science, Collaborative Innovation Center of Chemistry for Energy Materials(iChEM), Fudan University, Shanghai 200433, China \(^{4}\) School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China \(^{5}\) Beijing Key Laboratory of Optoelectronic Functional Materials & Micro- Nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China \(^{*}\) To whom correspondence should be addressed. Email address: bo_peng@uestc.edu.cn; denglj@uestc.edu.cn  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 467, 240, 485]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[147, 496, 851, 899]]<|/det|>
+Multiferroic materials with a coexistence of ferroelectric and magnetic order have been intensively pursued to achieve the mutual control of electric and magnetic properties toward energy- efficient memory and logic devices. The breakthrough progress of 2D van der Waals magnet and ferroelectric encourages the exploration of low dimensional multiferroics, which holds the promise to understand inscrutable magnetoelectric coupling and invent advanced spintronic devices. However, confirming ferroelectricity with optical techniques is challenging on 2D materials, particularly in conjunction with antiferromagnetic orders in a single- layer multiferroic. The prerequisite of ferroelectric is the electrically switchable spontaneous electric polarizations, which must be proven through reliable and direct electrical measurements. Here we report the discovery of 2D vdW multiferroic with out- of- plane ferroelectric polarization in trilayer NiI₂ device, as revealed by scanning reflective magnetic circular dichroism microscopy and ferroelectric hysteresis loop. The evolutions of between ferroelectric and antiferroelectric phase have been unambiguously observed. Moreover, the magnetoelectric interaction is directly probed by external electromagnetic field control of the multiferroic domains switching. This work opens up opportunities for exploring new multiferroic orders and multiferroic physics at the limit of single or few atomic layers, and for creating advanced magnetoelectronic devices.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 85, 851, 299]]<|/det|>
+Multiferroic materials with a coexistence of ferroelectric and magnetic orders has been diligently sought after for a long time to achieve the mutual control of electric and magnetic properties toward the energy- efficient memory and logic devices \(^{1 - 3}\) . But the two contrasting order parameters tend to be mutually exclusive in a single material \(^{4}\) . Nondisplacive mechanisms introduce a paradigm for constructing multiferroics beyond the traditional limits of mutual obstruction of the ferroelectric and magnetic orders \(^{5,6}\) . To date, the type I multiferroic BiFeO \(_3\) is the only known room- temperature single- phase multiferroic material. Alternatively, the helical magnetic orders break the spatial inversion symmetry and simultaneously lead to electric orders \(^{7,8}\) , giving rise to type- II multiferroics. The quest for a new single- phase multiferroic remains an open challenge.  
+
+<|ref|>text<|/ref|><|det|>[[147, 300, 851, 467]]<|/det|>
+The emergence of 2D vdW magnets and ferroelectrics has opened new avenues for exploring low- dimensional physics on magnetoelectric coupling \(^{9,10}\) . Diverse isolated vdW ferromagnets \(^{11 - 13}\) and ferroelectrics \(^{14,15}\) have enabled tantalizing opportunities to create 2D vdW spintronic devices with unprecedented performances at the limit of single or few atomic layers. Few of bulk crystals of transition- metal dihalides with a trigonal layered structure have been shown that the helical spin textures break inversion symmetries and induce an orthogonal ferroelectric polarization \(^{16,17}\) , but and definitive multiferroicity remains elusive at the limit of few atomic layers.  
+
+<|ref|>text<|/ref|><|det|>[[147, 469, 851, 765]]<|/det|>
+A recent work shows the possibility of discovery of type- II monolayer \(\mathrm{NiI_2}\) multiferroics using the optical measurements of second- harmonic- generation (SHG) and linear dichroism (LD) \(^{18}\) . Our work has pointed that all- optical characterizations are not sufficient to make a judgement of a few- and single- layer multiferroic at the presence of non- collinear and antiferromagnetic orders \(^{19}\) . The observed SHG and LD signals in few- layer \(\mathrm{NiI_2}\) originate from the magnetic- order- induced breaking of spatial- inversion \(^{19,20}\) . The prerequisite of ferroelectric polarization is the non- vanishing spontaneous electric polarizations, which must be proven through reliable and direct electrical measurements, such as polarization- and current- electric field (P- E and I- E) hysteresis loops. To date, 2D vdW multiferroic has not been directly uncovered at the limit of few layers. Here, we report fascinating vdW multiferroic with coexistence of ferroelectricity and antiferroelectricity in few layer \(\mathrm{NiI_2}\) based on magneto- optical- electric joint- measurements. In this 2D vdW multiferroics, an unprecedented magnetic control of switching dynamics of ferroelectric domain has been observed.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 775, 648, 796]]<|/det|>
+## Non-collinear antiferromagnetism in trilayer \(\mathrm{NiI_2}\)  
+
+<|ref|>text<|/ref|><|det|>[[148, 805, 851, 910]]<|/det|>
+Due to the high reactivity of \(\mathrm{NiI_2}\) flakes, \(\mathrm{NiI_2}\) exfoliation and encapsulation by graphene and hexagonal boron nitride (hBN) flakes were carried out in a glove box (Fig. 1a and Supplementary Fig. 1). \(\mathrm{NiI_2}\) crystal shows rhombohedral structure with a repeating stack of three (I- Ni- I) layers, where Ni and I ions form a triangular lattice in each layer (Fig. 1b). The rhombohedral stacking has been atomically identified (Fig. 1c). The atom
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 85, 851, 295]]<|/det|>
+arrangements of rhombohedral phase demonstrate signature hexagon- shaped periodic bright spots with equal contrast, validating the overlapping stack of I and Ni atoms along the \(c\) axis. The ADF- STEM and fast Fourier transform (FFT) show an interplanar spacing of \(1.9 \mathring{\mathrm{A}}\) , consistent with the (110) lattice plane of rhombohedral \(\mathrm{NiI}_2\) crystal. Circularly polarized Raman spectra in the parallel \((\sigma + / \sigma +\) and \(\sigma - / \sigma -\) ) configuration show only two distinct peaks in the \(\mathrm{NiI}_2\) device (Fig. 1d). The peak at \(\sim 124.7 \mathrm{cm}^{- 1}\) is assigned to the \(\mathrm{A_g}\) phonon modes \(^{22}\) , and this polarization behavior is consistent with Raman tensor analysis for the rhombohedral structure of \(\mathrm{NiI}_2^{23}\) . The Raman feature at \(\sim 20 \mathrm{cm}^{- 1}\) is assigned to the interlayer shear mode (SM), which suggests that the \(\mathrm{NiI}_2\) is trilayer \(^{20}\) .  
+
+<|ref|>text<|/ref|><|det|>[[147, 299, 851, 530]]<|/det|>
+For optimal optical response and sensitivity to probe the magnetic properties, the photon energy should be chosen near the absorption edge \(^{11,24}\) . Therefore, we first studied white- light magnetic circular dichroism (MCD) spectra of a trilayer \(\mathrm{NiI}_2\) device as a function of magnetic field perpendicular to the sample plane at \(10 \mathrm{K}\) (see Methods for details) \(^{25}\) . There is a strong peak near \(2.3 \mathrm{eV}\) along with two weak features around \(1.85 \mathrm{eV}\) and \(1.6 \mathrm{eV}\) (Fig. 1e). By means of ligand- field theory, the peaks are attributed to the absorption transitions of \(p\) - \(d\) exciton states \(^{26}\) . A pair of opposite MCD peaks with magnetic field manifestly appears at \(2.3 \mathrm{eV}\) , suggesting strong magneto- optical resonance. When the magnetic field is switched, MCD features is consistently reversed, and zero remanent MCD signal at \(\sim 2.3 \mathrm{eV}\) is distinctly observed at \(0 \mathrm{T}\) , indicating antiferromagnetic orders at \(10 \mathrm{K}\) .  
+
+<|ref|>text<|/ref|><|det|>[[147, 534, 851, 914]]<|/det|>
+To further validate the magnetic order, the scanning RMCD microscope was used to image and measure the magnetic domains of the as- exfoliated trilayer \(\mathrm{NiI}_2\) . The polar RMCD imaging is a reliable and powerful tool to unveil the 2D magnetism in the micro scale, and the RMCD intensity is proportional to the out- of- plane magnetization \(^{24}\) . All magneto- optical measurements were carried out using a \(2.33 \mathrm{eV}\) laser with optimal detection sensitivity (see Methods for details). Figure 2a shows RMCD maps of a trilayer \(\mathrm{NiI}_2\) sweeping between - 0.75 T and +0.75 T at \(10 \mathrm{K}\) . Remarkably, many micrometer- sized bimeron- like domains are observed in trilayer and another few- layer \(\mathrm{NiI}_2\) across the entire range of sweeping magnetic field \(^{27}\) . The spin- up and spin- down domains exist in pairs (Fig. 2a and Supplementary Fig. 2). One typical bimeron- like domains in trilayer \(\mathrm{NiI}_2\) at \(0 \mathrm{T}\) and \(10 \mathrm{K}\) are shown in Fig. 2b. The RMCD signals in each bimeron- like domain display opposite sign and nearly equal intensities. The magnetic moments point upwards or downwards in the core region and gradually decrease away from the core, and approaches zero near the perimeter (Fig. 2c). This magnetic moment distribution possibly indicates a pair of topological spin meron and antimeron with opposite chirality in a cycloid ground state \(^{28,29}\) . The bimeron- like magnetization textures remain robust in all magnetic field, indicating the bimeron- like domains are robust. The high stability of the bimeron- like magnetic domains probably
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 86, 851, 168]]<|/det|>
+originate from the topological protection, which also contributes to the preservation of magnetization even if upon a reversal magnetic field of 0.75 T. The formation of bimeron- like magnetic domains may be related to the localized stress at the interface. But further deep studies must be done to reveal the exact physical mechanism.  
+
+<|ref|>text<|/ref|><|det|>[[148, 172, 851, 403]]<|/det|>
+Fig. 2d shows the RMCD loops of the trilayer \(\mathrm{NiI}_2\) sweeping between \(+3\mathrm{T}\) and \(- 3\mathrm{T}\) at \(10\mathrm{K}\) . The RMCD loops show a highly nonlinear behavior with magnetic field and plateau behaviors for the out- of- plane magnetization. The RMCD intensity near \(0\mathrm{T}\) is suppressed and approaches zero, suggesting the vanishing remnant magnetization, which indicates a compensation of the out- of- plane magnetization and non- collinear AFM orders in the trilayer \(\mathrm{NiI}_2^{30}\) . And the gradual increases of the RMCD signal are observed with increasing magnetic field between \(\pm 1.2\) and \(\pm 2.6\mathrm{T}\) , suggesting a spin- flop process. The spin- flop behaviors of the magnetization curve imply that the interlayer antiferromagnetic coupling of the non- collinear spins is complicated. Similar magnetic hysteresis loops have been demonstrated in another few- layer \(\mathrm{NiI}_2\) , which show definite non- collinear AFM orders in the few- layer \(\mathrm{NiI}_2\) (Supplementary Fig. 2b).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 413, 530, 433]]<|/det|>
+## Ferroelectricity in trilayer \(\mathrm{NiI}_2\) device  
+
+<|ref|>text<|/ref|><|det|>[[147, 444, 851, 909]]<|/det|>
+To determine ferroelectricity in few- layer \(\mathrm{NiI}_2\) device, we performed the frequency- dependent measurement of electric polarization via \(I\) - \(E\) and \(P\) - \(E\) hysteresis loops, which allows an accurate estimation of the electric polarization. We fabricated two heterostructure devices of graphene/hBN/ \(\mathrm{NiI}_2\) /graphene/hBN (Fig. 1a and Supplementary Fig. 1). The hBN flake was used as an excellent insulating layer to prevent large leakage current and guarantee the detections of ferroelectric (FE) features \(^{31,32}\) (Supplementary Fig. 3). The hBN insulator shows a linear \(P\) - \(E\) behavior and a rectangle- shaped \(I\) - \(E\) loops (Supplementary Fig. 4), indicating excellent insulativity for ferroelectric hysteresis measurements (see Methods for details) \(^{33,34}\) . The frequency- dependent \(I\) - \(E\) and \(P\) - \(E\) loops at \(10\mathrm{K}\) are shown in Fig. 3, and the forward and backward scans of the electric polarization as a function of electric field show characteristic ferroelectric \(I\) - \(E\) and \(P\) - \(E\) hysteresis. Strikingly, a characteristic double- hysteresis loop of antiferroelectric (AFE) polarization emerges accompanied with decreasing remanent polarization \((P_r)\) . More importantly, a pair of opposite single peaks of switching current \((I)\) are observed when sweeping voltage at \(6.7\mathrm{Hz}\) , which is attribute to charge displacement and implies two stable states with inverse polarity (Fig. 3b and c). Whereas two pair of opposite bimodal peaks are observed when sweeping voltage at \(1.3\mathrm{Hz}\) , which is attribute to AFE- FE and FE- AFE transitions under electric field sweeping (Fig. 3c) \(^{35}\) . This suggests an evolution from FE to AFE polarization with frequency is observed \(^{36,37}\) , exhibiting the decisive evidence for coexistence of ferroelectric and antiferroelectric \(^{38,39}\) . This comprehensive frequency- dependent evolution behaviors also confirm the coexistence of FE and AFE in another a few layers
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 87, 380, 104]]<|/det|>
+\(\mathrm{NiI}_2\) (Supplementary Fig. 5).  
+
+<|ref|>text<|/ref|><|det|>[[147, 107, 852, 253]]<|/det|>
+The type- II multiferroicity has been demonstrated in the bulk \(\mathrm{NiI}_2\) . However, the multiferroic identification for few- layer \(\mathrm{NiI}_2\) remains challenging and elusive. All- optical methods are unreliable to make a judgement of a few- and single- layer multiferroic at the presence of non- collinear and antiferromagnetic orders<sup>19</sup>. The bulk \(\mathrm{NiI}_2\) displays a helimagnetic state below critical temperature<sup>16,17</sup>. From symmetry considerations and a Ginzburg- Landau perspective<sup>40,41</sup>, the helimagnetic state allows for the emergence of a ferroelectric polarization associated to the form:  
+
+<|ref|>equation<|/ref|><|det|>[[372, 257, 538, 275]]<|/det|>
+\[\mathbf{P} = \gamma \mathbf{e}\times \mathbf{q} \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 277, 852, 916]]<|/det|>
+where \(\mathbf{P}\) is the electric polarization, \(\mathbf{e}\) is the spin rotation axis, \(\mathbf{q}\) is the spin propagation vector of the spin spiral, and \(\gamma\) is a scalar parameter dependence with spin- orbit coupling. For monolayer \(\mathrm{NiI}_2\) , the helimagnetic order can be modeled with a 7axa supercell and an in- plane (x- y plane) spin cycloid, and the spin propagation vector \(\mathbf{q}\) is displayed along the [210] direction (in lattice vector units)<sup>42</sup>, as shown in in Fig. 3d. Thus, the in- plane (x- y plane) spin cycloid induces the in- plane electric polarization along the [010] direction (Fig. 3d). Actually, theoretical calculations have determined that the \(\mathbf{q}\) - vector in multi- layer and bulk \(\mathrm{NiI}_2\) is a consequence of the competition between magnetic exchange interactions between magnetic atoms<sup>42,43</sup>. In particular, intralayer ferromagnetic first- neighbor, intralayer antiferromagnetic third neighbor, and interlayer antiferromagnetic second- neighbor magnetic exchange interactions are the most relevant. In the monolayer limit, there are no interlayer interactions, hence the \(\mathbf{q}\) - vector is in- plane and determined by the competition between intralayer exchange interactions. For a trilayer \(\mathrm{NiI}_2\) , the \(\mathbf{q}\) - vector is modulated not only by intralayer exchange interactions but also by interlayer exchange interactions. Assuming that interlayer exchange interactions cause the tilting out- of- plane cycloidal spin configuration from in- plane (x- y plane) configuration (Fig. 3d), the \(\mathbf{e}\) - vector is no longer parallel to the z- axis, leading to an out- of- plane ferroelectric polarization component. Figure 3e illustrates the extreme case where the in- plane (x- y plane) cycloidal configuration tilts to x- z plane, resulting in an out- of- plane ferroelectric polarization. This scenario suggests the observed out- of- plane ferroelectric polarization in the trilayer \(\mathrm{NiI}_2\) device, but the precise mechanism remains to be further studied in the future. In particular, equation (1) shows that two spin spiral configurations with \(\mathbf{q}_1 = \mathbf{q}\) and \(\mathbf{q}_2 = -\mathbf{q}\) will give rise to opposite electric polarizations \(\mathbf{P} = -\mathbf{P}\) . The first principles calculations in spin configuration with both \(\mathbf{q}\) and \(-\mathbf{q}\) are energetically equivalent, and therefore show same energies with and without spin- orbit coupling<sup>42</sup>. Thus, the emergence of opposite electric dipoles can be directly observed in the total electronic density of the system. The energy of spin cycloidal configurations with positive and negative \(\mathbf{q}\) - vectors (positive and negative ferroelectric polarization \(\mathbf{P}\) ) is degenerate, which approve the coexistence of ferroelectric and antiferroelectric (Fig. 3f), consistent with the observed
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 87, 664, 103]]<|/det|>
+coexistence of ferroelectric and antiferroelectric in trilayer \(\mathrm{NiI_2}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 114, 504, 134]]<|/det|>
+## Magnetic control of ferroelectricity  
+
+<|ref|>text<|/ref|><|det|>[[147, 144, 851, 911]]<|/det|>
+To reveal the magnetoelectric coupling effect, we studied the magnetic control of ferroelectric properties in the trilayer \(\mathrm{NiI_2}\) device, as shown in Fig. 4. The \(P_r\) extracted from the \(P\) - \(E\) hysteresis loop is plotted as a function of out- of- plane magnetic field at different frequencies (Fig. 4a- c). The magnetic field causes a decrease in residual polarization at different frequencies (Fig. 4a- c and Supplementary Fig. 6), and the magnetic control of \(P_r\) shows frequency dependence of applied electric field (Fig. 4d). The magnetic control ratio reaches to \(\sim 7\%\) by detuning the frequency (24.5 Hz) at 7 T, which is remarkable feature of multiferroic. To better understand the magnetic control behavior, we briefly discuss the possible mechanism that leads to the decrease in \(P_r\) caused by the magnetic field from a microscopic perspective. We only discuss ferroelectric polarization flops in the model of spiral magnets<sup>40</sup>. In zero fields spins rotate in the easy x- z plane, so that the spin rotation axis \(\mathbf{e}\) is parallel to the y axis, and for \(\mathbf{q} / / \mathbf{x}\) - y plane, \(\mathbf{P} / / \mathbf{z}\) (Supplementary Fig. 7a and 7b). However, magnetic field in the z direction favors the rotation of spins in the x- y plane (Supplementary Fig. 7c and 7d), so that the spin rotation axis \(\mathbf{e}\) is parallel to the z axis, in which case, \(\mathbf{P} / / \mathbf{x}\) - y plane<sup>40</sup>. In short, applying a magnetic field parallel to the z- axis causes the spin rotation plane to tilt from the x- z plane to the x- y plane, and the corresponding ferroelectric polarization flops from the out- of- plane direction to the in- plane direction. Therefore, an out- of- plane magnetic field leads to a decrease of ferroelectric polarization in the out- of- plane direction, which is consistent with the observed decrease in \(P_r\) with increasing magnetic field. Furthermore, the decrease in the current peak accompanied by an increase in the coercive electric field due to the increased magnetic field is unambiguously observed (Fig. 4e and Supplementary Fig. 8). This is because the out- of- plane magnetic field causes the spin rotation plane to tilt from the x- z plane to the x- y plane, and the corresponding easy axis of ferroelectric polarization flops from the out- of- plane direction to the in- plane direction. The shifts of current peaks induced by ferroelectric switching vary with the magnetic field, but the background current remains constant, excluding the magnetoresistance effects (Fig. 4e and Supplementary Fig. 8). Finally, the switching time of ferroelectric domain under different magnetic fields at 10 K is calculated by KAI model<sup>44</sup> (Fig. 4f and 4g; Part A and B). The switching time \(\tau\) increase as magnetic field increase, which signifies an even symmetry with magnetic field (Fig. 4h), consistent with the above mechanisms. At 10 K, the switching time \(\tau\) , leading to a maximum enhancement of switching time by 20% (-7 T). This observation of robust control of ferroelectric properties by magnetic field, pointing to the potential use of few- layer \(\mathrm{NiI_2}\) as a research platform for studying the magneto- electric coupling physics in the two- dimensional limit and for fabricating advanced nano-
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[149, 87, 350, 103]]<|/det|>
+magnetoelectric devices.  
+
+<|ref|>text<|/ref|><|det|>[[148, 107, 851, 253]]<|/det|>
+In summary, we report a 2D vdW single- phase multiferroic \(\mathrm{NiI_2}\) few- layer crystal. We observed strong evidences for the coexistence of ferroelectric and non- collinear antiferromagnetism order via RMCD, \(P\) - \(E\) and \(I\) - \(E\) hysteresis loop. hysteresis loop. We achieve unprecedented magnetic control of ferroelectric properties in the \(\mathrm{NiI_2}\) trilayer. We envision that the 2D vdW single- phase multiferroic \(\mathrm{NiI_2}\) will provide numerous opportunities for exploring fundamental low- dimensional physics, and will introduce a paradigm shift for engineering new ultra- compact magnetoelectric devices.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 285, 240, 304]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 315, 315, 331]]<|/det|>
+## Sample fabrication  
+
+<|ref|>text<|/ref|><|det|>[[147, 336, 851, 504]]<|/det|>
+\(\mathrm{NiI_2}\) flakes were mechanically exfoliated from bulk crystals via PDMS films in a glovebox, which were synthesized by chemical vapor transport method from elemental precursors with molar ratio \(\mathrm{Ni:I} = 1:2\) . All exfoliated hBN, \(\mathrm{NiI_2}\) and graphene flakes were transferred onto pre- patterned Au electrodes on \(\mathrm{SiO_2 / Si}\) substrates one by one to create heterostructure in glovebox, which were further in- situ loaded into a microscopy optical cryostat for magneto- optical- electric joint- measurement. The whole process of \(\mathrm{NiI_2}\) sample fabrications and magneto- optical- electric measurements were kept out of atmosphere.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 529, 530, 546]]<|/det|>
+## Magneto-optical-electric joint-measurement  
+
+<|ref|>text<|/ref|><|det|>[[147, 550, 851, 715]]<|/det|>
+The polar RMCD, white- light MCD, Raman measurements and ferroelectric \(P\) - \(E\) and \(I\) - \(E\) measurements were performed on a powerful magneto- optical- electric joint- measurement scanning imaging system (MOEJSI) \(^{19}\) , with a spatial resolution reaching diffraction limit. The MOEJSI system was built based on a Witec Alpha 300R Plus low- wavenumber confocal Raman microscope, integrated with a closed cycle superconducting magnet (7 T) with a room temperature bore and a closed cycle cryogen- free microscopy optical cryostat (10 K) with a specially designed snout sample mount and electronic transport measurement assemblies.  
+
+<|ref|>text<|/ref|><|det|>[[147, 719, 851, 866]]<|/det|>
+The Raman signals were recorded by the Witec Alpha 300R Plus low- wavenumber confocal Raman microscope system, including a spectrometer (150, 600 and 1800/mm) and a TE- cooling Andor CCD. A 532 nm laser of \(\sim 0.2 \mathrm{mW}\) is parallel to the X- axis \((0^{\circ})\) and focused onto samples by a long working distance \(50 \times\) objective \((\mathrm{NA} = 0.55, \mathrm{Zeiss})\) after passing through a quarter- wave plate \((1 / 4 \lambda)\) . The circular polarization resolved Raman signals passed through the same \(1 / 4 \lambda\) waveplate and a linear polarizer, obtained by the spectrometer \((1800 / \mathrm{mm})\) and the CCD.  
+
+<|ref|>text<|/ref|><|det|>[[148, 869, 850, 908]]<|/det|>
+For white- light MCD measurements, white light with Kohler illumination from Witec Alpha 300R Plus microscope was linearly polarized at 0o by a visible wire grid
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 85, 851, 233]]<|/det|>
+polarizer, passed through an achromatic quarter- wave \((1 / 4\lambda)\) plate and focused onto samples by a long working distance \(50\times\) objective (Zeiss, \(\mathrm{NA} = 0.55\) ). The right- handed and left- handed circularly polarized white light was obtained by rotating \(1 / 4\lambda\) waveplate at \(+45^{\circ}\) and \(- 45^{\circ}\) . The white- light spectra were recorded by the Witec Alpha 300R Plus confocal Raman microscope system (spectrometer, \(150\mathrm{mm}\) ). The absorption spectra of right- handed and left- handed circularly polarized light in different magnetic field can be obtained as the previous work \(^{25}\) , giving corresponding MCD spectra.  
+
+<|ref|>text<|/ref|><|det|>[[147, 235, 851, 658]]<|/det|>
+For polar RMCD measurements, a free- space \(532\mathrm{nm}\) laser \((2.33\mathrm{eV})\) of \(\sim 2\mu \mathrm{W}\) modulated by photoelastic modulator (PEM, \(50\mathrm{KHz}\) ) was reflected by a non- polarizing beamsplitter cube \(\mathrm{(R / T = 30 / 70)}\) and then directly focused onto samples by a long working distance \(50\times\) objective \(\mathrm{(NA = 0.55}\) , Zeiss), with a diffraction limit spatial resolution of \(\sim 590\mathrm{nm}\) . The reflected beam which was collected by the same objective passed through the same non- polarizing beamsplitter cube and was detected by a photomultiplier (PMT), which was coupled with lock- in amplifier, Witec scanning imaging system, superconducting magnet, voltage source meter and ferroelectric tester. Ferroelectric \(P - E\) and \(I - E\) hysteresis loop of a \(\mathrm{NiI}_2\) device of \(\mathrm{Gr / hBN / NiI_2 / Gr}\) were measured by classical ferroelectric measurements and directly recorded by ferroelectric tester (Precision Premier II: Hysteresis measurement), which were contacted with the top and bottom graphene electrodes by patterned Au electrodes (Fig. 1a) through the electronic assemblies of the microscopy optical cryostat. The mechanism of ferroelectric measurement has been given by previous work \(^{45}\) . The detected signals include two components: a ferroelectric term of \(\mathrm{NiI}_2\) (2PrA) and a linear non- ferroelectric term of hBN insulator \((\sigma \mathrm{EAt})\) , \(\mathrm{Q} = \mathrm{QNiI} + \mathrm{QBN} = 2\mathrm{PrA} + \sigma \mathrm{EAt}\) . If only hBN insulator, a linear P- E loop take place, consistent with our experimental results of hBN flake (Supplementary Fig. 4). The linear hBN background have no effect on the ferroelectric features, and hBN flakes as excellent insulator suppress and overcome the leakage current, which for guarantee the detections of \(\mathrm{NiI}_2\) ferroelectric features \(^{31 - 34}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 683, 528, 700]]<|/det|>
+## STEM Imaging, Processing, and Simulation  
+
+<|ref|>text<|/ref|><|det|>[[147, 704, 851, 891]]<|/det|>
+Atomic- resolution ADF- STEM imaging was performed on an aberration- corrected JEOL ARM 200F microscope equipped with a cold field- emission gun operating at 80 kV. The convergence semiangle of the probe was around 30 mrad. Image simulations were performed with the Prismatic package, assuming an aberration- free probe with a probe size of approximately \(1\mathrm{\AA}\) . The convergence semiangle and accelerating voltage were in line with the experiments. The collection angle for ADF imaging was between 81 and 228 mrad. ADF- STEM images were filtered by Gaussian filters, and the positions of atomic columns were located by finding the local maxima of the filtered series.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[148, 93, 317, 113]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[148, 123, 850, 163]]<|/det|>
+The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 194, 261, 213]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[145, 222, 852, 905]]<|/det|>
+1 Fiebig, M., Lottermoser, T., Meier, D. & Trassin, M. The evolution of multiferroics. Nat. Rev. Mater. 1, 16046, (2016).  2 Chu, Y.- H. et al. Electric- field control of local ferromagnetism using a magnetoelectric multiferroic. Nat. Mater. 7, 478- 482, (2008).  3 Ponet, L. et al. Topologically protected magnetoelectric switching in a multiferroic. Nature 607, 81- 85, (2022).  4 Cheong, S.- W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13- 20, (2007).  5 Wang, J. et al. Epitaxial BiFeO₃ multiferroic thin film heterostructures. Science 299, 1719- 1722, (2003).  6 Guo, R. et al. Continuously controllable photoconductance in freestanding BiFeO₃ by the macroscopic flexoelectric effect. Nat. Commun. 11, 2571, (2020).  7 Kimura, T. et al. Magnetic control of ferroelectric polarization. Nature 426, 55- 58, (2003).  8 Hur, N. et al. Electric polarization reversal and memory in a multiferroic material induced by magnetic fields. Nature 429, 392- 395, (2004).  9 Rogée, L. et al. Ferroelectricity in untwisted heterobilayers of transition metal dichalcogenides. Science 376, 973- 978, (2022).  10 Yang, Q. et al. Ferroelectricity in layered bismuth oxide down to 1 nanometer. Science 379, 1218- 1224, (2023).  11 Huang, B. et al. Layer- dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270- 273, (2017).  12 Gong, C. et al. Discovery of intrinsic ferromagnetism in two- dimensional van der Waals crystals. Nature 546, 265- 269, (2017).  13 Deng, Y. et al. Gate- tunable room- temperature ferromagnetism in two- dimensional Fe₃GeTe₂. Nature 563, 94- 99, (2018).  14 Yuan, S. et al. Room- temperature ferroelectricity in MoTe₂ down to the atomic monolayer limit. Nat. Commun. 10, 1775, (2019).  15 Liu, F. et al. Room- temperature ferroelectricity in CuInP₂S₆ ultrathin flakes. Nat. Commun. 7, 12357, (2016).  16 Kurumaji, T. et al. Magnetoelectric responses induced by domain rearrangement and spin structural change in triangular- lattice helimagnets NiI₂ and CoI₂. Phys. Rev. B
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 87, 852, 916]]<|/det|>
+87, 014429, (2013).17 Zhao, L. et al. \(\mathrm{CuBr_2}\) – a new multiferroic material with high critical temperature. Adv. Mater. 24, 2469- 2473, (2012).18 Song, Q. et al. Evidence for a single-layer van der Waals multiferroic. Nature 602, 601- 605, (2022).19 Jiang, Y. et al. Dilemma in optical identification of single-layer multiferroics. Nature 619, E40- E43, (2023).20 Wu, S. et al. Layer thickness crossover of type- II multiferroic magnetism in \(\mathrm{NiI_2}\) . arXiv:2307.10686 (2023).21 Sun, Z. et al. Giant nonreciprocal second- harmonic generation from antiferromagnetic bilayer \(\mathrm{CrI_3}\) . Nature 572, 497- 501, (2019).22 Liu, H. et al. Vapor deposition of magnetic van der Waals \(\mathrm{NiI_2}\) crystals. ACS Nano 14, 10544- 10551, (2020).23 Guo, K. et al. Layer dependence of stacking order in nonencapsulated few- layer \(\mathrm{CrI_3}\) . Sci. China. Mater. 63, 413- 420, (2020).24 Wang, X. et al. Light- induced ferromagnetism in moiré superlattices. Nature 604, 468- 473, (2022).25 Mak, K. F. et al. Measurement of the optical conductivity of graphene. Phys. Rev. Lett. 101, 196405 (2008).26 Pollini, I., Thomas, J. & Lenselink, A. Optical properties of layered transition- metal iodides. Phys. Rev. B 30, 2140- 2148, (1984).27 Wu, X. et al. Topology- induced chiral photon emission from a large- scale meron lattice. Nat. Electron. 6, 516- 524, (2023).28 Wintz, S. et al. Topology and origin of effective spin meron pairs in ferromagnetic multilayer elements. Phys. Rev. Lett. 110, 177201, (2013).29 Xu, C. et al. Electric- field switching of magnetic topological charge in type- I multiferroics. Phys. Rev. Lett. 125, 037203, (2020).30 Xie, H. et al. Evidence of non- collinear spin texture in magnetic moiré superlattices. Nature Physics 19, 1150- 1155, (2023).31 Knobloch, T. et al. The performance limits of hexagonal boron nitride as an insulator for scaled CMOS devices based on two- dimensional materials. Nat. Electron. 4, 98- 108, (2021).32 Yang, T. H. et al. Ferroelectric transistors based on shear- transformation- mediated rhombohedral- stacked molybdenum disulfide. Nat. Electron. 7, 29- 38 (2024).33 Park, J. Y. et al. Revival of Ferroelectric Memories Based on Emerging Fluorite- Structured Ferroelectrics. Adv. Mater. 35, 2204904, (2023).34 Kim, Y., Min, K. K., Yu, J., Kwon, D. & Park, B.- G. Lamination method for improved polarization- leakage current relation in \(\mathrm{HfO_2}\) - based metal/ferroelectric/insulator/semiconductor structure. Semicond. Sci. Technol. 37,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 87, 283, 103]]<|/det|>
+045001, (2022).  
+
+<|ref|>text<|/ref|><|det|>[[147, 108, 850, 147]]<|/det|>
+35 Wu, Z. et al. Discovery of an above- room- temperature antiferroelectric in twodimensional hybrid perovskite. J. Am. Chem. Soc. 141, 3812- 3816, (2019).  
+
+<|ref|>text<|/ref|><|det|>[[147, 150, 850, 189]]<|/det|>
+36 Park, M. H. et al. Ferroelectricity and antiferroelectricity of doped thin \(\mathrm{HfO_2}\) - based films. Adv. Mater. 27, 1811- 1831, (2015).  
+
+<|ref|>text<|/ref|><|det|>[[147, 193, 850, 231]]<|/det|>
+37 Müller, J. et al. Ferroelectricity in Simple Binary \(\mathrm{ZrO_2}\) and \(\mathrm{HfO_2}\) . Nano Lett. 12, 4318- 4323, (2012).  
+
+<|ref|>text<|/ref|><|det|>[[147, 235, 850, 274]]<|/det|>
+38 Ko, K. et al. Operando electron microscopy investigation of polar domain dynamics in twisted van der Waals homobilayers. Nat. Mater. 22, 992- 998 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[147, 277, 850, 316]]<|/det|>
+39 Xu, B., Paillard, C., Dkhil, B. & Bellaiche, L. Pinched hysteresis loop in defect- free ferroelectric materials. Phys. Rev. B 94, 140101 (2016).  
+
+<|ref|>text<|/ref|><|det|>[[147, 320, 850, 358]]<|/det|>
+40 Mostovoy, M. Ferroelectricity in spiral magnets. Phys. Rev. Lett. 96, 067601, (2006).  
+
+<|ref|>text<|/ref|><|det|>[[147, 363, 850, 402]]<|/det|>
+41 Hohenberg, P. C. et al. An introduction to the Ginzburg- Landau theory of phase transitions and nonequilibrium patterns Phys. Rep. 572, 1- 42, (2015).  
+
+<|ref|>text<|/ref|><|det|>[[147, 405, 850, 444]]<|/det|>
+42 Fumega, A. O. et al. Microscopic origin of multiferroic order in monolayer \(\mathrm{NiI_2}\) . 2D Mater. 9, 025010, (2022).  
+
+<|ref|>text<|/ref|><|det|>[[147, 448, 850, 486]]<|/det|>
+43 Riedl, K. et al. Microscopic origin of magnetism in monolayer \(3d\) transition metal dihalides. Phys. Rev. B 106, 035156, (2022).  
+
+<|ref|>text<|/ref|><|det|>[[147, 490, 850, 529]]<|/det|>
+44 Zhao, D., Katsouras, I., Asadi, K., Blom, P. W. M. & de Leeuw, D. M. Switching dynamics in ferroelectric P(VDF- TrFE) thin films. Phys. Rev. B 92, 214115, (2015).  
+
+<|ref|>text<|/ref|><|det|>[[147, 532, 850, 571]]<|/det|>
+45 Scott, J. F. et al. Ferroelectrics go bananas. J. Phys.: Condens. Matter 20, 021001, (2008).  
+
+<|ref|>text<|/ref|><|det|>[[147, 575, 848, 614]]<|/det|>
+46 Golla, D. et al. Optical thickness determination of hexagonal boron nitride flakes. Appl. Phys. Lett. 102, 161906, (2013).  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 647, 335, 666]]<|/det|>
+## Acknowledgments  
+
+<|ref|>text<|/ref|><|det|>[[147, 677, 852, 909]]<|/det|>
+B.P. and L.D. acknowledge support from National Science Foundation of China (52021001). B.P. acknowledge support from National Science Foundation of China (62250073). R.C.C. acknowledge support from National Science Foundation of China (52231007). H.L. acknowledge support from National Science Foundation of China (51972046). L.D. acknowledge support from Sichuan Provincial Science and Technology Department (Grant No. 99203070). L.D. acknowledge support from Sichuan Provincial Science and Technology Department (Grant No. 9920 3070). L.Q. acknowledge support from National Science Foundation of China (520720591 and 11774044). J.W. thanks the National Natural Science Foundation of China (Grant No. 11974422), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB30000000).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[149, 93, 365, 112]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[148, 123, 851, 248]]<|/det|>
+B.P conceived the project. Y.W. prepared the samples and performed the magneto- optical- electric joint- measurements and Raman measurements assisted by B.P., and performed the ferroelectric measurements assisted by L.Q., and analyzed and interpreted the results assisted by H.L., N. L., W.J., L.D. and B.P.. C. Y, R.C, X.X. and X.H. performed the STEM measurements. Y.W. and B.P. wrote the paper with input from all authors. All authors discussed the results.  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 280, 353, 300]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[149, 310, 502, 327]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 359, 385, 378]]<|/det|>
+## Additional information  
+
+<|ref|>text<|/ref|><|det|>[[147, 388, 810, 408]]<|/det|>
+Supplementary information is available for this paper at xxx (will be provided).  
+
+<|ref|>text<|/ref|><|det|>[[149, 410, 750, 428]]<|/det|>
+Correspondence and requests for materials should be addressed to B.P.  
+
+<|ref|>text<|/ref|><|det|>[[148, 431, 850, 470]]<|/det|>
+Reprints and permission information is available online at http://www.nature.com/reprints.  
+
+<|ref|>text<|/ref|><|det|>[[148, 474, 844, 514]]<|/det|>
+Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[177, 88, 840, 504]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 512, 851, 787]]<|/det|>
+<center>Fig. 1 | Crystal structure, MCD measurements of trilayer \(\mathrm{NiI}_2\) at room temperature. a, Schematic of trilayer \(\mathrm{NiI}_2\) sandwiched between graphene and hBN. b, View of the in-plane and out-of-plane atomic lattice. The magnetic \(\mathrm{Ni}^{2 + }\) ions are surrounded by the octahedron of \(\mathrm{I}^{-}\) ions, and three \(\mathrm{NiI}_2\) layers as a repeating unit stack in a staggered fashion along the c axis. c, Atomic-resolution ADF-STEM image showing signature hexagonal patterns of rhombohedral stacking in few-layer \(\mathrm{NiI}_2\) crystals. The inset shows the corresponding FFT image. d, Circular polarization resolved Raman spectra of a trilayer \(\mathrm{NiI}_2\) device (Fig. 1a) at room temperature, excited by \(532\mathrm{nm}\) laser. “SM” indicates the interlayer shear mode of trilayer \(\mathrm{NiI}_2\) . e, The MCD spectra of trilayer \(\mathrm{NiI}_2\) at \(+3\mathrm{T}\) , \(0\mathrm{T}\) and -3T. MCD signals are sensitive to spin electronic transitions and magnetic moments in the electronic states. The MCD features are spin-sign dependent and reverse as magnetic field switch. The zero remanent MCD signals at \(\sim 2.3\mathrm{eV}\) at \(0\mathrm{T}\) suggest antiferromagnetic orders. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[160, 87, 833, 298]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 308, 852, 455]]<|/det|>
+<center>Fig. 2 | Non-collinear antiferromagnetism in trilayer NiI₂ device. a, Polar RMCD maps upon a 2.33 eV laser with diffraction-limited spatial resolution (see Methods), collected at room temperature and selected magnetic field. b, Schematic of the spin textures of bimerons-like domains and corresponding zoom-in RMCD images (white dashed-line box in Fig. 2a). c, The polar RMCD signals along with the line sections of RMCD map (b). d, The RMCD curves sweeping between \(+3\mathrm{T}\) and \(-3\mathrm{T}\) at \(10\mathrm{K}\) , suggesting a non-collinear antiferromagnetism. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[186, 78, 816, 675]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 680, 852, 910]]<|/det|>
+<center>Fig. 3 | Existence of ferroelectric and anti-ferroelectric orders in trilayer NiI2 device. a, b, \(P - E\) and \(I - E\) loops at various frequencies from device 1 (D1). c, Corresponding \(I - E\) loops from Fig. 3b subtracted the current background. Two pairs of current peaks (FE-AFE and AFE-FE switching peaks) were obtained by Lorentz fitting. An evolution from FE to AFE was observed. d, Schematic of the spin spiral configurations with in-plane (x-y plane) spin cycloid in monolayer NiI2, showing a periodicity of \(7\times 1\) unit cells. e, Extreme case where the in-plane (x-y plane) cycloidal configuration tilts to x-z plane caused by interlayer exchange interactions, resulting in an out-of-plane ferroelectric polarization. f, Schematic of the spin spiral configurations with opposite \(\mathbf{q}\) in trilayer NiI2, showing the coexistence of ferroelectric and antiferroelectric. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[161, 81, 828, 505]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 511, 852, 744]]<|/det|>
+<center>Fig. 4 | Magnetic control of ferroelectricity in trilayer NiI2 device. a-c, The \(P_r\) extracted from the \(P\) - \(E\) hysteresis loop is plotted as a function of out-of-plane magnetic field at different frequencies. The error bars are standard deviations of \(P_r\) . d, The magnetic control ratio \((P_r - P_{r0}) / P_{r0}\) are frequency dependent, where \(P_r\) and \(P_{r0}\) is remanent polarization in a magnetic field and without magnetic field, respectively. e, The \(I\) - \(E\) curves at different magnetic field. The decrease in the current peak accompanied by an increase in the coercive field due to the increased magnetic field is unambiguously observed. f, g, Fitting by KAI model for different magnetic field at 10 K, giving the switching time \(\tau\) . h, The \((\tau - \tau_0) / \tau_0\) as a function of magnetic field at 10 K, indicating a degree of magnetic control of switching time, where \(\tau\) and \(\tau_0\) is switching time in a magnetic field and without magnetic field, respectively. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[42, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[42, 92, 768, 112]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 137, 149]]<|/det|>
+- Sl.pdf
+
+<--- Page Split --->

preprint/preprint__00c2b94550129fb8f084bb495841a196a9f5afe6d5c14e29f461a9abeaa8a98e/images_list.json

@@ -0,0 +1,92 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "FIG. 1. Scheme for our Generator-Enhanced Optimization (GEO) strategy. The GEO framework leverages generative models to utilize previous samples coming from any quantum or classical solver. The trained quantum or classical generator is responsible for proposing candidate solutions which might be out of reach for conventional solvers. This seed data set (step 0) consists of observation bitstrings \\(\\{\\pmb{x}^{(i)}\\}_{\\mathrm{seed}}\\) and their respective costs \\(\\{\\sigma^{(i)}\\}_{\\mathrm{seed}}\\) . To give more weight to samples with low cost, the seed samples and their costs are used to construct a softmax function which serves as a surrogate to the cost function but in probabilistic domain. This softmax surrogate also serves as a prior distribution from which the training set samples are withdrawn to train the generative model (steps 1-3). As shown in the figure between steps 1 and 2, training samples from the softmax surrogate are biased favoring those with low cost value. For the work presented here, we implemented a tensor-network (TN)-based generative model. Therefore, we refer to this quantum-inspired instantiation of GEO as TN-GEO. Other families of generative models from classical, quantum, or hybrid quantum-classical can be explored as expounded in the main text. The quantum-inspired generator corresponds to a tensor-network Born machine (TNBM) model which is used to capture the main features in the training data, and to propose new solution candidates which are subsequently post selected before their costs \\(\\{\\sigma^{(i)}\\}_{\\mathrm{new}}\\) are evaluated (steps 4-6). The new set is merged with the seed data set (step 7) to form an updated seed data set (step 8) which is to be used in the next iteration of the algorithm. More algorithmic details for the two TN-GEO strategies proposed here, as a booster or as a stand-alone solver, can be found in the main text and in A5 and A6 respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        91,
+        65,
+        910,
+        372
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "FIG. 2. TN-GEO as a booster. Top: Strategies 1-3 correspond to the current options a user might explore when solving a combinatorial optimization problem with a suite of classical optimizers such as simulated annealing (SA), parallel tempering (PT), generic algorithms (GA), among others. In strategy 1, the user would use its computational budget with a preferred solver. In strategy 2-4 the user would inspect intermediate results and decide whether to keep trying with the same solver (strategy 2), try a new solver or a new setting of the same solver used to obtain the intermediate results (strategy 3), or, as proposed here, to use the acquired data to train a quantum or quantum-inspired generative model within a GEO framework such as TN-GEO (strategy 4). Bottom: Results showing the relative TN-GEO enhancement from TN-GEO over either strategy 1 or strategy 2. Positive values indicate runs where TN-GEO outperformed the respective classical strategies (see Eq. 1). The data represents bootstrapped medians from 20 independent runs of the experiments and error bars correspond to the 95% confidence intervals. The two instances presented here correspond to portfolio optimization instances where all the assets in the S&P 500 market index where included \\((N = 500)\\) , under two different cardinality constraints \\(\\kappa\\) . This cardinality constraint indicate the number of assets that can be included at a time in valid portfolios, yielding a search space of \\(M = \\binom{N}{\\kappa}\\) , with \\(M \\sim 10^{69}\\) portfolios candidates for \\(\\kappa = 50\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        90,
+        81,
+        480,
+        460
+      ]
+    ],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "FIG. 3. Generalization capabilities of our quantum-inspired generative model. Left panel corresponds to an investment universe with \\(N = 50\\) assets while the right panel corresponds to one with \\(N = 100\\) assets. The blue histogram represents the number of observations or portfolios obtained from the classical solver (seed data set). In orange we represent samples coming from our quantum generative model at the core of TN-GEO. The green dash line is positioned at the best risk value found in the seed data. This mark emphasizes all the new outstanding samples obtained with the quantum generative model and which correspond to lower portfolio risk value (better minima) than those available from the classical solver by itself. The number of outstanding samples in the case of \\(N = 50\\) is equal to 31, while 349 outstanding samples were obtained from the MPS generative model in the case of \\(N = 100\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        85,
+        75,
+        914,
+        324
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "FIG. 4. TN-GEO as a stand-alone solver: In this comparison of TN-GEO against four classical competing strategies, investment universes are constructed from subsets of the S&P 500 with a diversity in the number of assets (problem variables) ranging from \\(N = 30\\) to \\(N = 100\\) . The goal is to minimize the risk given an expected return which is one of the specifications in the combinatorial problem addressed here. Error bars and their 95% confidence intervals are calculated from bootstrapping over 100 independent random initializations for each solver on each problem. The main line for each solver corresponds to the bootstrapped median over these 100 repetitions, demonstrating the superior performance of TN-GEO over the classical solvers considered here. As specified in the text, with the exception of TN-GEO, the classical solvers use to their advantage the a priori information coming from the cardinality constraint imposed in the selection of valid portfolios.",
+    "footnote": [],
+    "bbox": [
+      [
+        200,
+        472,
+        777,
+        793
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "FIG. 5. A graphical demonstration of indices used for performance metrics calculation",
+    "footnote": [],
+    "bbox": [
+      [
+        515,
+        61,
+        916,
+        305
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "FIG. 6. Relative TN-GEO enhancement similar to those shown in the bottom panel of Fig. 2 in the main text. For these experiments, portfolio optimization instances with a number of variables ranging from \\(N = 30\\) to \\(N = 100\\) were used. Here, each panel correspond to a different investment universes corresponding to a random subset of the S&P 500 market index. Note the trend for a larger quantum-inspired enhancement as the number of variables (assets) becomes larger, with the largest enhancement obtained in the case on instances with all the assets from the S&P 500 ( \\(N = 500\\) ), as shown in Fig. 2",
+    "footnote": [],
+    "bbox": [
+      [
+        185,
+        60,
+        810,
+        732
+      ]
+    ],
+    "page_idx": 15
+  }
+]

preprint/preprint__00c2b94550129fb8f084bb495841a196a9f5afe6d5c14e29f461a9abeaa8a98e/preprint__00c2b94550129fb8f084bb495841a196a9f5afe6d5c14e29f461a9abeaa8a98e.mmd

@@ -0,0 +1,381 @@
+
+# GEO: Enhancing Combinatorial Optimization with Classical and Quantum Generative Models  
+
+Francisco Fernandez Alcazar  Alejandro Perdomo-Ortiz ( \(\square\) alejandro@zapatacomputing.com )  Zapata Computing Canada https://orcid.org/0000- 0001- 7176- 4719  
+
+Mohammad Ghazi Vakili  Zapata Computing Canada  
+
+Can Kalayci  Pamukkale University  
+
+Article  
+
+Keywords:  
+
+Posted Date: August 8th, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 241950/v1  
+
+License: © \(\circledcirc\) This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License
+
+<--- Page Split --->
+
+# GEO: Enhancing Combinatorial Optimization with Classical and Quantum Generative Models  
+
+Javier Alcazar, \(^{1}\) Mohammad Ghazi Vakili, \(^{1,2,3}\) Can B. Kalayci, \(^{1,4}\) and Alejandro Perdomo- Ortiz \(^{1,*}\)  
+
+\(^{1}\) Zapata Computing Canada Inc., 325 Front St W, Toronto, ON, M5V 2Y1 \(^{2}\) Department of Chemistry, University of Toronto, Toronto, ON, M5G 1Z8, Canada \(^{3}\) Department of Computer Science, University of Toronto, Toronto, Ontario M5S 2E4, Canada \(^{4}\) Department of Industrial Engineering, Pamukkale University, Kinikli Campus, 20160, Denizli, Turkey (Dated: July 2, 2022)  
+
+We introduce a new framework that leverages machine learning models known as generative models to solve optimization problems. Our Generator- Enhanced Optimization (GEO) strategy is flexible to adopt any generative model, from quantum to quantum- inspired or classical, such as Generative Adversarial Networks, Variational Autoencoders, or Quantum Circuit Born Machines, to name a few. Here, we focus on a quantum- inspired version of GEO relying on tensor- network Born machines, and referred to hereafter as TN- GEO. We present two prominent strategies for using TN- GEO. The first uses data points previously evaluated by any quantum or classical optimizer, and we show how TN- GEO improves the performance of the classical solver as a standalone strategy in hard- to- solve instances. The second strategy uses TN- GEO as a standalone solver, i.e., when no previous observations are available. Here, we show its superior performance when the goal is to find the best minimum given a fixed budget for the number of function calls. This might be ideal in situations where the cost function evaluation can be very expensive. To illustrate our results, we run these benchmarks in the context of the portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes. We show that TN- GEO can propose unseen candidates with lower cost function values than the candidates seen by classical solvers. This is the first demonstration of the generalization capabilities of quantum- inspired generative models that provide real value in the context of an industrial application. We also comprehensively compare state- of- the- art algorithms in a generalized version of the portfolio optimization problem. The results show that TN- GEO is among the best compared to these state- of- the- art algorithms; a remarkable outcome given the solvers used in the comparison have been fine- tuned for decades in this real- world industrial application. We see this as an important step toward a practical advantage with quantum- inspired models and, subsequently, with quantum generative models.  
+
+## I. INTRODUCTION  
+
+Along with machine learning and the simulation of materials, combinatorial optimization is one of top candidates for practical quantum advantage. That is, the moment where a quantum- assisted algorithm outperforms the best classical algorithms in the context of a real- world application with a commercial or scientific value. There is an ongoing portfolio of techniques to tackle optimization problems with quantum subroutines, ranging from algorithms tailored for quantum annealers (e.g., Refs. [1, 2]), gate- based quantum computers (e.g., Refs. [3, 4]) and quantum- inspired (QI) models based on tensor networks (e.g., Ref. [5]).  
+
+Regardless of the quantum optimization approach proposed to date, there is a need to translate the real- world problem into a polynomial unconstrained binary optimization (PUBO) expression - a task which is not necessarily straightforward and that usually results in an overhead in terms of the number of variables. Specific real- world use cases illustrating these PUBO mappings are depicted in Refs. [6] and [7]. Therefore, to achieve practical quantum advantage in the near- term, it would be ideal to find a quantum optimization strategy that can work on arbitrary objective functions, bypassing the translation and overhead limitations raised here.  
+
+In our work, we offer a solution to these challenges by proposing a novel generator- enhanced optimization (GEO) framework which leverage the power of (quantum or classical) generative models. This family of solvers can scale to large problems where combinatorial problems become intractable in real- world settings. Since our optimization strategy does not rely on the details of the objective function to be minimized, it is categorized in the group of so- called black- box solvers. Another highlight of our approach is that it can utilize available observations obtained from attempts to solve the optimization problem. These initial evaluations can come from any source, from random search trials to tailored state- of- the- art (SOTA) classical or quantum optimizers for the specific problem at hand.   
+
+Our GEO strategy is based on two key ideas. First, the generative- modeling component aims to capture the correlations from the previously observed data (step 0- 3 in Fig. 1). Second, since the focus here is on a minimization task, the (quantum) generative models need to be capable of generating new "unseen" solution candidates which have the potential to have a lower value for the objective function than those already "seen" and used as the training set (step 4- 6 in Fig. 1). This exploration towards unseen and valuable samples is by definition the fundamental concept behind generalization: the most desirable and important feature of any practical ML model. We will elaborate next on each of these components and demonstrate these two properties in the context of the tensor- network- based generative models and its application to a non- deterministic polynomial- time hard (NP- hard) version of the portfolio optimization in finance.  
+
+To the best of our knowledge, this is the first optimization strategy proposed to do an efficient blackbox exploration
+
+<--- Page Split --->
+
+of the objective- function landscape with the help of generative models. Although other proposal leveraging generative models as a subroutine within the optimizer have appeared recently since the publication of our manuscript (e.g., see GFlowNets [8] and the variational neural annealing [9] algorithms), our framework is the only capable of both, handling arbitrary cost functions and also with the possibility of swapping the generator for a quantum or quantum- inspired implementation. GEO also has the enhanced feature that the more data is available, the more information can be passed and used to train the (quantum) generator.  
+
+In this work, we highlight the different features of GEO by performing a comparison with alternative solvers, such as Bayesian optimizers and generic solvers like simulated annealing. In the case of the specific real- world large- scale application of portfolio optimization, we compare against the SOTA optimizers and show the competitiveness of our approach. These results are presented in Sec. III. Next, in Sec. II, we present the GEO approach and its range of applicability.  
+
+## II. QUANTUM-ENHANCED OPTIMIZATION WITH GENERATIVE MODELS  
+
+As shown in Fig. 1, depending on the GEO specifics we can construct an entire family of solvers whose generative modeling core range from classical, QI or quantum circuit (QC) enhanced, or hybrid quantum- classical model. These options can be realized by utilizing, for example, Boltzmann machines [10] or Generative Adversarial Networks (GAN) [11], Tensor- Network Born Machines (TNBm) [12], Quantum Circuit Born Machines (QCBM)[13] or Quantum- Circuit Associative Adversarial Networks (QC- AAN)[14] respectively, to name just a few of the many options for this probabilistic component.  
+
+QI algorithms come as an interesting alternative since these allow one to simulate larger scale quantum systems with the help of efficient tensor- network (TN) representations. Depending on the complexity of the TN used to build the quantum generative model, one can simulate from thousands of problem variables to a few tens, the latter being the limit of simulating an universal gate- based quantum computing model. This is, one can control the amount of quantum resources available in the quantum generative model by choosing the QI model.  
+
+Therefore, from all quantum generative model options, we chose to use a QI generative model based on TNs to test and scale our GEO strategy to instances with a number of variables commensurate with those found in industrial- scale scenarios. We refer to our solver hereafter as TN- GEO. For the training of our TN- GEO models we followed the work of Han et al. [15] where they proposed to use Matrix Product States (MPS) to build the unsupervised generative model. The latter extends the scope from early successes of quantum- inspired models in the context of supervised ML [16- 19].  
+
+In this paper we will discuss two modes of operation for our family of quantum- enhanced solvers:  
+
+- In TN-GEO as a "booster" we leverage past observa  
+
+tions from classical (or quantum) solvers. To illustrate this mode we use observations from simulated annealing (SA) runs. Simulation details are provided in Appendix A 5.  
+
+- In TN-GEO as a stand-alone solver all initial cost function evaluations are decided entirely by the quantum-inspired generative model, and a random prior is constructed just to give support to the target probability distribution the MPS model is aiming to capture. Simulation details are provided in Appendix A 6.  
+
+Both of these strategies are captured in the algorithm workflow diagram in Fig. 1 and described in more detail in Appendix A.  
+
+## III. RESULTS AND DISCUSSION  
+
+To illustrate the implementation for both of these settings we tested their performance on an NP- hard version of the portfolio optimization problem with cardinality constraints. The selection of optimal investment on a specific set of assets, or portfolios, is a problem of great interest in the area of quantitative finance. This problem is of practical importance for investors, whose objective is to allocate capital optimally among assets while respecting some investment restrictions. The goal of this optimization task, introduced by Markowitz [20], is to generate a set of portfolios that offers either the highest expected return (profit) for a defined level of risk or the lowest risk for a given level of expected return. In this work, we focus in two variants of this cardinality constrained optimization problem. The first scenario aims to choose portfolios which minimize the volatility or risk given a specific target return (more details are provided in Appendix A 1). To compare with the reported results from the best performing SOTA algorithms, we ran TN- GEO in a second scenario where the goal is to choose the best portfolio given a fixed level of risk aversion. This is the most commonly used version of this optimization problem when it comes to comparison among SOTA solvers in the literature (more details are provided in Appendix A 2).  
+
+### A. TN-GEO as a booster for any other combinatorial optimization solver  
+
+In Fig. 2 we present the experimental design and the results obtained from using TN- GEO as a booster. In these experiments we illustrate how using intermediate results from simulated annealing (SA) can be used as seed data for our TN- GEO algorithm. As described in Fig. 2, there are two strategies we explored (strategies 1 and 2) to compare with our TN- GEO strategy (strategy 4). To fairly compare each strategy, we provide each with approximately the same computational wall- clock time. For strategy 2, this translates into performing additional restarts of SA with the time allotted for TN- GEO. In the case of strategy 1, where we explored different settings for SA from the start compared to those used in strategy 2, this amounts to using the same total number
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>FIG. 1. Scheme for our Generator-Enhanced Optimization (GEO) strategy. The GEO framework leverages generative models to utilize previous samples coming from any quantum or classical solver. The trained quantum or classical generator is responsible for proposing candidate solutions which might be out of reach for conventional solvers. This seed data set (step 0) consists of observation bitstrings \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) and their respective costs \(\{\sigma^{(i)}\}_{\mathrm{seed}}\) . To give more weight to samples with low cost, the seed samples and their costs are used to construct a softmax function which serves as a surrogate to the cost function but in probabilistic domain. This softmax surrogate also serves as a prior distribution from which the training set samples are withdrawn to train the generative model (steps 1-3). As shown in the figure between steps 1 and 2, training samples from the softmax surrogate are biased favoring those with low cost value. For the work presented here, we implemented a tensor-network (TN)-based generative model. Therefore, we refer to this quantum-inspired instantiation of GEO as TN-GEO. Other families of generative models from classical, quantum, or hybrid quantum-classical can be explored as expounded in the main text. The quantum-inspired generator corresponds to a tensor-network Born machine (TNBM) model which is used to capture the main features in the training data, and to propose new solution candidates which are subsequently post selected before their costs \(\{\sigma^{(i)}\}_{\mathrm{new}}\) are evaluated (steps 4-6). The new set is merged with the seed data set (step 7) to form an updated seed data set (step 8) which is to be used in the next iteration of the algorithm. More algorithmic details for the two TN-GEO strategies proposed here, as a booster or as a stand-alone solver, can be found in the main text and in A5 and A6 respectively. </center>  
+
+of number of cost functions evaluations as those allocated to SA in strategy 2. For our experiments this number was set to 20,000 cost function evaluations for strategies 1 and 2. In strategy 4, the TN- GEO was initialized with a prior consisting of the best 1,000 observations out of the first 10,000 coming from strategy 2 (see Appendix A 5 for details). To evaluate the performance enhancement obtained from the TN- GEO strategy we compute the relative TN- GEO enhancement \(\eta\) , which we define as  
+
+\[\eta = \frac{C_{\mathrm{min}}^{\mathrm{cl}}}{C_{\mathrm{min}}^{\mathrm{cl}}} = \frac{C_{\mathrm{min}}^{\mathrm{TN - GEO}}}{C_{\mathrm{min}}^{\mathrm{cl}}}\times 100\% . \quad (1)\]  
+
+Here, \(C_{\mathrm{min}}^{\mathrm{cl}}\) is the lowest minimum value found by the classical strategy (e.g., strategies 1- 3) while \(C_{\mathrm{min}}^{\mathrm{TN - GEO}}\) corresponds to the lowest value found with the quantum- enhanced approach (e.g., with TN- GEO). Therefore, positive values reflect an improvement over the classical- only approaches, while negative values indicate cases where the classical solvers outperform the quantum- enhanced proposal.  
+
+As shown in the Fig. 2, we observe that TN- GEO outperforms on average both of the classical- only strategies imple  
+
+As shown in the Fig. 2, we observe that TN- GEO outperforms on average both of the classical- only strategies implemented. The quantum- inspired enhancement observed here, as well as the trend for a larger enhancement as the number of variables (assets) becomes larger, is confirmed in many other investment universes with a number of variables ranging from \(N = 30\) to \(N = 100\) (see Appendix B for more details). Although we show an enhancement compared to SA, similar results could be expected when other solvers are used, since our approach builds on solutions found by the solver and does not compete with it from the start of the search. Furthermore, the more data available, the better the expected performance of TN- GEO is. An important highlight of TN- GEO as a booster is that these previous observations can come from a combination of solvers, as different as purely quantum or classical, or hybrid.  
+
+The observed performance enhancement compared with the classical- only strategy must be coming from a better exploration of the relevant search space, i.e., the space of those bitstring configurations \(x\) representing portfolios which could yield a low risk value for a specified expected investment return. That is the intuition behind the construction of TN- GEO. The goal of the generative model is to capture the important
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>FIG. 2. TN-GEO as a booster. Top: Strategies 1-3 correspond to the current options a user might explore when solving a combinatorial optimization problem with a suite of classical optimizers such as simulated annealing (SA), parallel tempering (PT), generic algorithms (GA), among others. In strategy 1, the user would use its computational budget with a preferred solver. In strategy 2-4 the user would inspect intermediate results and decide whether to keep trying with the same solver (strategy 2), try a new solver or a new setting of the same solver used to obtain the intermediate results (strategy 3), or, as proposed here, to use the acquired data to train a quantum or quantum-inspired generative model within a GEO framework such as TN-GEO (strategy 4). Bottom: Results showing the relative TN-GEO enhancement from TN-GEO over either strategy 1 or strategy 2. Positive values indicate runs where TN-GEO outperformed the respective classical strategies (see Eq. 1). The data represents bootstrapped medians from 20 independent runs of the experiments and error bars correspond to the 95% confidence intervals. The two instances presented here correspond to portfolio optimization instances where all the assets in the S&P 500 market index where included \((N = 500)\) , under two different cardinality constraints \(\kappa\) . This cardinality constraint indicate the number of assets that can be included at a time in valid portfolios, yielding a search space of \(M = \binom{N}{\kappa}\) , with \(M \sim 10^{69}\) portfolios candidates for \(\kappa = 50\) . </center>  
+
+correlations in the previously observed data, and to use its generative capabilities to propose similar new candidates.  
+
+Generating new candidates is by no means a trivial task in ML and it determines the usefulness and power of the model since it measure its generalization capabilities. In this setting of QI generative models, one expects that the MPS- based  
+
+generative model at the core of TN- GEO is not simply memorizing the observations given as part of the training set, but that it will provide new unseen candidates. This is an idea which has been recently tested and demonstrated to some extent on synthetic data sets (see e.g., Refs. [21], [22] and [23]. In Fig. 3 we demonstrate that our quantum- inspired generative model is generalizing to new samples and that these add real value to the optimization search. To the best of our knowledge this is the first demonstration of the generalization capabilities of quantum generative models in the context of a real- world application in an industrial scale setting, and one of our main findings in our paper.  
+
+Note that our TN- based generative model not only produces better minima than the classical seed data, but it also generates a rich amount of samples in the low cost spectrum. This bias is imprinted in the design of our TN- GEO and it is the purpose of the softmax surrogate prior distribution shown in Fig. 1. This richness of new samples could be useful not only for the next iteration of the algorithm, but they may also be readily of value to the user solving the application. In some applications there is value as well in having information about the runnersup. Ultimately, the cost function is just a model of the system guiding the search, and the lowest cost does not translate to the best performance in the real- life investment strategy.  
+
+### B. Generator-Enhanced Optimization as a Stand-Alone Solver  
+
+Next, we explore the performance of our TN- GEO framework as a stand- alone solver. The focus is in combinatorial problems whose cost functions are expensive to evaluate and where finding the best minimum within the least number of calls to this function is desired. In Fig. 4 we present the comparison against four different classical optimization strategies. As the first solver, we use the random solver, which corresponds to a fully random search strategy over the \(2^{N}\) bitstrings of all possible portfolios, where \(N\) is the number of assets in our investment universe. As second solver, we use the conditioned random solver, which is a more sophisticated random strategy compared to the fully random search. The conditioned random strategy uses the a priori information that the search is restricted to bitstrings containing a fixed number of \(\kappa\) assets. Therefore the number of combinatorial possibilities is \(M = \binom{N}{\kappa}\) , which is significantly less than \(2^{N}\) . As expected, when this information is not used the performance of the random solver over the entire \(2^{N}\) search space is worse. The other two competing strategies considered here are SA and the Bayesian optimization library GPyOpt [24]. In both of these classical solvers, we adapted their search strategy to impose this cardinality constraint with fixed \(\kappa\) as well (details in Appendix. A 4). This raises the bar even higher for TN- GEO which is not using that a priori information to boost its performance [25]. As explained in Appendix A 6, we only use this information indirectly during the construction of the artificial seed data set which initializes the algorithm (step 0, Fig. 1), but it is not a strong constraint during the construction of the QI generative model (step 3, Fig. 1) or imposed to generate the new candidate samples coming from it (step 4,
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>FIG. 3. Generalization capabilities of our quantum-inspired generative model. Left panel corresponds to an investment universe with \(N = 50\) assets while the right panel corresponds to one with \(N = 100\) assets. The blue histogram represents the number of observations or portfolios obtained from the classical solver (seed data set). In orange we represent samples coming from our quantum generative model at the core of TN-GEO. The green dash line is positioned at the best risk value found in the seed data. This mark emphasizes all the new outstanding samples obtained with the quantum generative model and which correspond to lower portfolio risk value (better minima) than those available from the classical solver by itself. The number of outstanding samples in the case of \(N = 50\) is equal to 31, while 349 outstanding samples were obtained from the MPS generative model in the case of \(N = 100\) . </center>  
+
+![](images/Figure_4.jpg)
+
+<center>FIG. 4. TN-GEO as a stand-alone solver: In this comparison of TN-GEO against four classical competing strategies, investment universes are constructed from subsets of the S&P 500 with a diversity in the number of assets (problem variables) ranging from \(N = 30\) to \(N = 100\) . The goal is to minimize the risk given an expected return which is one of the specifications in the combinatorial problem addressed here. Error bars and their 95% confidence intervals are calculated from bootstrapping over 100 independent random initializations for each solver on each problem. The main line for each solver corresponds to the bootstrapped median over these 100 repetitions, demonstrating the superior performance of TN-GEO over the classical solvers considered here. As specified in the text, with the exception of TN-GEO, the classical solvers use to their advantage the a priori information coming from the cardinality constraint imposed in the selection of valid portfolios. </center>
+
+<--- Page Split --->
+
+Fig. 1). Post selection can be applied a posteriori such that only samples with the right cardinality are considered as valid candidates towards the selected set (step 5, Fig. 1).  
+
+In Fig. 4 we demonstrate the advantage of our TN- GEO stand- alone strategy compared to any of these widely- used solvers. In particular, it is interesting to note that the gap between TN- GEO and the other solvers seems to be larger for larger number of variables.  
+
+### C. Comparison with state-of-the-art algorithms  
+
+Finally, we compare TN- GEO with nine different leading SOTA optimizers covering a broad spectrum of algorithmic strategies for this specific combinatorial problem, based on and referred hereafter as: 1) GTS [26], the genetic algorithms, tabu search, and simulated annealing; 2) IPSO [27], an improved particle swarm optimization algorithm [27]; 3) IPSO- SA [28], a hybrid algorithm combining particle swarm optimization and simulated annealing; 4) PBILD [29], a population- based incremental learning and differential evolution algorithm; 5) GRASP [30], a greedy randomized adaptive solution procedure; 6) ABCFEIT [31], an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures; 7) HAAG [32], a hybrid algorithm integrating ant colony optimization, artificial bee colony and genetic algorithms; 8) VNSQP [33], a variable neighborhood search algorithm combined with quadratic programming; and, 9) RCABC [34], a rapidly converging artificial bee colony algorithm.  
+
+The test data used by the vast majority of researchers in the literature who have addressed the problem of cardinality- constrained portfolio optimization come from ORLibrary [35], which correspond to the weekly prices between March 1992 and September 1997 of the following indexes: Hang Seng in Hong Kong (31 assets); DAX 100 in Germany (85 assets); FTSE 100 in the United Kingdom (89 assets); S&P 100 in the United States (98 assets); and Nikkei 225 in Japan (225 assets).  
+
+Here we present the results obtained with TN- GEO and its comparison with the nine different SOTA metaheuristic algorithms mentioned above and whose results are publicly available from the literature. Table I shows the results of all algorithms and all performance metrics for each of the 5 index data sets (for more details on the evaluation metrics, see Appendix A 2). Each algorithm corresponds to a different column, with TN- GEO in the rightmost column. The values are shown in red if the TN- GEO algorithm performed better or equally well compared to the other algorithms on the corresponding performance metric. The numbers in bold mean that the algorithm found the best (lowest) value across all algorithms.  
+
+From all the entries in this table, \(67\%\) of them correspond to red entries, where TN- GEO either wins or draws, which is a significant percentage giving that these optimizers are among the best reported in the last decades.  
+
+In Table II we show a pairwise comparison of TN- GEO against each of the SOTA optimizers. This table reports the  
+
+number of times TN- GEO wins, loses, or draws compared to results reported for the other optimizer, across all the performance metrics and for all the 5 different market indexes. Note that since not all the performance metrics are reported for all the solvers and market indexes, the total number of wins, draws, or losses varies. Therefore, we report in the same table the overall percentage of wins plus draws in each case. We see that this percentage is greater than \(50\%\) in all the cases.  
+
+Furthermore, in Table II, we use the Wilcoxon signed- rank test [36], which is a widely used nonparametric statistical test used to evaluate and compare the performance of different algorithms in different benchmarks [37]. Therefore, to statistically validate the results, a Wilcoxon signed- rank test is performed to provide a meaningful comparison between the results from TN- GEO algorithm and the SOTA metaheuristic algorithms. The Wilcoxon signed- rank test tests the null hypothesis that the median of the differences between the results of the algorithms is equal to 0. Thus, it tests whether there is no significant difference between the performance of the algorithms. The null hypothesis is rejected if the significance value \((p)\) is less than the significance level \((\alpha)\) , which means that one of the algorithms performs better than the other. Otherwise, the hypothesis is retained.  
+
+As can be seen from the table, the TN- GEO algorithm significantly outperforms the GTS and PBILD methods on all performance metrics rejecting the null hypothesis at the 0.05 significance level. On the other hand, the null hypotheses are accepted at \(\alpha = 0.05\) for the TN- GEO algorithm over the other remaining algorithms. Thus, in terms of performance on all metrics combined, the results show that there is no significant difference between TN- GEO and these remaining seven SOTA optimizers (IPSO, IPSO- SA, GRASP, ABCFEIT, HAAG, VNSQP, and RCABC)  
+
+Overall, the results confirm the competitiveness of our quantum- inspired proposed approach against SOTA metaheuristic algorithms. This is remarkable given that these metaheuristics have been explored and fine- tuned for decades.  
+
+## IV. OUTLOOK  
+
+Compared to other quantum optimization strategies, an important feature of TN- GEO is its algorithmic flexibility. As shown here, unlike other proposals, our GEO framework can be applied to arbitrary cost functions, which opens the possibility of new applications that cannot be easily addressed by an explicit mapping to a polynomial unconstrained binary optimization (PUBO) problem. Our approach is also flexible with respect to the source of the seed samples, as they can come from any solver, possibly more efficient or even application- specific optimizers. The demonstrated generalization capabilities of the generative model that forms its core, helps TN- GEO build on the progress of previous experiments with other state- of- the- art solvers, and it provides new candidates that the classical optimizer may not be able to achieve on its own. We are optimistic that this flexible approach will open up the broad applicability of quantum and quantum- inspired generative models to real- world combinatorial optimization
+
+<--- Page Split --->
+
+
+TABLE I. Detailed comparison with SOTA algorithms for each of the five index data sets and on seven different performance indicators described in Appendix A 2. Entries in red correspond to cases where TN-GEO performed better or tied compared to the other algorithm. Entries in bold, corresponding to the best (lowest) value, for each specific indicator.   
+
+<table><tr><td>Data Set</td><td>Performance Indicator</td><td>GTS</td><td>IPSO</td><td>IPSO-SA</td><td>PBILD</td><td>GRASP</td><td>ABCFEIT</td><td>HAAG</td><td>VNSQP</td><td>RCABC</td><td>TN-GEO</td></tr><tr><td rowspan="7">Hang Seng</td><td>Mean</td><td>1.0957</td><td>1.0953</td><td>-</td><td>1.1431</td><td>1.0965</td><td>1.0953</td><td>1.0965</td><td>1.0964</td><td>1.0873</td><td>1.0958</td></tr><tr><td>Median</td><td>1.2181</td><td>-</td><td>-</td><td>1.2390</td><td>1.2155</td><td>1.2181</td><td>1.2181</td><td>1.2155</td><td>1.2154</td><td>1.2181</td></tr><tr><td>Min</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>Max</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.5538</td><td>1.5538</td><td>1.5538</td><td>1.5538</td><td>-</td><td>1.5538</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0001</td><td>-</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>-</td><td>0.0001</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>1.6368</td><td>-</td><td>1.6400</td><td>1.6432</td><td>1.6395</td><td>1.6397</td><td>1.6342</td><td>1.6392</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>0.6059</td><td>-</td><td>0.6060</td><td>0.6047</td><td>0.6085</td><td>0.6058</td><td>0.5964</td><td>0.6082</td></tr><tr><td rowspan="7">DAX100</td><td>Mean</td><td>2.5424</td><td>2.5417</td><td>-</td><td>2.4251</td><td>2.3126</td><td>2.3258</td><td>2.3130</td><td>2.3125</td><td>2.2898</td><td>2.3142</td></tr><tr><td>Median</td><td>2.5466</td><td>-</td><td>-</td><td>2.5866</td><td>2.5630</td><td>2.5678</td><td>2.5587</td><td>2.5630</td><td>2.5629</td><td>2.5660</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0059</td><td>0.0023</td><td>0.0023</td><td>0.0059</td><td>0.0059</td><td>0.0023</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>4.0275</td><td>4.0275</td><td>4.0275</td><td>4.0275</td><td>-</td><td>4.0275</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0001</td><td>-</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>-</td><td>0.0001</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>6.7806</td><td>-</td><td>6.7593</td><td>6.7925</td><td>6.7806</td><td>6.7583</td><td>6.8326</td><td>6.7540</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>1.2770</td><td>-</td><td>1.2769</td><td>1.2761</td><td>1.2780</td><td>1.2767</td><td>1.2357</td><td>1.2763</td></tr><tr><td rowspan="7">FTSE100</td><td>Mean</td><td>1.1076</td><td>1.0628</td><td>-</td><td>0.9706</td><td>0.8451</td><td>0.8481</td><td>0.8451</td><td>0.8453</td><td>0.8406</td><td>0.8445</td></tr><tr><td>Median</td><td>1.0841</td><td>-</td><td>-</td><td>1.0841</td><td>1.0841</td><td>1.0841</td><td>1.0841</td><td>-</td><td>1.0841</td><td>1.0841</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0016</td><td>0.0047</td><td>0.0006</td><td>0.0045</td><td>0.0016</td><td>0.0047</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>2.0576</td><td>2.0638</td><td>2.0605</td><td>2.0669</td><td>2.0670</td><td>2.0775</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0000</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>2.4701</td><td>-</td><td>2.4350</td><td>2.4397</td><td>2.4350</td><td>2.4349</td><td>2.4149</td><td>2.4342</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>0.3247</td><td>-</td><td>0.3245</td><td>0.3255</td><td>0.3186</td><td>0.3252</td><td>0.3207</td><td>0.3254</td></tr><tr><td rowspan="7">S&P100</td><td>Mean</td><td>1.9328</td><td>1.6890</td><td>-</td><td>1.6386</td><td>1.2937</td><td>1.2930</td><td>1.2930</td><td>1.2649</td><td>1.3464</td><td>1.2918</td></tr><tr><td>Median</td><td>1.1823</td><td>-</td><td>-</td><td>1.1692</td><td>1.1420</td><td>1.1369</td><td>1.1323</td><td>1.1323</td><td>1.1515</td><td>1.1452</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0009</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0009</td><td>0.0000</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>5.4551</td><td>5.4422</td><td>5.4642</td><td>5.4551</td><td>5.4520</td><td>5.4422</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0001</td><td>-</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>-</td><td>0.0001</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>2.6281</td><td>-</td><td>2.5211</td><td>2.5260</td><td>2.5255</td><td>2.5105</td><td>2.5364</td><td>2.5269</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>0.7846</td><td>-</td><td>0.9063</td><td>0.8885</td><td>0.7044</td><td>0.9072</td><td>0.8858</td><td>0.9117</td></tr><tr><td rowspan="7">Nikkei</td><td>Mean</td><td>0.6066</td><td>0.6870</td><td>-</td><td>0.5972</td><td>0.5782</td><td>0.5781</td><td>0.5781</td><td>0.5904</td><td>0.5665</td><td>0.5793</td></tr><tr><td>Median</td><td>0.6093</td><td>-</td><td>-</td><td>0.5896</td><td>0.5857</td><td>0.5856</td><td>0.5854</td><td>0.5857</td><td>0.5858</td><td>0.5855</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.1606</td><td>1.1606</td><td>1.1607</td><td>1.1606</td><td>1.1606</td><td>1.1606</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0000</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>0.9583</td><td>-</td><td>0.8359</td><td>0.8396</td><td>0.8191</td><td>0.8561</td><td>0.8314</td><td>0.8353</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>1.7090</td><td>-</td><td>0.4184</td><td>0.4147</td><td>0.4233</td><td>0.4217</td><td>0.4042</td><td>0.4229</td></tr></table>  
+
+TABLE II. Pairwise comparison of TN-GEO against each of the SOTA optimizers. The asymptotic significance is part of the Wilcoxon signedrank test results. The null hypothesis that the performance of the two algorithms is the same is tested at the \(95\%\) confidence level (significance level: \(\alpha = .05\) ). Results show that TN-GEO is on par with all the SOTA algorithms, and in two cases, GTS and PBILD, it significantly outperforms them. We also report the count for TN-GEO wins, losses, and ties, compared to each of the other algorithms.   
+
+<table><tr><td>TN-GEO vs Other:</td><td>GTS</td><td>IPSO</td><td>IPSO-SA</td><td>PBILD</td><td>GRASP</td><td>ABCFEIT</td><td>HAAG</td><td>VNSQP</td><td>RCABC</td></tr><tr><td>Wins(+)</td><td>6</td><td>4</td><td>6</td><td>9</td><td>12</td><td>10</td><td>11</td><td>11</td><td>8</td></tr><tr><td>Loss(-)</td><td>2</td><td>1</td><td>4</td><td>0</td><td>12</td><td>9</td><td>11</td><td>12</td><td>16</td></tr><tr><td>Ties</td><td>2</td><td>0</td><td>5</td><td>1</td><td>11</td><td>16</td><td>13</td><td>12</td><td>11</td></tr><tr><td>(Wins+Ties)/Total</td><td>80%</td><td>80%</td><td>67%</td><td>100%</td><td>66%</td><td>74%</td><td>69%</td><td>66%</td><td>54%</td></tr><tr><td>Asymptotic significance (p)</td><td>.036</td><td>.080</td><td>.308</td><td>.008</td><td>.247</td><td>.888</td><td>.363</td><td>.594</td><td>.110</td></tr><tr><td>Decision</td><td>Reject</td><td>Retain</td><td>Retain</td><td>Reject</td><td>Retain</td><td>Retain</td><td>Retain</td><td>Retain</td><td>Retain</td></tr></table>  
+
+problems at the industrial scale.  
+
+Although we have limited the scope of this work to tensor network- based generative quantum models, it would be a natural extension to consider other generative quantum models as well. For example, hybrid classical quantum models such as  
+
+quantum circuit associative adversarial networks (QC- AAN) [14] can be readily explored to harness the power of generative quantum models with so- called noisy intermediate- scale quantum (NISQ) devices [38]. In particular, the QC- AAN framework opens up the possibility of working with a larger
+
+<--- Page Split --->
+
+number of variables and going beyond discrete values (e.g., variables with continuous values). Both quantum- inspired and hybrid quantum- classical algorithms can be tested in this GEO framework in even larger problem sizes of this NP- hard version of the portfolio optimization problem or any other combinatorial optimization problem. As the number of qubits in NISQ devices increases, it would be interesting to explore generative models that can utilize more quantum resources, such as Quantum Circuit Born Machines (QCBM)[13]: a general framework to model arbitrary probability distributions and perform generative modeling tasks with gate- based quantum computers.  
+
+Increasing the expressive power of the quantum- inspired core of MPS to other more complex but still efficient QI approaches, such as tree- tensor networks [39], is another interesting research direction. Although we have fully demonstrated the relevance and scalability of our algorithm for industrial applications by increasing the performance of classical solvers on industrial scale instances (all 500 assets in the S&P 500 market index), there is a need to explore the performance improvement that could be achieved by more complex TN representations or on other combinatorial problems.  
+
+Although the goal of GEO was to show good behavior as a general black- box algorithm without considering the specifics of the study application, it is a worthwhile avenue to exploit the specifics of the problem formulation to improve its performance and runtime. In particular, for the portfolio optimization problem with a cardinality constraint, it is useful to incorporate this constraint as a natural MPS symmetry, thereby reducing the effective search space of feasible solutions from the size of the universe to the cardinality size.  
+
+Finally, our thorough comparison with SOTA algorithms, which have been fine- tuned for decades on this specific application, shows that our TN- GEO strategy manages to outperform a couple of these and is on par with the other seven optimizers. This is a remarkable feat for this new approach and hints at the possibility of finding commercial value in these quantum- inspired strategies in large- scale real- world problems, as the instances considered in this work. Also, it calls for more fundamental insights towards understanding when and where it would be beneficial to use this TN- GEO framework, which relies heavily on its quantum- inspired generative ML model. For example, understanding the intrinsic bias in these models, responsible for their remarkable performance, is another important milestone on the road to practical quantum advantage with quantum devices in the near future. The latter can be asserted given the tight connection of these quantum- inspired TN models to fully quantum models deployed on quantum hardware. And this question of when to go with quantum- inspired or fully quantum models is a challenging one that we are exploring in ongoing future work.  
+
+## ACKNOWLEDGMENTS  
+
+The authors would like to acknowledge Manuel S. Rudolph, Marta Mauri, Matthew J.S. Beach, Yudong Cao, Luis Serrano, Jhonathan Romero- Fontalvo, Brian Dellabetta, Matthew Kowalsky, Jacob Miller, John Realpe- Gomez, and Collin Farquhar for their feedback on an early version of this manuscript  
+
+[1] Tadashi Kadowaki and Hidetoshi Nishimori, "Quantum annealing in the transverse ising model," Phys. Rev. E. 58, 5355 (1998). [2] Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda, "A quantum adiabatic evolution algorithm applied to random instances of an NP- Complete problem," Science 292, 472- 475 (2001). [3] Sam Gutmann Edward Farhi, Jeffrey Goldstone, "A quantum approximate optimization algorithm," arXiv:1411.4028 (2014). [4] Stuart Hadfield, Zhihui Wang, Bryan O'Gorman, Eleanor G Rieffel, Davide Venturelli, and Rupak Biswas, "From the quantum approximate optimization algorithm to a quantum alternating operator ansatz," Algorithms 12, 34 (2019). [5] Samuel Mugel, Carlos Kuchkovsky, Escolastico Sanchez, Samuel Fernandez- Lorenzo, Jorge Luis- Hita, Enrique Lizaso, and Roman Orus, "Dynamic portfolio optimization with real datasets using quantum processors and quantum- inspired tensor networks," (2020), arXiv:2007.00017 [quant- ph]. [6] A. Perdomo- Ortiz, N. Dickson, M. Drew- Brook, G. Rose, and A. Aspuru- Guzik, "Finding low- energy conformations of lattice protein models by quantum annealing," Sci. Rep. 2, 571 (2012). [7] Alejandro Perdomo- Ortiz, Alexander Feldman, Asier Ozeta, Sergei V. Isakov, Zheng Zhu, Bryan O'Gorman, Helmut G. Katzgraber, Alexander Diedrich, Hartmut Neven, Johan de Kleer, Brad Lackey, and Rupak Biswas, "Readiness of quantum optimization machines for industrial applications,"  
+
+Phys. Rev. Applied 12, 014004 (2019). [8] Emmanuel Bengio, Moksh Jain, Maksym Korablyov, Doina Precup, and Yoshua Bengio, "Flow network based generative models for non- iterative diverse candidate generation," (2021). [9] Mohamed Hibat- Allah, Estelle M. Inack, Roeland Wiersema, Roger G. Melko, and Juan Carrasquilla, "Variational neural annealing," Nature Machine Intelligence 3, 952- 961 (2021). [10] Song Cheng, Jing Chen, and Lei Wang, "Information perspective to probabilistic modeling: Boltzmann machines versus born machines," Entropy 20, 583 (2018). [11] Ian J. Goodfellow, Jean Pouget- Abadie, Mehdi Mirza, Bing Xu, David Warde- Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio, "Generative adversarial networks," (2014), arXiv:1406.2661 [stat.ML]. [12] Song Cheng, Jing Chen, and Lei Wang, "Information perspective to probabilistic modeling: Boltzmann machines versus Born machines," Entropy 20 (2017). [13] Marcello Benedetti, Delfina Garcia- Pintos, Yunseong Nam, and Alejandro Perdomo- Ortiz, "A generative modeling approach for benchmarking and training shallow quantum circuits," npj Quantum Information 5 (2018), 10.1038/s41534- 019- 0157- 8. [14] Manuel S. Rudolph, Ntwali Toussaint Bashige, Amara Katabarwa, Sonika Johr, Borja Peropadre, and Alejandro Perdomo- Ortiz, "Generation of high resolution handwritten digits with an ion- trap quantum computer," (2020),
+
+<--- Page Split --->
+
+arXiv:2012.03924 [quant- ph]. [15] Zhao- Yu Han, Jun Wang, Heng Fan, Lei Wang, and Pan Zhang, "Unsupervised generative modeling using matrix product states," Phys. Rev. X 8, 031012 (2018). [16] Edwin Stoudenmire and David J Schwab, "Supervised learning with tensor networks," in Advances in Neural Information Processing Systems 29, edited by D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett (Curran Associates, Inc., 2016) pp. 4799- 4807. [17] Stavros Efthymiou, Jack Hidary, and Stefan Leichenauer, "TensorNetwork for machine learning," (2019), arXiv:1906.06329 [cs.LG]. [18] Chase Roberts, Ashley Milsted, Martin Ganahl, Adam Zalcman, Bruce Fontaine, Yijian Zou, Jack Hidary, Guifre Vidal, and Stefan Leichenauer, "TensorNetwork: A library for physics and machine learning," (2019), arXiv:1905.01330 [physics.comp- ph]. [19] Matthew Fishman, Steven R. White, and E. Miles Stoudenmire, "The ITensor software library for tensor network calculations," (2020), arXiv:2007.14822 [cs.MS]. [20] Harry Markowitz, "Portfolio selection," The Journal of Finance 7, 77- 91 (1952). [21] Tai- Danae Bradley, E M Stoudenmire, and John Terilla, "Modeling sequences with quantum states: a look under the hood," Machine Learning: Science and Technology 1, 035008 (2020). [22] James Stokes and John Terilla, "Probabilistic modeling with matrix product states," Entropy 21 (2019). [23] Jacob Miller, Guillaume Rabusseau, and John Terilla, "Tensor networks for probabilistic sequence modeling," (2020), arXiv:2003.01039 [cs.LG]. [24] The GPyOpt authors, "Gpyopt: A bayesian optimization framework in python," http://github.com/SheffieldML/GPyOpt (2016). [25] Specific adaptions of the MPS generative model could be implemented such that it conserves the number of assets by construction, borrowing ideas from condensed matter physics where one can impose MPS a conservation in the number of particles in the quantum state. [26] T- J Chang, Nigel Meade, John E Beasley, and Yazid M Sharaiha, "Heuristics for cardinality constrained portfolio optimisation," Computers & Operations Research 27, 1271- 1302 (2000). [27] Guang- Feng Deng, Woo- Tsong Lin, and Chih- Chung Lo, "Markowitz- based portfolio selection with cardinality constraints using improved particle swarm optimization," Expert Systems with Applications 39, 4558- 4566 (2012). [28] M Mozafari, F Jolai, and S Tafazzoli, "A new ipso- sa approach for cardinality constrained portfolio optimization," International Journal of Industrial Engineering Computations 2, 249- 262 (2011). [29] Khin Lwin and Rong Qu, "A hybrid algorithm for constrained portfolio selection problems," Applied intelligence 39, 251- 266 (2013). [30] Adil Baykasoğlu, Mualla Gonca Yunusoglu, and F Burcin Özsoydan, "A grasp based solution approach to solve cardinality constrained portfolio optimization problems," Computers & Industrial Engineering 90, 339- 351 (2015). [31] Can B Kalayci, Okkes Ertentice, Hasan Akyer, and Hakan Aygoren, "An artificial bee colony algorithm with feasibility enforcement and infeasibility tolerance procedures for cardinality constrained portfolio optimization," Expert Systems with Applications 85, 61- 75 (2017). [32] Can B Kalayci, Olcay Polat, and Mehmet A Akbay, "An efficient hybrid metaheuristic algorithm for cardinality constrained  
+
+portfolio optimization," Swarm and Evolutionary Computation 54, 100662 (2020). [33] Mehmet Anil Akbay, Can B Kalayci, and Olcay Polat, "A parallel variable neighborhood search algorithm with quadratic programming for cardinality constrained portfolio optimization," Knowledge- Based Systems 198, 105944 (2020). [34] Tunchan Cura, "A rapidly converging artificial bee colony algorithm for portfolio optimization," Knowledge- Based Systems 233, 107505 (2021). [35] John E Beasley, "Or- library: distributing test problems by electronic mail," Journal of the operational research society 41, 1069- 1072 (1990). [36] Frank Wilcoxon, "Individual comparisons by ranking methods," in Breakthroughs in statistics (Springer, 1992) pp. 196- 202. [37] Janez Demšar, "Statistical comparisons of classifiers over multiple data sets," Journal of Machine Learning Research 7, 1- 30 (2006). [38] John Preskill, "Quantum computing in the NISQ era and beyond," Quantum 2, 79 (2018). [39] Song Cheng, Lei Wang, Tao Xiang, and Pan Zhang, "Tree tensor networks for generative modeling," Phys. Rev. B 99, 155131 (2019). [40] Joachim Dahl Martin Andersen and Lieven Vandenberghe, "Python software for convex optimization," http://cvxopt.org (2020). [41] Tunchan Cura, "Particle swarm optimization approach to portfolio optimization," Nonlinear analysis: Real world applications 10, 2396- 2406 (2009). [42] Ignacio Cirac, David Perez- Garcia, Norbert Schuch, and Frank Verstraete, "Matrix product states and projected entangled pair states: Concepts, symmetries, and theorems," (2020), arXiv:2011.12127 [quant- ph]. [43] "Code for unsupervised generative modeling using matrix product states," https://github.com/congzllwag/UnsupGenModbyMPS (2018). [44] Matthew T. Perry and Richard J. Wagner, "Python module for simulated annealing," https://github.com/perrygeo/simanneal (2019). [45] Javier Alcazar, Vicente Leyton- Ortega, and Alejandro Perdomo- Ortiz, "Classical versus quantum models in machine learning: insights from a finance application," Machine Learning: Science and Technology 1, 035003 (2020).  
+
+## Appendix A: Methods  
+
+## 1. Generation of portfolio optimization instances  
+
+The portfolio optimization problem aims at determining the fractions \(w_{i}\) of a given capital to be invested in each asset \(i\) of a universe of \(N\) assets, such that the risk \(\sigma (w)\) for a given level \(\rho\) of the expected return \(\langle r(w)\rangle\) is minimized, constrained to \(\sum_{i}w_{i} = 1\) . The problem can be formulated as:  
+
+\[\min_{w}\{\sigma^{2}(w) = w^{T}\cdot \pmb {\Sigma}\cdot \pmb {w}:\langle r(w)\rangle = w\cdot \pmb {r} = \rho \} \mathrm{(A1)}\]  
+
+where the vectors \(w\) and \(r\) have dimensionality \(N\) , \(\pmb{\Sigma}\) is the sample covariance matrix obtained from the return time series of pair of asset \(i\) and \(j\) , and \(r\) is the vector of average return of the time series for each asset, with each daily return, \(r^{t}\) ,
+
+<--- Page Split --->
+
+calculated as the relative increment in asset price from its previous day (i.e., \(r^{t} = (p^{t} - p^{(t - 1)}) / p^{(t - 1)}\) , with \(p^{t}\) as the price for a particular asset at time \(t\) ). The solution to Eq. A1 for a given return level \(\rho\) corresponds to the optimal portfolio strategy \(\boldsymbol{w}^{*}\) and the minimal value of this objective function \(\sigma (\boldsymbol {w})\) correspond to the portfolio risk and will be denoted by \(\sigma_{\rho}^{*}\) .  
+
+Note that the optimization task in Eq. A1 has the potential outcome of investing small amounts in a large number of assets as an attempt to reduce the overall risk by "over diversifying" the portfolio. This type of investment strategy can be challenging to implement in practice: portfolios composed of a large number of assets are difficult to manage and may incur in high transaction costs. Therefore, several restrictions are usually imposed on the allocation of capital among assets, as a consequence of market rules and conditions for investment or to reflect investor profiles and preferences. For instance, constraints can be included to control the amount of desired diversification, i.e., modifying bound limits per asset \(i\) , denoted by \(\{l_{i}, u_{i}\}\) , to the proportion of capital invested in the investment on individual assets or a group of assets, thus the constraint \(l_{i} < w_{i} < u_{i}\) could be considered.  
+
+Additionally, a more realistic and common scenario is to include in the optimization task a cardinality constraint, which limits directly the number of assets to be transacted to a pre- specified number \(\kappa < N\) . Therefore, the number of different sets to be treated is \(M = \binom{N}{\kappa}\) . In this scenario, the problem can be formulated as a Mixed- Integer Quadratic Program (MIQP) with the addition of binary variables \(x_{i} \in \{0, 1\}\) per asset, for \(i = 1, \ldots , N\) , which are set to "1" when the \(i\) - th asset is included as part of the \(\kappa\) assets, or "0" if it is left out of this selected set. Therefore, valid portfolios would have a number \(\kappa\) of 1's, as specified in the cardinality constraint. For example, for \(N = 4\) and \(\kappa = 2\) , the six different valid configurations can be encoded as \(\{0011, 0101, 0110, 1001, 1010, 1100\}\) .  
+
+The optimization task can then be described as follows  
+
+\[\begin{array}{rl} & {\min_{\boldsymbol {w},\boldsymbol {x}}\{\sigma^2 (\boldsymbol {w}):}\\ & {\qquad \langle \boldsymbol {r}(\boldsymbol {w})\rangle = \rho ,}\\ & {\qquad l_i\boldsymbol {x}_i< w_i< u_i\boldsymbol {x}_i\quad i = 1,\dots ,N,}\\ & {\qquad \mathbf{1}\cdot \boldsymbol {x} = \kappa \} .} \end{array} \quad (A2)\]  
+
+In this reformulated problem we denote by \(\sigma_{\rho ,\kappa}^{*}\) the minimum portfolio risk outcome from Eq. A2 for a given return level \(\rho\) and cardinality \(\kappa\) . The optimal solution vectors \(\boldsymbol{w}^{*}\) and \(\boldsymbol{x}^{*}\) define the portfolio investment strategy. Adding the cardinality constraint and the investment bound limits transforms a simple convex optimization problem (Eq. A1) into a much harder non- convex NP- hard problem. For all the problem instance generation in this work we chose \(\kappa = N / 2\) and the combinatorial nature of the problems lies in the growth of the search space associated with the binary vector \(\boldsymbol{x}\) , which makes it intractable to exhaustively explore for a number of assets in the few hundreds. The size of the search space here is \(M = \binom{N}{N / 2}\)  
+
+It is important to note that given a selection of which assets belong to the portfolio by instantiating \(\boldsymbol{x}\) (say with a specific  
+
+\(\boldsymbol{x}^{(i)}\) ), solving the optimization problem in Eq. A2 to find the respective investment fractions \(\boldsymbol{w}^{(i)}\) and risk value \(\sigma_{\rho ,N / 2}^{(i)}\) can be efficiently achieved with conventional quadratic programming (QP) solvers. In this work we used the python module cvxopt [40] for solving this problem. Note that we exploit this fact to break this constrained portfolio optimization problem into a combinatorial intractable one (find best asset selection \(\boldsymbol{x}\) ), which we aim to solve with GEO, and a tractable subroutine which can be solved efficiently with available solvers.  
+
+The set of pairwise \((\sigma_{\rho}^{*}, \rho)\) , dubbed as the efficient frontier, is no longer convex neither continuous in contrast with the solution to problem in Eq. (A1).  
+
+## 2. Problem formulation for comparison with state-of-the-art algorithms  
+
+To carry out the comparison with State- of- the- Art Algorithms, in line with the formulation used there, we generalizes the problem in Eq. A2 releasing the constraint of a fix level of portfolio return, instead directly incorporating the portfolio return in the objective function, encompassing now two terms: the one on the left corresponding to the portfolio risk as beforehand the one on the right corresponding to the portfolio return. The goal is to balance out both terms such that return is maximized and risk minimized. Lambda is a hyperparameter, named risk averse, that controls if an investor wants to give more weight to risk or return. The new formulation reads as follows,  
+
+\[\begin{array}{rl} & {\min_{\boldsymbol {w},\boldsymbol {x}}\{\lambda \sigma^2 (\boldsymbol {w}) - (1 - \lambda)\langle \boldsymbol {r}(\boldsymbol {w})\rangle :}\\ & {l_i\boldsymbol {x}_i< w_i< u_i\boldsymbol {x}_i\quad i = 1,\dots ,N,}\\ & {\qquad \mathbf{1}\cdot \boldsymbol {x} = \kappa \} .} \end{array} \quad (A3)\]  
+
+With the rest of constraints and variables definition as in Appendix A1.  
+
+### a. Performance Metrics  
+
+To compare the performance of the proposed GEO with the SOTA metaheuristic algorithms in the literature, the most commonly used performance metrics for the cardinality constrained portfolio optimization problem are used. These metric formulations compute the distance between the heuristic efficient frontier and the unconstrained efficient frontier. Thus, the performance of the algorithms can be evaluated.  
+
+Four of these performance metrics (the Mean, Median, Minimum and Maximum in Table I) are based on the so- called Performance Deviation Errors \((PDE)\) . These \(PDE\) metrics were formulated by Chang [26] as follows:  
+
+\[PDE_{i} = min\left(\left|\frac{100(x_{i} - x_{i}^{*})}{x_{i}^{*}}\right|,\left|\frac{100(y_{i} - y_{i}^{*})}{y_{i}^{*}}\right|\right) \quad (A4)\]
+
+<--- Page Split --->
+
+\[\begin{array}{rl} & {x_{i}^{*} = X_{k_{y}} + \frac{(X_{j_{y}} - X_{k_{y}})(y_{i} - Y_{k_{y}})}{(Y_{j_{y}} - Y_{k_{y}})}}\\ & {y_{i}^{*} = Y_{k_{x}} + \frac{(Y_{j_{x}} - Y_{k_{x}})(x_{i} - X_{k_{x}})}{(X_{j_{x}} - X_{k_{x}})}}\\ & {j_{y} = \underset {l = 1,\dots ,\epsilon^{*}}{\arg \min}Y_{l}}\\ & {k_{y} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmax}}Y_{l}}\\ & {j_{x} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmin}}X_{l}}\\ & {k_{x} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmax}}X_{l}}\\ & {k_{x} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmax}}X_{l}} \end{array} \quad (A5)\]  
+
+where the pair \((X_{l},Y_{l})(l = 1,\dots ,\epsilon^{*})\) represents the point on the standard efficient frontier and the pair \((x_{i},y_{i})(i =\) \(1,\dots ,\epsilon)\) represents the point on the heuristic efficient frontier. Here, \(\epsilon^{*}\) denotes the number of points on the standard efficient frontier while \(\epsilon\) denotes the number of points on the heuristic efficient frontier. The mean, median, minimum, and maximum of the \(PDE\) can be used to compare the performance of the algorithms.  
+
+Later, three additional performance measures (MEUCD: Mean Euclidean Distance, VRE: Variance of Return Error, MRE: Mean Return Error) were formulated by Cura [41] as follows:  
+
+\[MEUCD = \frac{\sum_{i = 1}^{\epsilon}\sqrt{(X_{i}^{*} - x_{i}) + (Y_{i}^{*} - y_{i})}}{\epsilon} \quad (A6)\]  
+
+\[VRE = \frac{\sum_{i = 1}^{\epsilon}100|X_{i}^{*} - x_{i}| / x_{i}}{\epsilon} \quad (A7)\]  
+
+\[MRE = \frac{\sum_{i = 1}^{\epsilon}100|Y_{i}^{*} - y_{i}| / y_{i}}{\epsilon} \quad (A8)\]  
+
+where \((X_{i}^{*},Y_{i}^{*})\) is the standard point closest to the heuristic point \((x_{i},y_{i})\) . Figure 5 shows a graphical representation of the indices used to calculate the performance metrics for the convenience of the reader and the values for TN- GEO and all the other SOTA optimizers are reported in Table I.  
+
+## 3. Quantum-Inspired Generative Model in TN-GEO  
+
+The addition of a probabilistic component is inspired by the success of Bayesian Optimization (BO) techniques, which are among the most efficient solvers when the performance metric aims to find the lowest minimum possible within the least number of objective function evaluations. For example, within the family of BO solvers, GPyOpt [24] uses a Gaussian Process (GP) framework consisting of multivariate Gaussian distributions. This probabilistic framework aims to capture relationships among the previously observed data points (e.g., through tailored kernels), and it guides the decision of where  
+
+![](images/Figure_5.jpg)
+
+<center>FIG. 5. A graphical demonstration of indices used for performance metrics calculation </center>  
+
+to sample the next evaluation with the help of the so called acquisition function. GPyOpt is one of the solvers we use to benchmark the new quantum- enhanced strategies proposed here.  
+
+Although the GP framework in BO techniques is not a generative model, we explore here the powerful unsupervised machine learning framework of generative modeling in order to capture correlations from an initial set of observations and evaluations of the objective function (step 1- 4 in Fig. 1).  
+
+For the implementation of the quantum- inspired generative model at the core of TN- GEO we follow the procedure proposed and implemented in Ref. [15]. Inspired by the probabilistic interpretation of quantum physics via Born's rule, it was proposed that one can use the Born probabilities \(|\Psi (\pmb {x})|^2\) over the \(2^{N}\) states of an \(N\) qubit system to represent classical target probability distributions which would be obtained otherwise with generative machine learning models. Hence,  
+
+\[P(\pmb {x}) = \frac{|\Psi(\pmb{x})|^2}{Z},\mathrm{with}Z = \sum_{\pmb {x}\in \mathcal{S}}|\Psi (\pmb {x})|^2, \quad (A9)\]  
+
+with \(\Psi (\pmb {x}) = \langle \pmb {x}|\Psi \rangle\) and \(\pmb {x}\in \{0,1\}^{\otimes N}\) are in one- to- one correspondence with decision variables over the investment universe with \(N\) assets in our combinatorial problem of interest here. In Ref. [15] these quantum- inspired generative models were named as Born machines, but we will refer to them hereafter as tensor- network Born machines (TNBm) to differentiate it from the quantum circuit Born machines (QCBM) proposal [13] which was developed independently to achieve the same purpose but by leveraging quantum wave functions from quantum circuits in NISQ devices. As explained in the main text, either quantum generative model can be adapted for the purpose of our GEO algorithm.  
+
+On the grounds of computational efficiency and scalability towards problem instances with large number of variables (in the order of hundreds or more), following Ref. [15] we implemented the quantum- inspired generative model based on
+
+<--- Page Split --->
+
+Matrix Product States (MPS) to learn the target distributions \(|\Psi (\pmb {x})|^2\) .  
+
+MPS is a type of TN where the tensors are arranged in a one- dimensional geometry. Despite its simple structure, MPS can efficiently represent a large number of quantum states of interest extremely well [42]. Learning with the MPS is achieved by adjusting its parameters such that the distribution obtained via Born's rule is as close as possible to the data distribution. MPS enjoys a direct sampling method that is more efficient than other Machine Learning techniques, for instance, Boltzmann machines, which require Markov chain Monte Carlo (MCMC) process for data generation.  
+
+The key idea of the method to train the MPS, following the algorithm on paper [15], consists of adjusting the value of the tensors composing the MPS as well as the bond dimension among them, via the minimization of the negative log- likelihood function defined over the training dataset sampled from the target distribution. For more details on the implementation see Ref. [15] and for the respective code see Ref. [43].  
+
+## 4. Classical Optimizers  
+
+### a. GPyOpt Solver  
+
+GPyOpt [24] is a Python open- source library for Bayesian Optimization based on GPy and a Python framework for Gaussian process modelling. For the comparison exercise in TN- GEO as a stand- alone solver here are the hyperparameters we used for the GPyOpt solver:  
+
+- Domain: to deal with the exponential growth in dimensionality, the variable space for \(n\) number of assets was partitioned as the cartesian product of \(n\) 1-dimensional spaces.- Constraints: we added two inequalities in the number of assets in a portfolio solution to represent the cardinality condition.- Number of initial data points: 10- Acquisition function: Expected Improvement  
+
+### b. Simulated Annealing Solver  
+
+For simulated annealing (SA) we implemented a modified version from Ref. [44]. The main change consists of adapting the update rule such that new candidates are within the valid search space with fixed cardinality. The conventional update rule of single bit flips will change the Hamming weight of \(x\) which translates in a portfolio with different cardinality. The hyperparameters used are the following:  
+
+- Max temperature in thermalization: 1.0  
+
+- Min temperature in thermalization: 1e-4  
+
+### c. Conditioned Random Solver  
+
+This solver corresponds to the simplest and most naive approach, while still using the cardinality information of the problem. In the conditioned random solver, we generate, by construction, bitstrings which satisfy the cardinality constraint. Given the desired cardinality \(\kappa = N / 2\) used here, one starts from the bitstring with all zeros, \(x_0 = 0\dots 0\) , and flips only \(N / 2\) bits at random from positions containing 0's, resulting in a valid portfolio candidate \(x\) with cardinality \(N / 2\) .  
+
+### d. Random Solver  
+
+This solver corresponds to the simplest approach without even using the cardinality information of the problem. In the random solver, we generate, by construction, bitstrings randomly selected from the \(2^{N}\) bitstrings of all possible portfolios, where \(N\) is the number of assets in our investment universe.  
+
+## 5. Algorithm Methodology for TN-GEO as a booster  
+
+As explained in the main text, in this case it is assumed that the cost of evaluating the objective function is not the major computational bottleneck, and consequently there is no practical limitations in the number of observations to be considered.  
+
+Following the algorithmic scheme in Fig. 1, we describe next the details for each of the steps in our comparison benchmarks:  
+
+0 Build the seed data set, \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) and \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{seed}}\) . For each problem instance defined by \(\rho\) and a random subset with \(N\) assets from the S&P 500, gather all initial available data obtained from previous optimization attempts with classical solver(s). In our case, for each problem instances we collected 10,000 observations from the SA solver. These 10,000 observations corresponding to portfolio candidates \(\{\pmb{x}^{(i)}\}_{\mathrm{init}}\) and their respective risk evaluations \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{init}}\) were sorted and only the first \(n_{\mathrm{seed}} = 1,000\) portfolio candidates with the lowest risks were selected as the seed data set. This seed data set is the one labeled as \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) and \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{seed}}\) in the main text and hereafter. The idea of selecting a percentile of the original data is to provide the generative model inside GEO with samples which are the target samples to be generated. This percentile is a hyperparameter and we set it \(10\%\) of the initial data for our purposes.  
+
+1 Construct of the softmax surrogate distribution: Using the seed data from step 0, we construct a softmax multinomial distribution with \(n_{\mathrm{seed}}\) classes - one for each point on the seed data set. The probabilities outcome associated with each of these classes in the multinomial
+
+<--- Page Split --->
+
+is calculated as a Boltzmann weight, \(p_{i} = \frac{e^{-\overline{\sigma}_{i,\kappa}}}{\sum_{j = 1}^{n_{\mathrm{seed}}}e^{-\overline{\sigma}_{j,\kappa}}}\) .  
+
+Here, \(\overline{\sigma}_{\rho ,\kappa}^{(i)} = \sigma_{\rho ,\kappa}(\pmb{x}^{(i)}) / T\) , and \(T\) is a "temperature" hyperparameter. In our simulations, \(T\) was computed as the standard deviation of the risk values of this seed data set. In Bayesian optimization methods the surrogate function tracks the landscape associated with the values of the objective function (risk values here). This soft- max surrogate constructed here by design as a multinomial distribution from the seed data observations serves the purpose of representing the objective function landscape but in probability space. That is, it will assign higher probability to portfolio candidates with lower risk values. Since we will use this softmax surrogate to generate the training data set, this bias imprints a preference in the quantum- inspired generative model to favor low- cost configurations.  
+
+2 Sample from softmax surrogate. We will refer to these samples as the training set since these will be used to train the MPS- based generative model. For our experiments here we used \(n_{\mathrm{train}} = 10000\) samples.  
+
+3 Use the \(n_{\mathrm{train}}\) samples from the previous step to train the MPS generative model.  
+
+4 Obtain \(n_{\mathrm{MPS}}\) samples from the generative model which correspond to the new list of potential portfolio candidates. In our experiments, \(n_{\mathrm{MPS}} = 4000\) . For the case of 500 assets, as sampling takes sensibly longer because of the problem dimension, this value was reduced to 400 to match the time in SA.  
+
+5 Select new candidates: From the \(n_{\mathrm{MPS}}\) samples, select only those who fulfill the cardinality condition, and which have not been evaluated. These new portfolio candidates \(\{\pmb{x}^{(i)}\}_{\mathrm{new}}\) are saved for evaluation in the next step.  
+
+6 Obtain risk value for new selected samples: Solve Eq. A2 to evaluate the objective function (portfolio risks) for each of the new candidates \(\{\pmb{x}^{(i)}\}_{\mathrm{new}}\) . We will denote refer to the new cost function values by \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{new}}\) .  
+
+7 Merge the new portfolios, \(\{\pmb{x}^{(i)}\}_{\mathrm{new}}\) , and their respective cost function evaluations, \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{new}}\) with the seed portfolios, \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) , and their respective cost values, \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{seed}}\) , from step 0 above. This combined super set is the new initial data set.  
+
+8 Use the new initial data set from step 7 to start the algorithm from step 1. If a desired minimum is already found or if no more computational resources are available, one can decide to terminate the algorithm here. In all of our benchmark results reported here when using TN- GEO as a booster from SA intermediate results,  
+
+we only run the algorithm for this first cycle and the minima reported for the TN- GEO strategy is the lowest minimum obtained up to step 7 above.  
+
+## 6. Algorithm Methodology for TN-GEO as a stand-alone solver  
+
+This section presents the algorithm for the TN- GEO scheme as a stand- alone solver. In optimization problems where the objective function is inexpensive to evaluate, we can easily probe it at many points in the search for a minimum. However, if the cost function evaluation is expensive, e.g., tuning hyperparameters of a deep neural network, then it is important to minimize the number of evaluations drawn. This is the domain where optimization technique with a Bayesian flavour, where the search is being conducted based on new information gathered, are most useful, in the attempt to find the global optimum in a minimum number of steps.  
+
+The algorithmic steps for TN- GEO as a stand- alone solver follows the same logic as that of the solver as a booster described Sec. A5. The main differences between the two algorithms rely on step 0 during the construction of the initial data set and seed data set in step 0, the temperature use in the softmax surrogate in step 1, and a more stringent selection criteria in step 5. Since the other steps remain the same, we focus here to discuss the main changes to the algorithmic details provided in Sec. A5.  
+
+0 Build the seed data set: since evaluating the objective function could be the major bottleneck (assumed to be expensive) then we cannot rely on cost function evaluations to generate the seed data set. The strategy we adopted is to initialize the algorithm with samples of bitstrings which satisfy the hard constraints of the problem. In our specific example, we can easily generate \(n_{\mathrm{seed}}\) random samples, \(\mathcal{D}_0 = \{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) , which satisfy the cardinality constraint. Since all the elements in this data set hold the cardinality condition, then maximum length \(n_{\mathrm{seed}}\) of \(\mathcal{D}_0\) is \(\binom{N}{K}\) . In our experiments, we set the number of samples \(n_{\mathrm{init}} = 2,000\) , for all problems considered here up to \(N = 100\) assets  
+
+1 Construct the softmax surrogate distribution: start by constructing a uniform multinomial probability distribution where each sample in \(\mathcal{D}_0\) has the same probability. Therefore, for each point in the seed data set its probability is set to \(p_0 = 1 / n_{\mathrm{seed}}\) . As in TN- GEO as a booster, we will attempt to generate a softmax- like surrogate which favors samples with low cost value, but we will slowly build that information as new samples are evaluated. In this first iteration of the algorithm, we start by randomly selecting a point \(\pmb{x}^{(1)}\) from \(\mathcal{D}_0\) , and we evaluate the value of its objective function \(\sigma^{(1)}\) (its risk value in our specific finance example). To make this point \(\pmb{x}^{(1)}\) stand out from the other unevaluated samples, we set its probability to be twice that of any
+
+<--- Page Split --->
+
+of the remaining \(n_{\mathrm{seed}} - 1\) points in \(\mathcal{D}_0\) . Since we increase the probability of one of the points, we need to adjust the probability of the \(n_{\mathrm{seed}} - 1\) from \(p_0\) to \(p_0\) and if we assume the probability weights for observing each point follows a multinomial distribution with Boltzmann weights, under these assumptions, and making by fixing the temperature hyperparameter we can solve for the reference "risk" value \(\sigma^{(0)}\) associated to all the other \(n_{\mathrm{seed}} - 1\) points as shown below. It is important to note that \(\sigma^{(0)}\) is an artificial reference value which is calculated analytically and does not require a call to the objective function (in contrast to \(\sigma^{(1)}\) ). Here, \(\mathcal{N}\) is the normalization factor of the multinomial and \(T\) is the temperature hyperparameter which, as in the case of TN- GEO as a booster, can be adjusted later in the algorithm as more data is seen. Due to the lack of initial cost function values, in order to set a relevant typical "energy" scale in this problem, we follow the procedure in Ref. [45] where it is set to be the square root of the mean of the covariance matrix defined in Eq. A1, as this matrix encapsulates the risk information (volatility) as stated in the Markowitz's model.  
+
+\[\left\{ \begin{array}{ll}(n_{\mathrm{seed}} - 1)p_0' + p_1 = 1 & \Rightarrow \left\{ \begin{array}{ll}p_0' = 1 / (1 + n_{\mathrm{seed}}) \\ p_1 = 2 / (1 + n_{\mathrm{seed}}) \end{array} \right.\\ \displaystyle \left\{ \begin{array}{ll}\mathcal{N} = (n_{\mathrm{seed}} - 1)e^{-\sigma^{(0)} / T} + e^{-\sigma^{(1)} / T} & \\ p_1 = e^{-\sigma^{(1)} / T} / \mathcal{N} & \\ p_0' = e^{-\sigma^{(0)} / T} / \mathcal{N} & \end{array} \right. \end{array} \right.\]  
+
+2 Generate training set: same as in TN- GEO as a booster (see Appendix A 5).  
+
+3 Train MPS: same as in TN- GEO as a booster (see Appendix A 5).  
+
+4 Generate samples from trained MPS: same as in TN- GEO as a booster (see Appendix A 5).  
+
+5 Select new candidates from trained MPS: In contrast to TN- GEO as a booster we cannot afford to evaluate all new candidates coming from the MPS samples. In our procedure we selected only two new candidates which must meet the cardinality constraint. For our procedure these two candidates correspond to the most frequent sample ("exploitation") and the least frequent sample ("exploration"). If all new samples appeared with the same frequency, then we can select two samples at random. In the case where no new samples were generated, we choose them from the unevaluated samples of the original seed data set in \(\mathcal{D}_0\)  
+
+6 Obtain risk value for new selected samples: same as in TN- GEO as a booster (see Appendix A 5).  
+
+7 Merge the new portfolios with seed data set from step 0 same as in TN- GEO as a booster (see Appendix A 5).  
+
+8 Restart next cycle of the algorithm with the merge data set as the new seed data set: same as in TN- GEO as a booster (see Appendix A 5).  
+
+## Appendix B: Relative TN-GEO Enhancement  
+
+Figure 6 represents the relative performance within the strategies 1 and 2 referred to subsection III A.
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>FIG. 6. Relative TN-GEO enhancement similar to those shown in the bottom panel of Fig. 2 in the main text. For these experiments, portfolio optimization instances with a number of variables ranging from \(N = 30\) to \(N = 100\) were used. Here, each panel correspond to a different investment universes corresponding to a random subset of the S&P 500 market index. Note the trend for a larger quantum-inspired enhancement as the number of variables (assets) becomes larger, with the largest enhancement obtained in the case on instances with all the assets from the S&P 500 ( \(N = 500\) ), as shown in Fig. 2 </center>
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+summarycomparisonTNGEOvsalI.pdf
+
+<--- Page Split --->

preprint/preprint__00c2b94550129fb8f084bb495841a196a9f5afe6d5c14e29f461a9abeaa8a98e/preprint__00c2b94550129fb8f084bb495841a196a9f5afe6d5c14e29f461a9abeaa8a98e_det.mmd

@@ -0,0 +1,530 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 896, 175]]<|/det|>
+# GEO: Enhancing Combinatorial Optimization with Classical and Quantum Generative Models  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 652, 260]]<|/det|>
+Francisco Fernandez Alcazar  Alejandro Perdomo-Ortiz ( \(\square\) alejandro@zapatacomputing.com )  Zapata Computing Canada https://orcid.org/0000- 0001- 7176- 4719  
+
+<|ref|>text<|/ref|><|det|>[[44, 265, 295, 305]]<|/det|>
+Mohammad Ghazi Vakili  Zapata Computing Canada  
+
+<|ref|>text<|/ref|><|det|>[[44, 311, 245, 351]]<|/det|>
+Can Kalayci  Pamukkale University  
+
+<|ref|>text<|/ref|><|det|>[[44, 392, 102, 410]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 430, 137, 449]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 468, 310, 488]]<|/det|>
+Posted Date: August 8th, 2022  
+
+<|ref|>text<|/ref|><|det|>[[44, 506, 463, 526]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 241950/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 543, 909, 586]]<|/det|>
+License: © \(\circledcirc\) This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[105, 63, 900, 82]]<|/det|>
+# GEO: Enhancing Combinatorial Optimization with Classical and Quantum Generative Models  
+
+<|ref|>text<|/ref|><|det|>[[171, 94, 830, 111]]<|/det|>
+Javier Alcazar, \(^{1}\) Mohammad Ghazi Vakili, \(^{1,2,3}\) Can B. Kalayci, \(^{1,4}\) and Alejandro Perdomo- Ortiz \(^{1,*}\)  
+
+<|ref|>text<|/ref|><|det|>[[194, 114, 810, 180]]<|/det|>
+\(^{1}\) Zapata Computing Canada Inc., 325 Front St W, Toronto, ON, M5V 2Y1 \(^{2}\) Department of Chemistry, University of Toronto, Toronto, ON, M5G 1Z8, Canada \(^{3}\) Department of Computer Science, University of Toronto, Toronto, Ontario M5S 2E4, Canada \(^{4}\) Department of Industrial Engineering, Pamukkale University, Kinikli Campus, 20160, Denizli, Turkey (Dated: July 2, 2022)  
+
+<|ref|>text<|/ref|><|det|>[[175, 188, 829, 452]]<|/det|>
+We introduce a new framework that leverages machine learning models known as generative models to solve optimization problems. Our Generator- Enhanced Optimization (GEO) strategy is flexible to adopt any generative model, from quantum to quantum- inspired or classical, such as Generative Adversarial Networks, Variational Autoencoders, or Quantum Circuit Born Machines, to name a few. Here, we focus on a quantum- inspired version of GEO relying on tensor- network Born machines, and referred to hereafter as TN- GEO. We present two prominent strategies for using TN- GEO. The first uses data points previously evaluated by any quantum or classical optimizer, and we show how TN- GEO improves the performance of the classical solver as a standalone strategy in hard- to- solve instances. The second strategy uses TN- GEO as a standalone solver, i.e., when no previous observations are available. Here, we show its superior performance when the goal is to find the best minimum given a fixed budget for the number of function calls. This might be ideal in situations where the cost function evaluation can be very expensive. To illustrate our results, we run these benchmarks in the context of the portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes. We show that TN- GEO can propose unseen candidates with lower cost function values than the candidates seen by classical solvers. This is the first demonstration of the generalization capabilities of quantum- inspired generative models that provide real value in the context of an industrial application. We also comprehensively compare state- of- the- art algorithms in a generalized version of the portfolio optimization problem. The results show that TN- GEO is among the best compared to these state- of- the- art algorithms; a remarkable outcome given the solvers used in the comparison have been fine- tuned for decades in this real- world industrial application. We see this as an important step toward a practical advantage with quantum- inspired models and, subsequently, with quantum generative models.  
+
+<|ref|>sub_title<|/ref|><|det|>[[215, 479, 357, 492]]<|/det|>
+## I. INTRODUCTION  
+
+<|ref|>text<|/ref|><|det|>[[86, 510, 486, 668]]<|/det|>
+Along with machine learning and the simulation of materials, combinatorial optimization is one of top candidates for practical quantum advantage. That is, the moment where a quantum- assisted algorithm outperforms the best classical algorithms in the context of a real- world application with a commercial or scientific value. There is an ongoing portfolio of techniques to tackle optimization problems with quantum subroutines, ranging from algorithms tailored for quantum annealers (e.g., Refs. [1, 2]), gate- based quantum computers (e.g., Refs. [3, 4]) and quantum- inspired (QI) models based on tensor networks (e.g., Ref. [5]).  
+
+<|ref|>text<|/ref|><|det|>[[86, 670, 486, 828]]<|/det|>
+Regardless of the quantum optimization approach proposed to date, there is a need to translate the real- world problem into a polynomial unconstrained binary optimization (PUBO) expression - a task which is not necessarily straightforward and that usually results in an overhead in terms of the number of variables. Specific real- world use cases illustrating these PUBO mappings are depicted in Refs. [6] and [7]. Therefore, to achieve practical quantum advantage in the near- term, it would be ideal to find a quantum optimization strategy that can work on arbitrary objective functions, bypassing the translation and overhead limitations raised here.  
+
+<|ref|>text<|/ref|><|det|>[[86, 830, 486, 857], [516, 479, 916, 650]]<|/det|>
+In our work, we offer a solution to these challenges by proposing a novel generator- enhanced optimization (GEO) framework which leverage the power of (quantum or classical) generative models. This family of solvers can scale to large problems where combinatorial problems become intractable in real- world settings. Since our optimization strategy does not rely on the details of the objective function to be minimized, it is categorized in the group of so- called black- box solvers. Another highlight of our approach is that it can utilize available observations obtained from attempts to solve the optimization problem. These initial evaluations can come from any source, from random search trials to tailored state- of- the- art (SOTA) classical or quantum optimizers for the specific problem at hand.   
+
+<|ref|>text<|/ref|><|det|>[[516, 653, 916, 881]]<|/det|>
+Our GEO strategy is based on two key ideas. First, the generative- modeling component aims to capture the correlations from the previously observed data (step 0- 3 in Fig. 1). Second, since the focus here is on a minimization task, the (quantum) generative models need to be capable of generating new "unseen" solution candidates which have the potential to have a lower value for the objective function than those already "seen" and used as the training set (step 4- 6 in Fig. 1). This exploration towards unseen and valuable samples is by definition the fundamental concept behind generalization: the most desirable and important feature of any practical ML model. We will elaborate next on each of these components and demonstrate these two properties in the context of the tensor- network- based generative models and its application to a non- deterministic polynomial- time hard (NP- hard) version of the portfolio optimization in finance.  
+
+<|ref|>text<|/ref|><|det|>[[515, 884, 916, 911]]<|/det|>
+To the best of our knowledge, this is the first optimization strategy proposed to do an efficient blackbox exploration
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[86, 66, 487, 225]]<|/det|>
+of the objective- function landscape with the help of generative models. Although other proposal leveraging generative models as a subroutine within the optimizer have appeared recently since the publication of our manuscript (e.g., see GFlowNets [8] and the variational neural annealing [9] algorithms), our framework is the only capable of both, handling arbitrary cost functions and also with the possibility of swapping the generator for a quantum or quantum- inspired implementation. GEO also has the enhanced feature that the more data is available, the more information can be passed and used to train the (quantum) generator.  
+
+<|ref|>text<|/ref|><|det|>[[86, 226, 487, 341]]<|/det|>
+In this work, we highlight the different features of GEO by performing a comparison with alternative solvers, such as Bayesian optimizers and generic solvers like simulated annealing. In the case of the specific real- world large- scale application of portfolio optimization, we compare against the SOTA optimizers and show the competitiveness of our approach. These results are presented in Sec. III. Next, in Sec. II, we present the GEO approach and its range of applicability.  
+
+<|ref|>sub_title<|/ref|><|det|>[[106, 367, 465, 395]]<|/det|>
+## II. QUANTUM-ENHANCED OPTIMIZATION WITH GENERATIVE MODELS  
+
+<|ref|>text<|/ref|><|det|>[[86, 412, 487, 570]]<|/det|>
+As shown in Fig. 1, depending on the GEO specifics we can construct an entire family of solvers whose generative modeling core range from classical, QI or quantum circuit (QC) enhanced, or hybrid quantum- classical model. These options can be realized by utilizing, for example, Boltzmann machines [10] or Generative Adversarial Networks (GAN) [11], Tensor- Network Born Machines (TNBm) [12], Quantum Circuit Born Machines (QCBM)[13] or Quantum- Circuit Associative Adversarial Networks (QC- AAN)[14] respectively, to name just a few of the many options for this probabilistic component.  
+
+<|ref|>text<|/ref|><|det|>[[86, 571, 487, 715]]<|/det|>
+QI algorithms come as an interesting alternative since these allow one to simulate larger scale quantum systems with the help of efficient tensor- network (TN) representations. Depending on the complexity of the TN used to build the quantum generative model, one can simulate from thousands of problem variables to a few tens, the latter being the limit of simulating an universal gate- based quantum computing model. This is, one can control the amount of quantum resources available in the quantum generative model by choosing the QI model.  
+
+<|ref|>text<|/ref|><|det|>[[86, 716, 487, 860]]<|/det|>
+Therefore, from all quantum generative model options, we chose to use a QI generative model based on TNs to test and scale our GEO strategy to instances with a number of variables commensurate with those found in industrial- scale scenarios. We refer to our solver hereafter as TN- GEO. For the training of our TN- GEO models we followed the work of Han et al. [15] where they proposed to use Matrix Product States (MPS) to build the unsupervised generative model. The latter extends the scope from early successes of quantum- inspired models in the context of supervised ML [16- 19].  
+
+<|ref|>text<|/ref|><|det|>[[85, 861, 487, 889]]<|/det|>
+In this paper we will discuss two modes of operation for our family of quantum- enhanced solvers:  
+
+<|ref|>text<|/ref|><|det|>[[113, 897, 487, 912]]<|/det|>
+- In TN-GEO as a "booster" we leverage past observa  
+
+<|ref|>text<|/ref|><|det|>[[555, 66, 917, 123]]<|/det|>
+tions from classical (or quantum) solvers. To illustrate this mode we use observations from simulated annealing (SA) runs. Simulation details are provided in Appendix A 5.  
+
+<|ref|>text<|/ref|><|det|>[[545, 133, 917, 218]]<|/det|>
+- In TN-GEO as a stand-alone solver all initial cost function evaluations are decided entirely by the quantum-inspired generative model, and a random prior is constructed just to give support to the target probability distribution the MPS model is aiming to capture. Simulation details are provided in Appendix A 6.  
+
+<|ref|>text<|/ref|><|det|>[[515, 231, 916, 275]]<|/det|>
+Both of these strategies are captured in the algorithm workflow diagram in Fig. 1 and described in more detail in Appendix A.  
+
+<|ref|>sub_title<|/ref|><|det|>[[601, 302, 830, 315]]<|/det|>
+## III. RESULTS AND DISCUSSION  
+
+<|ref|>text<|/ref|><|det|>[[515, 334, 917, 650]]<|/det|>
+To illustrate the implementation for both of these settings we tested their performance on an NP- hard version of the portfolio optimization problem with cardinality constraints. The selection of optimal investment on a specific set of assets, or portfolios, is a problem of great interest in the area of quantitative finance. This problem is of practical importance for investors, whose objective is to allocate capital optimally among assets while respecting some investment restrictions. The goal of this optimization task, introduced by Markowitz [20], is to generate a set of portfolios that offers either the highest expected return (profit) for a defined level of risk or the lowest risk for a given level of expected return. In this work, we focus in two variants of this cardinality constrained optimization problem. The first scenario aims to choose portfolios which minimize the volatility or risk given a specific target return (more details are provided in Appendix A 1). To compare with the reported results from the best performing SOTA algorithms, we ran TN- GEO in a second scenario where the goal is to choose the best portfolio given a fixed level of risk aversion. This is the most commonly used version of this optimization problem when it comes to comparison among SOTA solvers in the literature (more details are provided in Appendix A 2).  
+
+<|ref|>sub_title<|/ref|><|det|>[[545, 678, 887, 706]]<|/det|>
+### A. TN-GEO as a booster for any other combinatorial optimization solver  
+
+<|ref|>text<|/ref|><|det|>[[515, 724, 916, 912]]<|/det|>
+In Fig. 2 we present the experimental design and the results obtained from using TN- GEO as a booster. In these experiments we illustrate how using intermediate results from simulated annealing (SA) can be used as seed data for our TN- GEO algorithm. As described in Fig. 2, there are two strategies we explored (strategies 1 and 2) to compare with our TN- GEO strategy (strategy 4). To fairly compare each strategy, we provide each with approximately the same computational wall- clock time. For strategy 2, this translates into performing additional restarts of SA with the time allotted for TN- GEO. In the case of strategy 1, where we explored different settings for SA from the start compared to those used in strategy 2, this amounts to using the same total number
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[91, 65, 910, 372]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[84, 390, 919, 578]]<|/det|>
+<center>FIG. 1. Scheme for our Generator-Enhanced Optimization (GEO) strategy. The GEO framework leverages generative models to utilize previous samples coming from any quantum or classical solver. The trained quantum or classical generator is responsible for proposing candidate solutions which might be out of reach for conventional solvers. This seed data set (step 0) consists of observation bitstrings \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) and their respective costs \(\{\sigma^{(i)}\}_{\mathrm{seed}}\) . To give more weight to samples with low cost, the seed samples and their costs are used to construct a softmax function which serves as a surrogate to the cost function but in probabilistic domain. This softmax surrogate also serves as a prior distribution from which the training set samples are withdrawn to train the generative model (steps 1-3). As shown in the figure between steps 1 and 2, training samples from the softmax surrogate are biased favoring those with low cost value. For the work presented here, we implemented a tensor-network (TN)-based generative model. Therefore, we refer to this quantum-inspired instantiation of GEO as TN-GEO. Other families of generative models from classical, quantum, or hybrid quantum-classical can be explored as expounded in the main text. The quantum-inspired generator corresponds to a tensor-network Born machine (TNBM) model which is used to capture the main features in the training data, and to propose new solution candidates which are subsequently post selected before their costs \(\{\sigma^{(i)}\}_{\mathrm{new}}\) are evaluated (steps 4-6). The new set is merged with the seed data set (step 7) to form an updated seed data set (step 8) which is to be used in the next iteration of the algorithm. More algorithmic details for the two TN-GEO strategies proposed here, as a booster or as a stand-alone solver, can be found in the main text and in A5 and A6 respectively. </center>  
+
+<|ref|>text<|/ref|><|det|>[[86, 605, 488, 735]]<|/det|>
+of number of cost functions evaluations as those allocated to SA in strategy 2. For our experiments this number was set to 20,000 cost function evaluations for strategies 1 and 2. In strategy 4, the TN- GEO was initialized with a prior consisting of the best 1,000 observations out of the first 10,000 coming from strategy 2 (see Appendix A 5 for details). To evaluate the performance enhancement obtained from the TN- GEO strategy we compute the relative TN- GEO enhancement \(\eta\) , which we define as  
+
+<|ref|>equation<|/ref|><|det|>[[173, 736, 487, 777]]<|/det|>
+\[\eta = \frac{C_{\mathrm{min}}^{\mathrm{cl}}}{C_{\mathrm{min}}^{\mathrm{cl}}} = \frac{C_{\mathrm{min}}^{\mathrm{TN - GEO}}}{C_{\mathrm{min}}^{\mathrm{cl}}}\times 100\% . \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[86, 780, 488, 884]]<|/det|>
+Here, \(C_{\mathrm{min}}^{\mathrm{cl}}\) is the lowest minimum value found by the classical strategy (e.g., strategies 1- 3) while \(C_{\mathrm{min}}^{\mathrm{TN - GEO}}\) corresponds to the lowest value found with the quantum- enhanced approach (e.g., with TN- GEO). Therefore, positive values reflect an improvement over the classical- only approaches, while negative values indicate cases where the classical solvers outperform the quantum- enhanced proposal.  
+
+<|ref|>text<|/ref|><|det|>[[86, 884, 487, 912]]<|/det|>
+As shown in the Fig. 2, we observe that TN- GEO outperforms on average both of the classical- only strategies imple  
+
+<|ref|>text<|/ref|><|det|>[[515, 605, 917, 810]]<|/det|>
+As shown in the Fig. 2, we observe that TN- GEO outperforms on average both of the classical- only strategies implemented. The quantum- inspired enhancement observed here, as well as the trend for a larger enhancement as the number of variables (assets) becomes larger, is confirmed in many other investment universes with a number of variables ranging from \(N = 30\) to \(N = 100\) (see Appendix B for more details). Although we show an enhancement compared to SA, similar results could be expected when other solvers are used, since our approach builds on solutions found by the solver and does not compete with it from the start of the search. Furthermore, the more data available, the better the expected performance of TN- GEO is. An important highlight of TN- GEO as a booster is that these previous observations can come from a combination of solvers, as different as purely quantum or classical, or hybrid.  
+
+<|ref|>text<|/ref|><|det|>[[515, 812, 916, 912]]<|/det|>
+The observed performance enhancement compared with the classical- only strategy must be coming from a better exploration of the relevant search space, i.e., the space of those bitstring configurations \(x\) representing portfolios which could yield a low risk value for a specified expected investment return. That is the intuition behind the construction of TN- GEO. The goal of the generative model is to capture the important
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[90, 81, 480, 460]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[85, 480, 488, 785]]<|/det|>
+<center>FIG. 2. TN-GEO as a booster. Top: Strategies 1-3 correspond to the current options a user might explore when solving a combinatorial optimization problem with a suite of classical optimizers such as simulated annealing (SA), parallel tempering (PT), generic algorithms (GA), among others. In strategy 1, the user would use its computational budget with a preferred solver. In strategy 2-4 the user would inspect intermediate results and decide whether to keep trying with the same solver (strategy 2), try a new solver or a new setting of the same solver used to obtain the intermediate results (strategy 3), or, as proposed here, to use the acquired data to train a quantum or quantum-inspired generative model within a GEO framework such as TN-GEO (strategy 4). Bottom: Results showing the relative TN-GEO enhancement from TN-GEO over either strategy 1 or strategy 2. Positive values indicate runs where TN-GEO outperformed the respective classical strategies (see Eq. 1). The data represents bootstrapped medians from 20 independent runs of the experiments and error bars correspond to the 95% confidence intervals. The two instances presented here correspond to portfolio optimization instances where all the assets in the S&P 500 market index where included \((N = 500)\) , under two different cardinality constraints \(\kappa\) . This cardinality constraint indicate the number of assets that can be included at a time in valid portfolios, yielding a search space of \(M = \binom{N}{\kappa}\) , with \(M \sim 10^{69}\) portfolios candidates for \(\kappa = 50\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[85, 821, 487, 850]]<|/det|>
+correlations in the previously observed data, and to use its generative capabilities to propose similar new candidates.  
+
+<|ref|>text<|/ref|><|det|>[[85, 854, 487, 912]]<|/det|>
+Generating new candidates is by no means a trivial task in ML and it determines the usefulness and power of the model since it measure its generalization capabilities. In this setting of QI generative models, one expects that the MPS- based  
+
+<|ref|>text<|/ref|><|det|>[[515, 66, 917, 238]]<|/det|>
+generative model at the core of TN- GEO is not simply memorizing the observations given as part of the training set, but that it will provide new unseen candidates. This is an idea which has been recently tested and demonstrated to some extent on synthetic data sets (see e.g., Refs. [21], [22] and [23]. In Fig. 3 we demonstrate that our quantum- inspired generative model is generalizing to new samples and that these add real value to the optimization search. To the best of our knowledge this is the first demonstration of the generalization capabilities of quantum generative models in the context of a real- world application in an industrial scale setting, and one of our main findings in our paper.  
+
+<|ref|>text<|/ref|><|det|>[[515, 240, 917, 414]]<|/det|>
+Note that our TN- based generative model not only produces better minima than the classical seed data, but it also generates a rich amount of samples in the low cost spectrum. This bias is imprinted in the design of our TN- GEO and it is the purpose of the softmax surrogate prior distribution shown in Fig. 1. This richness of new samples could be useful not only for the next iteration of the algorithm, but they may also be readily of value to the user solving the application. In some applications there is value as well in having information about the runnersup. Ultimately, the cost function is just a model of the system guiding the search, and the lowest cost does not translate to the best performance in the real- life investment strategy.  
+
+<|ref|>sub_title<|/ref|><|det|>[[515, 446, 915, 460]]<|/det|>
+### B. Generator-Enhanced Optimization as a Stand-Alone Solver  
+
+<|ref|>text<|/ref|><|det|>[[515, 479, 917, 912]]<|/det|>
+Next, we explore the performance of our TN- GEO framework as a stand- alone solver. The focus is in combinatorial problems whose cost functions are expensive to evaluate and where finding the best minimum within the least number of calls to this function is desired. In Fig. 4 we present the comparison against four different classical optimization strategies. As the first solver, we use the random solver, which corresponds to a fully random search strategy over the \(2^{N}\) bitstrings of all possible portfolios, where \(N\) is the number of assets in our investment universe. As second solver, we use the conditioned random solver, which is a more sophisticated random strategy compared to the fully random search. The conditioned random strategy uses the a priori information that the search is restricted to bitstrings containing a fixed number of \(\kappa\) assets. Therefore the number of combinatorial possibilities is \(M = \binom{N}{\kappa}\) , which is significantly less than \(2^{N}\) . As expected, when this information is not used the performance of the random solver over the entire \(2^{N}\) search space is worse. The other two competing strategies considered here are SA and the Bayesian optimization library GPyOpt [24]. In both of these classical solvers, we adapted their search strategy to impose this cardinality constraint with fixed \(\kappa\) as well (details in Appendix. A 4). This raises the bar even higher for TN- GEO which is not using that a priori information to boost its performance [25]. As explained in Appendix A 6, we only use this information indirectly during the construction of the artificial seed data set which initializes the algorithm (step 0, Fig. 1), but it is not a strong constraint during the construction of the QI generative model (step 3, Fig. 1) or imposed to generate the new candidate samples coming from it (step 4,
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[85, 75, 914, 324]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[84, 335, 920, 430]]<|/det|>
+<center>FIG. 3. Generalization capabilities of our quantum-inspired generative model. Left panel corresponds to an investment universe with \(N = 50\) assets while the right panel corresponds to one with \(N = 100\) assets. The blue histogram represents the number of observations or portfolios obtained from the classical solver (seed data set). In orange we represent samples coming from our quantum generative model at the core of TN-GEO. The green dash line is positioned at the best risk value found in the seed data. This mark emphasizes all the new outstanding samples obtained with the quantum generative model and which correspond to lower portfolio risk value (better minima) than those available from the classical solver by itself. The number of outstanding samples in the case of \(N = 50\) is equal to 31, while 349 outstanding samples were obtained from the MPS generative model in the case of \(N = 100\) . </center>  
+
+<|ref|>image<|/ref|><|det|>[[200, 472, 777, 793]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[84, 808, 920, 902]]<|/det|>
+<center>FIG. 4. TN-GEO as a stand-alone solver: In this comparison of TN-GEO against four classical competing strategies, investment universes are constructed from subsets of the S&P 500 with a diversity in the number of assets (problem variables) ranging from \(N = 30\) to \(N = 100\) . The goal is to minimize the risk given an expected return which is one of the specifications in the combinatorial problem addressed here. Error bars and their 95% confidence intervals are calculated from bootstrapping over 100 independent random initializations for each solver on each problem. The main line for each solver corresponds to the bootstrapped median over these 100 repetitions, demonstrating the superior performance of TN-GEO over the classical solvers considered here. As specified in the text, with the exception of TN-GEO, the classical solvers use to their advantage the a priori information coming from the cardinality constraint imposed in the selection of valid portfolios. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 66, 488, 110]]<|/det|>
+Fig. 1). Post selection can be applied a posteriori such that only samples with the right cardinality are considered as valid candidates towards the selected set (step 5, Fig. 1).  
+
+<|ref|>text<|/ref|><|det|>[[86, 111, 488, 181]]<|/det|>
+In Fig. 4 we demonstrate the advantage of our TN- GEO stand- alone strategy compared to any of these widely- used solvers. In particular, it is interesting to note that the gap between TN- GEO and the other solvers seems to be larger for larger number of variables.  
+
+<|ref|>sub_title<|/ref|><|det|>[[133, 214, 440, 227]]<|/det|>
+### C. Comparison with state-of-the-art algorithms  
+
+<|ref|>text<|/ref|><|det|>[[86, 246, 488, 504]]<|/det|>
+Finally, we compare TN- GEO with nine different leading SOTA optimizers covering a broad spectrum of algorithmic strategies for this specific combinatorial problem, based on and referred hereafter as: 1) GTS [26], the genetic algorithms, tabu search, and simulated annealing; 2) IPSO [27], an improved particle swarm optimization algorithm [27]; 3) IPSO- SA [28], a hybrid algorithm combining particle swarm optimization and simulated annealing; 4) PBILD [29], a population- based incremental learning and differential evolution algorithm; 5) GRASP [30], a greedy randomized adaptive solution procedure; 6) ABCFEIT [31], an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures; 7) HAAG [32], a hybrid algorithm integrating ant colony optimization, artificial bee colony and genetic algorithms; 8) VNSQP [33], a variable neighborhood search algorithm combined with quadratic programming; and, 9) RCABC [34], a rapidly converging artificial bee colony algorithm.  
+
+<|ref|>text<|/ref|><|det|>[[86, 506, 488, 635]]<|/det|>
+The test data used by the vast majority of researchers in the literature who have addressed the problem of cardinality- constrained portfolio optimization come from ORLibrary [35], which correspond to the weekly prices between March 1992 and September 1997 of the following indexes: Hang Seng in Hong Kong (31 assets); DAX 100 in Germany (85 assets); FTSE 100 in the United Kingdom (89 assets); S&P 100 in the United States (98 assets); and Nikkei 225 in Japan (225 assets).  
+
+<|ref|>text<|/ref|><|det|>[[86, 637, 488, 823]]<|/det|>
+Here we present the results obtained with TN- GEO and its comparison with the nine different SOTA metaheuristic algorithms mentioned above and whose results are publicly available from the literature. Table I shows the results of all algorithms and all performance metrics for each of the 5 index data sets (for more details on the evaluation metrics, see Appendix A 2). Each algorithm corresponds to a different column, with TN- GEO in the rightmost column. The values are shown in red if the TN- GEO algorithm performed better or equally well compared to the other algorithms on the corresponding performance metric. The numbers in bold mean that the algorithm found the best (lowest) value across all algorithms.  
+
+<|ref|>text<|/ref|><|det|>[[85, 825, 488, 882]]<|/det|>
+From all the entries in this table, \(67\%\) of them correspond to red entries, where TN- GEO either wins or draws, which is a significant percentage giving that these optimizers are among the best reported in the last decades.  
+
+<|ref|>text<|/ref|><|det|>[[85, 884, 488, 911]]<|/det|>
+In Table II we show a pairwise comparison of TN- GEO against each of the SOTA optimizers. This table reports the  
+
+<|ref|>text<|/ref|><|det|>[[516, 66, 917, 181]]<|/det|>
+number of times TN- GEO wins, loses, or draws compared to results reported for the other optimizer, across all the performance metrics and for all the 5 different market indexes. Note that since not all the performance metrics are reported for all the solvers and market indexes, the total number of wins, draws, or losses varies. Therefore, we report in the same table the overall percentage of wins plus draws in each case. We see that this percentage is greater than \(50\%\) in all the cases.  
+
+<|ref|>text<|/ref|><|det|>[[516, 183, 917, 398]]<|/det|>
+Furthermore, in Table II, we use the Wilcoxon signed- rank test [36], which is a widely used nonparametric statistical test used to evaluate and compare the performance of different algorithms in different benchmarks [37]. Therefore, to statistically validate the results, a Wilcoxon signed- rank test is performed to provide a meaningful comparison between the results from TN- GEO algorithm and the SOTA metaheuristic algorithms. The Wilcoxon signed- rank test tests the null hypothesis that the median of the differences between the results of the algorithms is equal to 0. Thus, it tests whether there is no significant difference between the performance of the algorithms. The null hypothesis is rejected if the significance value \((p)\) is less than the significance level \((\alpha)\) , which means that one of the algorithms performs better than the other. Otherwise, the hypothesis is retained.  
+
+<|ref|>text<|/ref|><|det|>[[516, 400, 917, 544]]<|/det|>
+As can be seen from the table, the TN- GEO algorithm significantly outperforms the GTS and PBILD methods on all performance metrics rejecting the null hypothesis at the 0.05 significance level. On the other hand, the null hypotheses are accepted at \(\alpha = 0.05\) for the TN- GEO algorithm over the other remaining algorithms. Thus, in terms of performance on all metrics combined, the results show that there is no significant difference between TN- GEO and these remaining seven SOTA optimizers (IPSO, IPSO- SA, GRASP, ABCFEIT, HAAG, VNSQP, and RCABC)  
+
+<|ref|>text<|/ref|><|det|>[[516, 545, 917, 602]]<|/det|>
+Overall, the results confirm the competitiveness of our quantum- inspired proposed approach against SOTA metaheuristic algorithms. This is remarkable given that these metaheuristics have been explored and fine- tuned for decades.  
+
+<|ref|>sub_title<|/ref|><|det|>[[661, 634, 770, 647]]<|/det|>
+## IV. OUTLOOK  
+
+<|ref|>text<|/ref|><|det|>[[516, 666, 917, 911]]<|/det|>
+Compared to other quantum optimization strategies, an important feature of TN- GEO is its algorithmic flexibility. As shown here, unlike other proposals, our GEO framework can be applied to arbitrary cost functions, which opens the possibility of new applications that cannot be easily addressed by an explicit mapping to a polynomial unconstrained binary optimization (PUBO) problem. Our approach is also flexible with respect to the source of the seed samples, as they can come from any solver, possibly more efficient or even application- specific optimizers. The demonstrated generalization capabilities of the generative model that forms its core, helps TN- GEO build on the progress of previous experiments with other state- of- the- art solvers, and it provides new candidates that the classical optimizer may not be able to achieve on its own. We are optimistic that this flexible approach will open up the broad applicability of quantum and quantum- inspired generative models to real- world combinatorial optimization
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[115, 113, 883, 604]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[85, 74, 920, 115]]<|/det|>
+TABLE I. Detailed comparison with SOTA algorithms for each of the five index data sets and on seven different performance indicators described in Appendix A 2. Entries in red correspond to cases where TN-GEO performed better or tied compared to the other algorithm. Entries in bold, corresponding to the best (lowest) value, for each specific indicator.   
+
+<table><tr><td>Data Set</td><td>Performance Indicator</td><td>GTS</td><td>IPSO</td><td>IPSO-SA</td><td>PBILD</td><td>GRASP</td><td>ABCFEIT</td><td>HAAG</td><td>VNSQP</td><td>RCABC</td><td>TN-GEO</td></tr><tr><td rowspan="7">Hang Seng</td><td>Mean</td><td>1.0957</td><td>1.0953</td><td>-</td><td>1.1431</td><td>1.0965</td><td>1.0953</td><td>1.0965</td><td>1.0964</td><td>1.0873</td><td>1.0958</td></tr><tr><td>Median</td><td>1.2181</td><td>-</td><td>-</td><td>1.2390</td><td>1.2155</td><td>1.2181</td><td>1.2181</td><td>1.2155</td><td>1.2154</td><td>1.2181</td></tr><tr><td>Min</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>Max</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.5538</td><td>1.5538</td><td>1.5538</td><td>1.5538</td><td>-</td><td>1.5538</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0001</td><td>-</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>-</td><td>0.0001</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>1.6368</td><td>-</td><td>1.6400</td><td>1.6432</td><td>1.6395</td><td>1.6397</td><td>1.6342</td><td>1.6392</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>0.6059</td><td>-</td><td>0.6060</td><td>0.6047</td><td>0.6085</td><td>0.6058</td><td>0.5964</td><td>0.6082</td></tr><tr><td rowspan="7">DAX100</td><td>Mean</td><td>2.5424</td><td>2.5417</td><td>-</td><td>2.4251</td><td>2.3126</td><td>2.3258</td><td>2.3130</td><td>2.3125</td><td>2.2898</td><td>2.3142</td></tr><tr><td>Median</td><td>2.5466</td><td>-</td><td>-</td><td>2.5866</td><td>2.5630</td><td>2.5678</td><td>2.5587</td><td>2.5630</td><td>2.5629</td><td>2.5660</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0059</td><td>0.0023</td><td>0.0023</td><td>0.0059</td><td>0.0059</td><td>0.0023</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>4.0275</td><td>4.0275</td><td>4.0275</td><td>4.0275</td><td>-</td><td>4.0275</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0001</td><td>-</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>-</td><td>0.0001</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>6.7806</td><td>-</td><td>6.7593</td><td>6.7925</td><td>6.7806</td><td>6.7583</td><td>6.8326</td><td>6.7540</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>1.2770</td><td>-</td><td>1.2769</td><td>1.2761</td><td>1.2780</td><td>1.2767</td><td>1.2357</td><td>1.2763</td></tr><tr><td rowspan="7">FTSE100</td><td>Mean</td><td>1.1076</td><td>1.0628</td><td>-</td><td>0.9706</td><td>0.8451</td><td>0.8481</td><td>0.8451</td><td>0.8453</td><td>0.8406</td><td>0.8445</td></tr><tr><td>Median</td><td>1.0841</td><td>-</td><td>-</td><td>1.0841</td><td>1.0841</td><td>1.0841</td><td>1.0841</td><td>-</td><td>1.0841</td><td>1.0841</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0016</td><td>0.0047</td><td>0.0006</td><td>0.0045</td><td>0.0016</td><td>0.0047</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>2.0576</td><td>2.0638</td><td>2.0605</td><td>2.0669</td><td>2.0670</td><td>2.0775</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0000</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>2.4701</td><td>-</td><td>2.4350</td><td>2.4397</td><td>2.4350</td><td>2.4349</td><td>2.4149</td><td>2.4342</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>0.3247</td><td>-</td><td>0.3245</td><td>0.3255</td><td>0.3186</td><td>0.3252</td><td>0.3207</td><td>0.3254</td></tr><tr><td rowspan="7">S&P100</td><td>Mean</td><td>1.9328</td><td>1.6890</td><td>-</td><td>1.6386</td><td>1.2937</td><td>1.2930</td><td>1.2930</td><td>1.2649</td><td>1.3464</td><td>1.2918</td></tr><tr><td>Median</td><td>1.1823</td><td>-</td><td>-</td><td>1.1692</td><td>1.1420</td><td>1.1369</td><td>1.1323</td><td>1.1323</td><td>1.1515</td><td>1.1452</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0009</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0009</td><td>0.0000</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>5.4551</td><td>5.4422</td><td>5.4642</td><td>5.4551</td><td>5.4520</td><td>5.4422</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0001</td><td>-</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>0.0001</td><td>-</td><td>0.0001</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>2.6281</td><td>-</td><td>2.5211</td><td>2.5260</td><td>2.5255</td><td>2.5105</td><td>2.5364</td><td>2.5269</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>0.7846</td><td>-</td><td>0.9063</td><td>0.8885</td><td>0.7044</td><td>0.9072</td><td>0.8858</td><td>0.9117</td></tr><tr><td rowspan="7">Nikkei</td><td>Mean</td><td>0.6066</td><td>0.6870</td><td>-</td><td>0.5972</td><td>0.5782</td><td>0.5781</td><td>0.5781</td><td>0.5904</td><td>0.5665</td><td>0.5793</td></tr><tr><td>Median</td><td>0.6093</td><td>-</td><td>-</td><td>0.5896</td><td>0.5857</td><td>0.5856</td><td>0.5854</td><td>0.5857</td><td>0.5858</td><td>0.5855</td></tr><tr><td>Minimum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>Maximum</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.1606</td><td>1.1606</td><td>1.1607</td><td>1.1606</td><td>1.1606</td><td>1.1606</td></tr><tr><td>MEUCD</td><td>-</td><td>-</td><td>0.0000</td><td>-</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>0.0000</td><td>-</td><td>0.0000</td></tr><tr><td>VRE</td><td>-</td><td>-</td><td>0.9583</td><td>-</td><td>0.8359</td><td>0.8396</td><td>0.8191</td><td>0.8561</td><td>0.8314</td><td>0.8353</td></tr><tr><td>MRE</td><td>-</td><td>-</td><td>1.7090</td><td>-</td><td>0.4184</td><td>0.4147</td><td>0.4233</td><td>0.4217</td><td>0.4042</td><td>0.4229</td></tr></table>  
+
+<|ref|>table<|/ref|><|det|>[[85, 680, 919, 807]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[85, 625, 919, 680]]<|/det|>
+TABLE II. Pairwise comparison of TN-GEO against each of the SOTA optimizers. The asymptotic significance is part of the Wilcoxon signedrank test results. The null hypothesis that the performance of the two algorithms is the same is tested at the \(95\%\) confidence level (significance level: \(\alpha = .05\) ). Results show that TN-GEO is on par with all the SOTA algorithms, and in two cases, GTS and PBILD, it significantly outperforms them. We also report the count for TN-GEO wins, losses, and ties, compared to each of the other algorithms.   
+
+<table><tr><td>TN-GEO vs Other:</td><td>GTS</td><td>IPSO</td><td>IPSO-SA</td><td>PBILD</td><td>GRASP</td><td>ABCFEIT</td><td>HAAG</td><td>VNSQP</td><td>RCABC</td></tr><tr><td>Wins(+)</td><td>6</td><td>4</td><td>6</td><td>9</td><td>12</td><td>10</td><td>11</td><td>11</td><td>8</td></tr><tr><td>Loss(-)</td><td>2</td><td>1</td><td>4</td><td>0</td><td>12</td><td>9</td><td>11</td><td>12</td><td>16</td></tr><tr><td>Ties</td><td>2</td><td>0</td><td>5</td><td>1</td><td>11</td><td>16</td><td>13</td><td>12</td><td>11</td></tr><tr><td>(Wins+Ties)/Total</td><td>80%</td><td>80%</td><td>67%</td><td>100%</td><td>66%</td><td>74%</td><td>69%</td><td>66%</td><td>54%</td></tr><tr><td>Asymptotic significance (p)</td><td>.036</td><td>.080</td><td>.308</td><td>.008</td><td>.247</td><td>.888</td><td>.363</td><td>.594</td><td>.110</td></tr><tr><td>Decision</td><td>Reject</td><td>Retain</td><td>Retain</td><td>Reject</td><td>Retain</td><td>Retain</td><td>Retain</td><td>Retain</td><td>Retain</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[87, 831, 293, 846]]<|/det|>
+problems at the industrial scale.  
+
+<|ref|>text<|/ref|><|det|>[[86, 854, 488, 913]]<|/det|>
+Although we have limited the scope of this work to tensor network- based generative quantum models, it would be a natural extension to consider other generative quantum models as well. For example, hybrid classical quantum models such as  
+
+<|ref|>text<|/ref|><|det|>[[515, 830, 917, 904]]<|/det|>
+quantum circuit associative adversarial networks (QC- AAN) [14] can be readily explored to harness the power of generative quantum models with so- called noisy intermediate- scale quantum (NISQ) devices [38]. In particular, the QC- AAN framework opens up the possibility of working with a larger
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[86, 66, 487, 240]]<|/det|>
+number of variables and going beyond discrete values (e.g., variables with continuous values). Both quantum- inspired and hybrid quantum- classical algorithms can be tested in this GEO framework in even larger problem sizes of this NP- hard version of the portfolio optimization problem or any other combinatorial optimization problem. As the number of qubits in NISQ devices increases, it would be interesting to explore generative models that can utilize more quantum resources, such as Quantum Circuit Born Machines (QCBM)[13]: a general framework to model arbitrary probability distributions and perform generative modeling tasks with gate- based quantum computers.  
+
+<|ref|>text<|/ref|><|det|>[[86, 240, 487, 384]]<|/det|>
+Increasing the expressive power of the quantum- inspired core of MPS to other more complex but still efficient QI approaches, such as tree- tensor networks [39], is another interesting research direction. Although we have fully demonstrated the relevance and scalability of our algorithm for industrial applications by increasing the performance of classical solvers on industrial scale instances (all 500 assets in the S&P 500 market index), there is a need to explore the performance improvement that could be achieved by more complex TN representations or on other combinatorial problems.  
+
+<|ref|>text<|/ref|><|det|>[[86, 384, 487, 514]]<|/det|>
+Although the goal of GEO was to show good behavior as a general black- box algorithm without considering the specifics of the study application, it is a worthwhile avenue to exploit the specifics of the problem formulation to improve its performance and runtime. In particular, for the portfolio optimization problem with a cardinality constraint, it is useful to incorporate this constraint as a natural MPS symmetry, thereby reducing the effective search space of feasible solutions from the size of the universe to the cardinality size.  
+
+<|ref|>text<|/ref|><|det|>[[515, 67, 916, 356]]<|/det|>
+Finally, our thorough comparison with SOTA algorithms, which have been fine- tuned for decades on this specific application, shows that our TN- GEO strategy manages to outperform a couple of these and is on par with the other seven optimizers. This is a remarkable feat for this new approach and hints at the possibility of finding commercial value in these quantum- inspired strategies in large- scale real- world problems, as the instances considered in this work. Also, it calls for more fundamental insights towards understanding when and where it would be beneficial to use this TN- GEO framework, which relies heavily on its quantum- inspired generative ML model. For example, understanding the intrinsic bias in these models, responsible for their remarkable performance, is another important milestone on the road to practical quantum advantage with quantum devices in the near future. The latter can be asserted given the tight connection of these quantum- inspired TN models to fully quantum models deployed on quantum hardware. And this question of when to go with quantum- inspired or fully quantum models is a challenging one that we are exploring in ongoing future work.  
+
+<|ref|>sub_title<|/ref|><|det|>[[636, 407, 797, 420]]<|/det|>
+## ACKNOWLEDGMENTS  
+
+<|ref|>text<|/ref|><|det|>[[515, 442, 916, 513]]<|/det|>
+The authors would like to acknowledge Manuel S. Rudolph, Marta Mauri, Matthew J.S. Beach, Yudong Cao, Luis Serrano, Jhonathan Romero- Fontalvo, Brian Dellabetta, Matthew Kowalsky, Jacob Miller, John Realpe- Gomez, and Collin Farquhar for their feedback on an early version of this manuscript  
+
+<|ref|>text<|/ref|><|det|>[[90, 567, 490, 911]]<|/det|>
+[1] Tadashi Kadowaki and Hidetoshi Nishimori, "Quantum annealing in the transverse ising model," Phys. Rev. E. 58, 5355 (1998). [2] Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda, "A quantum adiabatic evolution algorithm applied to random instances of an NP- Complete problem," Science 292, 472- 475 (2001). [3] Sam Gutmann Edward Farhi, Jeffrey Goldstone, "A quantum approximate optimization algorithm," arXiv:1411.4028 (2014). [4] Stuart Hadfield, Zhihui Wang, Bryan O'Gorman, Eleanor G Rieffel, Davide Venturelli, and Rupak Biswas, "From the quantum approximate optimization algorithm to a quantum alternating operator ansatz," Algorithms 12, 34 (2019). [5] Samuel Mugel, Carlos Kuchkovsky, Escolastico Sanchez, Samuel Fernandez- Lorenzo, Jorge Luis- Hita, Enrique Lizaso, and Roman Orus, "Dynamic portfolio optimization with real datasets using quantum processors and quantum- inspired tensor networks," (2020), arXiv:2007.00017 [quant- ph]. [6] A. Perdomo- Ortiz, N. Dickson, M. Drew- Brook, G. Rose, and A. Aspuru- Guzik, "Finding low- energy conformations of lattice protein models by quantum annealing," Sci. Rep. 2, 571 (2012). [7] Alejandro Perdomo- Ortiz, Alexander Feldman, Asier Ozeta, Sergei V. Isakov, Zheng Zhu, Bryan O'Gorman, Helmut G. Katzgraber, Alexander Diedrich, Hartmut Neven, Johan de Kleer, Brad Lackey, and Rupak Biswas, "Readiness of quantum optimization machines for industrial applications,"  
+
+<|ref|>text<|/ref|><|det|>[[515, 567, 918, 911]]<|/det|>
+Phys. Rev. Applied 12, 014004 (2019). [8] Emmanuel Bengio, Moksh Jain, Maksym Korablyov, Doina Precup, and Yoshua Bengio, "Flow network based generative models for non- iterative diverse candidate generation," (2021). [9] Mohamed Hibat- Allah, Estelle M. Inack, Roeland Wiersema, Roger G. Melko, and Juan Carrasquilla, "Variational neural annealing," Nature Machine Intelligence 3, 952- 961 (2021). [10] Song Cheng, Jing Chen, and Lei Wang, "Information perspective to probabilistic modeling: Boltzmann machines versus born machines," Entropy 20, 583 (2018). [11] Ian J. Goodfellow, Jean Pouget- Abadie, Mehdi Mirza, Bing Xu, David Warde- Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio, "Generative adversarial networks," (2014), arXiv:1406.2661 [stat.ML]. [12] Song Cheng, Jing Chen, and Lei Wang, "Information perspective to probabilistic modeling: Boltzmann machines versus Born machines," Entropy 20 (2017). [13] Marcello Benedetti, Delfina Garcia- Pintos, Yunseong Nam, and Alejandro Perdomo- Ortiz, "A generative modeling approach for benchmarking and training shallow quantum circuits," npj Quantum Information 5 (2018), 10.1038/s41534- 019- 0157- 8. [14] Manuel S. Rudolph, Ntwali Toussaint Bashige, Amara Katabarwa, Sonika Johr, Borja Peropadre, and Alejandro Perdomo- Ortiz, "Generation of high resolution handwritten digits with an ion- trap quantum computer," (2020),
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 70, 490, 910]]<|/det|>
+arXiv:2012.03924 [quant- ph]. [15] Zhao- Yu Han, Jun Wang, Heng Fan, Lei Wang, and Pan Zhang, "Unsupervised generative modeling using matrix product states," Phys. Rev. X 8, 031012 (2018). [16] Edwin Stoudenmire and David J Schwab, "Supervised learning with tensor networks," in Advances in Neural Information Processing Systems 29, edited by D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett (Curran Associates, Inc., 2016) pp. 4799- 4807. [17] Stavros Efthymiou, Jack Hidary, and Stefan Leichenauer, "TensorNetwork for machine learning," (2019), arXiv:1906.06329 [cs.LG]. [18] Chase Roberts, Ashley Milsted, Martin Ganahl, Adam Zalcman, Bruce Fontaine, Yijian Zou, Jack Hidary, Guifre Vidal, and Stefan Leichenauer, "TensorNetwork: A library for physics and machine learning," (2019), arXiv:1905.01330 [physics.comp- ph]. [19] Matthew Fishman, Steven R. White, and E. Miles Stoudenmire, "The ITensor software library for tensor network calculations," (2020), arXiv:2007.14822 [cs.MS]. [20] Harry Markowitz, "Portfolio selection," The Journal of Finance 7, 77- 91 (1952). [21] Tai- Danae Bradley, E M Stoudenmire, and John Terilla, "Modeling sequences with quantum states: a look under the hood," Machine Learning: Science and Technology 1, 035008 (2020). [22] James Stokes and John Terilla, "Probabilistic modeling with matrix product states," Entropy 21 (2019). [23] Jacob Miller, Guillaume Rabusseau, and John Terilla, "Tensor networks for probabilistic sequence modeling," (2020), arXiv:2003.01039 [cs.LG]. [24] The GPyOpt authors, "Gpyopt: A bayesian optimization framework in python," http://github.com/SheffieldML/GPyOpt (2016). [25] Specific adaptions of the MPS generative model could be implemented such that it conserves the number of assets by construction, borrowing ideas from condensed matter physics where one can impose MPS a conservation in the number of particles in the quantum state. [26] T- J Chang, Nigel Meade, John E Beasley, and Yazid M Sharaiha, "Heuristics for cardinality constrained portfolio optimisation," Computers & Operations Research 27, 1271- 1302 (2000). [27] Guang- Feng Deng, Woo- Tsong Lin, and Chih- Chung Lo, "Markowitz- based portfolio selection with cardinality constraints using improved particle swarm optimization," Expert Systems with Applications 39, 4558- 4566 (2012). [28] M Mozafari, F Jolai, and S Tafazzoli, "A new ipso- sa approach for cardinality constrained portfolio optimization," International Journal of Industrial Engineering Computations 2, 249- 262 (2011). [29] Khin Lwin and Rong Qu, "A hybrid algorithm for constrained portfolio selection problems," Applied intelligence 39, 251- 266 (2013). [30] Adil Baykasoğlu, Mualla Gonca Yunusoglu, and F Burcin Özsoydan, "A grasp based solution approach to solve cardinality constrained portfolio optimization problems," Computers & Industrial Engineering 90, 339- 351 (2015). [31] Can B Kalayci, Okkes Ertentice, Hasan Akyer, and Hakan Aygoren, "An artificial bee colony algorithm with feasibility enforcement and infeasibility tolerance procedures for cardinality constrained portfolio optimization," Expert Systems with Applications 85, 61- 75 (2017). [32] Can B Kalayci, Olcay Polat, and Mehmet A Akbay, "An efficient hybrid metaheuristic algorithm for cardinality constrained  
+
+<|ref|>text<|/ref|><|det|>[[512, 68, 919, 640]]<|/det|>
+portfolio optimization," Swarm and Evolutionary Computation 54, 100662 (2020). [33] Mehmet Anil Akbay, Can B Kalayci, and Olcay Polat, "A parallel variable neighborhood search algorithm with quadratic programming for cardinality constrained portfolio optimization," Knowledge- Based Systems 198, 105944 (2020). [34] Tunchan Cura, "A rapidly converging artificial bee colony algorithm for portfolio optimization," Knowledge- Based Systems 233, 107505 (2021). [35] John E Beasley, "Or- library: distributing test problems by electronic mail," Journal of the operational research society 41, 1069- 1072 (1990). [36] Frank Wilcoxon, "Individual comparisons by ranking methods," in Breakthroughs in statistics (Springer, 1992) pp. 196- 202. [37] Janez Demšar, "Statistical comparisons of classifiers over multiple data sets," Journal of Machine Learning Research 7, 1- 30 (2006). [38] John Preskill, "Quantum computing in the NISQ era and beyond," Quantum 2, 79 (2018). [39] Song Cheng, Lei Wang, Tao Xiang, and Pan Zhang, "Tree tensor networks for generative modeling," Phys. Rev. B 99, 155131 (2019). [40] Joachim Dahl Martin Andersen and Lieven Vandenberghe, "Python software for convex optimization," http://cvxopt.org (2020). [41] Tunchan Cura, "Particle swarm optimization approach to portfolio optimization," Nonlinear analysis: Real world applications 10, 2396- 2406 (2009). [42] Ignacio Cirac, David Perez- Garcia, Norbert Schuch, and Frank Verstraete, "Matrix product states and projected entangled pair states: Concepts, symmetries, and theorems," (2020), arXiv:2011.12127 [quant- ph]. [43] "Code for unsupervised generative modeling using matrix product states," https://github.com/congzllwag/UnsupGenModbyMPS (2018). [44] Matthew T. Perry and Richard J. Wagner, "Python module for simulated annealing," https://github.com/perrygeo/simanneal (2019). [45] Javier Alcazar, Vicente Leyton- Ortega, and Alejandro Perdomo- Ortiz, "Classical versus quantum models in machine learning: insights from a finance application," Machine Learning: Science and Technology 1, 035003 (2020).  
+
+<|ref|>sub_title<|/ref|><|det|>[[647, 664, 785, 678]]<|/det|>
+## Appendix A: Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[560, 694, 874, 708]]<|/det|>
+## 1. Generation of portfolio optimization instances  
+
+<|ref|>text<|/ref|><|det|>[[515, 725, 918, 810]]<|/det|>
+The portfolio optimization problem aims at determining the fractions \(w_{i}\) of a given capital to be invested in each asset \(i\) of a universe of \(N\) assets, such that the risk \(\sigma (w)\) for a given level \(\rho\) of the expected return \(\langle r(w)\rangle\) is minimized, constrained to \(\sum_{i}w_{i} = 1\) . The problem can be formulated as:  
+
+<|ref|>equation<|/ref|><|det|>[[546, 821, 916, 848]]<|/det|>
+\[\min_{w}\{\sigma^{2}(w) = w^{T}\cdot \pmb {\Sigma}\cdot \pmb {w}:\langle r(w)\rangle = w\cdot \pmb {r} = \rho \} \mathrm{(A1)}\]  
+
+<|ref|>text<|/ref|><|det|>[[515, 854, 918, 911]]<|/det|>
+where the vectors \(w\) and \(r\) have dimensionality \(N\) , \(\pmb{\Sigma}\) is the sample covariance matrix obtained from the return time series of pair of asset \(i\) and \(j\) , and \(r\) is the vector of average return of the time series for each asset, with each daily return, \(r^{t}\) ,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 66, 488, 153]]<|/det|>
+calculated as the relative increment in asset price from its previous day (i.e., \(r^{t} = (p^{t} - p^{(t - 1)}) / p^{(t - 1)}\) , with \(p^{t}\) as the price for a particular asset at time \(t\) ). The solution to Eq. A1 for a given return level \(\rho\) corresponds to the optimal portfolio strategy \(\boldsymbol{w}^{*}\) and the minimal value of this objective function \(\sigma (\boldsymbol {w})\) correspond to the portfolio risk and will be denoted by \(\sigma_{\rho}^{*}\) .  
+
+<|ref|>text<|/ref|><|det|>[[85, 155, 488, 369]]<|/det|>
+Note that the optimization task in Eq. A1 has the potential outcome of investing small amounts in a large number of assets as an attempt to reduce the overall risk by "over diversifying" the portfolio. This type of investment strategy can be challenging to implement in practice: portfolios composed of a large number of assets are difficult to manage and may incur in high transaction costs. Therefore, several restrictions are usually imposed on the allocation of capital among assets, as a consequence of market rules and conditions for investment or to reflect investor profiles and preferences. For instance, constraints can be included to control the amount of desired diversification, i.e., modifying bound limits per asset \(i\) , denoted by \(\{l_{i}, u_{i}\}\) , to the proportion of capital invested in the investment on individual assets or a group of assets, thus the constraint \(l_{i} < w_{i} < u_{i}\) could be considered.  
+
+<|ref|>text<|/ref|><|det|>[[85, 370, 488, 569]]<|/det|>
+Additionally, a more realistic and common scenario is to include in the optimization task a cardinality constraint, which limits directly the number of assets to be transacted to a pre- specified number \(\kappa < N\) . Therefore, the number of different sets to be treated is \(M = \binom{N}{\kappa}\) . In this scenario, the problem can be formulated as a Mixed- Integer Quadratic Program (MIQP) with the addition of binary variables \(x_{i} \in \{0, 1\}\) per asset, for \(i = 1, \ldots , N\) , which are set to "1" when the \(i\) - th asset is included as part of the \(\kappa\) assets, or "0" if it is left out of this selected set. Therefore, valid portfolios would have a number \(\kappa\) of 1's, as specified in the cardinality constraint. For example, for \(N = 4\) and \(\kappa = 2\) , the six different valid configurations can be encoded as \(\{0011, 0101, 0110, 1001, 1010, 1100\}\) .  
+
+<|ref|>text<|/ref|><|det|>[[100, 572, 460, 586]]<|/det|>
+The optimization task can then be described as follows  
+
+<|ref|>equation<|/ref|><|det|>[[132, 612, 488, 696]]<|/det|>
+\[\begin{array}{rl} & {\min_{\boldsymbol {w},\boldsymbol {x}}\{\sigma^2 (\boldsymbol {w}):}\\ & {\qquad \langle \boldsymbol {r}(\boldsymbol {w})\rangle = \rho ,}\\ & {\qquad l_i\boldsymbol {x}_i< w_i< u_i\boldsymbol {x}_i\quad i = 1,\dots ,N,}\\ & {\qquad \mathbf{1}\cdot \boldsymbol {x} = \kappa \} .} \end{array} \quad (A2)\]  
+
+<|ref|>text<|/ref|><|det|>[[85, 708, 488, 883]]<|/det|>
+In this reformulated problem we denote by \(\sigma_{\rho ,\kappa}^{*}\) the minimum portfolio risk outcome from Eq. A2 for a given return level \(\rho\) and cardinality \(\kappa\) . The optimal solution vectors \(\boldsymbol{w}^{*}\) and \(\boldsymbol{x}^{*}\) define the portfolio investment strategy. Adding the cardinality constraint and the investment bound limits transforms a simple convex optimization problem (Eq. A1) into a much harder non- convex NP- hard problem. For all the problem instance generation in this work we chose \(\kappa = N / 2\) and the combinatorial nature of the problems lies in the growth of the search space associated with the binary vector \(\boldsymbol{x}\) , which makes it intractable to exhaustively explore for a number of assets in the few hundreds. The size of the search space here is \(M = \binom{N}{N / 2}\)  
+
+<|ref|>text<|/ref|><|det|>[[85, 884, 488, 912]]<|/det|>
+It is important to note that given a selection of which assets belong to the portfolio by instantiating \(\boldsymbol{x}\) (say with a specific  
+
+<|ref|>text<|/ref|><|det|>[[515, 65, 917, 200]]<|/det|>
+\(\boldsymbol{x}^{(i)}\) ), solving the optimization problem in Eq. A2 to find the respective investment fractions \(\boldsymbol{w}^{(i)}\) and risk value \(\sigma_{\rho ,N / 2}^{(i)}\) can be efficiently achieved with conventional quadratic programming (QP) solvers. In this work we used the python module cvxopt [40] for solving this problem. Note that we exploit this fact to break this constrained portfolio optimization problem into a combinatorial intractable one (find best asset selection \(\boldsymbol{x}\) ), which we aim to solve with GEO, and a tractable subroutine which can be solved efficiently with available solvers.  
+
+<|ref|>text<|/ref|><|det|>[[515, 201, 917, 245]]<|/det|>
+The set of pairwise \((\sigma_{\rho}^{*}, \rho)\) , dubbed as the efficient frontier, is no longer convex neither continuous in contrast with the solution to problem in Eq. (A1).  
+
+<|ref|>sub_title<|/ref|><|det|>[[520, 278, 910, 305]]<|/det|>
+## 2. Problem formulation for comparison with state-of-the-art algorithms  
+
+<|ref|>text<|/ref|><|det|>[[515, 324, 917, 494]]<|/det|>
+To carry out the comparison with State- of- the- Art Algorithms, in line with the formulation used there, we generalizes the problem in Eq. A2 releasing the constraint of a fix level of portfolio return, instead directly incorporating the portfolio return in the objective function, encompassing now two terms: the one on the left corresponding to the portfolio risk as beforehand the one on the right corresponding to the portfolio return. The goal is to balance out both terms such that return is maximized and risk minimized. Lambda is a hyperparameter, named risk averse, that controls if an investor wants to give more weight to risk or return. The new formulation reads as follows,  
+
+<|ref|>equation<|/ref|><|det|>[[603, 523, 917, 585]]<|/det|>
+\[\begin{array}{rl} & {\min_{\boldsymbol {w},\boldsymbol {x}}\{\lambda \sigma^2 (\boldsymbol {w}) - (1 - \lambda)\langle \boldsymbol {r}(\boldsymbol {w})\rangle :}\\ & {l_i\boldsymbol {x}_i< w_i< u_i\boldsymbol {x}_i\quad i = 1,\dots ,N,}\\ & {\qquad \mathbf{1}\cdot \boldsymbol {x} = \kappa \} .} \end{array} \quad (A3)\]  
+
+<|ref|>text<|/ref|><|det|>[[515, 601, 917, 630]]<|/det|>
+With the rest of constraints and variables definition as in Appendix A1.  
+
+<|ref|>sub_title<|/ref|><|det|>[[640, 662, 792, 675]]<|/det|>
+### a. Performance Metrics  
+
+<|ref|>text<|/ref|><|det|>[[515, 695, 917, 796]]<|/det|>
+To compare the performance of the proposed GEO with the SOTA metaheuristic algorithms in the literature, the most commonly used performance metrics for the cardinality constrained portfolio optimization problem are used. These metric formulations compute the distance between the heuristic efficient frontier and the unconstrained efficient frontier. Thus, the performance of the algorithms can be evaluated.  
+
+<|ref|>text<|/ref|><|det|>[[515, 798, 917, 856]]<|/det|>
+Four of these performance metrics (the Mean, Median, Minimum and Maximum in Table I) are based on the so- called Performance Deviation Errors \((PDE)\) . These \(PDE\) metrics were formulated by Chang [26] as follows:  
+
+<|ref|>equation<|/ref|><|det|>[[525, 877, 917, 916]]<|/det|>
+\[PDE_{i} = min\left(\left|\frac{100(x_{i} - x_{i}^{*})}{x_{i}^{*}}\right|,\left|\frac{100(y_{i} - y_{i}^{*})}{y_{i}^{*}}\right|\right) \quad (A4)\]
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[155, 87, 488, 280]]<|/det|>
+\[\begin{array}{rl} & {x_{i}^{*} = X_{k_{y}} + \frac{(X_{j_{y}} - X_{k_{y}})(y_{i} - Y_{k_{y}})}{(Y_{j_{y}} - Y_{k_{y}})}}\\ & {y_{i}^{*} = Y_{k_{x}} + \frac{(Y_{j_{x}} - Y_{k_{x}})(x_{i} - X_{k_{x}})}{(X_{j_{x}} - X_{k_{x}})}}\\ & {j_{y} = \underset {l = 1,\dots ,\epsilon^{*}}{\arg \min}Y_{l}}\\ & {k_{y} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmax}}Y_{l}}\\ & {j_{x} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmin}}X_{l}}\\ & {k_{x} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmax}}X_{l}}\\ & {k_{x} = \underset {l = 1,\dots ,\epsilon^{*}}{\mathrm{argmax}}X_{l}} \end{array} \quad (A5)\]  
+
+<|ref|>text<|/ref|><|det|>[[85, 289, 488, 404]]<|/det|>
+where the pair \((X_{l},Y_{l})(l = 1,\dots ,\epsilon^{*})\) represents the point on the standard efficient frontier and the pair \((x_{i},y_{i})(i =\) \(1,\dots ,\epsilon)\) represents the point on the heuristic efficient frontier. Here, \(\epsilon^{*}\) denotes the number of points on the standard efficient frontier while \(\epsilon\) denotes the number of points on the heuristic efficient frontier. The mean, median, minimum, and maximum of the \(PDE\) can be used to compare the performance of the algorithms.  
+
+<|ref|>text<|/ref|><|det|>[[85, 404, 488, 464]]<|/det|>
+Later, three additional performance measures (MEUCD: Mean Euclidean Distance, VRE: Variance of Return Error, MRE: Mean Return Error) were formulated by Cura [41] as follows:  
+
+<|ref|>equation<|/ref|><|det|>[[113, 484, 487, 519]]<|/det|>
+\[MEUCD = \frac{\sum_{i = 1}^{\epsilon}\sqrt{(X_{i}^{*} - x_{i}) + (Y_{i}^{*} - y_{i})}}{\epsilon} \quad (A6)\]  
+
+<|ref|>equation<|/ref|><|det|>[[174, 540, 487, 575]]<|/det|>
+\[VRE = \frac{\sum_{i = 1}^{\epsilon}100|X_{i}^{*} - x_{i}| / x_{i}}{\epsilon} \quad (A7)\]  
+
+<|ref|>equation<|/ref|><|det|>[[174, 591, 487, 625]]<|/det|>
+\[MRE = \frac{\sum_{i = 1}^{\epsilon}100|Y_{i}^{*} - y_{i}| / y_{i}}{\epsilon} \quad (A8)\]  
+
+<|ref|>text<|/ref|><|det|>[[85, 634, 488, 710]]<|/det|>
+where \((X_{i}^{*},Y_{i}^{*})\) is the standard point closest to the heuristic point \((x_{i},y_{i})\) . Figure 5 shows a graphical representation of the indices used to calculate the performance metrics for the convenience of the reader and the values for TN- GEO and all the other SOTA optimizers are reported in Table I.  
+
+<|ref|>sub_title<|/ref|><|det|>[[117, 736, 456, 750]]<|/det|>
+## 3. Quantum-Inspired Generative Model in TN-GEO  
+
+<|ref|>text<|/ref|><|det|>[[86, 767, 488, 912]]<|/det|>
+The addition of a probabilistic component is inspired by the success of Bayesian Optimization (BO) techniques, which are among the most efficient solvers when the performance metric aims to find the lowest minimum possible within the least number of objective function evaluations. For example, within the family of BO solvers, GPyOpt [24] uses a Gaussian Process (GP) framework consisting of multivariate Gaussian distributions. This probabilistic framework aims to capture relationships among the previously observed data points (e.g., through tailored kernels), and it guides the decision of where  
+
+<|ref|>image<|/ref|><|det|>[[515, 61, 916, 305]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[514, 320, 917, 346]]<|/det|>
+<center>FIG. 5. A graphical demonstration of indices used for performance metrics calculation </center>  
+
+<|ref|>text<|/ref|><|det|>[[515, 369, 917, 426]]<|/det|>
+to sample the next evaluation with the help of the so called acquisition function. GPyOpt is one of the solvers we use to benchmark the new quantum- enhanced strategies proposed here.  
+
+<|ref|>text<|/ref|><|det|>[[515, 426, 917, 500]]<|/det|>
+Although the GP framework in BO techniques is not a generative model, we explore here the powerful unsupervised machine learning framework of generative modeling in order to capture correlations from an initial set of observations and evaluations of the objective function (step 1- 4 in Fig. 1).  
+
+<|ref|>text<|/ref|><|det|>[[515, 500, 917, 615]]<|/det|>
+For the implementation of the quantum- inspired generative model at the core of TN- GEO we follow the procedure proposed and implemented in Ref. [15]. Inspired by the probabilistic interpretation of quantum physics via Born's rule, it was proposed that one can use the Born probabilities \(|\Psi (\pmb {x})|^2\) over the \(2^{N}\) states of an \(N\) qubit system to represent classical target probability distributions which would be obtained otherwise with generative machine learning models. Hence,  
+
+<|ref|>equation<|/ref|><|det|>[[576, 631, 916, 670]]<|/det|>
+\[P(\pmb {x}) = \frac{|\Psi(\pmb{x})|^2}{Z},\mathrm{with}Z = \sum_{\pmb {x}\in \mathcal{S}}|\Psi (\pmb {x})|^2, \quad (A9)\]  
+
+<|ref|>text<|/ref|><|det|>[[515, 678, 917, 853]]<|/det|>
+with \(\Psi (\pmb {x}) = \langle \pmb {x}|\Psi \rangle\) and \(\pmb {x}\in \{0,1\}^{\otimes N}\) are in one- to- one correspondence with decision variables over the investment universe with \(N\) assets in our combinatorial problem of interest here. In Ref. [15] these quantum- inspired generative models were named as Born machines, but we will refer to them hereafter as tensor- network Born machines (TNBm) to differentiate it from the quantum circuit Born machines (QCBM) proposal [13] which was developed independently to achieve the same purpose but by leveraging quantum wave functions from quantum circuits in NISQ devices. As explained in the main text, either quantum generative model can be adapted for the purpose of our GEO algorithm.  
+
+<|ref|>text<|/ref|><|det|>[[515, 854, 917, 912]]<|/det|>
+On the grounds of computational efficiency and scalability towards problem instances with large number of variables (in the order of hundreds or more), following Ref. [15] we implemented the quantum- inspired generative model based on
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 66, 487, 95]]<|/det|>
+Matrix Product States (MPS) to learn the target distributions \(|\Psi (\pmb {x})|^2\) .  
+
+<|ref|>text<|/ref|><|det|>[[86, 96, 488, 240]]<|/det|>
+MPS is a type of TN where the tensors are arranged in a one- dimensional geometry. Despite its simple structure, MPS can efficiently represent a large number of quantum states of interest extremely well [42]. Learning with the MPS is achieved by adjusting its parameters such that the distribution obtained via Born's rule is as close as possible to the data distribution. MPS enjoys a direct sampling method that is more efficient than other Machine Learning techniques, for instance, Boltzmann machines, which require Markov chain Monte Carlo (MCMC) process for data generation.  
+
+<|ref|>text<|/ref|><|det|>[[86, 241, 488, 356]]<|/det|>
+The key idea of the method to train the MPS, following the algorithm on paper [15], consists of adjusting the value of the tensors composing the MPS as well as the bond dimension among them, via the minimization of the negative log- likelihood function defined over the training dataset sampled from the target distribution. For more details on the implementation see Ref. [15] and for the respective code see Ref. [43].  
+
+<|ref|>sub_title<|/ref|><|det|>[[210, 386, 365, 399]]<|/det|>
+## 4. Classical Optimizers  
+
+<|ref|>sub_title<|/ref|><|det|>[[228, 417, 345, 430]]<|/det|>
+### a. GPyOpt Solver  
+
+<|ref|>text<|/ref|><|det|>[[86, 448, 488, 522]]<|/det|>
+GPyOpt [24] is a Python open- source library for Bayesian Optimization based on GPy and a Python framework for Gaussian process modelling. For the comparison exercise in TN- GEO as a stand- alone solver here are the hyperparameters we used for the GPyOpt solver:  
+
+<|ref|>text<|/ref|><|det|>[[113, 532, 488, 700]]<|/det|>
+- Domain: to deal with the exponential growth in dimensionality, the variable space for \(n\) number of assets was partitioned as the cartesian product of \(n\) 1-dimensional spaces.- Constraints: we added two inequalities in the number of assets in a portfolio solution to represent the cardinality condition.- Number of initial data points: 10- Acquisition function: Expected Improvement  
+
+<|ref|>sub_title<|/ref|><|det|>[[192, 728, 382, 741]]<|/det|>
+### b. Simulated Annealing Solver  
+
+<|ref|>text<|/ref|><|det|>[[86, 760, 488, 860]]<|/det|>
+For simulated annealing (SA) we implemented a modified version from Ref. [44]. The main change consists of adapting the update rule such that new candidates are within the valid search space with fixed cardinality. The conventional update rule of single bit flips will change the Hamming weight of \(x\) which translates in a portfolio with different cardinality. The hyperparameters used are the following:  
+
+<|ref|>text<|/ref|><|det|>[[113, 871, 390, 884]]<|/det|>
+- Max temperature in thermalization: 1.0  
+
+<|ref|>text<|/ref|><|det|>[[113, 896, 390, 911]]<|/det|>
+- Min temperature in thermalization: 1e-4  
+
+<|ref|>sub_title<|/ref|><|det|>[[620, 68, 812, 80]]<|/det|>
+### c. Conditioned Random Solver  
+
+<|ref|>text<|/ref|><|det|>[[515, 100, 917, 213]]<|/det|>
+This solver corresponds to the simplest and most naive approach, while still using the cardinality information of the problem. In the conditioned random solver, we generate, by construction, bitstrings which satisfy the cardinality constraint. Given the desired cardinality \(\kappa = N / 2\) used here, one starts from the bitstring with all zeros, \(x_0 = 0\dots 0\) , and flips only \(N / 2\) bits at random from positions containing 0's, resulting in a valid portfolio candidate \(x\) with cardinality \(N / 2\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[657, 245, 775, 258]]<|/det|>
+### d. Random Solver  
+
+<|ref|>text<|/ref|><|det|>[[515, 277, 917, 363]]<|/det|>
+This solver corresponds to the simplest approach without even using the cardinality information of the problem. In the random solver, we generate, by construction, bitstrings randomly selected from the \(2^{N}\) bitstrings of all possible portfolios, where \(N\) is the number of assets in our investment universe.  
+
+<|ref|>sub_title<|/ref|><|det|>[[544, 393, 885, 407]]<|/det|>
+## 5. Algorithm Methodology for TN-GEO as a booster  
+
+<|ref|>text<|/ref|><|det|>[[515, 440, 917, 498]]<|/det|>
+As explained in the main text, in this case it is assumed that the cost of evaluating the objective function is not the major computational bottleneck, and consequently there is no practical limitations in the number of observations to be considered.  
+
+<|ref|>text<|/ref|><|det|>[[515, 499, 917, 541]]<|/det|>
+Following the algorithmic scheme in Fig. 1, we describe next the details for each of the steps in our comparison benchmarks:  
+
+<|ref|>text<|/ref|><|det|>[[540, 554, 917, 828]]<|/det|>
+0 Build the seed data set, \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) and \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{seed}}\) . For each problem instance defined by \(\rho\) and a random subset with \(N\) assets from the S&P 500, gather all initial available data obtained from previous optimization attempts with classical solver(s). In our case, for each problem instances we collected 10,000 observations from the SA solver. These 10,000 observations corresponding to portfolio candidates \(\{\pmb{x}^{(i)}\}_{\mathrm{init}}\) and their respective risk evaluations \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{init}}\) were sorted and only the first \(n_{\mathrm{seed}} = 1,000\) portfolio candidates with the lowest risks were selected as the seed data set. This seed data set is the one labeled as \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) and \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{seed}}\) in the main text and hereafter. The idea of selecting a percentile of the original data is to provide the generative model inside GEO with samples which are the target samples to be generated. This percentile is a hyperparameter and we set it \(10\%\) of the initial data for our purposes.  
+
+<|ref|>text<|/ref|><|det|>[[540, 840, 917, 911]]<|/det|>
+1 Construct of the softmax surrogate distribution: Using the seed data from step 0, we construct a softmax multinomial distribution with \(n_{\mathrm{seed}}\) classes - one for each point on the seed data set. The probabilities outcome associated with each of these classes in the multinomial
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[125, 65, 490, 115]]<|/det|>
+is calculated as a Boltzmann weight, \(p_{i} = \frac{e^{-\overline{\sigma}_{i,\kappa}}}{\sum_{j = 1}^{n_{\mathrm{seed}}}e^{-\overline{\sigma}_{j,\kappa}}}\) .  
+
+<|ref|>text<|/ref|><|det|>[[125, 117, 488, 336]]<|/det|>
+Here, \(\overline{\sigma}_{\rho ,\kappa}^{(i)} = \sigma_{\rho ,\kappa}(\pmb{x}^{(i)}) / T\) , and \(T\) is a "temperature" hyperparameter. In our simulations, \(T\) was computed as the standard deviation of the risk values of this seed data set. In Bayesian optimization methods the surrogate function tracks the landscape associated with the values of the objective function (risk values here). This soft- max surrogate constructed here by design as a multinomial distribution from the seed data observations serves the purpose of representing the objective function landscape but in probability space. That is, it will assign higher probability to portfolio candidates with lower risk values. Since we will use this softmax surrogate to generate the training data set, this bias imprints a preference in the quantum- inspired generative model to favor low- cost configurations.  
+
+<|ref|>text<|/ref|><|det|>[[112, 347, 488, 404]]<|/det|>
+2 Sample from softmax surrogate. We will refer to these samples as the training set since these will be used to train the MPS- based generative model. For our experiments here we used \(n_{\mathrm{train}} = 10000\) samples.  
+
+<|ref|>text<|/ref|><|det|>[[111, 416, 488, 446]]<|/det|>
+3 Use the \(n_{\mathrm{train}}\) samples from the previous step to train the MPS generative model.  
+
+<|ref|>text<|/ref|><|det|>[[111, 457, 488, 544]]<|/det|>
+4 Obtain \(n_{\mathrm{MPS}}\) samples from the generative model which correspond to the new list of potential portfolio candidates. In our experiments, \(n_{\mathrm{MPS}} = 4000\) . For the case of 500 assets, as sampling takes sensibly longer because of the problem dimension, this value was reduced to 400 to match the time in SA.  
+
+<|ref|>text<|/ref|><|det|>[[111, 555, 488, 628]]<|/det|>
+5 Select new candidates: From the \(n_{\mathrm{MPS}}\) samples, select only those who fulfill the cardinality condition, and which have not been evaluated. These new portfolio candidates \(\{\pmb{x}^{(i)}\}_{\mathrm{new}}\) are saved for evaluation in the next step.  
+
+<|ref|>text<|/ref|><|det|>[[111, 638, 488, 716]]<|/det|>
+6 Obtain risk value for new selected samples: Solve Eq. A2 to evaluate the objective function (portfolio risks) for each of the new candidates \(\{\pmb{x}^{(i)}\}_{\mathrm{new}}\) . We will denote refer to the new cost function values by \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{new}}\) .  
+
+<|ref|>text<|/ref|><|det|>[[111, 728, 488, 815]]<|/det|>
+7 Merge the new portfolios, \(\{\pmb{x}^{(i)}\}_{\mathrm{new}}\) , and their respective cost function evaluations, \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{new}}\) with the seed portfolios, \(\{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) , and their respective cost values, \(\{\sigma_{\rho ,N / 2}^{(i)}\}_{\mathrm{seed}}\) , from step 0 above. This combined super set is the new initial data set.  
+
+<|ref|>text<|/ref|><|det|>[[110, 826, 488, 912]]<|/det|>
+8 Use the new initial data set from step 7 to start the algorithm from step 1. If a desired minimum is already found or if no more computational resources are available, one can decide to terminate the algorithm here. In all of our benchmark results reported here when using TN- GEO as a booster from SA intermediate results,  
+
+<|ref|>text<|/ref|><|det|>[[555, 66, 917, 110]]<|/det|>
+we only run the algorithm for this first cycle and the minima reported for the TN- GEO strategy is the lowest minimum obtained up to step 7 above.  
+
+<|ref|>sub_title<|/ref|><|det|>[[533, 142, 899, 169]]<|/det|>
+## 6. Algorithm Methodology for TN-GEO as a stand-alone solver  
+
+<|ref|>text<|/ref|><|det|>[[513, 202, 917, 362]]<|/det|>
+This section presents the algorithm for the TN- GEO scheme as a stand- alone solver. In optimization problems where the objective function is inexpensive to evaluate, we can easily probe it at many points in the search for a minimum. However, if the cost function evaluation is expensive, e.g., tuning hyperparameters of a deep neural network, then it is important to minimize the number of evaluations drawn. This is the domain where optimization technique with a Bayesian flavour, where the search is being conducted based on new information gathered, are most useful, in the attempt to find the global optimum in a minimum number of steps.  
+
+<|ref|>text<|/ref|><|det|>[[513, 363, 917, 492]]<|/det|>
+The algorithmic steps for TN- GEO as a stand- alone solver follows the same logic as that of the solver as a booster described Sec. A5. The main differences between the two algorithms rely on step 0 during the construction of the initial data set and seed data set in step 0, the temperature use in the softmax surrogate in step 1, and a more stringent selection criteria in step 5. Since the other steps remain the same, we focus here to discuss the main changes to the algorithmic details provided in Sec. A5.  
+
+<|ref|>text<|/ref|><|det|>[[540, 508, 917, 696]]<|/det|>
+0 Build the seed data set: since evaluating the objective function could be the major bottleneck (assumed to be expensive) then we cannot rely on cost function evaluations to generate the seed data set. The strategy we adopted is to initialize the algorithm with samples of bitstrings which satisfy the hard constraints of the problem. In our specific example, we can easily generate \(n_{\mathrm{seed}}\) random samples, \(\mathcal{D}_0 = \{\pmb{x}^{(i)}\}_{\mathrm{seed}}\) , which satisfy the cardinality constraint. Since all the elements in this data set hold the cardinality condition, then maximum length \(n_{\mathrm{seed}}\) of \(\mathcal{D}_0\) is \(\binom{N}{K}\) . In our experiments, we set the number of samples \(n_{\mathrm{init}} = 2,000\) , for all problems considered here up to \(N = 100\) assets  
+
+<|ref|>text<|/ref|><|det|>[[540, 710, 917, 912]]<|/det|>
+1 Construct the softmax surrogate distribution: start by constructing a uniform multinomial probability distribution where each sample in \(\mathcal{D}_0\) has the same probability. Therefore, for each point in the seed data set its probability is set to \(p_0 = 1 / n_{\mathrm{seed}}\) . As in TN- GEO as a booster, we will attempt to generate a softmax- like surrogate which favors samples with low cost value, but we will slowly build that information as new samples are evaluated. In this first iteration of the algorithm, we start by randomly selecting a point \(\pmb{x}^{(1)}\) from \(\mathcal{D}_0\) , and we evaluate the value of its objective function \(\sigma^{(1)}\) (its risk value in our specific finance example). To make this point \(\pmb{x}^{(1)}\) stand out from the other unevaluated samples, we set its probability to be twice that of any
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[125, 66, 488, 386]]<|/det|>
+of the remaining \(n_{\mathrm{seed}} - 1\) points in \(\mathcal{D}_0\) . Since we increase the probability of one of the points, we need to adjust the probability of the \(n_{\mathrm{seed}} - 1\) from \(p_0\) to \(p_0\) and if we assume the probability weights for observing each point follows a multinomial distribution with Boltzmann weights, under these assumptions, and making by fixing the temperature hyperparameter we can solve for the reference "risk" value \(\sigma^{(0)}\) associated to all the other \(n_{\mathrm{seed}} - 1\) points as shown below. It is important to note that \(\sigma^{(0)}\) is an artificial reference value which is calculated analytically and does not require a call to the objective function (in contrast to \(\sigma^{(1)}\) ). Here, \(\mathcal{N}\) is the normalization factor of the multinomial and \(T\) is the temperature hyperparameter which, as in the case of TN- GEO as a booster, can be adjusted later in the algorithm as more data is seen. Due to the lack of initial cost function values, in order to set a relevant typical "energy" scale in this problem, we follow the procedure in Ref. [45] where it is set to be the square root of the mean of the covariance matrix defined in Eq. A1, as this matrix encapsulates the risk information (volatility) as stated in the Markowitz's model.  
+
+<|ref|>equation<|/ref|><|det|>[[100, 405, 460, 568]]<|/det|>
+\[\left\{ \begin{array}{ll}(n_{\mathrm{seed}} - 1)p_0' + p_1 = 1 & \Rightarrow \left\{ \begin{array}{ll}p_0' = 1 / (1 + n_{\mathrm{seed}}) \\ p_1 = 2 / (1 + n_{\mathrm{seed}}) \end{array} \right.\\ \displaystyle \left\{ \begin{array}{ll}\mathcal{N} = (n_{\mathrm{seed}} - 1)e^{-\sigma^{(0)} / T} + e^{-\sigma^{(1)} / T} & \\ p_1 = e^{-\sigma^{(1)} / T} / \mathcal{N} & \\ p_0' = e^{-\sigma^{(0)} / T} / \mathcal{N} & \end{array} \right. \end{array} \right.\]  
+
+<|ref|>text<|/ref|><|det|>[[112, 590, 488, 620]]<|/det|>
+2 Generate training set: same as in TN- GEO as a booster (see Appendix A 5).  
+
+<|ref|>text<|/ref|><|det|>[[111, 627, 488, 657]]<|/det|>
+3 Train MPS: same as in TN- GEO as a booster (see Appendix A 5).  
+
+<|ref|>text<|/ref|><|det|>[[111, 664, 488, 694]]<|/det|>
+4 Generate samples from trained MPS: same as in TN- GEO as a booster (see Appendix A 5).  
+
+<|ref|>text<|/ref|><|det|>[[111, 702, 488, 875]]<|/det|>
+5 Select new candidates from trained MPS: In contrast to TN- GEO as a booster we cannot afford to evaluate all new candidates coming from the MPS samples. In our procedure we selected only two new candidates which must meet the cardinality constraint. For our procedure these two candidates correspond to the most frequent sample ("exploitation") and the least frequent sample ("exploration"). If all new samples appeared with the same frequency, then we can select two samples at random. In the case where no new samples were generated, we choose them from the unevaluated samples of the original seed data set in \(\mathcal{D}_0\)  
+
+<|ref|>text<|/ref|><|det|>[[111, 883, 488, 913]]<|/det|>
+6 Obtain risk value for new selected samples: same as in TN- GEO as a booster (see Appendix A 5).  
+
+<|ref|>text<|/ref|><|det|>[[540, 66, 917, 96]]<|/det|>
+7 Merge the new portfolios with seed data set from step 0 same as in TN- GEO as a booster (see Appendix A 5).  
+
+<|ref|>text<|/ref|><|det|>[[540, 105, 917, 150]]<|/det|>
+8 Restart next cycle of the algorithm with the merge data set as the new seed data set: same as in TN- GEO as a booster (see Appendix A 5).  
+
+<|ref|>sub_title<|/ref|><|det|>[[574, 177, 859, 191]]<|/det|>
+## Appendix B: Relative TN-GEO Enhancement  
+
+<|ref|>text<|/ref|><|det|>[[511, 208, 916, 238]]<|/det|>
+Figure 6 represents the relative performance within the strategies 1 and 2 referred to subsection III A.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[185, 60, 810, 732]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[84, 742, 920, 812]]<|/det|>
+<center>FIG. 6. Relative TN-GEO enhancement similar to those shown in the bottom panel of Fig. 2 in the main text. For these experiments, portfolio optimization instances with a number of variables ranging from \(N = 30\) to \(N = 100\) were used. Here, each panel correspond to a different investment universes corresponding to a random subset of the S&P 500 market index. Note the trend for a larger quantum-inspired enhancement as the number of variables (assets) becomes larger, with the largest enhancement obtained in the case on instances with all the assets from the S&P 500 ( \(N = 500\) ), as shown in Fig. 2 </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 410, 150]]<|/det|>
+summarycomparisonTNGEOvsalI.pdf
+
+<--- Page Split --->

preprint/preprint__00d0f482762f2f37431ca49a939480fc54bdd5eb053d5ac8ce0b474c9dacda22/images_list.json

@@ -0,0 +1,77 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
+    "footnote": [],
+    "bbox": [
+      [
+        50,
+        40,
+        640,
+        787
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2",
+    "footnote": [],
+    "bbox": [
+      [
+        62,
+        81,
+        928,
+        780
+      ]
+    ],
+    "page_idx": 19
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3",
+    "footnote": [],
+    "bbox": [
+      [
+        61,
+        70,
+        700,
+        789
+      ]
+    ],
+    "page_idx": 21
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4",
+    "footnote": [],
+    "bbox": [
+      [
+        63,
+        70,
+        792,
+        777
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5",
+    "footnote": [],
+    "bbox": [
+      [
+        50,
+        66,
+        789,
+        787
+      ]
+    ],
+    "page_idx": 25
+  }
+]

preprint/preprint__00d0f482762f2f37431ca49a939480fc54bdd5eb053d5ac8ce0b474c9dacda22/preprint__00d0f482762f2f37431ca49a939480fc54bdd5eb053d5ac8ce0b474c9dacda22.mmd

@@ -0,0 +1,362 @@
+
+# An integrin-targeting AAV developed using a novel computational rational design methodology presents improved targeting of the skeletal muscle and reduced liver tropism  
+
+Ai Vu Hong  
+
+avuhong@genethon.fr  
+
+Genethon https://orcid.org/0000- 0002- 0872- 4295  
+
+Laurence Suel  
+
+Genethon  
+
+Jérôme Poupiot  
+
+Genethon  
+
+Isabelle Richard  
+
+Genethon  
+
+## Article  
+
+Keywords:  
+
+Posted Date: October 27th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3466229/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: Yes there is potential Competing Interest. A.H.V. and I.R. are inventors on PCT application EP2023/065499 for the integration of RGLxxL/I motif in AAV capsid for enhanced muscle transduction efficiency. I.R. is a part- time employee of Atamyo Therapeutics. The other authors declare no competing interests.  
+
+Version of Record: A version of this preprint was published at Nature Communications on September 11th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 52002- 4.
+
+<--- Page Split --->
+
+## Abstract  
+
+Current adeno- associated virus (AAV) gene therapy using nature- derived AAVs is limited by non- optimal tissue targeting. In the treatment of muscular diseases (MD), high doses are therefore often required, but can lead to severe adverse effects. To lower treatment doses, we rationally designed an AAV that specifically targets skeletal muscle. We employed a novel computational design that integrated binding motifs of integrin alpha V beta 6 (αVβ6) into a liver- detargeting AAV capsid backbone to target the human αVβ6 complex – a selected AAV receptor for skeletal muscle. After sampling the low- energy capsid mutants, all in silico designed AAVs showed higher productivity compared to their parent. We confirmed in vitro that the enhanced transduction is due to the binding to the αVβ6 complex. Thanks to inclusion of αVβ6- binding motifs, the designed AAVs exhibited enhanced transduction efficacy in human differentiated myotubes as well as in murine skeletal muscles in vivo. One notable variant, LICA1, showed similar muscle transduction to other published myotropic AAVs, while being significantly more strongly liver- detargeted. We further examined the efficacy of LICA1, in comparison to AAV9, in delivering therapeutic transgenes in two mouse MD models at a low dose of 5E12 vg/kg. At this dose, AAV9 was suboptimal, while LICA1 transduced effectively and significantly better than AAV9 in all tested muscles. Consequently, LICA1 corrected the myopathology, restored global transcriptomic dysregulation, and improved muscle functionality. These results underline the potential of our design method for AAV engineering and demonstrate the relevance of the novel AAV variant for gene therapy treatment of MD.  
+
+## One Sentence Summary  
+
+We developed a novel computationally AAV design method resulting in a new myotropic AAV, which allows low- dose AAV treatment for muscular dystrophies.  
+
+## INTRODUCTION  
+
+Over 50 years since their discovery, adeno- associated viruses (AAVs) have shown great promise as an effective viral vector for gene delivery and gene therapy, leading to recent approval of therapeutic products \(^{1,2}\) . Due to unmet medical needs and natural AAV tropism, many AAV- based gene therapies focus on treating muscle diseases (MD) \(^{3}\) . Systemic treatment in such diseases aims to primarily target skeletal muscle, which accounts for more than 40% of body mass, and therefore often requires very high doses (≥1E14 vg/kg) to achieve meaningful therapeutic efficacy \(^{3- 6}\) . In addition, most recombinant AAVs built on natural- occurring variants lack specificity and often accumulate in the liver, with the concomitant risk of hepatotoxicity \(^{7}\) . Other key challenges of rAAV use persist, including manufacturing, immunological barriers, and associated toxicity \(^{1,2,8,9}\) .  
+
+AAV is a small non- pathogenic single- stranded DNA parvovirus. Multiple open reading frames (ORFs) were identified in its genome, including Rep, Cap, AAP and MAAP \(^{1,10}\) . The single Cap ORF expresses three capsid proteins - virion protein 1 (VP1), VP2 and VP3, which assemble into an icosahedral 60- mer capsid. Structurally, the VP3 monomer core contains a highly conserved eight- stranded β- barrel motif \(^{11}\) .
+
+<--- Page Split --->
+
+Inserted between the \(\beta\) - strands, nine surface- exposed variable regions (VR1- 9) result in local topological differences between serotypes and dictate virus- host interaction. Consequently, genetically modifying VRs can drastically change the AAV, transduction, antigenic profile, and fitness \(^{10,12,13}\) . VR4 and VR8, that cluster together spatially, forming the most prominent protrusion at the 3- fold axis, have been widely subjected to modifications, notably by inserting short peptides into the loop apices \(^{14}\) . This resulted in some highly efficient capsid variants for transducing a variety of cell types and tissues \(^{1,12}\) . Among these, remarkably, AAVMYOs \(^{15,16}\) and MYOAAVs \(^{17}\) transduce skeletal muscles, deliver therapeutic transgenes efficiently, and were shown to correct dystrophic phenotypes in MD mouse models at relatively low doses (2E12 – 1E13 vg/kg).  
+
+Importantly, the myotropic AAVs \(^{15 - 17}\) identified by muscle- directed high- throughput screening (HTS) were shown to share an Arg- Gly- Asp (RGD) motif, presumably targeting the integrin complex \(^{17 - 20}\) . Integrins are a group of heterodimeric proteins composed of an \(\alpha\) - and a \(\beta\) subunit that serve various cellular functions, including cell adhesion, cell migration, and cell signaling \(^{21}\) . As adhesion molecules, integrins also mediate cell- pathogen interactions, and are therefore exploited by many viruses, including natural AAV, to infect cells \(^{22 - 24}\) . Indeed, many of these viruses use an RGD motif on their viral envelope glycoproteins or capsids for cell attachment, endocytosis, entry, and endosomal escape \(^{18,22,25}\) . The discovery that RGD- dependent integrin- targeting AAV variants can acquire myotropism therefore represents a novel potential candidate approach for a rational design to target skeletal muscle.  
+
+This study introduces a novel computational method for a rational AAV design targeting skeletal muscle, which resulted in a novel myotropic vector for MD gene therapy. First, the human skeletal muscle- enriched integrin complex alpha V beta 6 (αVβ6) was selected as the target receptor. Inspired by one- sided protein design \(^{26,27}\) , we computationally designed a previously developed liver- detargeting hybrid capsid between AAV9 and AAVrh74 (Cap9rh74) as an αVβ6 binder. The VR4 loop was completely modified, in which new sequences were iteratively selected to simultaneously optimize for free energy, while hosting αVβ6- binding RGDLLXL/I motifs. All designed AAVs were well- produced, at higher titers than their parent. The designed AAVs were confirmed to require αVβ6 binding for cellular transduction. The most promising variant, renamed LICA1, was selected for further analysis and showed superior transduction in human differentiated myotubes and strong myotropism in several mouse models. We evaluated this variant by delivering therapeutic transgenes in two MD mouse models at a very low dose of 5E12 vg/kg, in comparison to AAV9. In both cases, LICA1 presents higher efficacy than AAV9 in correcting dystrophic phenotypes, global transcriptomic changes and restoring muscle function, thanks to improved transduction and transgene expression in skeletal muscles. Collectively, the study provides a proof- of- concept for a new rational AAV design pipeline leveraging protein design tools, which resulted in a novel myotropic AAV with high potential for gene therapy for muscle diseases.  
+
+## RESULTS  
+
+## 1. Selection of the cellular receptor for rational design
+
+<--- Page Split --->
+
+Several myotrophic AAVs have recently been developed, notably, the insertion into the AAV9 VR- VIII loop of P1 peptide (RGDLLGS) \(^{15,16}\) , and a series of RGD- containing sequences identified by directed evolution \(^{17}\) . Importantly, these modified capsids shared a common RGD motif, which suggested their affinity to integrin (ITG), cell- surface heterocomplexes that interact with the extracellular matrix \(^{28}\) . Using publicly available datasets, we aimed to select relevant integrin subunits for a subsequent rational AAV design targeting skeletal muscle.  
+
+Chemello and colleagues previously performed single- nucleus RNA sequencing, comparing gene expression of all cell types in the skeletal muscle of wild- type (WT) and Duchenne muscular dystrophy mouse models (D51) \(^{29}\) . We extracted RNA levels of all integrin alpha and beta genes from these data (Figure S1A). Among all subunits, only the \(\alpha\) - subunits Itgav, Itga7 and the \(\beta\) - subunits Itgb6, Itgb1, and Itgb5 show relatively high expression in the myogenic nuclei. Of interest is the fact that the expression level of Itgb6 is highly enriched in myonuclei, and significantly upregulated in the dystrophic condition, whereas Itgb1 and Itgb5 expression are ubiquitous in all cell types, and significantly lower than the Itgb6 level in all myonuclei. Among the two expressed \(\alpha\) - subunits, only Itgav was known to associate with Itgb6 to form avβ6 heterocomplexes – a member of the RGD- binding integrin family \(^{30}\) . Furthermore, bulk RNA sequencing data from multiple human tissues confirmed high expression of Itgav and Itgb6 in skeletal muscle, and low expression of Itgb6 in the liver and spleen, two preferred targets of natural AAV (Figure S1B, GTEx V8, dbGaP Accession phs000424.v8.p2). We therefore hypothesize that AAV transduction in skeletal muscle can be improved by rationally designing an AAV capsid that specifically binds to avβ6.  
+
+## 2. Rational design of a hybrid capsid, Cap9rh74, with a high affinity to the \(\mathbb{V}\mathbb{B}\beta 6\) complex  
+
+As we aim to specifically target the skeletal muscle, we selected a hybrid capsid that we previously developed and that has a liver- detargeting property as the parental capsid in our design (Patent Number: EP18305399.0). This hybrid capsid of AAV9 and AAV.rh74 (AAV9rh74) was constructed by replacing the AAV9 sequence of VR4 to VR8 with that of AAV- rh74. The hybrid capsid showed similar infectivity in skeletal and cardiac muscles but was strongly de- targeted from the liver. The latter property is of particular interest in skeletal muscle gene transfer since the majority of administrated viral vector will not accumulate in the liver, as is the case for natural AAVs \(^{31,32}\) .  
+
+After selection of the cellular receptor of interest and capsid backbone, AAV capsids were computationally engineered (Fig. 1A). First, the 3D structure of the parental capsid, of with structure was unknown, was modeled using AlphaFold2 \(^{33,34}\) . The structural prediction of the Cap9rh74 aa 219–737 monomer performed using AlphaFold2 was at a high level of confidence, with predicted local distance difference test (IDDT- Ca), a per- residue measure of local confidence, of 97.04 and low predicted aligned error (PEA) of 4.32 (Fig S1C- D). This structure is thus suitable for the next steps in the design.  
+
+Second, we extracted the 3D structure or sequences of binding motifs of the human integrin complex from PDB. Importantly, avβ6 was previously shown to bind with high affinity to the RGDLLXL/1 motif
+
+<--- Page Split --->
+
+found in the human TGF- \(\beta 1\) and TGF- \(\beta 3\) prodomains \(^{35,36}\) . Binding peptides with eight amino acid residues, aa214- 221 in TGF- \(\beta 1\) (PDB: 5ffo) and aa240- 247 in TGF- \(\beta 3\) (PDB: 4um9), were isolated from the corresponding crystal structures before grafting into the Cap9rh74 VR4 loop. Both motifs bind to \(\alpha \beta 6\) dimer at a very similar position (Fig S1E).  
+
+Third, the defined binding motifs were then grafted into the VR4 loop (residues 453- 459) of the capsid protein based on the RosettaRemodel protocol \(^{37}\) . In the grafting- remodel process, many rounds of backbone optimization and sequence design iteratively search for low- energy sequence- structure pairs (Fig. 1B). The lowest- energy designs in grafting experiments of each TGF- \(\beta\) motif showed convergence in both structure and sequence (Fig. 1C- D, S1F- G). The new VR4 loops include the binding peptide and two flanking 2- amino acid linkers and retain the LXXL/I motif as an \(\alpha\) - helix, which is important to bind in the \(\beta 6\) subunit's pocket \(^{36}\) .  
+
+Retrospective docking simulations of the two AAV_ITGs with the best scores, namely Cap9rh74_5ffo and Cap9rh74_4um9, on the \(\alpha \beta 6\) complex showed highly similar binding positions of the new VR4 loop to its corresponding inserted motifs (Fig. 1E- F). This suggests that the new capsids can bind to \(\alpha \beta 6\) thanks to VR4- included RGDLLXXL/I motif. Sequences with the best scores, which reflect the thermodynamic stability of one static protein conformation \(^{38}\) , were subjected to experimental validation.  
+
+## 3. All designed AAV_ITGs showed higher productivity and enhanced cellular transduction via \(\alpha \beta 6\) binding.  
+
+The two AAVs with the best design were then tested for productivity and the effectiveness of using \(\alpha \beta 6\) as a cellular receptor. They were produced by tri- transfection with pITR- CMV- GFP- Luciferase as the expression cassette. Thanks to energy optimization, all the designed AAV- ITG variants significantly increase their titers compared to their parental hybrid capsid, to levels similar to those for AAV9 (Fig. 2A, S2A). In addition, all modified AAV- ITG variants retain proportions of VP1, VP2, VP3 capsid proteins with a similar ratio of AAV9 (Fig. 2B). This suggests that the designed sequences result in more stable AAV capsid complexes thanks to their estimated low energy structure, and therefore better production efficacy.  
+
+Next, we examined whether these AAV- ITGs can effectively use \(\alpha \beta 6\) as a cellular receptor upon infection. First, a HEK293 cell line (293_ \(\alpha \beta 6\) ) constitutively overexpressing both integrin subunits, \(\alpha\) and \(\beta 6\) , was created using the PiggyBac system (Fig S2B- C). The designed AAVs were then tested for their infectivity in this cell line. As expected, infection of AAV_ITGs in 293_ \(\alpha \beta 6\) cells, as defined by vector copy numbers (VCN), was higher than for AAV9 and AAV9rh74 (Fig. 2C). Both AAV_ITGs dramatically improved the luciferase activity ( \(\mathrm{FC}_{9\mathrm{rh74\_4um9 / AAV9}} = 60.50\) , \(\mathrm{FC}_{9\mathrm{rh74\_5ffo / AAV9}} = 25.99\) , \(\mathrm{FC}_{9\mathrm{rh74\_4um9 / 9rh74}} = 63.99\) , and \(\mathrm{FC}_{9\mathrm{rh74\_4um9 / 9rh74 = 27.49}}\) , Fig. 2D). To investigate how specific AAV_ITGs used \(\alpha \beta 6\) as a cellular receptor, we tested their infectivity under binding competition conditions. The number of AAV_ITG viral vectors entering the cells was significantly reduced when blocked by the recombinant protein \(\alpha \beta 6\) before viral infection, but no change occurred with AAV9 or AAV9rh74
+
+<--- Page Split --->
+
+(Fig. 2E). This result suggests that efficient transduction of AAV_ITGs requires specific binding to a \(\alpha \beta \delta\) complex.  
+
+During myogenesis, \(\alpha \beta \delta\) is only expressed in late differentiation, but not in the myoblast stage (Fig S1A, S2D). We therefore hypothesized an enhanced transduction of AAV_ITGs in differentiated myotubes, but not myoblasts. We infected both human myoblasts and myotubes with AAV_ITGs. Low levels of luciferase activity were observed in all AAVs tested in human myoblasts (Fig. 2G,I). On the other hand, in human differentiated myotubes (hMT), VCN and luciferase activities in both AAV9rh74_4um9 and _5ff0 were significantly higher than for AAV9 or AAV9rh74 (Fig. 2F,H,K). In particular, variant AAV9rh74_4um9 showed a 16.56 (p < 0.0001) and 25.02- fold (p < 0.0001) improvement in luciferase activity compared to AAV9 and AAV9rh74, respectively, which is in agreement with its superior transduction efficiency and transgene expression seen in 293_αVβ6 cells.  
+
+In summary, the two designed AAV_ITGs were both well- produced and function via \(\alpha \beta \delta\) - specific binding, thus enhancing their transduction efficiency in 293_αVβ6 and human differentiated myotubes.  
+
+## 4. AAV_ITGs enhanced transduction in skeletal muscle following systematic administration  
+
+AAV_ITGs, together with AAV9 and AAV9rh74, were administrated systematically via intravenous injection (transgene: CMV_GFP- Luciferase, dose: 1E13 vg/kg, age at injection: 6 weeks, n = 4) in C57Bl6 mice to examine their biodistribution 3 weeks post- injection (Fig. 3A).  
+
+In agreement with a previous study, AAV9rh74 slightly reduces transduction in skeletal muscle compared to AAV9 but accumulates much less in the liver (Fig. 3B- D). Thanks to the liver- detargeting capsid and in accordance with the fact that \(\alpha \beta \delta\) is weakly expressed in the liver, we expected poor entry into the liver for designed AAV_ITGs. Indeed, AAV_ITGs is strongly detargeted from the liver, both at VCN and mRNA levels, even further than the parental capsid (Fig. 3C- D). In contrast, enhanced transduction was observed in all skeletal muscles that were tested, including the tibialis anterior (TA), quadriceps (Qua) and diaphragm (Dia) (Fig. 3B- D). The two AAV_ITGs both showed a substantial increase in VCN and luciferase activity compared to both AAV9 and AAV9rh74. Similar to the results obtained in in vitro models, AAV9rh74_4um9 is the best transducer among the two AAV_ITGs. Compared to AAV9, the variant 9rh74_4um9 significantly increased VCN 5.31/7.21/2.48- fold and increased luciferase activity 15.2/13.2/23.57- fold in Qua, TA, and Dia (p < 0.05), respectively. Compared to the original backbone AAV9rh74, this variant even magnified the difference by increasing VCN 5.53/2.85/7.69- fold and increasing luciferase activity 152.35/106.68/60.43- fold (p < 0.05). Furthermore, AAV9rh74_4um9, but not AAV9rh74_5ffo, significantly increased transduction in the heart (FCVCN=4.15, FCLLC=15.43, p < 0.05). All AAVs that were tested showed poor delivery and transgene expression in the lungs and kidneys. No alteration of TGFβ and integrin signaling was observed at one- month post- injection in all AAVs being tested (Fig S2F- G). Overall, these data indicate that AAV_ITGs, especially the 9rh74_4um9 variant, are strongly liver- detargeted and exhibit enhanced tropism towards skeletal and cardiac muscles.
+
+<--- Page Split --->
+
+## 5. AAV9rh74_4um9 transduced skeletal muscle similarly, but detargeted the liver more strongly than other myotropic AAVs  
+
+Several engineered myotropic AAVs (mAAVs), including AAVMYO \(^{15}\) , MYOAAV- 1A and - 2A \(^{17}\) , have demonstrated superior efficacy for in vivo delivery of muscle compared to natural AAVs. To evaluate the properties of these AAVs compared to ours, we performed in vitro and in vivo experiments. Viral preparations were produced using the same reporter transgene (CMV_GFP- Luc). All mAAVs were well- produced in 400ml suspension, with higher titers than AAV9rh74. However, MYOAAV productivity was significantly lower than 9rh74_ITGs and MYOAAVs (Fig S3A). Since all investigated mAAVs shared a common integrin- targeting RGD motif, these AAVs were then evaluated for their transduction via integrin complexes in myotubes and in cell lines where integrin complexes were stably overexpressed by the PiggyBac system. In 293_αVβ6 cells as well as in hMT, where αVβ6 is highly expressed, AAV9rh74_4um9 showed the highest transduction among the tested myotropic AAVs, with the sole exception that luciferase activity of MYOAAV2A was higher in hMT (Fig S3B- C). We also tested AAV transduction efficiency in two other cell lines, 293_WT, where αVβ6 expression is low, and 293_α7β1 that stably overexpresses a non- RGD- targeting α7β1 integrin. In both conditions, MYOAAV2A and AAV9rh74_4um9 showed the highest transduction (Fig S3D- E). These results suggest that, as intended with the rational design, AAV9rh74_4um9 uses αVβ6 more preferentially for cellular transduction than others, yet it can also efficiently use other integrin(s) similar to MYOAAV2A.  
+
+Following in vivo injection in the same setting as described above (6- week- old WT mice, dose: 1E13 \(\mathrm{vg / kg}\) , \(\mathrm{n} = 4\) ), the three mAAVs and 9rh74_4um9 all showed strong liver- detargeting, high enrichment in both skeletal and cardiac muscles, and negligible transduction levels in other organs that were tested (kidneys, lungs, and brain) (Fig. 3G- H). No significant difference was observed in either VCN or luciferase activity between all three mAAVs and 9rh74_4um9 in the skeletal muscles that were tested. In heart muscle, MYOAAV2A showed a significant increase in VCN compared to other myotropic vectors, but no difference in luciferase activity, in agreement with the original observation \(^{17}\) . The most striking difference is the level of liver- detargeting between these vectors. The VCN for 9rh74_4um9 in liver is 3.34/22.05/13.85 times lower than for AAVMYO ( \(\mathrm{p} = 0.0022\) ), MYOAAV- 1A ( \(\mathrm{p} = 0.0013\) ) and - 2A ( \(\mathrm{p} = 0.033\) ), respectively (Fig. 3G), and is therefore the only vector that accumulates less in liver than skeletal muscles (Fig S3F- G). These data indicate higher muscle specificity for the 9rh74_4um9 variant compared to other myotropic vectors that have been investigated to date.  
+
+In summary, the 9rh74_4um9 variant, hereafter referred to as LICA1 (linked- integrin- complex AAV), consistently showed enhanced transduction and strongest liver- detargeting. Therefore, we then attempted to evaluate LICA1 as a delivery vector for muscular dystrophies, in comparison with AAV9. Two different setups will be investigated: the transfer of microdystrophin (μDys) – an incomplete transgene - in mdx, a mild mouse model of Duchenne muscular dystrophy (DMD) and of the full- length human α- sarcoglycan (SGCA) in a severe mouse model of limb- girdle muscular dystrophy R3 (LGMD- R3).
+
+<--- Page Split --->
+
+## 6. Low-dose LICA1-μDys gene transfer is effective in specifically overexpressing microdystrophin in dystrophic muscle but not sufficient to fully correct the underlying pathology  
+
+DMD is caused by mutations in the DMD gene, which encodes for dystrophin protein - a key player in the dystrophin- glycoprotein complex (DGC), which is critical for the structural stability of skeletal muscle fibers \(^{39}\) . Lack of dystrophin can result in progressive loss of muscle function, respiratory defects, and cardiomyopathy. The most commonly used DMD animal model is the mdx mouse, with a lifespan reduced by \(25\%\) , milder clinical symptoms than those seen in human patients, with the exception of the diaphragm muscle \(^{40}\) . Among many therapeutic strategies to restore dystrophin expression, high- dose AAV- based gene transfer of shortened functional forms of the dystrophin ORF provided excellent results in animal models, but unsatisfactory conflicting data in current clinical trials \(^{6}\) . Severe toxicities, even patient death, have been reported from these trials (NCT03368742, NCT04281485), assumed to be related to the dose of \(\geq 1E14\) vg/kg. We therefore explored the possibility of low- dose μDys gene transfer \(^{41}\) in mdx mice using LICA1 in comparison to AAV9 (Fig S4A, age at injection: 4 weeks, dose: 5E12 vg/kg, treatment duration: 4 weeks, \(n = 5\) ). Three muscles with increasing levels of severity - TA, Qua, and Dia - were used to study AAV transduction and treatment efficacy.  
+
+LICA1 showed better μDys gene transfer than AAV9 in this model. LICA1- treated mice exhibited a significantly higher VCN in all 3 muscles that were tested, 1.85/2.02/1.07 times higher in TA ( \(p < 0.0001\) ), Qua ( \(p < 0.0001\) ), and Dia ( \(p = 0.020\) ), respectively (Fig. 4A). RNA levels indicated even greater differences and were 4.56- 7.57 times higher in the LICA1- treated group (Fig. 4B; TA: FC = 4.56, \(p < 0.0001\) ; Qua: FC = 5.46, \(p = 0.0001\) ; Dia: 7.57, \(p = 0.05\) ). Consequently, LICA1 can transduce almost \(100\%\) in TA and Qua, and \(49.98\%\) in Dia, while substantially lower numbers were seen in AAV9- treated muscles, at \(73.22\%\) ( \(p = 0.0001\) ), \(57.8\%\) ( \(p < 0.0001\) ), \(10.34\%\) ( \(p < 0.0001\) ) in TA, Qua, Dia, respectively (Fig. 4C, Fig S4B). Furthermore, while infection levels and expression of the transgene in liver were high for the AAV9 vector (despite the use of muscle- specific promoter), the VCN and mRNA levels in LICA1- treated liver were extremely low (Fig. 4A- B, FCVCN:AAV9/LICA1=36.8, \(p = 0.0002\) ; FCmRNA:AAV9/LICA1=64.7, \(p < 0.0001\) ). These data again confirmed the transduction efficiency and specificity towards skeletal muscle for the LICA1 vector, even with low- dose treatment.  
+
+The histological features and muscle functionality after AAV treatment were restored accordingly. The centronucleation index (percentage of centronucleated fibers) - an indicator of the regeneration/degeneration process - did not change with AAV9 (except in TA) but was significantly reduced upon LICA1 treatment (reduction of \(21.68\%\) , \(19.05\%\) , \(22.88\%\) in TA, Qua, Dia, respectively) (Fig. 4D, Fig S4C). Similarly, the fibrosis level in two severely affected muscles, Qua and Dia, only exhibited a significant reduction with LICA1, but not AAV9 (Fig. 4E, Fig S4D). The serum biomarker MYOM3 level, an indicator of muscle damage \(^{42}\) , showed a reduction for both AAV treatments, with a considerable further reduction seen in the LICA1- treated group (Fig. 4F, FCAAV9/KO=0.75, FC-LICA/KO=0.43, PAAV9- LICA1>0.0001). More importantly, AAV9 treatment did not affect any muscle functionality being tested (Fig. 4G- I), while significant improvements with LICA1- μDys treatment were observed in escape
+
+<--- Page Split --->
+
+test – a measure of global force (Fig. 4G, \(\mathrm{FC}_{\mathrm{LICA1 / mdx}} = 1.19\) , \(\mathrm{P}_{\mathrm{LICA1 / mdx}} = 0.02\) ) and in situ TA mechanical force measurement (Fig. 4H, \(\mathrm{FC}_{\mathrm{LICA1 / mdx}} = 1.14\) , \(\mathrm{P}_{\mathrm{LICA1 / mdx}} = 0.0006\) ). However, none of the treatment normalized to the WT functional levels. These data indicate that LICA1 is better than AAV9 at restoring dystrophic histological features and muscle functions.  
+
+We also investigated the molecular alteration in Qua upon AAV treatment using RNA- seq. On the two first principal components (PCs) of the PCA, a clear distinction between four transcriptome groups (WT, mdx, AAV9, LICA1) was observed, while LICA1- treated muscles were clustered closer to the WTs than others (Fig S4E). To our surprise, despite excellent transgene expression by LICA1, global transcriptomic restoration was relatively modest (Fig. 4K). Nevertheless, a substantial improvement can still be seen for LICA1 compared to AAV9. Among 4216 down- and 4501 upregulated differentially expressed genes (DEGs) identified in mdx muscle, 1515 (35.9%) and 1728 (38.4%) were restored by AAV9, while LICA1 was able to correct 1736 (41.2%) and 1980 (44.0%), respectively (Fig. 4L- M). In addition, a greater number of genes were either not or insufficiently corrected by AAV9 than by LICA1 (Fig. 4N). A total of 2572 genes were downregulated (61.0%) and 2620 (58.2%) incompletely restored, while significantly lower numbers were seen for LICA, with 2094 (49.67%) down- and 2019 (44.86%) upregulated. Interestingly, some known dysregulated pathways, including \(\alpha\) - and Y- interferon responses and oxidative phosphorylation, were significantly better normalized by LICA1 than by AAV9 (Fig S4F).  
+
+In summary, at 5E12 vg/kg, LICA1- \(\mu\) Dys, but not AAV9, was efficient in transducing close to 100% myofibers, except in the diaphragm. This effective improvement in transduction can significantly reduce some dystrophic features in all muscles that were tested, yet restoration in the global transcriptome remains modest. However, greater improvements in functional, histological, and transcriptomic restoration were achieved with LICA1 compared to AAV9.  
+
+## 7. Low-dose LICA1-SGCA treatment restored the muscle functionality, dystrophic phenotypes, and transcriptomic dysregulation in a severe SGCA mouse model.  
+
+LGMDR3 is caused by mutations in the SGCA gene \(^{43}\) – another component of the DGC complex. Defects in the SGCA protein therefore lead to muscle weakness and wasting. A LGMDR3 mouse model has been established, which closely represents patient's clinical phenotypes \(^{44}\) . Similar to the setting in mdx mice, low- dose AAV treatment with 5E12 vg/kg was investigated in this mouse model. AAV9 or LICA1 encoding human SGCA (hSGCA) under control of a muscle- specific human Acta1 promoter were injected into 4- week- old SGCA- KO mice (Fig. 5A). Analysis was performed 4 weeks post- treatment.  
+
+In all three muscles that were tested, TA, Qua, Dia (in order of increasing severity), transduction in various measures, VCN, mRNA level, and percentage of SGCA + myofibers, was significantly greater in the LICA1- treated group than for AAV9 (Fig. 5B- D, Fig S5A). Of note is the fact that the differences in transduction efficacy (%SGCA + myofibers) between LICA1 and AAV9 are greater in more severely affected muscles (Fig. 5D). At such a low dose, AAV9 was able to transduce > 80% myofibers in TA while LICA1 can reach close to 100% (p < 0.0001). While LICA1 still transduced almost 100% of fibers in Qua (the muscle
+
+<--- Page Split --->
+
+affected with intermediate severity), only \(58.1\%\) fibers were transduced by AAV9 on average \((p < 0.0001)\) . In the most severely affected muscle, Dia, both vectors displayed reduced efficiency; however, LICA1 continued to demonstrate much better transduction \((\mu_{\mathrm{AAV9}} = 22.1\%, \mu_{\mathrm{LICA1}} = 59.5\%, \mathrm{p} < 0.0001)\) .  
+
+The differences in transgene delivery and expression positively correlated with levels of histological and functional restoration. Different dystrophic histological features, including percentage of centronucleated fibers (Fig. 5E, Fig S5B), percentage of fibrosis area (Fig. 5F, Fig S5C), and fiber size distribution (Fig. 5G), were all significantly better normalized by LICA1 than AAV9, especially in more severely affected muscles. Importantly, no significant improvement was observed in the AAV9- treated group in centronucleation index and fibrosis level in Dia, while LICA1 reduced these parameters by half (Fig. 5E- F). Fiber sizes were also restored to near- WT distribution by LICA1 in this muscle (Fig. 5G). No difference in body weight was seen between groups with or without AAV treatment (Fig S5D). At the functional level, however, the escape test – a measure of global force – showed a significant increase in AAV9- treated mice \((FC = 1.42, \mathrm{p} = 0.0072)\) and was even higher in LICA1- treated group \((FC = 1.72, \mathrm{p} < 0.0001)\) (Fig. 5H). On the other hand, in situ TA mechanical forces were both improved in the two AAV groups at similar levels (Fig. 5I), possibly due to \(>80\%\) transduction rate by both vectors. Similar to the global force, the serum MYOM3 level was greatly reduced in the LICA1- treated group but not for AAV9, indicating less muscle damage (Fig. 5K). No difference was seen in the anti- capsid antibody between the two AAV treatments (Fig S5E). These results indicate that better and significant functional and histological restoration in the LICA1- treated mice was achieved, even at low- dose treatment, thanks to superior transduction efficacy.  
+
+We further investigated the molecular alterations following AAV treatment by transcriptomic profiling of the quadriceps muscle. The first principal component (PCs) of the PCA was able to separate a group including WT and LICA1 with a group including SGCA- KO and AAV9, suggesting close proximity between elements within these 2 groups (Fig S5F). A heatmap of all 8591 significant DEGs (4035 downregulated and 4556 upregulated) further highlighted the restorative effect of LICA1 on gene expression levels (Fig. 5L). LICA1- treated muscles, in particular, demonstrated a significant correction of \(69.9\%\) (2821/4035) and \(66.5\%\) (3028/4556) of down- and upregulated DEGs, respectively, compared to \(12.4\%\) (500/4035) and \(9.21\%\) (420/4556) corrected by AAV9 treatment (Fig. 5M- N). Conversely, not all DEGs were significantly restored or returned to WT levels. The number of such transcripts in AAV9- treated muscles was much higher than in the LICA1- treated group (Fig. 5O): 2541 (63.0%) downregulated DEGs and 3045 (66.8%) upregulated DEGs for AAV9, with only 483 (12.0%) downregulated DEGs and 1038 (22.8%) upregulated DEGs in the LICA1- treated group. These data illustrate that low- dose LICA1 treatment can effectively normalize the majority of the dysregulated transcriptome and is much more efficient in correcting gene expression dysregulation than AAV9 at the same dose.  
+
+In summary, low- dose (5E12 vg/kg) AAV gene transfer using LICA1 in the LGMDR3 mouse model is effective in restoring muscle function, dystrophic histology, and the dysregulated transcriptome. The efficacy was much greater than for AAV9 at the same dose due to enhanced transduction.
+
+<--- Page Split --->
+
+## DISCUSSION  
+
+Given the severe complications observed with very high dose AAV treatment, lowering the dose by increasing vector specificity via capsid modification is one way to address these issues. This study investigated the possibility of altering AAV tropism towards skeletal muscle by targeting integrin. We designed an AAV as a \(\alpha \mathrm{V}\beta 6\) binder, which resulted in a novel myotropic AAV variant, namely LICA1. LICA1 showed greatly enhanced transduction in skeletal muscle in WT and two MD mouse models. Consequently, by improving the delivery of therapeutic transgenes (hSGCA and \(\mu \mathrm{Dys}\) ) in these MD mouse models, LICA1 was able to correct dystrophic phenotypes, global transcriptional dysregulations and significantly restore muscle function.  
+
+## AAV capsid sequence design method that ensures high AAV production  
+
+AAV tropism is commonly altered by inserting a small peptide into the VR4 or VR8 loop without any sequence constraints. Since no consideration regarding AAV capsid stability is included in this method, the resulting AAV can suffer from instability, reduced productivity, and increased AAV genome fragmentation \(^{17,45}\) (ASGCT 2023). In the current study, a physics- based protein sequence design method was used to graft the binding motifs from TGF \(\beta\) - 1 and - 3 into the VR4 loop of the hybrid capsid AAV9rh74. The major differences to the classical peptide insertion method are that the entire VR4 loop was modified to include a new binding motif and the amino acids around this motif (linkers) were selected to minimize the potential energy. Low- energy sequences ensure the stability and intended folding of the designed proteins, presumably leading to improved stability of the AAV particle \(^{38}\) . Six AAVs designed using this method were tested experimentally and all showed better productivity than their parent, Cap9rh74, and similar levels to well- produced AAV9. This suggests that low Rosetta energy correlates with high stability of capsid protein, and thereby high AAV production.  
+
+## Integrin \(\alpha \mathrm{V}\beta 6\) as a myotropic AAV receptor for skeletal muscle  
+
+Virus- host interaction is the foundation for improved viral vectors, yet skeletal muscle receptors that allow effective AAV transduction are poorly defined. However, top hits from two independent studies with different screening schemes identified myotropic AAVs with a common RGD motif, \(^{15,17,19}\) . In addition, it has previously been described that integrin functions as cellular receptor for natural AAV \(^{23,24}\) . Coincident with our screening for possible integrin receptor, only \(\alpha \mathrm{V}\beta 6\) is highly expressed and enriched in skeletal muscle (Fig S1). By including \(\alpha \mathrm{V}\beta 6\) binding motifs, AAV_ITGs efficiently utilized \(\alpha \mathrm{V}\beta 6\) for cellular infection. Enhanced transduction was observed in conditions with high (either ectopic or natural) \(\alpha \mathrm{V}\beta 6\) expression, including human differentiated myotubes and murine skeletal muscles of WT and two other MD mouse models. In most cases, the improved transduction was evident at the VCN level, indicating better cell entry via \(\alpha \mathrm{V}\beta 6\) binding.  
+
+In addition, we conducted a study comparing LICA1 and three other published myotropic AAVs. No significant differences in skeletal muscle transduction were observed on either VCN or transgene expression levels. However, the liver infection rate was significantly lower with LICA1 compared to the
+
+<--- Page Split --->
+
+other mAAVs, presumably due to the use of a liver- detargeted backbone and the low expression level of \(\alpha \mathrm{V}\beta 6\) in liver. As a result, the LICA1 vector exhibited the highest muscle/liver transduction ratio among all AAVs tested, suggesting increased specificity towards skeletal muscle. This finding highlights the importance of selecting an appropriate targeting receptor for rational design and further supports \(\alpha \mathrm{V}\beta 6\) as a promising candidate for targeting skeletal muscle.  
+
+## LICA1 is a potential vector for muscular diseases  
+
+AAV gene therapy in muscle diseases typically requires very high doses \((\geq 1E14 \mathrm{vg / kg})\) for functional benefits \(^{41,46}\) , yet can result in severe and even fatal adverse events \(^{7}\) . In this study, we explored low dose (5E12 vg/kg) treatment using the LICA1 vector in two MD mouse models, DMD and LGMDR3. Of note is that this dose is at least 20 times lower than the doses currently used in clinical trials for neuromuscular diseases \(^{3}\) . In both models, LICA1 was significantly better than AAV9 in delivering and expressing therapeutic transgenes, consequently restoring better histological dystrophic phenotypes. In TA and Qua, LICA1 was able to transduce more than \(80\%\) of fibers. It was still a challenge to effectively transduce diaphragm muscle at this dose, yet more than \(50\%\) of Dia fibers were positive for transgene expression with LICA1 in both models while AAV9 transduced very poorly. This improvement in transgene expression translates directly into improved histological restoration, including centronucleation index and fibrosis level. In particular, with only more than \(50\%\) successfully transduced fibers, LICA1 was able to reduce diaphragm fibrosis by \(42.8 - 47.0\%\) (mdx and SGCA \(^{- / - }\) models respectively), whereas no change was seen in AAV9- treated groups. The biomarker for muscle damage level, MYOM3, was reduced by \(57.5 - 67.2\%\) (mdx and SGCA \(^{- / - }\) models respectively) by LICA1 and significantly greater than AAV9. Similarly, global muscle force was significantly restored to a higher level with LICA1 than with AAV9 in SGCA- KO mice. These data confirmed superior muscle transduction by LICA1 and resulting therapeutic benefits were obtained even at low- dose treatment in two MD models.  
+
+However, treatment efficacy varies between two disease models at molecular levels. We profiled transcriptomic changes in Qua following AAV treatment in both MD models. Despite similar transduction efficiency of LICA1 in the two models, restoration of dystrophic transcriptional changes in SGCA- KO was significantly greater. It is noteworthy that \(\mu \mathrm{Dys}\) is an incomplete form of dystrophin. The \(\mu \mathrm{Dys}\) used in the present study lacks several functional domains, including multiple spectrin- like repeats that bind to nNOS, F- actin, sarcomeric lipid and microtubules, and a dystrobrevin- and syntrophin- binding C- terminus \(^{41}\) . This might explain the inadequate efficacy in restoring global gene expression in \(\mu \mathrm{Dys}\) gene therapy trials, in spite of highly effective gene transfer. Similarly, despite excellent functional restoration by microdystrophin gene transfer in various animal models, outcomes from these clinical trials are unsatisfactory \(^{6}\) . Therefore, careful assessment of molecular restoration should be included for evaluating gene therapy efficacy.  
+
+In summary, this study presents an alternative computational method that aids rational AAV design and ensures high- production AAV variants. The proof- of- concept design targeting skeletal muscle resulted in a high- productivity myotropic AAV, thereby effectively delivering therapeutic transgenes and restoring
+
+<--- Page Split --->
+
+dystrophic phenotypes in two MD mouse models at a low dose. This work contributes to the ongoing efforts to reduce AAV treatment doses and further advance AAV engineering, paving the way for more effective and accessible gene therapies in the future.  
+
+## MATERIALS AND METHODS  
+
+## Study Design  
+
+The primary objective of the study was to design a novel myotropic AAV capsid with a high production yield by using a computationally rational design. The secondary aim was to investigate the possibility of low- dose AAV treatment using a designed AAV in animal models of muscular dystrophies, which typically require an alarmingly high dose \((\geq 1E14\) vg/kg). We used publicly available datasets to identify possible receptors for skeletal muscle and protein design tools to engineer AAV capsid protein. Resulting variants were characterized for their productivity and transduction efficiency in various in vitro cell lines and multiple mouse models. Experiments were performed at least three times, unless noted otherwise. The AAV injection and infection experiments were conducted in a nonblinded fashion. The blinding approach was used during dissection, histological validation, immunostaining analysis, in vivo functional tests, and biomarker analysis. No data were excluded. Details on experimental procedures are presented in Supplementary Materials and Methods.  
+
+## Animal care and use  
+
+All animals were handled according to French and European guidelines for human care and the use of experimental animals. All procedures on animals were approved by the local ethics committee and the regulatory affairs of the French Ministry of Research (MESRI) under the numbers 2018- 024- B #19736, 2022- 004 #35896. C57Bl/6, B6Ros.Cg- Dmdmdx- 4Cv/J mice were obtained from the Jackson Laboratory. A knockout mouse model of \(\alpha\) - sarcoglycan was obtained from the Kevin Campbell laboratory (University of Iowa, USA) \(^{44}\) . Mice were housed in a SPF barrier facility with 12- h light, 12- h dark cycles, and were provided with food and water ad libitum. Only male mice were used in the present study. Well- being and weights of the animals were monitored for the duration of the study. The animals were anesthetized with a mix of ketamine (100 mg/kg) and xylazine (10 mg/kg), or with isoflurane (4%) for blood samples. For AAV intravenous injections, a maximum volume of 150 μl containing AAV vectors was injected via the sinus route after the animals had been anesthetized with isoflurane. The AAV intravenous doses used in the present study were 5E12 or 1E13 vg/kg.  
+
+## Cell culture and in vitro study  
+
+Adherent HEK293- T cells were maintained in the proliferating medium containing DMEM (Thermo Fisher Scientific), supplied with 10% fetal bovine serum and 1X gentamycin at \(37^{\circ}C\) , 5% CO2. Human immortalized myoblasts (AB1190 cell line) were maintained in Skeletal Muscle Cell Growth Medium (PromoCell, C23060) and differentiated in Skeletal Muscle Differentiation Medium (PromoCell, C23061).
+
+<--- Page Split --->
+
+In vitro AAV infection was performed by directly adding AAV into culture medium at the dose of 1E9 or 1E10 vg per 24- well plate well. After 48h post- infection, cells were washed and subjected to VCN and gene expression analysis.  
+
+To inhibit AAV infection, AAVs were incubated with recombinant hTGAV- hITGB6 protein (Bio- Techné, 3817- AV- 050) at \(37^{\circ}C\) for 30 minutes, at a concentration of \(1\mu g\) protein per 5E9vg AAV before addition to the cells (1E4 vg per cell). The same condition treated with recombinant hSGCA protein served as a control for the comparison.  
+
+## Statistical Analysis  
+
+Results are presented as mean \(\pm\) SEM, unless noted otherwise. Significance of differences in multiple pairwise comparisons of more than two groups was determined by one- way ANOVA. The significance of differences in pairwise comparisons of multiple groups with multiple treatments was determined by two- way ANOVA. To account for multiple testing and control the false discovery rate (FDR) across the numerous pairwise comparisons, the Benjamini- Hochberg (BH) procedure was applied with an FDR threshold of 0.05. Statistical tests were performed using GraphPad Prism 9. Results were considered significant when p- values or adjusted p- values were less than 0.05.  
+
+## DECLARATIONS  
+
+Acknowledgments: The authors are Genopole's members, first French biocluster dedicated to genetic, biotechnologies and biotherapies. We are grateful to the "Imaging and Cytometry Core Facility" and to the in vivo evaluation, services of Genethon for technical support, to Ile- de- France Region, to Conseil Départemental de l'Essonne (ASTRE), INSERM and GIP Genopole, Evry for the purchase of the equipment. We would like to acknowledge the technical help of Carolina Pacheco Algalan and Alejandro Arco Hierves. The Genotype- Tissue Expression (GTEx) Project was supported by the Common Fund of the Office of the Director of the National Institutes of Health, and by NCI, NHGRI, NHLBI, NIDA, NIMH, and NINDS.  
+
+Funding: This work was supported by the "Association Française contre les Myopathies" (AFM), and "Institut National de la Santé Et de la Recherche Médicale" (INSERM, FranceRelance N°221513A10).  
+
+Author contributions: The project was conceptualized by A.H.V. and I.R. A.H.V., L.S.P., and J.P. conducted experiments and performed data analysis. Funding supporting this project was obtained by I.R. A.H.V. and I.R. supervised the project. The manuscript was written by A.H.V. and I.R.  
+
+Competing interests: A.H.V. and I.R. are inventors on PCT application EP2023/065499 for the integration of RGDlxxL/I motif in AAV capsid for enhanced muscle transduction efficiency. I.R. is a part- time employee of Atamyo Therapeutics. The other authors declare that they have no competing interests.  
+
+Data and materials availability: All data associated with this study are present in the paper or the Supplementary Materials. All transcriptomic data will be deposited in the NCBI Sequence Read Archive
+
+<--- Page Split --->
+
+(SRA) upon publication. Processed data including differential gene expression analysis are available in data file S1 and S2. The plasmid constructs and reagents generated as part of this study are available under a material transfer agreement from the corresponding authors.  
+
+## REFERENCES  
+
+1. Wang, D., Tai, P.W.L. & Gao, G. Adeno-associated virus vector as a platform for gene therapy delivery. Nat Rev Drug Discov 18, 358-378 (2019).  
+2. Pupo, A. et al. AAV vectors: The Rubik's cube of human gene therapy. Molecular therapy: the journal of the American Society of Gene Therapy 30, 3515-3541 (2022).  
+3. Crudele, J.M. & Chamberlain, J.S. AAV-based gene therapies for the muscular dystrophies. Hum Mol Genet 28, R102-R107 (2019).  
+4. Duan, D. Systemic AAV Micro-dystrophin Gene Therapy for Duchenne Muscular Dystrophy. Molecular therapy: the journal of the American Society of Gene Therapy 26, 2337-2356 (2018).  
+5. Mack, D.L. et al. Systemic AAV8-Mediated Gene Therapy Drives Whole-Body Correction of Myotubular Myopathy in Dogs. Molecular therapy: the journal of the American Society of Gene Therapy 25, 839-854 (2017).  
+6. Mercuri, E., Bonnemann, C.G. & Muntoni, F. Muscular dystrophies. Lancet 394, 2025-2038 (2019).  
+7. Ertl, H.C.J. Immunogenicity and toxicity of AAV gene therapy. Front Immunol 13, 975803 (2022).  
+8. Verdera, H.C., Kuranda, K. & Mingozzi, F. AAV Vector Immunogenicity in Humans: A Long Journey to Successful Gene Transfer. Molecular therapy: the journal of the American Society of Gene Therapy 28, 723-746 (2020).  
+9. High-dose AAV gene therapy deaths. Nature biotechnology 38, 910 (2020).  
+10. Ogden, P.J., Kelsic, E.D., Sinai, S. & Church, G.M. Comprehensive AAV capsid fitness landscape reveals a viral gene and enables machine-guided design. Science 366, 1139-1143 (2019).  
+11. DiMattia, M.A. et al. Structural insight into the unique properties of adeno-associated virus serotype 9. Journal of virology 86, 6947-6958 (2012).  
+12. Li, C. & Samulski, R.J. Engineering adeno-associated virus vectors for gene therapy. Nat Rev Genet 21, 255-272 (2020).  
+13. Tseng, Y.S. & Agbandje-McKenna, M. Mapping the AAV Capsid Host Antibody Response toward the Development of Second Generation Gene Delivery Vectors. Front Immunol 5, 9 (2014).  
+14. Buning, H. & Srivastava, A. Capsid Modifications for Targeting and Improving the Efficacy of AAV Vectors. Molecular therapy. Methods & clinical development 12, 248-265 (2019).  
+15. Weinmann, J. et al. Identification of a myotropic AAV by massively parallel in vivo evaluation of barcoded capsid variants. Nature communications 11, 5432 (2020).  
+16. El Andari, J. et al. Semirational bioengineering of AAV vectors with increased potency and specificity for systemic gene therapy of muscle disorders. Science advances 8, eabn4704 (2022).
+
+<--- Page Split --->
+
+17. Tabebordbar, M. et al. Directed evolution of a family of AAV capsid variants enabling potent muscle-directed gene delivery across species. Cell 184, 4919-4938 e4922 (2021).  
+
+18. Ruoslahti, E. & Pierschbacher, M.D. Arg-Gly-Asp: a versatile cell recognition signal. Cell 44, 517-518 (1986).  
+
+19. Bauer, A. et al. Molecular Signature of Astrocytes for Gene Delivery by the Synthetic Adenoc- Associated Viral Vector rAAV9P1. Adv Sci (Weinh) 9, e2104979 (2022).  
+
+20. Zolotukhin, S., Trivedi, P.D., Corti, M. & Byrne, B.J. Scratching the surface of RGD-directed AAV capsid engineering. Molecular therapy: the journal of the American Society of Gene Therapy 29, 3099-3100 (2021).  
+
+21. Hynes, R.O. Integrins: a family of cell surface receptors. Cell 48, 549-554 (1987).  
+
+22. Hussein, H.A. et al. Beyond RGD: virus interactions with integrins. Arch Virol 160, 2669-2681 (2015).  
+
+23. Asokan, A., Hamra, J.B., Govindasamy, L., Agbandje-McKenna, M. & Samulski, R.J. Adeno-associated virus type 2 contains an integrin alpha5beta1 binding domain essential for viral cell entry. Journal of virology 80, 8961-8969 (2006).  
+
+24. Summerford, C., Bartlett, J.S. & Samulski, R.J. AlphaVbeta5 integrin: a co-receptor for adeno-associated virus type 2 infection. Nat Med 5, 78-82 (1999).  
+
+25. Stewart, P.L. & Nemerow, G.R. Cell integrins: commonly used receptors for diverse viral pathogens. Trends Microbiol 15, 500-507 (2007).  
+
+26. Strauch, E.M. et al. Computational design of trimeric influenza-neutralizing proteins targeting the hemagglutinin receptor binding site. Nature biotechnology 35, 667-671 (2017).  
+
+27. Cao, L. et al. Design of protein-binding proteins from the target structure alone. Nature 605, 551-560 (2022).  
+
+28. Ruoslahti, E. RGD and other recognition sequences for integrins. Annual review of cell and developmental biology 12, 697-715 (1996).  
+
+29. Chemello, F. et al. Degenerative and regenerative pathways underlying Duchenne muscular dystrophy revealed by single-nucleus RNA sequencing. Proceedings of the National Academy of Sciences of the United States of America 117, 29691-29701 (2020).  
+
+30. Pang, X. et al. Targeting integrin pathways: mechanisms and advances in therapy. Signal Transduct Target Ther 8, 1 (2023).  
+
+31. Shen, X., Storm, T. & Kay, M.A. Characterization of the relationship of AAV capsid domain swapping to liver transduction efficiency. Molecular therapy: the journal of the American Society of Gene Therapy 15, 1955-1962 (2007).  
+
+32. Ballon, D.J. et al. Quantitative Whole-Body Imaging of I-124-Labeled Adeno-Associated Viral Vector Biodistribution in Nonhuman Primates. Human gene therapy 31, 1237-1259 (2020).  
+
+33. Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583-589 (2021).
+
+<--- Page Split --->
+
+34. Mirdita, M. et al. ColabFold: making protein folding accessible to all. Nature methods 19, 679-682 (2022).35. Dong, X. et al. Force interacts with macromolecular structure in activation of TGF-beta. Nature 542, 55-59 (2017).36. Dong, X., Hudson, N.E., Lu, C. & Springer, T.A. Structural determinants of integrin beta-subunit specificity for latent TGF-beta. Nature structural & molecular biology 21, 1091-1096 (2014).37. Huang, P.S. et al. RosettaRemodel: a generalized framework for flexible backbone protein design. PloS one 6, e24109 (2011).38. Alford, R.F. et al. The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design. Journal of chemical theory and computation 13, 3031-3048 (2017).39. Duan, D., Goemans, N., Takeda, S., Mercuri, E. & Aartsma-Rus, A. Duchenne muscular dystrophy. Nat Rev Dis Primers 7, 13 (2021).40. Stedman, H.H. et al. The mdx mouse diaphragm reproduces the degenerative changes of Duchenne muscular dystrophy. Nature 352, 536-539 (1991).41. Bourg, N. et al. Co-Administration of Simvastatin Does Not Potentiate the Benefit of Gene Therapy in the mdx Mouse Model for Duchenne Muscular Dystrophy. Int J Mol Sci 23 (2022).42. Rouillon, J. et al. Serum proteomic profiling reveals fragments of MYOM3 as potential biomarkers for monitoring the outcome of therapeutic interventions in muscular dystrophies. Hum Mol Genet 24, 4916-4932 (2015).43. Eymard, B. et al. Primary adhalinopathy (alpha-sarcoglycanopathy): clinical, pathologic, and genetic correlation in 20 patients with autosomal recessive muscular dystrophy. Neurology 48, 1227-1234 (1997).44. Duclos, F. et al. Progressive muscular dystrophy in alpha-sarcoglycan-deficient mice. The Journal of cell biology 142, 1461-1471 (1998).45. Bryant, D.H. et al. Deep diversification of an AAV capsid protein by machine learning. Nature biotechnology 39, 691-696 (2021).46. Israeli, D. et al. An AAV-SGCG Dose-Response Study in a gamma-Sarcoglycanopathy Mouse Model in the Context of Mechanical Stress. Molecular therapy. Methods & clinical development 13, 494-502 (2019).  
+
+## Figures
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+## Computational rational AAV capsid design to bind to \(\alpha \beta \beta\) integrin  
+
+A. Overview of the design pipeline, including three steps: 1. Capsid 3D structures were obtained either from the PDB database or predicted by AlphaFold2. 2. The capsid VR4 loop was completely replaced by integrating the binding motif, which was extracted from receptor's natural binder, using RosettaRemodel
+
+<--- Page Split --->
+
+protocol. 3. Top scored designs from the previous grafting step were docked onto the intended receptor in silico to verify the binding potential of the designed capsid. B. An illustration of the sampling for low- energy sequence- structure pairs during motif- grafting process. Capsid VR4 after removing the loop was colored in blue, extracted binding motif was colored in red. The sampled linkers and sequences (Fig. S1F) were labeled in green. C- D. The three lowest energy designs after grafting TGFβ3 (C) and TGFβ1 (D) into the capsid VR4. All top designs showed convergence in structures and sequences, suggesting sampling approached the global optimum. E- F. Retrospective docking of motif- grafted capsids (E. Cap9rh74_4um9 and F. Cap9rh74_5ffo) onto the αVβ6 structure. The left panels are illustrations of the structures with the lowest energy at the interface of capsid and integrin proteins (dG_separated: difference in free energy of two proteins). Both two newly designed VR4s (colored in green) were predicted to bind to the αVβ6 complex at very similar positions to natural binding motifs (colored in red). The right panels are scatter plots of dG_separated energy versus root-mean- square deviation (RMSD) from the lowest energy structure of all sampled docking positions.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 </center>  
+
+<center>Figure 2 </center>  
+
+Designed AAV_ITGs were well- produced and improved transduction via aVβ6 binding.  
+
+A. AAV titers of different AAV variants in bulked small-scale production in suspension three-day post-triple-transfection (2ml production, \(n = 6\) , one-way ANOVA). B. Western blot of VP proteins from purified AAVs showed similar VP ratios for designed AAV_ITGs capsids compared to AAV9 and AAV9rh74,
+
+<--- Page Split --->
+
+suggesting successful capsid assembly. C- D. VCN (C) and luciferase activity (D) of 293_aVβ6 after AAV infection (n=3- 4, one- way ANOVA). Both the two designed AAV_ITGs showed enhanced VCN and luciferase activities compared to AAV9rh74 and AAV9. E. Inhibition of cell entry of designed AAV_ITGs, but not for AAV9 or AAV9rh74, in 293_aVβ6 cells by aVβ6 recombinant protein. AAVs were preincubated with aVβ6 recombinant protein (r.ITGAV- B6) for 30 minutes at 37°C before infection (n=3, two- way ANOVA). SGCA recombinant protein (r.SGCA) was used as the control. F- K. Enhanced transduction of AAV_ITGs in in vitro human differentiated myotubes, but not in myoblasts. F. Representative images of the GFP signal of myotubes 48 hours post- infection (scale bar: 400μm). G- K. VCN and luciferase activities of AAV_ITGs in comparison with AAV9 and AAV9rh74 in myoblasts (G,I) and myotubes (H,K) (n=3- 4, one- way ANOVA).
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 </center>  
+
+<center>Figure 3 </center>  
+
+Designed AAV_ITGs showed enhanced transduction in skeletal and cardiac muscles while strongly liver- detargeted in vivo.  
+
+A. Scheme of in vivo experiment. AAVs (CMV_GFP-Luciferase) were injected intravenously into 6wo C57BL6 mice (n=4) at the dose of 1E13 vg/kg. B. Representative images of the bioluminescence signal
+
+<--- Page Split --->
+
+20 days post- infection. C- D. VCN (C) and gene expression (D) (GFP mRNA level in the liver and luciferase activity in other organs) for different AAVs in liver, skeletal muscles, heart, lung, and kidney (n=4, one- way ANOVA). Both designed AAV_ITGs strongly detargeted from the liver compared to AAV9, while they significantly improved VCN and luciferase activities over AAV9rh74 (and AAV9 with AAV9rh74_4um9 variant) in skeletal and cardiac muscles, and were detected and expressed at low levels in lung and kidney. E- H. Comparison of the AAV9rh74_4um9 variant with other public myotropic AAVs (mAAVs) \(^{15,17}\) . E. Illustration of the differences between mAAVs and AAV9rh74_4um9 at modification sites in capsid protein and modification methods. F. The VR8 loop sequences of mAAVs compared to VR8 of their backbone AAV9, and VR4 of AAV9rh74_4um9 compared to VR4 of AAV9rh74. G- H. VCN (G) and gene expression (H) (GFP mRNA level in liver and luciferase activity in other organs) of different AAVs in liver, skeletal muscles, heart, lung, kidney, and brain (n=4, one- way ANOVA). AAV9rh74_4um9 showed similar VCN and gene expression in skeletal muscle to other mAAVs, while being significantly more strongly detargeted from the liver.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 </center>  
+
+<center>Figure 4 </center>  
+
+Low- dose gene transfer by LICA1 was more effective and better at restoring dystrophic phenotypes than AAV9 in the DMD mouse model.  
+
+A- B. Comparison of transduction efficacy between AAV9 and LICA1 in all three muscles that were tested, in terms of VCN (A), and \(\mu\) Dys RNA level (B). C. Comparison of percentage of successfully transduced
+
+<--- Page Split --->
+
+(dystrophin- positive) fibers in all three muscles that were tested. Note that TA, Qua, Dia muscles are presented in increasing order of severity. D- E. Comparison of restoration levels in dystrophic histological features between AAV9 and LICA1 in all three muscles that were tested, in terms of percentage of centro- nucleated fibers (D) and fibrosis level (E). Illustrated images in C- E are of quadriceps muscles (scale bar: \(100\mu \mathrm{m}\) ). F. Serum MYOM3 level – indicator of muscle damage – 4 weeks post- injection ( \(n = 5\) , one- way ANOVA). G- I. Comparison of functional restoration between AAV9 and LICA1 by Escape test – global force measurement (G, \(n = 6\) ), tetanus force of TA muscle (H, \(n = 10 - 12\) ), and twitch force of TA muscle (I, \(n = 9 - 12\) ). K- N. Comparison of restoration in global transcriptomic changes in quadriceps muscle between AAV9 and LICA1 ( \(n = 4\) , adjusted p- values \(< 0.05\) ). K. The heatmap presents the log2 fold change (log2FC) in comparison to WT muscle for all 8717 DEGs found in mdx muscle (compared to WT). The log2FC values are illustrated in row Z- scores, colored from blue to red, arranged from lowest to highest. L- N. Volcano plots of multiple comparisons illustrate transcriptomic changes before and after AAV treatment. As a reference, 4216 downregulated and 4501 upregulated DEGs found in mdx were colored blue and red, respectively, in all volcano plots. Among these DEGs, the number of genes found to be significantly different in each pair- wise comparison were labeled in the upper corners. L. Volcano plots comparing mdx/WT transcriptomes. M. Volcano plots comparing mdx to AAV- treated transcriptomes, in which significant DEGs are the genes correctly restored after AAV treatment. N. Volcano plots comparing AAV treatment to WT, in which significant DEGs are the genes that are not or incompletely restored after AAV treatment.
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 </center>  
+
+<center>Figure 5 </center>  
+
+Low- dose gene transfer by LICA1 was better at restoring dystrophic phenotypes and functionality than AAV9 in the LGMDR3 mouse model.  
+
+A. Scheme of in vivo experiment: LICA1 (9rh74_4um9) or AAV9 were injected intravenously into a 4wo SGCA-KO mouse model at the dose of 5E12 vg/kg (expression cassette: hACTA1_hSGCA_HBB2-pA, n=3-
+
+<--- Page Split --->
+
+5). Three skeletal muscles in increasing order of severity, TA, Qua, and Dia, were analysed 4 weeks postinjection. B-D. Comparison of transduction efficacy between AAV9 and LICA1 in all three muscles that were tested in terms of VCN (B), hSGCA mRNA level (C), and percentage of succesfully transduced (SGCA- positive) fibers (D). E-G. Comparison of restoration levels in dystrophic histological features between AAV9 and LICA1 in all three muscles that were tested in terms of percentage of centro- nucleated fibers (E), fibrosis level (F), and fiber size distribution (G). Illustrated images in D-F are of quadriceps muscles (scale bar: \(100 \mu m\) ). H-K. Comparison of functional restoration between AAV9 and LICA1 using the escape test – global force measurement (H), tetanus force of TA muscle (I), and serum MYOM3 level – indicator of muscle damage (K). L-O. Comparison of restoration in global transcriptomic changes in quadriceps muscle between AAV9 and LICA1 (n=4, adjusted p values < 0.05). L. The heatmap presents the log2 fold change (log2FC) in comparison to WT muscle for all 8591 DEGs found in KO muscle (compared to WT). The log2FC values are illustrated by row Z-scores, colored from blue to red, arranged from lowest to highest. M-O. Volcano plots of multiple comparisons illustrate transcriptomic changes before and after AAV treatment. As a reference, 4035 downregulated and 4556 upregulated DEGs found in KO were colored blue and red, respectively, in all volcano plots. Among these DEGs, the number of genes found to be significantly different in each pair-wise comparison were labeled in the upper corners. M. Volcano plots comparing KO/WT transcriptomes. N. Volcano plots comparing KO to AAV-treated transcriptomes, in which significant DEGs are the genes correctly restored after AAV treatment. O. Volcano plots comparing AAV treatment to WT, in which significant DEGs are the genes that are not or incompletely restored after AAV treatment.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- ALICA1supp.pdf- DatafileS2DEGSGCA.xlsx- DatafileS1DEGDMD.xlsx
+
+<--- Page Split --->

preprint/preprint__00d0f482762f2f37431ca49a939480fc54bdd5eb053d5ac8ce0b474c9dacda22/preprint__00d0f482762f2f37431ca49a939480fc54bdd5eb053d5ac8ce0b474c9dacda22_det.mmd

@@ -0,0 +1,475 @@
+<|ref|>title<|/ref|><|det|>[[42, 106, 928, 243]]<|/det|>
+# An integrin-targeting AAV developed using a novel computational rational design methodology presents improved targeting of the skeletal muscle and reduced liver tropism  
+
+<|ref|>text<|/ref|><|det|>[[44, 263, 166, 283]]<|/det|>
+Ai Vu Hong  
+
+<|ref|>text<|/ref|><|det|>[[53, 291, 266, 309]]<|/det|>
+avuhong@genethon.fr  
+
+<|ref|>text<|/ref|><|det|>[[44, 336, 501, 355]]<|/det|>
+Genethon https://orcid.org/0000- 0002- 0872- 4295  
+
+<|ref|>text<|/ref|><|det|>[[44, 361, 170, 380]]<|/det|>
+Laurence Suel  
+
+<|ref|>text<|/ref|><|det|>[[52, 385, 141, 401]]<|/det|>
+Genethon  
+
+<|ref|>text<|/ref|><|det|>[[44, 408, 185, 426]]<|/det|>
+Jérôme Poupiot  
+
+<|ref|>text<|/ref|><|det|>[[52, 432, 141, 448]]<|/det|>
+Genethon  
+
+<|ref|>text<|/ref|><|det|>[[44, 455, 185, 473]]<|/det|>
+Isabelle Richard  
+
+<|ref|>text<|/ref|><|det|>[[52, 479, 141, 494]]<|/det|>
+Genethon  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 536, 103, 553]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 574, 136, 592]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 611, 328, 630]]<|/det|>
+Posted Date: October 27th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 650, 475, 669]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3466229/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 687, 916, 730]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 747, 936, 836]]<|/det|>
+Additional Declarations: Yes there is potential Competing Interest. A.H.V. and I.R. are inventors on PCT application EP2023/065499 for the integration of RGLxxL/I motif in AAV capsid for enhanced muscle transduction efficiency. I.R. is a part- time employee of Atamyo Therapeutics. The other authors declare no competing interests.  
+
+<|ref|>text<|/ref|><|det|>[[42, 870, 921, 914]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on September 11th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 52002- 4.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 41, 157, 66]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[39, 81, 955, 468]]<|/det|>
+Current adeno- associated virus (AAV) gene therapy using nature- derived AAVs is limited by non- optimal tissue targeting. In the treatment of muscular diseases (MD), high doses are therefore often required, but can lead to severe adverse effects. To lower treatment doses, we rationally designed an AAV that specifically targets skeletal muscle. We employed a novel computational design that integrated binding motifs of integrin alpha V beta 6 (αVβ6) into a liver- detargeting AAV capsid backbone to target the human αVβ6 complex – a selected AAV receptor for skeletal muscle. After sampling the low- energy capsid mutants, all in silico designed AAVs showed higher productivity compared to their parent. We confirmed in vitro that the enhanced transduction is due to the binding to the αVβ6 complex. Thanks to inclusion of αVβ6- binding motifs, the designed AAVs exhibited enhanced transduction efficacy in human differentiated myotubes as well as in murine skeletal muscles in vivo. One notable variant, LICA1, showed similar muscle transduction to other published myotropic AAVs, while being significantly more strongly liver- detargeted. We further examined the efficacy of LICA1, in comparison to AAV9, in delivering therapeutic transgenes in two mouse MD models at a low dose of 5E12 vg/kg. At this dose, AAV9 was suboptimal, while LICA1 transduced effectively and significantly better than AAV9 in all tested muscles. Consequently, LICA1 corrected the myopathology, restored global transcriptomic dysregulation, and improved muscle functionality. These results underline the potential of our design method for AAV engineering and demonstrate the relevance of the novel AAV variant for gene therapy treatment of MD.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 490, 360, 516]]<|/det|>
+## One Sentence Summary  
+
+<|ref|>text<|/ref|><|det|>[[42, 530, 908, 574]]<|/det|>
+We developed a novel computationally AAV design method resulting in a new myotropic AAV, which allows low- dose AAV treatment for muscular dystrophies.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 595, 255, 622]]<|/det|>
+## INTRODUCTION  
+
+<|ref|>text<|/ref|><|det|>[[41, 635, 952, 850]]<|/det|>
+Over 50 years since their discovery, adeno- associated viruses (AAVs) have shown great promise as an effective viral vector for gene delivery and gene therapy, leading to recent approval of therapeutic products \(^{1,2}\) . Due to unmet medical needs and natural AAV tropism, many AAV- based gene therapies focus on treating muscle diseases (MD) \(^{3}\) . Systemic treatment in such diseases aims to primarily target skeletal muscle, which accounts for more than 40% of body mass, and therefore often requires very high doses (≥1E14 vg/kg) to achieve meaningful therapeutic efficacy \(^{3- 6}\) . In addition, most recombinant AAVs built on natural- occurring variants lack specificity and often accumulate in the liver, with the concomitant risk of hepatotoxicity \(^{7}\) . Other key challenges of rAAV use persist, including manufacturing, immunological barriers, and associated toxicity \(^{1,2,8,9}\) .  
+
+<|ref|>text<|/ref|><|det|>[[41, 866, 945, 960]]<|/det|>
+AAV is a small non- pathogenic single- stranded DNA parvovirus. Multiple open reading frames (ORFs) were identified in its genome, including Rep, Cap, AAP and MAAP \(^{1,10}\) . The single Cap ORF expresses three capsid proteins - virion protein 1 (VP1), VP2 and VP3, which assemble into an icosahedral 60- mer capsid. Structurally, the VP3 monomer core contains a highly conserved eight- stranded β- barrel motif \(^{11}\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[40, 44, 953, 257]]<|/det|>
+Inserted between the \(\beta\) - strands, nine surface- exposed variable regions (VR1- 9) result in local topological differences between serotypes and dictate virus- host interaction. Consequently, genetically modifying VRs can drastically change the AAV, transduction, antigenic profile, and fitness \(^{10,12,13}\) . VR4 and VR8, that cluster together spatially, forming the most prominent protrusion at the 3- fold axis, have been widely subjected to modifications, notably by inserting short peptides into the loop apices \(^{14}\) . This resulted in some highly efficient capsid variants for transducing a variety of cell types and tissues \(^{1,12}\) . Among these, remarkably, AAVMYOs \(^{15,16}\) and MYOAAVs \(^{17}\) transduce skeletal muscles, deliver therapeutic transgenes efficiently, and were shown to correct dystrophic phenotypes in MD mouse models at relatively low doses (2E12 – 1E13 vg/kg).  
+
+<|ref|>text<|/ref|><|det|>[[40, 273, 944, 487]]<|/det|>
+Importantly, the myotropic AAVs \(^{15 - 17}\) identified by muscle- directed high- throughput screening (HTS) were shown to share an Arg- Gly- Asp (RGD) motif, presumably targeting the integrin complex \(^{17 - 20}\) . Integrins are a group of heterodimeric proteins composed of an \(\alpha\) - and a \(\beta\) subunit that serve various cellular functions, including cell adhesion, cell migration, and cell signaling \(^{21}\) . As adhesion molecules, integrins also mediate cell- pathogen interactions, and are therefore exploited by many viruses, including natural AAV, to infect cells \(^{22 - 24}\) . Indeed, many of these viruses use an RGD motif on their viral envelope glycoproteins or capsids for cell attachment, endocytosis, entry, and endosomal escape \(^{18,22,25}\) . The discovery that RGD- dependent integrin- targeting AAV variants can acquire myotropism therefore represents a novel potential candidate approach for a rational design to target skeletal muscle.  
+
+<|ref|>text<|/ref|><|det|>[[39, 503, 951, 867]]<|/det|>
+This study introduces a novel computational method for a rational AAV design targeting skeletal muscle, which resulted in a novel myotropic vector for MD gene therapy. First, the human skeletal muscle- enriched integrin complex alpha V beta 6 (αVβ6) was selected as the target receptor. Inspired by one- sided protein design \(^{26,27}\) , we computationally designed a previously developed liver- detargeting hybrid capsid between AAV9 and AAVrh74 (Cap9rh74) as an αVβ6 binder. The VR4 loop was completely modified, in which new sequences were iteratively selected to simultaneously optimize for free energy, while hosting αVβ6- binding RGDLLXL/I motifs. All designed AAVs were well- produced, at higher titers than their parent. The designed AAVs were confirmed to require αVβ6 binding for cellular transduction. The most promising variant, renamed LICA1, was selected for further analysis and showed superior transduction in human differentiated myotubes and strong myotropism in several mouse models. We evaluated this variant by delivering therapeutic transgenes in two MD mouse models at a very low dose of 5E12 vg/kg, in comparison to AAV9. In both cases, LICA1 presents higher efficacy than AAV9 in correcting dystrophic phenotypes, global transcriptomic changes and restoring muscle function, thanks to improved transduction and transgene expression in skeletal muscles. Collectively, the study provides a proof- of- concept for a new rational AAV design pipeline leveraging protein design tools, which resulted in a novel myotropic AAV with high potential for gene therapy for muscle diseases.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 890, 164, 916]]<|/det|>
+## RESULTS  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 930, 512, 951]]<|/det|>
+## 1. Selection of the cellular receptor for rational design
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 953, 185]]<|/det|>
+Several myotrophic AAVs have recently been developed, notably, the insertion into the AAV9 VR- VIII loop of P1 peptide (RGDLLGS) \(^{15,16}\) , and a series of RGD- containing sequences identified by directed evolution \(^{17}\) . Importantly, these modified capsids shared a common RGD motif, which suggested their affinity to integrin (ITG), cell- surface heterocomplexes that interact with the extracellular matrix \(^{28}\) . Using publicly available datasets, we aimed to select relevant integrin subunits for a subsequent rational AAV design targeting skeletal muscle.  
+
+<|ref|>text<|/ref|><|det|>[[40, 202, 955, 522]]<|/det|>
+Chemello and colleagues previously performed single- nucleus RNA sequencing, comparing gene expression of all cell types in the skeletal muscle of wild- type (WT) and Duchenne muscular dystrophy mouse models (D51) \(^{29}\) . We extracted RNA levels of all integrin alpha and beta genes from these data (Figure S1A). Among all subunits, only the \(\alpha\) - subunits Itgav, Itga7 and the \(\beta\) - subunits Itgb6, Itgb1, and Itgb5 show relatively high expression in the myogenic nuclei. Of interest is the fact that the expression level of Itgb6 is highly enriched in myonuclei, and significantly upregulated in the dystrophic condition, whereas Itgb1 and Itgb5 expression are ubiquitous in all cell types, and significantly lower than the Itgb6 level in all myonuclei. Among the two expressed \(\alpha\) - subunits, only Itgav was known to associate with Itgb6 to form avβ6 heterocomplexes – a member of the RGD- binding integrin family \(^{30}\) . Furthermore, bulk RNA sequencing data from multiple human tissues confirmed high expression of Itgav and Itgb6 in skeletal muscle, and low expression of Itgb6 in the liver and spleen, two preferred targets of natural AAV (Figure S1B, GTEx V8, dbGaP Accession phs000424.v8.p2). We therefore hypothesize that AAV transduction in skeletal muscle can be improved by rationally designing an AAV capsid that specifically binds to avβ6.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 539, 805, 561]]<|/det|>
+## 2. Rational design of a hybrid capsid, Cap9rh74, with a high affinity to the \(\mathbb{V}\mathbb{B}\beta 6\) complex  
+
+<|ref|>text<|/ref|><|det|>[[41, 578, 955, 737]]<|/det|>
+As we aim to specifically target the skeletal muscle, we selected a hybrid capsid that we previously developed and that has a liver- detargeting property as the parental capsid in our design (Patent Number: EP18305399.0). This hybrid capsid of AAV9 and AAV.rh74 (AAV9rh74) was constructed by replacing the AAV9 sequence of VR4 to VR8 with that of AAV- rh74. The hybrid capsid showed similar infectivity in skeletal and cardiac muscles but was strongly de- targeted from the liver. The latter property is of particular interest in skeletal muscle gene transfer since the majority of administrated viral vector will not accumulate in the liver, as is the case for natural AAVs \(^{31,32}\) .  
+
+<|ref|>text<|/ref|><|det|>[[42, 753, 950, 891]]<|/det|>
+After selection of the cellular receptor of interest and capsid backbone, AAV capsids were computationally engineered (Fig. 1A). First, the 3D structure of the parental capsid, of with structure was unknown, was modeled using AlphaFold2 \(^{33,34}\) . The structural prediction of the Cap9rh74 aa 219–737 monomer performed using AlphaFold2 was at a high level of confidence, with predicted local distance difference test (IDDT- Ca), a per- residue measure of local confidence, of 97.04 and low predicted aligned error (PEA) of 4.32 (Fig S1C- D). This structure is thus suitable for the next steps in the design.  
+
+<|ref|>text<|/ref|><|det|>[[42, 908, 925, 951]]<|/det|>
+Second, we extracted the 3D structure or sequences of binding motifs of the human integrin complex from PDB. Importantly, avβ6 was previously shown to bind with high affinity to the RGDLLXL/1 motif
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 44, 955, 137]]<|/det|>
+found in the human TGF- \(\beta 1\) and TGF- \(\beta 3\) prodomains \(^{35,36}\) . Binding peptides with eight amino acid residues, aa214- 221 in TGF- \(\beta 1\) (PDB: 5ffo) and aa240- 247 in TGF- \(\beta 3\) (PDB: 4um9), were isolated from the corresponding crystal structures before grafting into the Cap9rh74 VR4 loop. Both motifs bind to \(\alpha \beta 6\) dimer at a very similar position (Fig S1E).  
+
+<|ref|>text<|/ref|><|det|>[[41, 152, 955, 314]]<|/det|>
+Third, the defined binding motifs were then grafted into the VR4 loop (residues 453- 459) of the capsid protein based on the RosettaRemodel protocol \(^{37}\) . In the grafting- remodel process, many rounds of backbone optimization and sequence design iteratively search for low- energy sequence- structure pairs (Fig. 1B). The lowest- energy designs in grafting experiments of each TGF- \(\beta\) motif showed convergence in both structure and sequence (Fig. 1C- D, S1F- G). The new VR4 loops include the binding peptide and two flanking 2- amino acid linkers and retain the LXXL/I motif as an \(\alpha\) - helix, which is important to bind in the \(\beta 6\) subunit's pocket \(^{36}\) .  
+
+<|ref|>text<|/ref|><|det|>[[41, 330, 955, 446]]<|/det|>
+Retrospective docking simulations of the two AAV_ITGs with the best scores, namely Cap9rh74_5ffo and Cap9rh74_4um9, on the \(\alpha \beta 6\) complex showed highly similar binding positions of the new VR4 loop to its corresponding inserted motifs (Fig. 1E- F). This suggests that the new capsids can bind to \(\alpha \beta 6\) thanks to VR4- included RGDLLXXL/I motif. Sequences with the best scores, which reflect the thermodynamic stability of one static protein conformation \(^{38}\) , were subjected to experimental validation.  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 460, 899, 505]]<|/det|>
+## 3. All designed AAV_ITGs showed higher productivity and enhanced cellular transduction via \(\alpha \beta 6\) binding.  
+
+<|ref|>text<|/ref|><|det|>[[41, 521, 951, 703]]<|/det|>
+The two AAVs with the best design were then tested for productivity and the effectiveness of using \(\alpha \beta 6\) as a cellular receptor. They were produced by tri- transfection with pITR- CMV- GFP- Luciferase as the expression cassette. Thanks to energy optimization, all the designed AAV- ITG variants significantly increase their titers compared to their parental hybrid capsid, to levels similar to those for AAV9 (Fig. 2A, S2A). In addition, all modified AAV- ITG variants retain proportions of VP1, VP2, VP3 capsid proteins with a similar ratio of AAV9 (Fig. 2B). This suggests that the designed sequences result in more stable AAV capsid complexes thanks to their estimated low energy structure, and therefore better production efficacy.  
+
+<|ref|>text<|/ref|><|det|>[[40, 719, 930, 950]]<|/det|>
+Next, we examined whether these AAV- ITGs can effectively use \(\alpha \beta 6\) as a cellular receptor upon infection. First, a HEK293 cell line (293_ \(\alpha \beta 6\) ) constitutively overexpressing both integrin subunits, \(\alpha\) and \(\beta 6\) , was created using the PiggyBac system (Fig S2B- C). The designed AAVs were then tested for their infectivity in this cell line. As expected, infection of AAV_ITGs in 293_ \(\alpha \beta 6\) cells, as defined by vector copy numbers (VCN), was higher than for AAV9 and AAV9rh74 (Fig. 2C). Both AAV_ITGs dramatically improved the luciferase activity ( \(\mathrm{FC}_{9\mathrm{rh74\_4um9 / AAV9}} = 60.50\) , \(\mathrm{FC}_{9\mathrm{rh74\_5ffo / AAV9}} = 25.99\) , \(\mathrm{FC}_{9\mathrm{rh74\_4um9 / 9rh74}} = 63.99\) , and \(\mathrm{FC}_{9\mathrm{rh74\_4um9 / 9rh74 = 27.49}}\) , Fig. 2D). To investigate how specific AAV_ITGs used \(\alpha \beta 6\) as a cellular receptor, we tested their infectivity under binding competition conditions. The number of AAV_ITG viral vectors entering the cells was significantly reduced when blocked by the recombinant protein \(\alpha \beta 6\) before viral infection, but no change occurred with AAV9 or AAV9rh74
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 951, 88]]<|/det|>
+(Fig. 2E). This result suggests that efficient transduction of AAV_ITGs requires specific binding to a \(\alpha \beta \delta\) complex.  
+
+<|ref|>text<|/ref|><|det|>[[40, 104, 950, 308]]<|/det|>
+During myogenesis, \(\alpha \beta \delta\) is only expressed in late differentiation, but not in the myoblast stage (Fig S1A, S2D). We therefore hypothesized an enhanced transduction of AAV_ITGs in differentiated myotubes, but not myoblasts. We infected both human myoblasts and myotubes with AAV_ITGs. Low levels of luciferase activity were observed in all AAVs tested in human myoblasts (Fig. 2G,I). On the other hand, in human differentiated myotubes (hMT), VCN and luciferase activities in both AAV9rh74_4um9 and _5ff0 were significantly higher than for AAV9 or AAV9rh74 (Fig. 2F,H,K). In particular, variant AAV9rh74_4um9 showed a 16.56 (p < 0.0001) and 25.02- fold (p < 0.0001) improvement in luciferase activity compared to AAV9 and AAV9rh74, respectively, which is in agreement with its superior transduction efficiency and transgene expression seen in 293_αVβ6 cells.  
+
+<|ref|>text<|/ref|><|det|>[[42, 324, 933, 369]]<|/det|>
+In summary, the two designed AAV_ITGs were both well- produced and function via \(\alpha \beta \delta\) - specific binding, thus enhancing their transduction efficiency in 293_αVβ6 and human differentiated myotubes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 385, 835, 407]]<|/det|>
+## 4. AAV_ITGs enhanced transduction in skeletal muscle following systematic administration  
+
+<|ref|>text<|/ref|><|det|>[[42, 423, 940, 490]]<|/det|>
+AAV_ITGs, together with AAV9 and AAV9rh74, were administrated systematically via intravenous injection (transgene: CMV_GFP- Luciferase, dose: 1E13 vg/kg, age at injection: 6 weeks, n = 4) in C57Bl6 mice to examine their biodistribution 3 weeks post- injection (Fig. 3A).  
+
+<|ref|>text<|/ref|><|det|>[[39, 504, 950, 916]]<|/det|>
+In agreement with a previous study, AAV9rh74 slightly reduces transduction in skeletal muscle compared to AAV9 but accumulates much less in the liver (Fig. 3B- D). Thanks to the liver- detargeting capsid and in accordance with the fact that \(\alpha \beta \delta\) is weakly expressed in the liver, we expected poor entry into the liver for designed AAV_ITGs. Indeed, AAV_ITGs is strongly detargeted from the liver, both at VCN and mRNA levels, even further than the parental capsid (Fig. 3C- D). In contrast, enhanced transduction was observed in all skeletal muscles that were tested, including the tibialis anterior (TA), quadriceps (Qua) and diaphragm (Dia) (Fig. 3B- D). The two AAV_ITGs both showed a substantial increase in VCN and luciferase activity compared to both AAV9 and AAV9rh74. Similar to the results obtained in in vitro models, AAV9rh74_4um9 is the best transducer among the two AAV_ITGs. Compared to AAV9, the variant 9rh74_4um9 significantly increased VCN 5.31/7.21/2.48- fold and increased luciferase activity 15.2/13.2/23.57- fold in Qua, TA, and Dia (p < 0.05), respectively. Compared to the original backbone AAV9rh74, this variant even magnified the difference by increasing VCN 5.53/2.85/7.69- fold and increasing luciferase activity 152.35/106.68/60.43- fold (p < 0.05). Furthermore, AAV9rh74_4um9, but not AAV9rh74_5ffo, significantly increased transduction in the heart (FCVCN=4.15, FCLLC=15.43, p < 0.05). All AAVs that were tested showed poor delivery and transgene expression in the lungs and kidneys. No alteration of TGFβ and integrin signaling was observed at one- month post- injection in all AAVs being tested (Fig S2F- G). Overall, these data indicate that AAV_ITGs, especially the 9rh74_4um9 variant, are strongly liver- detargeted and exhibit enhanced tropism towards skeletal and cardiac muscles.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[42, 44, 914, 88]]<|/det|>
+## 5. AAV9rh74_4um9 transduced skeletal muscle similarly, but detargeted the liver more strongly than other myotropic AAVs  
+
+<|ref|>text<|/ref|><|det|>[[39, 105, 951, 469]]<|/det|>
+Several engineered myotropic AAVs (mAAVs), including AAVMYO \(^{15}\) , MYOAAV- 1A and - 2A \(^{17}\) , have demonstrated superior efficacy for in vivo delivery of muscle compared to natural AAVs. To evaluate the properties of these AAVs compared to ours, we performed in vitro and in vivo experiments. Viral preparations were produced using the same reporter transgene (CMV_GFP- Luc). All mAAVs were well- produced in 400ml suspension, with higher titers than AAV9rh74. However, MYOAAV productivity was significantly lower than 9rh74_ITGs and MYOAAVs (Fig S3A). Since all investigated mAAVs shared a common integrin- targeting RGD motif, these AAVs were then evaluated for their transduction via integrin complexes in myotubes and in cell lines where integrin complexes were stably overexpressed by the PiggyBac system. In 293_αVβ6 cells as well as in hMT, where αVβ6 is highly expressed, AAV9rh74_4um9 showed the highest transduction among the tested myotropic AAVs, with the sole exception that luciferase activity of MYOAAV2A was higher in hMT (Fig S3B- C). We also tested AAV transduction efficiency in two other cell lines, 293_WT, where αVβ6 expression is low, and 293_α7β1 that stably overexpresses a non- RGD- targeting α7β1 integrin. In both conditions, MYOAAV2A and AAV9rh74_4um9 showed the highest transduction (Fig S3D- E). These results suggest that, as intended with the rational design, AAV9rh74_4um9 uses αVβ6 more preferentially for cellular transduction than others, yet it can also efficiently use other integrin(s) similar to MYOAAV2A.  
+
+<|ref|>text<|/ref|><|det|>[[39, 484, 950, 759]]<|/det|>
+Following in vivo injection in the same setting as described above (6- week- old WT mice, dose: 1E13 \(\mathrm{vg / kg}\) , \(\mathrm{n} = 4\) ), the three mAAVs and 9rh74_4um9 all showed strong liver- detargeting, high enrichment in both skeletal and cardiac muscles, and negligible transduction levels in other organs that were tested (kidneys, lungs, and brain) (Fig. 3G- H). No significant difference was observed in either VCN or luciferase activity between all three mAAVs and 9rh74_4um9 in the skeletal muscles that were tested. In heart muscle, MYOAAV2A showed a significant increase in VCN compared to other myotropic vectors, but no difference in luciferase activity, in agreement with the original observation \(^{17}\) . The most striking difference is the level of liver- detargeting between these vectors. The VCN for 9rh74_4um9 in liver is 3.34/22.05/13.85 times lower than for AAVMYO ( \(\mathrm{p} = 0.0022\) ), MYOAAV- 1A ( \(\mathrm{p} = 0.0013\) ) and - 2A ( \(\mathrm{p} = 0.033\) ), respectively (Fig. 3G), and is therefore the only vector that accumulates less in liver than skeletal muscles (Fig S3F- G). These data indicate higher muscle specificity for the 9rh74_4um9 variant compared to other myotropic vectors that have been investigated to date.  
+
+<|ref|>text<|/ref|><|det|>[[41, 775, 950, 911]]<|/det|>
+In summary, the 9rh74_4um9 variant, hereafter referred to as LICA1 (linked- integrin- complex AAV), consistently showed enhanced transduction and strongest liver- detargeting. Therefore, we then attempted to evaluate LICA1 as a delivery vector for muscular dystrophies, in comparison with AAV9. Two different setups will be investigated: the transfer of microdystrophin (μDys) – an incomplete transgene - in mdx, a mild mouse model of Duchenne muscular dystrophy (DMD) and of the full- length human α- sarcoglycan (SGCA) in a severe mouse model of limb- girdle muscular dystrophy R3 (LGMD- R3).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[42, 44, 905, 89]]<|/det|>
+## 6. Low-dose LICA1-μDys gene transfer is effective in specifically overexpressing microdystrophin in dystrophic muscle but not sufficient to fully correct the underlying pathology  
+
+<|ref|>text<|/ref|><|det|>[[39, 105, 950, 408]]<|/det|>
+DMD is caused by mutations in the DMD gene, which encodes for dystrophin protein - a key player in the dystrophin- glycoprotein complex (DGC), which is critical for the structural stability of skeletal muscle fibers \(^{39}\) . Lack of dystrophin can result in progressive loss of muscle function, respiratory defects, and cardiomyopathy. The most commonly used DMD animal model is the mdx mouse, with a lifespan reduced by \(25\%\) , milder clinical symptoms than those seen in human patients, with the exception of the diaphragm muscle \(^{40}\) . Among many therapeutic strategies to restore dystrophin expression, high- dose AAV- based gene transfer of shortened functional forms of the dystrophin ORF provided excellent results in animal models, but unsatisfactory conflicting data in current clinical trials \(^{6}\) . Severe toxicities, even patient death, have been reported from these trials (NCT03368742, NCT04281485), assumed to be related to the dose of \(\geq 1E14\) vg/kg. We therefore explored the possibility of low- dose μDys gene transfer \(^{41}\) in mdx mice using LICA1 in comparison to AAV9 (Fig S4A, age at injection: 4 weeks, dose: 5E12 vg/kg, treatment duration: 4 weeks, \(n = 5\) ). Three muscles with increasing levels of severity - TA, Qua, and Dia - were used to study AAV transduction and treatment efficacy.  
+
+<|ref|>text<|/ref|><|det|>[[39, 424, 956, 699]]<|/det|>
+LICA1 showed better μDys gene transfer than AAV9 in this model. LICA1- treated mice exhibited a significantly higher VCN in all 3 muscles that were tested, 1.85/2.02/1.07 times higher in TA ( \(p < 0.0001\) ), Qua ( \(p < 0.0001\) ), and Dia ( \(p = 0.020\) ), respectively (Fig. 4A). RNA levels indicated even greater differences and were 4.56- 7.57 times higher in the LICA1- treated group (Fig. 4B; TA: FC = 4.56, \(p < 0.0001\) ; Qua: FC = 5.46, \(p = 0.0001\) ; Dia: 7.57, \(p = 0.05\) ). Consequently, LICA1 can transduce almost \(100\%\) in TA and Qua, and \(49.98\%\) in Dia, while substantially lower numbers were seen in AAV9- treated muscles, at \(73.22\%\) ( \(p = 0.0001\) ), \(57.8\%\) ( \(p < 0.0001\) ), \(10.34\%\) ( \(p < 0.0001\) ) in TA, Qua, Dia, respectively (Fig. 4C, Fig S4B). Furthermore, while infection levels and expression of the transgene in liver were high for the AAV9 vector (despite the use of muscle- specific promoter), the VCN and mRNA levels in LICA1- treated liver were extremely low (Fig. 4A- B, FCVCN:AAV9/LICA1=36.8, \(p = 0.0002\) ; FCmRNA:AAV9/LICA1=64.7, \(p < 0.0001\) ). These data again confirmed the transduction efficiency and specificity towards skeletal muscle for the LICA1 vector, even with low- dose treatment.  
+
+<|ref|>text<|/ref|><|det|>[[39, 714, 940, 947]]<|/det|>
+The histological features and muscle functionality after AAV treatment were restored accordingly. The centronucleation index (percentage of centronucleated fibers) - an indicator of the regeneration/degeneration process - did not change with AAV9 (except in TA) but was significantly reduced upon LICA1 treatment (reduction of \(21.68\%\) , \(19.05\%\) , \(22.88\%\) in TA, Qua, Dia, respectively) (Fig. 4D, Fig S4C). Similarly, the fibrosis level in two severely affected muscles, Qua and Dia, only exhibited a significant reduction with LICA1, but not AAV9 (Fig. 4E, Fig S4D). The serum biomarker MYOM3 level, an indicator of muscle damage \(^{42}\) , showed a reduction for both AAV treatments, with a considerable further reduction seen in the LICA1- treated group (Fig. 4F, FCAAV9/KO=0.75, FC-LICA/KO=0.43, PAAV9- LICA1>0.0001). More importantly, AAV9 treatment did not affect any muscle functionality being tested (Fig. 4G- I), while significant improvements with LICA1- μDys treatment were observed in escape
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 43, 935, 137]]<|/det|>
+test – a measure of global force (Fig. 4G, \(\mathrm{FC}_{\mathrm{LICA1 / mdx}} = 1.19\) , \(\mathrm{P}_{\mathrm{LICA1 / mdx}} = 0.02\) ) and in situ TA mechanical force measurement (Fig. 4H, \(\mathrm{FC}_{\mathrm{LICA1 / mdx}} = 1.14\) , \(\mathrm{P}_{\mathrm{LICA1 / mdx}} = 0.0006\) ). However, none of the treatment normalized to the WT functional levels. These data indicate that LICA1 is better than AAV9 at restoring dystrophic histological features and muscle functions.  
+
+<|ref|>text<|/ref|><|det|>[[39, 153, 951, 449]]<|/det|>
+We also investigated the molecular alteration in Qua upon AAV treatment using RNA- seq. On the two first principal components (PCs) of the PCA, a clear distinction between four transcriptome groups (WT, mdx, AAV9, LICA1) was observed, while LICA1- treated muscles were clustered closer to the WTs than others (Fig S4E). To our surprise, despite excellent transgene expression by LICA1, global transcriptomic restoration was relatively modest (Fig. 4K). Nevertheless, a substantial improvement can still be seen for LICA1 compared to AAV9. Among 4216 down- and 4501 upregulated differentially expressed genes (DEGs) identified in mdx muscle, 1515 (35.9%) and 1728 (38.4%) were restored by AAV9, while LICA1 was able to correct 1736 (41.2%) and 1980 (44.0%), respectively (Fig. 4L- M). In addition, a greater number of genes were either not or insufficiently corrected by AAV9 than by LICA1 (Fig. 4N). A total of 2572 genes were downregulated (61.0%) and 2620 (58.2%) incompletely restored, while significantly lower numbers were seen for LICA, with 2094 (49.67%) down- and 2019 (44.86%) upregulated. Interestingly, some known dysregulated pathways, including \(\alpha\) - and Y- interferon responses and oxidative phosphorylation, were significantly better normalized by LICA1 than by AAV9 (Fig S4F).  
+
+<|ref|>text<|/ref|><|det|>[[41, 463, 945, 576]]<|/det|>
+In summary, at 5E12 vg/kg, LICA1- \(\mu\) Dys, but not AAV9, was efficient in transducing close to 100% myofibers, except in the diaphragm. This effective improvement in transduction can significantly reduce some dystrophic features in all muscles that were tested, yet restoration in the global transcriptome remains modest. However, greater improvements in functional, histological, and transcriptomic restoration were achieved with LICA1 compared to AAV9.  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 592, 894, 637]]<|/det|>
+## 7. Low-dose LICA1-SGCA treatment restored the muscle functionality, dystrophic phenotypes, and transcriptomic dysregulation in a severe SGCA mouse model.  
+
+<|ref|>text<|/ref|><|det|>[[41, 654, 955, 794]]<|/det|>
+LGMDR3 is caused by mutations in the SGCA gene \(^{43}\) – another component of the DGC complex. Defects in the SGCA protein therefore lead to muscle weakness and wasting. A LGMDR3 mouse model has been established, which closely represents patient's clinical phenotypes \(^{44}\) . Similar to the setting in mdx mice, low- dose AAV treatment with 5E12 vg/kg was investigated in this mouse model. AAV9 or LICA1 encoding human SGCA (hSGCA) under control of a muscle- specific human Acta1 promoter were injected into 4- week- old SGCA- KO mice (Fig. 5A). Analysis was performed 4 weeks post- treatment.  
+
+<|ref|>text<|/ref|><|det|>[[41, 809, 953, 945]]<|/det|>
+In all three muscles that were tested, TA, Qua, Dia (in order of increasing severity), transduction in various measures, VCN, mRNA level, and percentage of SGCA + myofibers, was significantly greater in the LICA1- treated group than for AAV9 (Fig. 5B- D, Fig S5A). Of note is the fact that the differences in transduction efficacy (%SGCA + myofibers) between LICA1 and AAV9 are greater in more severely affected muscles (Fig. 5D). At such a low dose, AAV9 was able to transduce > 80% myofibers in TA while LICA1 can reach close to 100% (p < 0.0001). While LICA1 still transduced almost 100% of fibers in Qua (the muscle
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 44, 950, 111]]<|/det|>
+affected with intermediate severity), only \(58.1\%\) fibers were transduced by AAV9 on average \((p < 0.0001)\) . In the most severely affected muscle, Dia, both vectors displayed reduced efficiency; however, LICA1 continued to demonstrate much better transduction \((\mu_{\mathrm{AAV9}} = 22.1\%, \mu_{\mathrm{LICA1}} = 59.5\%, \mathrm{p} < 0.0001)\) .  
+
+<|ref|>text<|/ref|><|det|>[[39, 128, 955, 515]]<|/det|>
+The differences in transgene delivery and expression positively correlated with levels of histological and functional restoration. Different dystrophic histological features, including percentage of centronucleated fibers (Fig. 5E, Fig S5B), percentage of fibrosis area (Fig. 5F, Fig S5C), and fiber size distribution (Fig. 5G), were all significantly better normalized by LICA1 than AAV9, especially in more severely affected muscles. Importantly, no significant improvement was observed in the AAV9- treated group in centronucleation index and fibrosis level in Dia, while LICA1 reduced these parameters by half (Fig. 5E- F). Fiber sizes were also restored to near- WT distribution by LICA1 in this muscle (Fig. 5G). No difference in body weight was seen between groups with or without AAV treatment (Fig S5D). At the functional level, however, the escape test – a measure of global force – showed a significant increase in AAV9- treated mice \((FC = 1.42, \mathrm{p} = 0.0072)\) and was even higher in LICA1- treated group \((FC = 1.72, \mathrm{p} < 0.0001)\) (Fig. 5H). On the other hand, in situ TA mechanical forces were both improved in the two AAV groups at similar levels (Fig. 5I), possibly due to \(>80\%\) transduction rate by both vectors. Similar to the global force, the serum MYOM3 level was greatly reduced in the LICA1- treated group but not for AAV9, indicating less muscle damage (Fig. 5K). No difference was seen in the anti- capsid antibody between the two AAV treatments (Fig S5E). These results indicate that better and significant functional and histological restoration in the LICA1- treated mice was achieved, even at low- dose treatment, thanks to superior transduction efficacy.  
+
+<|ref|>text<|/ref|><|det|>[[39, 530, 947, 848]]<|/det|>
+We further investigated the molecular alterations following AAV treatment by transcriptomic profiling of the quadriceps muscle. The first principal component (PCs) of the PCA was able to separate a group including WT and LICA1 with a group including SGCA- KO and AAV9, suggesting close proximity between elements within these 2 groups (Fig S5F). A heatmap of all 8591 significant DEGs (4035 downregulated and 4556 upregulated) further highlighted the restorative effect of LICA1 on gene expression levels (Fig. 5L). LICA1- treated muscles, in particular, demonstrated a significant correction of \(69.9\%\) (2821/4035) and \(66.5\%\) (3028/4556) of down- and upregulated DEGs, respectively, compared to \(12.4\%\) (500/4035) and \(9.21\%\) (420/4556) corrected by AAV9 treatment (Fig. 5M- N). Conversely, not all DEGs were significantly restored or returned to WT levels. The number of such transcripts in AAV9- treated muscles was much higher than in the LICA1- treated group (Fig. 5O): 2541 (63.0%) downregulated DEGs and 3045 (66.8%) upregulated DEGs for AAV9, with only 483 (12.0%) downregulated DEGs and 1038 (22.8%) upregulated DEGs in the LICA1- treated group. These data illustrate that low- dose LICA1 treatment can effectively normalize the majority of the dysregulated transcriptome and is much more efficient in correcting gene expression dysregulation than AAV9 at the same dose.  
+
+<|ref|>text<|/ref|><|det|>[[42, 864, 915, 930]]<|/det|>
+In summary, low- dose (5E12 vg/kg) AAV gene transfer using LICA1 in the LGMDR3 mouse model is effective in restoring muscle function, dystrophic histology, and the dysregulated transcriptome. The efficacy was much greater than for AAV9 at the same dose due to enhanced transduction.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 213, 68]]<|/det|>
+## DISCUSSION  
+
+<|ref|>text<|/ref|><|det|>[[41, 83, 955, 263]]<|/det|>
+Given the severe complications observed with very high dose AAV treatment, lowering the dose by increasing vector specificity via capsid modification is one way to address these issues. This study investigated the possibility of altering AAV tropism towards skeletal muscle by targeting integrin. We designed an AAV as a \(\alpha \mathrm{V}\beta 6\) binder, which resulted in a novel myotropic AAV variant, namely LICA1. LICA1 showed greatly enhanced transduction in skeletal muscle in WT and two MD mouse models. Consequently, by improving the delivery of therapeutic transgenes (hSGCA and \(\mu \mathrm{Dys}\) ) in these MD mouse models, LICA1 was able to correct dystrophic phenotypes, global transcriptional dysregulations and significantly restore muscle function.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 280, 666, 301]]<|/det|>
+## AAV capsid sequence design method that ensures high AAV production  
+
+<|ref|>text<|/ref|><|det|>[[40, 317, 951, 592]]<|/det|>
+AAV tropism is commonly altered by inserting a small peptide into the VR4 or VR8 loop without any sequence constraints. Since no consideration regarding AAV capsid stability is included in this method, the resulting AAV can suffer from instability, reduced productivity, and increased AAV genome fragmentation \(^{17,45}\) (ASGCT 2023). In the current study, a physics- based protein sequence design method was used to graft the binding motifs from TGF \(\beta\) - 1 and - 3 into the VR4 loop of the hybrid capsid AAV9rh74. The major differences to the classical peptide insertion method are that the entire VR4 loop was modified to include a new binding motif and the amino acids around this motif (linkers) were selected to minimize the potential energy. Low- energy sequences ensure the stability and intended folding of the designed proteins, presumably leading to improved stability of the AAV particle \(^{38}\) . Six AAVs designed using this method were tested experimentally and all showed better productivity than their parent, Cap9rh74, and similar levels to well- produced AAV9. This suggests that low Rosetta energy correlates with high stability of capsid protein, and thereby high AAV production.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 608, 586, 629]]<|/det|>
+## Integrin \(\alpha \mathrm{V}\beta 6\) as a myotropic AAV receptor for skeletal muscle  
+
+<|ref|>text<|/ref|><|det|>[[40, 646, 955, 877]]<|/det|>
+Virus- host interaction is the foundation for improved viral vectors, yet skeletal muscle receptors that allow effective AAV transduction are poorly defined. However, top hits from two independent studies with different screening schemes identified myotropic AAVs with a common RGD motif, \(^{15,17,19}\) . In addition, it has previously been described that integrin functions as cellular receptor for natural AAV \(^{23,24}\) . Coincident with our screening for possible integrin receptor, only \(\alpha \mathrm{V}\beta 6\) is highly expressed and enriched in skeletal muscle (Fig S1). By including \(\alpha \mathrm{V}\beta 6\) binding motifs, AAV_ITGs efficiently utilized \(\alpha \mathrm{V}\beta 6\) for cellular infection. Enhanced transduction was observed in conditions with high (either ectopic or natural) \(\alpha \mathrm{V}\beta 6\) expression, including human differentiated myotubes and murine skeletal muscles of WT and two other MD mouse models. In most cases, the improved transduction was evident at the VCN level, indicating better cell entry via \(\alpha \mathrm{V}\beta 6\) binding.  
+
+<|ref|>text<|/ref|><|det|>[[42, 893, 928, 960]]<|/det|>
+In addition, we conducted a study comparing LICA1 and three other published myotropic AAVs. No significant differences in skeletal muscle transduction were observed on either VCN or transgene expression levels. However, the liver infection rate was significantly lower with LICA1 compared to the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 953, 155]]<|/det|>
+other mAAVs, presumably due to the use of a liver- detargeted backbone and the low expression level of \(\alpha \mathrm{V}\beta 6\) in liver. As a result, the LICA1 vector exhibited the highest muscle/liver transduction ratio among all AAVs tested, suggesting increased specificity towards skeletal muscle. This finding highlights the importance of selecting an appropriate targeting receptor for rational design and further supports \(\alpha \mathrm{V}\beta 6\) as a promising candidate for targeting skeletal muscle.  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 174, 472, 194]]<|/det|>
+## LICA1 is a potential vector for muscular diseases  
+
+<|ref|>text<|/ref|><|det|>[[39, 210, 955, 604]]<|/det|>
+AAV gene therapy in muscle diseases typically requires very high doses \((\geq 1E14 \mathrm{vg / kg})\) for functional benefits \(^{41,46}\) , yet can result in severe and even fatal adverse events \(^{7}\) . In this study, we explored low dose (5E12 vg/kg) treatment using the LICA1 vector in two MD mouse models, DMD and LGMDR3. Of note is that this dose is at least 20 times lower than the doses currently used in clinical trials for neuromuscular diseases \(^{3}\) . In both models, LICA1 was significantly better than AAV9 in delivering and expressing therapeutic transgenes, consequently restoring better histological dystrophic phenotypes. In TA and Qua, LICA1 was able to transduce more than \(80\%\) of fibers. It was still a challenge to effectively transduce diaphragm muscle at this dose, yet more than \(50\%\) of Dia fibers were positive for transgene expression with LICA1 in both models while AAV9 transduced very poorly. This improvement in transgene expression translates directly into improved histological restoration, including centronucleation index and fibrosis level. In particular, with only more than \(50\%\) successfully transduced fibers, LICA1 was able to reduce diaphragm fibrosis by \(42.8 - 47.0\%\) (mdx and SGCA \(^{- / - }\) models respectively), whereas no change was seen in AAV9- treated groups. The biomarker for muscle damage level, MYOM3, was reduced by \(57.5 - 67.2\%\) (mdx and SGCA \(^{- / - }\) models respectively) by LICA1 and significantly greater than AAV9. Similarly, global muscle force was significantly restored to a higher level with LICA1 than with AAV9 in SGCA- KO mice. These data confirmed superior muscle transduction by LICA1 and resulting therapeutic benefits were obtained even at low- dose treatment in two MD models.  
+
+<|ref|>text<|/ref|><|det|>[[40, 620, 955, 875]]<|/det|>
+However, treatment efficacy varies between two disease models at molecular levels. We profiled transcriptomic changes in Qua following AAV treatment in both MD models. Despite similar transduction efficiency of LICA1 in the two models, restoration of dystrophic transcriptional changes in SGCA- KO was significantly greater. It is noteworthy that \(\mu \mathrm{Dys}\) is an incomplete form of dystrophin. The \(\mu \mathrm{Dys}\) used in the present study lacks several functional domains, including multiple spectrin- like repeats that bind to nNOS, F- actin, sarcomeric lipid and microtubules, and a dystrobrevin- and syntrophin- binding C- terminus \(^{41}\) . This might explain the inadequate efficacy in restoring global gene expression in \(\mu \mathrm{Dys}\) gene therapy trials, in spite of highly effective gene transfer. Similarly, despite excellent functional restoration by microdystrophin gene transfer in various animal models, outcomes from these clinical trials are unsatisfactory \(^{6}\) . Therefore, careful assessment of molecular restoration should be included for evaluating gene therapy efficacy.  
+
+<|ref|>text<|/ref|><|det|>[[41, 890, 950, 958]]<|/det|>
+In summary, this study presents an alternative computational method that aids rational AAV design and ensures high- production AAV variants. The proof- of- concept design targeting skeletal muscle resulted in a high- productivity myotropic AAV, thereby effectively delivering therapeutic transgenes and restoring
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 928, 110]]<|/det|>
+dystrophic phenotypes in two MD mouse models at a low dose. This work contributes to the ongoing efforts to reduce AAV treatment doses and further advance AAV engineering, paving the way for more effective and accessible gene therapies in the future.  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 133, 415, 159]]<|/det|>
+## MATERIALS AND METHODS  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 175, 160, 195]]<|/det|>
+## Study Design  
+
+<|ref|>text<|/ref|><|det|>[[40, 211, 955, 460]]<|/det|>
+The primary objective of the study was to design a novel myotropic AAV capsid with a high production yield by using a computationally rational design. The secondary aim was to investigate the possibility of low- dose AAV treatment using a designed AAV in animal models of muscular dystrophies, which typically require an alarmingly high dose \((\geq 1E14\) vg/kg). We used publicly available datasets to identify possible receptors for skeletal muscle and protein design tools to engineer AAV capsid protein. Resulting variants were characterized for their productivity and transduction efficiency in various in vitro cell lines and multiple mouse models. Experiments were performed at least three times, unless noted otherwise. The AAV injection and infection experiments were conducted in a nonblinded fashion. The blinding approach was used during dissection, histological validation, immunostaining analysis, in vivo functional tests, and biomarker analysis. No data were excluded. Details on experimental procedures are presented in Supplementary Materials and Methods.  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 477, 223, 497]]<|/det|>
+## Animal care and use  
+
+<|ref|>text<|/ref|><|det|>[[40, 514, 952, 787]]<|/det|>
+All animals were handled according to French and European guidelines for human care and the use of experimental animals. All procedures on animals were approved by the local ethics committee and the regulatory affairs of the French Ministry of Research (MESRI) under the numbers 2018- 024- B #19736, 2022- 004 #35896. C57Bl/6, B6Ros.Cg- Dmdmdx- 4Cv/J mice were obtained from the Jackson Laboratory. A knockout mouse model of \(\alpha\) - sarcoglycan was obtained from the Kevin Campbell laboratory (University of Iowa, USA) \(^{44}\) . Mice were housed in a SPF barrier facility with 12- h light, 12- h dark cycles, and were provided with food and water ad libitum. Only male mice were used in the present study. Well- being and weights of the animals were monitored for the duration of the study. The animals were anesthetized with a mix of ketamine (100 mg/kg) and xylazine (10 mg/kg), or with isoflurane (4%) for blood samples. For AAV intravenous injections, a maximum volume of 150 μl containing AAV vectors was injected via the sinus route after the animals had been anesthetized with isoflurane. The AAV intravenous doses used in the present study were 5E12 or 1E13 vg/kg.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 804, 297, 824]]<|/det|>
+## Cell culture and in vitro study  
+
+<|ref|>text<|/ref|><|det|>[[42, 841, 949, 930]]<|/det|>
+Adherent HEK293- T cells were maintained in the proliferating medium containing DMEM (Thermo Fisher Scientific), supplied with 10% fetal bovine serum and 1X gentamycin at \(37^{\circ}C\) , 5% CO2. Human immortalized myoblasts (AB1190 cell line) were maintained in Skeletal Muscle Cell Growth Medium (PromoCell, C23060) and differentiated in Skeletal Muscle Differentiation Medium (PromoCell, C23061).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 44, 931, 110]]<|/det|>
+In vitro AAV infection was performed by directly adding AAV into culture medium at the dose of 1E9 or 1E10 vg per 24- well plate well. After 48h post- infection, cells were washed and subjected to VCN and gene expression analysis.  
+
+<|ref|>text<|/ref|><|det|>[[42, 127, 950, 216]]<|/det|>
+To inhibit AAV infection, AAVs were incubated with recombinant hTGAV- hITGB6 protein (Bio- Techné, 3817- AV- 050) at \(37^{\circ}C\) for 30 minutes, at a concentration of \(1\mu g\) protein per 5E9vg AAV before addition to the cells (1E4 vg per cell). The same condition treated with recombinant hSGCA protein served as a control for the comparison.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 234, 211, 254]]<|/det|>
+## Statistical Analysis  
+
+<|ref|>text<|/ref|><|det|>[[42, 271, 950, 428]]<|/det|>
+Results are presented as mean \(\pm\) SEM, unless noted otherwise. Significance of differences in multiple pairwise comparisons of more than two groups was determined by one- way ANOVA. The significance of differences in pairwise comparisons of multiple groups with multiple treatments was determined by two- way ANOVA. To account for multiple testing and control the false discovery rate (FDR) across the numerous pairwise comparisons, the Benjamini- Hochberg (BH) procedure was applied with an FDR threshold of 0.05. Statistical tests were performed using GraphPad Prism 9. Results were considered significant when p- values or adjusted p- values were less than 0.05.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 451, 257, 477]]<|/det|>
+## DECLARATIONS  
+
+<|ref|>text<|/ref|><|det|>[[41, 492, 951, 670]]<|/det|>
+Acknowledgments: The authors are Genopole's members, first French biocluster dedicated to genetic, biotechnologies and biotherapies. We are grateful to the "Imaging and Cytometry Core Facility" and to the in vivo evaluation, services of Genethon for technical support, to Ile- de- France Region, to Conseil Départemental de l'Essonne (ASTRE), INSERM and GIP Genopole, Evry for the purchase of the equipment. We would like to acknowledge the technical help of Carolina Pacheco Algalan and Alejandro Arco Hierves. The Genotype- Tissue Expression (GTEx) Project was supported by the Common Fund of the Office of the Director of the National Institutes of Health, and by NCI, NHGRI, NHLBI, NIDA, NIMH, and NINDS.  
+
+<|ref|>text<|/ref|><|det|>[[42, 689, 914, 733]]<|/det|>
+Funding: This work was supported by the "Association Française contre les Myopathies" (AFM), and "Institut National de la Santé Et de la Recherche Médicale" (INSERM, FranceRelance N°221513A10).  
+
+<|ref|>text<|/ref|><|det|>[[42, 750, 949, 815]]<|/det|>
+Author contributions: The project was conceptualized by A.H.V. and I.R. A.H.V., L.S.P., and J.P. conducted experiments and performed data analysis. Funding supporting this project was obtained by I.R. A.H.V. and I.R. supervised the project. The manuscript was written by A.H.V. and I.R.  
+
+<|ref|>text<|/ref|><|det|>[[42, 832, 947, 899]]<|/det|>
+Competing interests: A.H.V. and I.R. are inventors on PCT application EP2023/065499 for the integration of RGDlxxL/I motif in AAV capsid for enhanced muscle transduction efficiency. I.R. is a part- time employee of Atamyo Therapeutics. The other authors declare that they have no competing interests.  
+
+<|ref|>text<|/ref|><|det|>[[42, 916, 936, 959]]<|/det|>
+Data and materials availability: All data associated with this study are present in the paper or the Supplementary Materials. All transcriptomic data will be deposited in the NCBI Sequence Read Archive
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 933, 110]]<|/det|>
+(SRA) upon publication. Processed data including differential gene expression analysis are available in data file S1 and S2. The plasmid constructs and reagents generated as part of this study are available under a material transfer agreement from the corresponding authors.  
+
+<|ref|>sub_title<|/ref|><|det|>[[43, 133, 224, 158]]<|/det|>
+## REFERENCES  
+
+<|ref|>text<|/ref|><|det|>[[50, 174, 951, 940]]<|/det|>
+1. Wang, D., Tai, P.W.L. & Gao, G. Adeno-associated virus vector as a platform for gene therapy delivery. Nat Rev Drug Discov 18, 358-378 (2019).  
+2. Pupo, A. et al. AAV vectors: The Rubik's cube of human gene therapy. Molecular therapy: the journal of the American Society of Gene Therapy 30, 3515-3541 (2022).  
+3. Crudele, J.M. & Chamberlain, J.S. AAV-based gene therapies for the muscular dystrophies. Hum Mol Genet 28, R102-R107 (2019).  
+4. Duan, D. Systemic AAV Micro-dystrophin Gene Therapy for Duchenne Muscular Dystrophy. Molecular therapy: the journal of the American Society of Gene Therapy 26, 2337-2356 (2018).  
+5. Mack, D.L. et al. Systemic AAV8-Mediated Gene Therapy Drives Whole-Body Correction of Myotubular Myopathy in Dogs. Molecular therapy: the journal of the American Society of Gene Therapy 25, 839-854 (2017).  
+6. Mercuri, E., Bonnemann, C.G. & Muntoni, F. Muscular dystrophies. Lancet 394, 2025-2038 (2019).  
+7. Ertl, H.C.J. Immunogenicity and toxicity of AAV gene therapy. Front Immunol 13, 975803 (2022).  
+8. Verdera, H.C., Kuranda, K. & Mingozzi, F. AAV Vector Immunogenicity in Humans: A Long Journey to Successful Gene Transfer. Molecular therapy: the journal of the American Society of Gene Therapy 28, 723-746 (2020).  
+9. High-dose AAV gene therapy deaths. Nature biotechnology 38, 910 (2020).  
+10. Ogden, P.J., Kelsic, E.D., Sinai, S. & Church, G.M. Comprehensive AAV capsid fitness landscape reveals a viral gene and enables machine-guided design. Science 366, 1139-1143 (2019).  
+11. DiMattia, M.A. et al. Structural insight into the unique properties of adeno-associated virus serotype 9. Journal of virology 86, 6947-6958 (2012).  
+12. Li, C. & Samulski, R.J. Engineering adeno-associated virus vectors for gene therapy. Nat Rev Genet 21, 255-272 (2020).  
+13. Tseng, Y.S. & Agbandje-McKenna, M. Mapping the AAV Capsid Host Antibody Response toward the Development of Second Generation Gene Delivery Vectors. Front Immunol 5, 9 (2014).  
+14. Buning, H. & Srivastava, A. Capsid Modifications for Targeting and Improving the Efficacy of AAV Vectors. Molecular therapy. Methods & clinical development 12, 248-265 (2019).  
+15. Weinmann, J. et al. Identification of a myotropic AAV by massively parallel in vivo evaluation of barcoded capsid variants. Nature communications 11, 5432 (2020).  
+16. El Andari, J. et al. Semirational bioengineering of AAV vectors with increased potency and specificity for systemic gene therapy of muscle disorders. Science advances 8, eabn4704 (2022).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[47, 42, 951, 92]]<|/det|>
+17. Tabebordbar, M. et al. Directed evolution of a family of AAV capsid variants enabling potent muscle-directed gene delivery across species. Cell 184, 4919-4938 e4922 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[47, 95, 940, 140]]<|/det|>
+18. Ruoslahti, E. & Pierschbacher, M.D. Arg-Gly-Asp: a versatile cell recognition signal. Cell 44, 517-518 (1986).  
+
+<|ref|>text<|/ref|><|det|>[[47, 144, 875, 188]]<|/det|>
+19. Bauer, A. et al. Molecular Signature of Astrocytes for Gene Delivery by the Synthetic Adenoc- Associated Viral Vector rAAV9P1. Adv Sci (Weinh) 9, e2104979 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[47, 192, 951, 260]]<|/det|>
+20. Zolotukhin, S., Trivedi, P.D., Corti, M. & Byrne, B.J. Scratching the surface of RGD-directed AAV capsid engineering. Molecular therapy: the journal of the American Society of Gene Therapy 29, 3099-3100 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[47, 264, 777, 286]]<|/det|>
+21. Hynes, R.O. Integrins: a family of cell surface receptors. Cell 48, 549-554 (1987).  
+
+<|ref|>text<|/ref|><|det|>[[47, 290, 950, 312]]<|/det|>
+22. Hussein, H.A. et al. Beyond RGD: virus interactions with integrins. Arch Virol 160, 2669-2681 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[47, 317, 952, 384]]<|/det|>
+23. Asokan, A., Hamra, J.B., Govindasamy, L., Agbandje-McKenna, M. & Samulski, R.J. Adeno-associated virus type 2 contains an integrin alpha5beta1 binding domain essential for viral cell entry. Journal of virology 80, 8961-8969 (2006).  
+
+<|ref|>text<|/ref|><|det|>[[47, 388, 888, 433]]<|/det|>
+24. Summerford, C., Bartlett, J.S. & Samulski, R.J. AlphaVbeta5 integrin: a co-receptor for adeno-associated virus type 2 infection. Nat Med 5, 78-82 (1999).  
+
+<|ref|>text<|/ref|><|det|>[[47, 437, 936, 481]]<|/det|>
+25. Stewart, P.L. & Nemerow, G.R. Cell integrins: commonly used receptors for diverse viral pathogens. Trends Microbiol 15, 500-507 (2007).  
+
+<|ref|>text<|/ref|><|det|>[[47, 486, 925, 531]]<|/det|>
+26. Strauch, E.M. et al. Computational design of trimeric influenza-neutralizing proteins targeting the hemagglutinin receptor binding site. Nature biotechnology 35, 667-671 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[47, 535, 949, 580]]<|/det|>
+27. Cao, L. et al. Design of protein-binding proteins from the target structure alone. Nature 605, 551-560 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[47, 585, 867, 629]]<|/det|>
+28. Ruoslahti, E. RGD and other recognition sequences for integrins. Annual review of cell and developmental biology 12, 697-715 (1996).  
+
+<|ref|>text<|/ref|><|det|>[[47, 633, 920, 700]]<|/det|>
+29. Chemello, F. et al. Degenerative and regenerative pathways underlying Duchenne muscular dystrophy revealed by single-nucleus RNA sequencing. Proceedings of the National Academy of Sciences of the United States of America 117, 29691-29701 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[47, 705, 941, 750]]<|/det|>
+30. Pang, X. et al. Targeting integrin pathways: mechanisms and advances in therapy. Signal Transduct Target Ther 8, 1 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[47, 755, 940, 823]]<|/det|>
+31. Shen, X., Storm, T. & Kay, M.A. Characterization of the relationship of AAV capsid domain swapping to liver transduction efficiency. Molecular therapy: the journal of the American Society of Gene Therapy 15, 1955-1962 (2007).  
+
+<|ref|>text<|/ref|><|det|>[[47, 827, 940, 872]]<|/det|>
+32. Ballon, D.J. et al. Quantitative Whole-Body Imaging of I-124-Labeled Adeno-Associated Viral Vector Biodistribution in Nonhuman Primates. Human gene therapy 31, 1237-1259 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[47, 876, 925, 921]]<|/det|>
+33. Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583-589 (2021).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[45, 44, 936, 752]]<|/det|>
+34. Mirdita, M. et al. ColabFold: making protein folding accessible to all. Nature methods 19, 679-682 (2022).35. Dong, X. et al. Force interacts with macromolecular structure in activation of TGF-beta. Nature 542, 55-59 (2017).36. Dong, X., Hudson, N.E., Lu, C. & Springer, T.A. Structural determinants of integrin beta-subunit specificity for latent TGF-beta. Nature structural & molecular biology 21, 1091-1096 (2014).37. Huang, P.S. et al. RosettaRemodel: a generalized framework for flexible backbone protein design. PloS one 6, e24109 (2011).38. Alford, R.F. et al. The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design. Journal of chemical theory and computation 13, 3031-3048 (2017).39. Duan, D., Goemans, N., Takeda, S., Mercuri, E. & Aartsma-Rus, A. Duchenne muscular dystrophy. Nat Rev Dis Primers 7, 13 (2021).40. Stedman, H.H. et al. The mdx mouse diaphragm reproduces the degenerative changes of Duchenne muscular dystrophy. Nature 352, 536-539 (1991).41. Bourg, N. et al. Co-Administration of Simvastatin Does Not Potentiate the Benefit of Gene Therapy in the mdx Mouse Model for Duchenne Muscular Dystrophy. Int J Mol Sci 23 (2022).42. Rouillon, J. et al. Serum proteomic profiling reveals fragments of MYOM3 as potential biomarkers for monitoring the outcome of therapeutic interventions in muscular dystrophies. Hum Mol Genet 24, 4916-4932 (2015).43. Eymard, B. et al. Primary adhalinopathy (alpha-sarcoglycanopathy): clinical, pathologic, and genetic correlation in 20 patients with autosomal recessive muscular dystrophy. Neurology 48, 1227-1234 (1997).44. Duclos, F. et al. Progressive muscular dystrophy in alpha-sarcoglycan-deficient mice. The Journal of cell biology 142, 1461-1471 (1998).45. Bryant, D.H. et al. Deep diversification of an AAV capsid protein by machine learning. Nature biotechnology 39, 691-696 (2021).46. Israeli, D. et al. An AAV-SGCG Dose-Response Study in a gamma-Sarcoglycanopathy Mouse Model in the Context of Mechanical Stress. Molecular therapy. Methods & clinical development 13, 494-502 (2019).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 770, 143, 797]]<|/det|>
+## Figures
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[50, 40, 640, 787]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 802, 115, 821]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 843, 621, 864]]<|/det|>
+## Computational rational AAV capsid design to bind to \(\alpha \beta \beta\) integrin  
+
+<|ref|>text<|/ref|><|det|>[[42, 881, 944, 947]]<|/det|>
+A. Overview of the design pipeline, including three steps: 1. Capsid 3D structures were obtained either from the PDB database or predicted by AlphaFold2. 2. The capsid VR4 loop was completely replaced by integrating the binding motif, which was extracted from receptor's natural binder, using RosettaRemodel
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 44, 950, 338]]<|/det|>
+protocol. 3. Top scored designs from the previous grafting step were docked onto the intended receptor in silico to verify the binding potential of the designed capsid. B. An illustration of the sampling for low- energy sequence- structure pairs during motif- grafting process. Capsid VR4 after removing the loop was colored in blue, extracted binding motif was colored in red. The sampled linkers and sequences (Fig. S1F) were labeled in green. C- D. The three lowest energy designs after grafting TGFβ3 (C) and TGFβ1 (D) into the capsid VR4. All top designs showed convergence in structures and sequences, suggesting sampling approached the global optimum. E- F. Retrospective docking of motif- grafted capsids (E. Cap9rh74_4um9 and F. Cap9rh74_5ffo) onto the αVβ6 structure. The left panels are illustrations of the structures with the lowest energy at the interface of capsid and integrin proteins (dG_separated: difference in free energy of two proteins). Both two newly designed VR4s (colored in green) were predicted to bind to the αVβ6 complex at very similar positions to natural binding motifs (colored in red). The right panels are scatter plots of dG_separated energy versus root-mean- square deviation (RMSD) from the lowest energy structure of all sampled docking positions.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[62, 81, 928, 780]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[45, 50, 128, 72]]<|/det|>
+<center>Fig. 2 </center>  
+<|ref|>image_caption<|/ref|><|det|>[[44, 802, 118, 821]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[44, 845, 785, 867]]<|/det|>
+Designed AAV_ITGs were well- produced and improved transduction via aVβ6 binding.  
+
+<|ref|>text<|/ref|><|det|>[[42, 882, 930, 947]]<|/det|>
+A. AAV titers of different AAV variants in bulked small-scale production in suspension three-day post-triple-transfection (2ml production, \(n = 6\) , one-way ANOVA). B. Western blot of VP proteins from purified AAVs showed similar VP ratios for designed AAV_ITGs capsids compared to AAV9 and AAV9rh74,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 44, 945, 271]]<|/det|>
+suggesting successful capsid assembly. C- D. VCN (C) and luciferase activity (D) of 293_aVβ6 after AAV infection (n=3- 4, one- way ANOVA). Both the two designed AAV_ITGs showed enhanced VCN and luciferase activities compared to AAV9rh74 and AAV9. E. Inhibition of cell entry of designed AAV_ITGs, but not for AAV9 or AAV9rh74, in 293_aVβ6 cells by aVβ6 recombinant protein. AAVs were preincubated with aVβ6 recombinant protein (r.ITGAV- B6) for 30 minutes at 37°C before infection (n=3, two- way ANOVA). SGCA recombinant protein (r.SGCA) was used as the control. F- K. Enhanced transduction of AAV_ITGs in in vitro human differentiated myotubes, but not in myoblasts. F. Representative images of the GFP signal of myotubes 48 hours post- infection (scale bar: 400μm). G- K. VCN and luciferase activities of AAV_ITGs in comparison with AAV9 and AAV9rh74 in myoblasts (G,I) and myotubes (H,K) (n=3- 4, one- way ANOVA).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[61, 70, 700, 789]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[52, 49, 106, 66]]<|/det|>
+<center>Fig. 3 </center>  
+<|ref|>image_caption<|/ref|><|det|>[[42, 803, 117, 821]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 844, 944, 887]]<|/det|>
+Designed AAV_ITGs showed enhanced transduction in skeletal and cardiac muscles while strongly liver- detargeted in vivo.  
+
+<|ref|>text<|/ref|><|det|>[[42, 904, 937, 947]]<|/det|>
+A. Scheme of in vivo experiment. AAVs (CMV_GFP-Luciferase) were injected intravenously into 6wo C57BL6 mice (n=4) at the dose of 1E13 vg/kg. B. Representative images of the bioluminescence signal
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 44, 955, 340]]<|/det|>
+20 days post- infection. C- D. VCN (C) and gene expression (D) (GFP mRNA level in the liver and luciferase activity in other organs) for different AAVs in liver, skeletal muscles, heart, lung, and kidney (n=4, one- way ANOVA). Both designed AAV_ITGs strongly detargeted from the liver compared to AAV9, while they significantly improved VCN and luciferase activities over AAV9rh74 (and AAV9 with AAV9rh74_4um9 variant) in skeletal and cardiac muscles, and were detected and expressed at low levels in lung and kidney. E- H. Comparison of the AAV9rh74_4um9 variant with other public myotropic AAVs (mAAVs) \(^{15,17}\) . E. Illustration of the differences between mAAVs and AAV9rh74_4um9 at modification sites in capsid protein and modification methods. F. The VR8 loop sequences of mAAVs compared to VR8 of their backbone AAV9, and VR4 of AAV9rh74_4um9 compared to VR4 of AAV9rh74. G- H. VCN (G) and gene expression (H) (GFP mRNA level in liver and luciferase activity in other organs) of different AAVs in liver, skeletal muscles, heart, lung, kidney, and brain (n=4, one- way ANOVA). AAV9rh74_4um9 showed similar VCN and gene expression in skeletal muscle to other mAAVs, while being significantly more strongly detargeted from the liver.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[63, 70, 792, 777]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 50, 115, 70]]<|/det|>
+<center>Fig. 4 </center>  
+<|ref|>image_caption<|/ref|><|det|>[[42, 803, 118, 821]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 844, 949, 887]]<|/det|>
+Low- dose gene transfer by LICA1 was more effective and better at restoring dystrophic phenotypes than AAV9 in the DMD mouse model.  
+
+<|ref|>text<|/ref|><|det|>[[42, 903, 950, 946]]<|/det|>
+A- B. Comparison of transduction efficacy between AAV9 and LICA1 in all three muscles that were tested, in terms of VCN (A), and \(\mu\) Dys RNA level (B). C. Comparison of percentage of successfully transduced
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 45, 953, 476]]<|/det|>
+(dystrophin- positive) fibers in all three muscles that were tested. Note that TA, Qua, Dia muscles are presented in increasing order of severity. D- E. Comparison of restoration levels in dystrophic histological features between AAV9 and LICA1 in all three muscles that were tested, in terms of percentage of centro- nucleated fibers (D) and fibrosis level (E). Illustrated images in C- E are of quadriceps muscles (scale bar: \(100\mu \mathrm{m}\) ). F. Serum MYOM3 level – indicator of muscle damage – 4 weeks post- injection ( \(n = 5\) , one- way ANOVA). G- I. Comparison of functional restoration between AAV9 and LICA1 by Escape test – global force measurement (G, \(n = 6\) ), tetanus force of TA muscle (H, \(n = 10 - 12\) ), and twitch force of TA muscle (I, \(n = 9 - 12\) ). K- N. Comparison of restoration in global transcriptomic changes in quadriceps muscle between AAV9 and LICA1 ( \(n = 4\) , adjusted p- values \(< 0.05\) ). K. The heatmap presents the log2 fold change (log2FC) in comparison to WT muscle for all 8717 DEGs found in mdx muscle (compared to WT). The log2FC values are illustrated in row Z- scores, colored from blue to red, arranged from lowest to highest. L- N. Volcano plots of multiple comparisons illustrate transcriptomic changes before and after AAV treatment. As a reference, 4216 downregulated and 4501 upregulated DEGs found in mdx were colored blue and red, respectively, in all volcano plots. Among these DEGs, the number of genes found to be significantly different in each pair- wise comparison were labeled in the upper corners. L. Volcano plots comparing mdx/WT transcriptomes. M. Volcano plots comparing mdx to AAV- treated transcriptomes, in which significant DEGs are the genes correctly restored after AAV treatment. N. Volcano plots comparing AAV treatment to WT, in which significant DEGs are the genes that are not or incompletely restored after AAV treatment.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[50, 66, 789, 787]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[48, 50, 111, 68]]<|/det|>
+<center>Fig. 5 </center>  
+<|ref|>image_caption<|/ref|><|det|>[[44, 803, 118, 821]]<|/det|>
+<center>Figure 5 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 844, 931, 887]]<|/det|>
+Low- dose gene transfer by LICA1 was better at restoring dystrophic phenotypes and functionality than AAV9 in the LGMDR3 mouse model.  
+
+<|ref|>text<|/ref|><|det|>[[42, 904, 949, 946]]<|/det|>
+A. Scheme of in vivo experiment: LICA1 (9rh74_4um9) or AAV9 were injected intravenously into a 4wo SGCA-KO mouse model at the dose of 5E12 vg/kg (expression cassette: hACTA1_hSGCA_HBB2-pA, n=3-
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 45, 951, 500]]<|/det|>
+5). Three skeletal muscles in increasing order of severity, TA, Qua, and Dia, were analysed 4 weeks postinjection. B-D. Comparison of transduction efficacy between AAV9 and LICA1 in all three muscles that were tested in terms of VCN (B), hSGCA mRNA level (C), and percentage of succesfully transduced (SGCA- positive) fibers (D). E-G. Comparison of restoration levels in dystrophic histological features between AAV9 and LICA1 in all three muscles that were tested in terms of percentage of centro- nucleated fibers (E), fibrosis level (F), and fiber size distribution (G). Illustrated images in D-F are of quadriceps muscles (scale bar: \(100 \mu m\) ). H-K. Comparison of functional restoration between AAV9 and LICA1 using the escape test – global force measurement (H), tetanus force of TA muscle (I), and serum MYOM3 level – indicator of muscle damage (K). L-O. Comparison of restoration in global transcriptomic changes in quadriceps muscle between AAV9 and LICA1 (n=4, adjusted p values < 0.05). L. The heatmap presents the log2 fold change (log2FC) in comparison to WT muscle for all 8591 DEGs found in KO muscle (compared to WT). The log2FC values are illustrated by row Z-scores, colored from blue to red, arranged from lowest to highest. M-O. Volcano plots of multiple comparisons illustrate transcriptomic changes before and after AAV treatment. As a reference, 4035 downregulated and 4556 upregulated DEGs found in KO were colored blue and red, respectively, in all volcano plots. Among these DEGs, the number of genes found to be significantly different in each pair-wise comparison were labeled in the upper corners. M. Volcano plots comparing KO/WT transcriptomes. N. Volcano plots comparing KO to AAV-treated transcriptomes, in which significant DEGs are the genes correctly restored after AAV treatment. O. Volcano plots comparing AAV treatment to WT, in which significant DEGs are the genes that are not or incompletely restored after AAV treatment.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 519, 312, 547]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 570, 767, 590]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 607, 300, 681]]<|/det|>
+- ALICA1supp.pdf- DatafileS2DEGSGCA.xlsx- DatafileS1DEGDMD.xlsx
+
+<--- Page Split --->

preprint/preprint__00d7abe0a4b5c990501df86cac16b26584184537e4e60f6f33e33b81c4a5b14a/images_list.json

@@ -0,0 +1,55 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "FIG. 2. Protocols and bubble observation. a) Experimental protocol. Ellipses illustrate the cloud magnetization at different \\(t\\) and the two sketches show the energy landscape for positive (up) and negative (down) \\(\\delta\\) . b) Collection of integrated magnetization profiles \\(Z(x)\\) after different waiting times \\(t\\) . For each value of \\(t\\) , 7 different realizations are shown. c) Magnetization profiles for the realizations marked with arrows in panel (b). d) Measured probability \\(P\\) (empty circles) to observe a shot with a bubble at fixed time is shown. The probability is well fitted to an exponential curve (grey continuous line) until it saturates to 1.",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "FIG. 3. Measurement of the evolution of \\(Z(x)\\) in time after the ramp on \\(\\delta\\) for \\(\\Omega_{R} / 2\\pi = 300\\mathrm{Hz}\\) , for \\(\\delta_{f} / \\Omega_{R} = -1.70\\) in (a) and \\(-1.79\\) in (b). c) Value of \\(F_{\\mathrm{t}}\\) evaluated in the \\(20\\mu \\mathrm{m}\\) central region of the cloud are fitted by the empirical expression reported in the text (squares for data in (a) and pentagons for (b)). Error bars are the standard deviation over up to ten repetitions. d-e) Numerical simulations for \\(\\delta_{f} / \\Omega_{R} = -1.52\\) in (d) and \\(-1.585\\) in (e). Value of \\(F_{\\mathrm{t}}\\) for the simulations (triangles for data in (d) and stars for (e)). The red dashed lined are linear fits in the exponentially decaying part. g) Experimental \\(\\tau\\) and numerical \\(\\tau_{\\mathrm{sim}}\\) timescale of the bubble formation as a function of \\((\\delta_{f} - \\delta_{c}) / |\\kappa |n\\) . Error bars include statistical uncertainties on the fit and uncertainty on the \\(\\delta_{f} - \\delta_{c}\\) coming from magnetic field stability and calibration. Numerical timescale of the bubble formation \\(\\tau_{\\mathrm{sim}}\\) is shown before (light symbols) and after (dark symbol) rescaling. The empty triangle is an experimental point taken with a preparation ramp twice slower than the others, to verify the impact on the nucleation time resulting from a residual non-adiabaticity in the preparation of the sample.",
+    "footnote": [],
+    "bbox": [
+      [
+        270,
+        92,
+        710,
+        500
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "FIG. 4. Decay time \\(\\tau\\) and \\(\\tau_{\\mathrm{sim}}\\) and instanton theory. Experimental \\(\\tau\\) and simulations \\(\\tau_{\\mathrm{sim}}\\) are obtained as explained in the text for \\(\\Omega_{R} / 2\\pi = 300,400,600\\) and \\(800\\mathrm{Hz}\\) . A rescaling common to all \\(\\Omega_{R}\\) is applied to the horizontal axes of the simulation; see text. Dashed and full curves are fits of the experimental and simulation data according to the instanton formula. Full markers stand for simulation results while empty markers for experimental data. Error bars include statistical uncertainties on the fit and uncertainty on the \\(\\delta_{f}\\) due to on the magnetic field stability.",
+    "footnote": [],
+    "bbox": [
+      [
+        272,
+        92,
+        720,
+        422
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "FIG. M1. \\(\\tau\\) vs \\(\\tau_{50\\%}\\) for experimental (a) and numerical (b) results. The two quantity are compatible to each other within error bars in experimental results and show only small deviation in simulation data. Color code for the points is the same used in the main text and the blue line marks \\(\\tau = \\tau_{50\\%}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        270,
+        663,
+        725,
+        840
+      ]
+    ],
+    "page_idx": 9
+  }
+]

preprint/preprint__00d7abe0a4b5c990501df86cac16b26584184537e4e60f6f33e33b81c4a5b14a/preprint__00d7abe0a4b5c990501df86cac16b26584184537e4e60f6f33e33b81c4a5b14a.mmd

@@ -0,0 +1,349 @@
+
+# Observation of false vacuum decay via bubble formation in ferromagnetic superfluids  
+
+Anna Berti  CNR- INO, Pitaevskii BEC Center, Università di Trento  https://orcid.org/0000- 0003- 3073- 9554  
+
+Riccardo Cominotti  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+Chiara Rogora  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+Ian Moss  School of Mathematics, Statistics and Physics, Newcastle University  
+
+Thomas Billam  Newcastle University  
+
+Iacopo Carusotto  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+Giacomo Lamporesi  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+Alessio Recati  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+Gabriele Ferrari  Universita' di Trento and INO- CNR BEC Center  https://orcid.org/0000- 0003- 1827- 5048  
+
+Alessandro Zenesini ( \(\boxed{ \begin{array}{r l} \end{array} }\) alessandro.zenesini@ino.it)  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+Article  
+
+Keywords:  
+
+Posted Date: June 8th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 2923763/v1  
+
+License: © \(\circledast\) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.
+
+<--- Page Split --->
+
+Version of Record: A version of this preprint was published at Nature Physics on January 22nd, 2024. See the published version at https://doi.org/10.1038/s41567-023-02345-4.
+
+<--- Page Split --->
+
+# Observation of false vacuum decay via bubble formation in ferromagnetic superfluids  
+
+A. Zenesini \(^{1,2}\) , 
+A. Berti \(^{1}\) , 
+R. Cominotti \(^{1}\) , 
+C. Rogora \(^{1}\) , 
+I. 
+G. Moss \(^{3}\) , 
+T. 
+P. Billam \(^{4}\) , 
+I. Carusotto \(^{1}\) , 
+G. Lamporesi \(^{1,2}\) , 
+A. Recati \(^{1}\) , and 
+G. Ferrari \(^{1,2}\) \(^{1}\) Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, 38123 Trento, Italy \(^{2}\) Trento Institute for Fundamental Physics and Applications, INFN, 38123 Trento, Italy \(^{3}\) School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK and \(^{4}\) Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK (Dated: May 22, 2023)  
+
+Metastability is ubiquitous in nature and is observed through the crossing of an energy barrier toward a configuration of lower energy as, for example, in chemical processes [1] or electron field ionization [2]. In classical many- body systems, metastability naturally emerges in the presence of a first- order phase transition and finds a prototypical example in supercooled vapour. In the last decades, the extension to quantum field theory and quantum many- body systems has attracted significant interest in the context of statistical physics [3, 4], protein folding [5, 6], and cosmology [7- 9], where thermal and quantum fluctuations are expected to trigger the transition from the metastable state (false vacuum) to the ground state (real vacuum) via the probabilistic nucleation of spatially localized bubbles [10, 11]. However, the long- standing theoretical progress in estimating the relaxation rate of the metastable field via bubble nucleation has not yet found a counterpart in terms of experimental observations. Here we experimentally observe and characterize bubble nucleation in isolated and coherently- coupled atomic superfluids, and support our observations with numerical simulations. The agreement between our results and a novel analytic formula based on instanton theory confirms the quantum- field character of the observed decay, and promotes coherently- coupled atomic superfluids as emulators of out- of- equilibrium quantum field phenomena.  
+
+A supercooled gas is a classic example of a metastable state which exists just across a first order phase transition. The passage to the ground state (the liquid phase) is mediated by resonant bubble nucleation when the energy gain provided by the liquid bulk is compensated by the cost of the surface tension. This energy balance leads to a critical bubble size and a stochastic
+
+<--- Page Split --->
+
+formation of the bubble typically occurs around nucleation spots given by impurities in the gas or imperfections at the container. The extension of this idea to a quantum many- body or a quantum field system has attracted extensive attention in a wide range of scenarios and length scales, from the understanding of early universe [7- 9] to the characterization of spin chains [3, 4]. In all these models, the metastable state at the origin of the bubble nucleation, is identified as "false vacuum" and the role of surface tension is taken by a genuinely quantum term. In the purest form, the false vacuum decay into the ground state would take place through quantum vacuum fluctuations [10, 11] (similarly to impurities in the classical case). However, as for example in the early universe, the tunnelling is equally likely to be boosted by thermal fluctuations, and the process would be of the type styled "vacuum decay at finite temperature" [12] (see [13, 14] for a review).  
+
+In the cosmological case, the energy scales are well above any that are accessible to experiments, and the phenomenon of false vacuum decay remains one of the most important yet untested processes considered in theoretical high energy physics. Recently, the extreme flexibility of neutral and charged atoms tabletop experiments and the advances of classical and quantum computer algorithms have paved the way for the proposal of experimental environments [15- 22] and virtual simulators [23, 24]. Up to now only numerical results have been achieved and the experimental observation of an analogue to false vacuum decay would therefore be of high significance.  
+
+In tabletop experiments, the observation of bubble nucleation requires several ingredients which are difficult to arrange simultaneously. First, a mean- field interaction- induced energy landscape composed of an asymmetric double well represents the minimal requirement for the decay from the metastable state to the absolute ground state via macroscopic tunneling across the energy barrier, followed by relaxation; see sketch in Fig. 1. Second, unlike in the ordinary quantum tunneling of a single particle [1, 25, 26], it is an effective field describing the system that changes state. Third, the time resolution of the experiment should cover many orders of magnitude to allow for the investigation of the predicted exponential time- dependence on the tuning parameters. This must be associated to a high stability and accuracy of the tuning parameters. An extended ferromagnetic superfluid [27] possesses the ideal properties to act as a field simulator, in particular its first order phase transition character, the long range coherence and the flexibility to control its experimental parameters within a stable and isolated environment. In tight analogy with supercooling, in an extended quantum system the presence of a spatial region with different magnetization to the bulk carries a positive kinetic energy due to the winding of the field at the interface, see Fig. 1.  
+
+In this letter, we present the experimental observation of bubble formation via false vacuum decay in a quantum system. We observe that the bubble nucleation time scales exponentially with
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+  
+
+FIG. 1. Mean- field energy and bubble formation. The cloud is initially prepared with all the atoms in \(|\uparrow \rangle\) (A). While the single \(|\downarrow \rangle\) spin state is energetically lower ( \(E_{\downarrow} < E_{\uparrow}\) ) in the center of the cloud, in the low density tails the situation is opposite. The interface has a positive energy which adds up to the double minimum energy landscape emerging from the ferromagnetic interaction. Macroscopic quantum tunneling can take place resonantly to the bubble state (B) which has a \(|\downarrow \rangle\) bubble in the center, whose core energy gain compensates for the interface energy cost. The barrier crossing can be triggered by quantum fluctuations in the zero- temperature case (dashed arrow) or by thermal fluctuations at finite temperature (empty arrow). After the tunneling process, in the presence of dissipation, the bubble increases in size to reach the ground state (C), without coming back to (A).  
+
+an experimental parameter that is connected to the energy barrier properties. Theoretical and numerical simulations support our observations and allow us to confirm the quantum field origin of the decay and its thermal activation.  
+
+The experimental platform is composed of a bosonic gas of \(^{23}\mathrm{Na}\) atoms, optically trapped and cooled below the condensation temperature. The gas is initially prepared in the internal state \(|F,m_{F}\rangle = |1, - 1\rangle = |\downarrow \rangle\) , where \(F\) is the total angular momentum and \(m_{F}\) its projection on the quantization axis. A microwave radiation with amplitude \(\Omega_{R}\) coherently couples the \(|\downarrow \rangle\) state to \(|2, - 2\rangle = |\uparrow \rangle\) . The relevant scattering lengths for such a two- level system are \(a_{\downarrow \downarrow} = 54.5a_{0}\) , \(a_{\uparrow \uparrow} = 64.3a_{0}\) , and \(a_{\downarrow \uparrow} = 54.5a_{0}\) , and lead to the condition \(\Delta a = (a_{\uparrow \uparrow} + a_{\downarrow \downarrow}) / 2 - a_{\downarrow \uparrow} < 0\) , i.e., to a system with a ferromagnetic ground state [27].  
+
+The trapping potential is axially symmetric and harmonic in all three directions, but strongly asymmetric (axial and radial trapping frequencies \(\omega_{x} / 2\pi = 20\mathrm{Hz}\) and \(\omega_{\rho} / 2\pi = 2\mathrm{kHz}\) ), producing an elongated system with inhomogeneous density and spatial size given by the longitudinal and
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>FIG. 2. Protocols and bubble observation. a) Experimental protocol. Ellipses illustrate the cloud magnetization at different \(t\) and the two sketches show the energy landscape for positive (up) and negative (down) \(\delta\) . b) Collection of integrated magnetization profiles \(Z(x)\) after different waiting times \(t\) . For each value of \(t\) , 7 different realizations are shown. c) Magnetization profiles for the realizations marked with arrows in panel (b). d) Measured probability \(P\) (empty circles) to observe a shot with a bubble at fixed time is shown. The probability is well fitted to an exponential curve (grey continuous line) until it saturates to 1. </center>  
+
+radial Thomas- Fermi radius \(R_{\mathrm{x}} = 200\mu \mathrm{m}\) and \(R_{\rho} = 2.5\mu \mathrm{m}\) . At the end of each experimental realization, we image the two spin states independently and extract their density distributions. The transverse confinement is tight enough to suppress the radial spin dynamics of the condensate. We therefore integrate each image along the transverse direction and obtain the integrated 1D density profiles \(n_{\uparrow}(x)\) and \(n_{\downarrow}(x)\) , from which we extract the profile of the relative magnetization \(Z(x) = [n_{\uparrow}(x) - n_{\downarrow}(x)] / [n_{\uparrow}(x) + n_{\downarrow}(x)]\) .  
+
+The coupled two- level system can be studied by separately treating the total density ( \(n = n_{\uparrow} + n_{\downarrow}\) ) and the spin ( \(n_{\uparrow} - n_{\downarrow} = nZ\) ) degrees of freedom. While the density is simply dominated by a continuity equation, the spin degree of freedom is ruled by a magnetic mean- field Hamiltonian, which shows a first- order phase transition in the central region of the cloud for \(\Omega_{R} < |\kappa |n\) , where
+
+<--- Page Split --->
+
+\(\kappa \propto \Delta a\) is the relevant interaction parameter; see Methods.  
+
+The first- order phase transition originates from a symmetry breaking when the energy landscape as a function of the magnetization \(Z\) goes from a single to a double minimum at \(\Omega_{R}< |\kappa |n =\) \(2\pi \times 1150\mathrm{Hz}\) . At fixed \(\Omega_{R}\) , the experimentally tunable parameter is the detuning \(\delta\) between the two- level system and the coupling radiation. For small enough \(|\delta |\) , the energy landscape \(E(Z)\) is represented by an asymmetric double well, that turns symmetric for \(\delta = 0\) . In particular, for positive \(\delta\) , the energy is minimized by positive values of \(Z\) , and viceversa The relevant parameter for the bubble nucleation is the shape (height and width) of the energy barrier separating the two wells that the system needs to overcome as a field, i.e., in a macroscopic manner. This depends on \(\delta\) , \(n\) and \(\Omega_{R}\) . When \(|\delta |\) exceeds a critical value \(\delta_{c}\) , the metastable well disappears [27]. Borrowing the nomenclature from ferromagnetism, \(\pm \delta_{c}\) correspond to the edges of the hysteresis region and their value depends both on \(\Omega_{R}\) and \(|\kappa |n\) .  
+
+Figure 2(a) illustrates the experimental protocol. We first transfer the whole system from \(|\downarrow \rangle\) to \(|\uparrow \rangle\) with a \(\pi\) pulse. While keeping \(\Omega_{R}\) constant, \(\delta\) is linearly ramped down from \(\delta_{i} / 2\pi = 5.5\mathrm{kHz}\) to a variable \(\delta_{f}\) on a timescale between 20 and 60 ms. Since the ramp starts with \(\delta \gg \Omega_{R}\) , the system follows the spin rotation remaining in the local ground state until \(\delta < 0\) when such a local ground state becomes a metastable state; see inset in Fig. 2(a). Once \(\delta_{f}\) is reached, the states are independently imaged after a variable waiting time \(t\) .  
+
+If \(\delta_{f} > 0\) , the whole system is and remains in the absolute ground state \(|\uparrow \rangle\) , whereas for \(\delta_{f}< 0\) , after a variable time, a macroscopic region in the central part of the system flips to \(|\downarrow \rangle\) , generating a bubble; see examples in Fig. 2(b) and magnetization profiles in (c). On average the bubble occurrence probability is larger if the waiting time is longer [see Fig. 2(b) and (d)]. For a quantitative analysis, at each \(t\) , we repeat the measurement up to 10 times in order to investigate the statistical formation of bubbles. Note that, while in uniform systems the bubbles would stochastically nucleate in random spatial positions, our nonuniform density profile of the atomic sample strongly favors the nucleation at the center of the cloud, where \(\delta_{f}\) is closest to \(\delta_{c}\) .  
+
+A useful quantity to characterize the bubble nucleation in time is \(F_{t} = (1 + \langle Z\rangle_{t} / \langle Z\rangle_{t = 0}) / 2\) , which was used in Ref. [3] to compare an exact diagonalization approach in a zero- temperature spin chain to instanton predictions. Here \(\langle \cdot \rangle_{t}\) stands for \(Z\) measured at time \(t\) and averaged over many realizations. In Fig. 3(a) and (b), we show the average magnetization \(\langle Z\rangle_{t}\) profile as a function of waiting time for two values of detuning. Since the bubble appears always in the center of the system, to compute \(F_{t}\) , we extract the mean magnetization \(\langle Z\rangle_{t}\) in the central 20- \(\mu \mathrm{m}\) - wide region \((\approx R_{x} / 10)\) . The resulting \(F_{t}\) , plotted in panel (c), initially remains flat, and then it exponentially
+
+<--- Page Split --->
+
+decays because of the bubble nucleation. Both features were also observed in Ref. [3] and the understanding of the starting plateau is still an open question from the theoretical point of view. We find that the measured \(F_{t}\) is well described by the empirical function \((1 - \epsilon) / \sqrt{1 + (e^{t / \tau} - 1)^{2}} + \epsilon\) , which is 1 for \(t = 0\) , scales as \(t^{2}\) for small \(t\) and is exponentially decaying to \(\epsilon\) for large \(t\) . The two fitting parameters are \(\tau\) , that describes the characteristic timescale for the bubble formation, and \(\epsilon\) , that takes into account that the asymptotic magnetization \(Z_{t = \infty}\) can be different from the one of the ground state, \(Z_{TV}\) ( \(F = 0\) ). Note that the timescale \(\tau\) is related to the exponential decay, while the empirical formula takes into account an initial plateau present in the averaged magnetisation \(F_{t}\) . (in Methods we show that the plateau length and \(\tau\) are strictly connected).  
+
+Numerical simulations based on 1D Gross- Pitaevskii equations, reported in Fig. 3(d) and (e), qualitatively reproduce the experimental observations. In the numerics, classical noise is included to simulate the effect of a finite temperature (more details can be found in Methods). Data in Fig. 3(d) and (e) are obtained by averaging over 1000 different noisy realizations of the real- time dynamics: the large statistics allows us to directly extract the exponential decay time \(\tau_{\mathrm{sim}}\) through a linear fit of \(\ln (F_{t})\) .  
+
+In Fig. 3(g), we report six experimental values of \(\tau\) obtained for \(\Omega_{R} = 2\pi \times 300 \mathrm{Hz}\) , plotted as a function of the distance from the critical detuning, \((\delta_{f} - \delta_{c}) / |\kappa |n\) . The results show an exponential dependence on the tuning parameter over two orders of magnitude, from a few to hundreds of ms. Such a sensitivity to a parameter is remarkable for ultracold atoms experiments. In particular, the experimental observation of the quasi- exponential dependence of \(\tau\) with respect to \(\delta_{f}\) in an interval of the order of \(100 \mathrm{Hz}\) critically relies on the magnetic field stability better than a few tens of \(\mu \mathrm{G}\) [28].  
+
+The values of \(\tau_{\mathrm{sim}}\) for the simulations [light symbols in Fig. 3(g)] qualitatively show the same behaviour of the experimental data. The agreement becomes even quantitative [dark symbols in Fig. 3(g)], by using a rescaling of \(|\kappa |n\) and a small shift of \(\delta\) . The need for such a rescaling was demonstrated in Ref. [27], as a consequence of dimensionality, noise and non complete adiabaticity of the preparation protocol. In Fig. 4, we compare experimental \(\tau\) and rescaled numerical \(\tau_{\mathrm{sim}}\) , for four different values of \(\Omega_{R}\) , by using the same rescaling for all four panels.  
+
+Our observations are consistent with the scenario of a condensate spinor field initially in a ferromagnetic metastable state, which decays via macroscopic tunneling to bubbles (domains) of the ferromagnetic ground state. The escape of a quantum field from the false vacuum, occurring via macroscopic tunneling, and the bubble formation finds a suitable description in terms of an instanton, or critical solution to the field equations in imaginary time [10–12]. Such a theory
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>FIG. 3. Measurement of the evolution of \(Z(x)\) in time after the ramp on \(\delta\) for \(\Omega_{R} / 2\pi = 300\mathrm{Hz}\) , for \(\delta_{f} / \Omega_{R} = -1.70\) in (a) and \(-1.79\) in (b). c) Value of \(F_{\mathrm{t}}\) evaluated in the \(20\mu \mathrm{m}\) central region of the cloud are fitted by the empirical expression reported in the text (squares for data in (a) and pentagons for (b)). Error bars are the standard deviation over up to ten repetitions. d-e) Numerical simulations for \(\delta_{f} / \Omega_{R} = -1.52\) in (d) and \(-1.585\) in (e). Value of \(F_{\mathrm{t}}\) for the simulations (triangles for data in (d) and stars for (e)). The red dashed lined are linear fits in the exponentially decaying part. g) Experimental \(\tau\) and numerical \(\tau_{\mathrm{sim}}\) timescale of the bubble formation as a function of \((\delta_{f} - \delta_{c}) / |\kappa |n\) . Error bars include statistical uncertainties on the fit and uncertainty on the \(\delta_{f} - \delta_{c}\) coming from magnetic field stability and calibration. Numerical timescale of the bubble formation \(\tau_{\mathrm{sim}}\) is shown before (light symbols) and after (dark symbol) rescaling. The empty triangle is an experimental point taken with a preparation ramp twice slower than the others, to verify the impact on the nucleation time resulting from a residual non-adiabaticity in the preparation of the sample. </center>  
+
+provides a threshold energy scale, below (above) which quantum (thermal) fluctuations dominate: zero- \(T\) quantum tunneling is expected to be dominant when \(T\) is below the critical temperature \(T^{*} = \hbar |\kappa |n / k_{B}\) . Considering the peak density in our system, we estimate \(T^{*} \simeq 50 \mathrm{nK}\) . Although the temperature of our condensates is \(T = 1.5 \mu \mathrm{K} \gg T^{*}\) , given the harmonic confinement and the
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+<center>FIG. 4. Decay time \(\tau\) and \(\tau_{\mathrm{sim}}\) and instanton theory. Experimental \(\tau\) and simulations \(\tau_{\mathrm{sim}}\) are obtained as explained in the text for \(\Omega_{R} / 2\pi = 300,400,600\) and \(800\mathrm{Hz}\) . A rescaling common to all \(\Omega_{R}\) is applied to the horizontal axes of the simulation; see text. Dashed and full curves are fits of the experimental and simulation data according to the instanton formula. Full markers stand for simulation results while empty markers for experimental data. Error bars include statistical uncertainties on the fit and uncertainty on the \(\delta_{f}\) due to on the magnetic field stability. </center>  
+
+exchange interaction which pushes the thermal component away from the condensate, we estimate an effective local temperature of about \(250\mathrm{nK}\) in the condensate region which is still larger than \(T^{*}\) in the region where the bubbles appear. Therefore we expect the macroscopic tunneling to be in the thermally activated regime.  
+
+Within the instanton approach, the bubble nucleation probability has the characteristic timescale \(\tau\) , which has an exponential dependence \(A(E_{c} / k_{B}T)^{- 1 / 2}e^{E_{c} / k_{B}T}\) . \(E_{c}(\delta ,\kappa n,\Omega_{R})\) is the energy of the critical solution and strongly depends on the shape of the many- body potential and in particular on the barrier height (Fig. 1). The pre- factor \(A\) depends on fluctuations about the critical solution, but there are very few models for which this factor is calculable, at present. We therefore regard the pre- factor \(A\) as a fitting parameter in the following analysis. We can estimate \(E_{c}\) , and provide an analytical expression in the limit of vanishing metastable well (small \(\delta_{f} - \delta_{c}\) ), by considering a homogeneous 1D system. The potential for the magnetization field \(Z\) can be
+
+<--- Page Split --->
+
+written as (see, e.g., Ref.[27] )  
+
+\[V(Z) = \kappa n Z^{2} - 2\Omega (1 - Z^{2})^{1 / 2} - 2\delta_{f}Z \quad (1)\]  
+
+and the instanton energy reads  
+
+\[\frac{E_{c}}{\hbar|\kappa|n} = \sqrt{\frac{\hbar n}{2m|\kappa|}}\int_{Z_{T P}}^{Z_{F V}}\left[\frac{V(Z) - V(Z_{F V})}{|\kappa|n(1 - Z^{2})}\right]^{1 / 2}d Z, \quad (2)\]  
+
+where \(Z_{T P}\) is the classical turning point (in the inverted potential \(V\) ) and \(Z_{F(alse)V(acuum)}\) the value of the magnetization of the metastable state. Most of our data are taken in a regime where the barrier is much smaller than the depth of the ground state well. In this limiting case the instanton energy reads  
+
+\[\frac{E_{c}}{\hbar|\kappa|n}\propto \sqrt{\frac{\hbar n}{2m|\kappa|}}\left(\frac{\delta_{f} - \delta_{c}}{|\kappa|n}\right)^{\frac{5}{4}}\left(\frac{\Omega_{R}}{|\kappa|n}\right)^{\frac{1}{6}}\left(\frac{|\delta_{c}|}{|\kappa|n}\right)^{-\frac{1}{4}}, \quad (3)\]  
+
+where \(\delta_{c} = \kappa n[1 - (\Omega /(|\kappa |n))^{\frac{2}{3}}]^{\frac{3}{2}}\) : see Methods. We compare the previous expression to the experimental data and numerical simulations using a two- parameter fit \(\ln \tau = \ln A + b\hat{E}_{c} + \ln (b\hat{E}_{c}) / 2\) , where \(\hat{E}_{c} = \sqrt{2m|\kappa| / (\hbar n)} E_{c} / \hbar |\kappa |n\) is the rescaled energy. The results are shown in Fig. 4. Considering the approximations used to derive Eq. (3) – in particular the absence of the trapping potential, no phase fluctuations and small barrier – the agreement is remarkable and the instanton theory appears to capture the main dependence of the false vacuum decay rate on the microscopic parameter \(\delta_{f}\) which is responsible for the broken \(\mathbb{Z}_{2}\) symmetry.  
+
+In this paper, we present solid evidence of the thermally- induced macroscopic tunneling of a coherent quantum field, manifested by bubbles of true vacuum phase nucleating in a false vacuum state. The true and false vacua are the local and global energy minimum of a ferromagnetic atomic Bose- Einstein condensate, respectively. The experimental results clearly show an exponential dependence of the decay rate on the microscopic parameters and the hysteric region width. Such a dependence is successfully captured by numerical simulations and more remarkably by a simple instanton theory based on a reduced energy functional for the magnetisation. Our platform paves the way to explore the process of bubble formation and growth in intricate detail, and to build a new bridge between low energy and high energy phenomena characterized by metastability within a first order phase transition. In this spirit our work opens up new avenues in the understanding of early universe, as well as ferromagnetic quantum phase transitions. The possibility of engineering the barrier properties via injection of tailored noise and of deterministically seeding bubbles are promising future directions for experimental investigations with focus on the role of dissipation,
+
+<--- Page Split --->
+
+the existence of shortcut- to- adiabaticity [29, 30], the creation of entanglement, of domain wall confinement [31], and relativistic and non relativistic aspects of the bubble nucleation and dynamics. Furthermore an experimental effort towards colder systems would allow us to reach the tunneling regime dominated by quantum fluctuations. A natural extension of the present work goes to dimensionality larger than one, where the theoretical treatment is challenging.  
+
+Acknowledgements - We thank A. Biella and P. Hauke for fruitful discussions. We acknowledge funding from Provincia Autonoma di Trento, from INFN through the FISH project, from the Italian MIUR under the PRIN2017 project CEnTraL (Protocol Number 20172H2SC4), from the European Union's Horizon 2020 research and innovation Programme through the STAQS project of QuantERA II (Grant Agreement No. 101017733), from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 804305), from the UK Quantum Technologies for Fundamental Physics programme (grants ST/T00584X/1 and ST/W006162/1) and from PNRR MUR project PE0000023- NQSTI. This work was supported by Q@TN, the joint lab between University of Trento, FBK - Fondazione Bruno Kessler, INFN - National Institute for Nuclear Physics and CNR - National Research Council.  
+
+Author contribution - G.F., G.L. and A.Z. conceived the project. R.C., C.R., and A.Z. performed the experiments and analyzed the data. A.B., I.C., I.M., T.B., and A.R. performed the theoretical analysis. A.B. developed the numerical code and performed the simulations. G.F. supervised the project. All authors contributed to the discussion and interpretation of the results and paper writing.  
+
+Data availability - Data in paper figures are available in Extended data. Two dimensional raw atomic cloud pictures from all experimental runs and analysis code are available upon request to A.Z.  
+
+Corresponding author - Correspondence to A.Z., G.L. and A.R.  
+
+Ethics declarations: Competing interests - The authors declare no competing interests.
+
+<--- Page Split --->
+
+## METHODS  
+
+### I. FERROMAGNETISM IN ELONGATED MIXTURES  
+
+The ferromagnetic properties of atomic superfluid coupled mixtures are experimentally measured and discussed in [27]. Here we summarize the key ingredients which help understanding the results presented in the main text of the article.  
+
+Our system is composed of two sodium hyperfine states \(|F,m_{F}\rangle = |2, - 2\rangle \equiv |\uparrow \rangle\) and \(|1, - 1\rangle \equiv\) \(|\downarrow \rangle\) , where \(F\) is the total angular momentum and \(m_{F}\) its projection. The two populations \(n_{\uparrow}(x,y)\) and \(n_{\downarrow}(x,y)\) are independently measured by shadow imaging. Starting from the two two- dimensional pictures of the cloud, we determine the relative magnetization \(Z(x)\) as \(Z(x) =\) \((n_{\uparrow}(x) - n_{\downarrow}(x)) / n(x)\) , where \(n_{\uparrow ,(\downarrow)}(x) = \int n_{\uparrow ,(\downarrow)}(x,y)dy\) and \(n(x) = \int (n_{\uparrow}(x,y) + n_{\downarrow}(x,y))dy\) are the 1D integrated densities. The integration along \(y\) takes advantage of the suppressed radial dynamics. In local density approximation (LDA), the energy per particle associated to the spin channel of the mixture is  
+
+\[E(Z,\phi)\propto -\frac{\delta_{f}}{2} Z + \frac{\kappa n}{2} Z^{2} - \Omega_{\mathrm{R}}\sqrt{1 - Z^{2}}\cos \phi \quad (4)\]  
+
+where the phase \(\phi\) is the relative phase between \(|\uparrow \rangle\) and \(|\downarrow \rangle\) . The detuning \(\delta_{f}\) used in the text is equal to \(\delta_{\mathrm{B}} + n\Delta\) where \(\delta_{\mathrm{B}}\) is the experimental controllable detuning. The quantity \(\kappa\) and \(\Delta\) are associated to the collisional proprieties of the mixture and are  
+
+\[\begin{array}{l}\Delta \equiv \frac{g_{\downarrow\downarrow} - g_{\uparrow\uparrow}}{2\hbar} < 0\\ \kappa \equiv \frac{g_{\downarrow\downarrow} + g_{\uparrow\uparrow}}{2\hbar} -\frac{g_{\downarrow\uparrow}}{\hbar} < 0 \end{array} \quad (6)\]  
+
+where \(g_{\downarrow \downarrow},g_{\uparrow \uparrow}\) and \(g_{\downarrow \uparrow}\) are the two intra species and the inter species coupling constants. Note that \(n\Delta\) derives from the \(|\uparrow \rangle\) and \(|\downarrow \rangle\) self interaction asymmetry.  
+
+In an elongated cloud having a parabolic Thomas Fermi density profile, the ferromagnetic phase is located in the center of the cloud where the non liner term \(|\kappa |nZ^{2} / 2\) is maximal. Under the condition \(|\kappa |n< \Omega\) , in fact, the energy per particle is characterized by a symmetric double minimum structures a signature of the symmetry breaking typical of the ferromagnetic phase. At non zero detuning, the symmetry of the two wells is broken. Thanks to the tuning knob \(\delta_{B}\) , which is linearly proportional to the applied magnetic field, one can change the relative energy difference between the two energy minima, converting one or the other state into the absolute ground state or the metastable state. The tails of the cloud remain in the paramagnetic regime, having smaller density, and \(Z\) of the only energy minimum is unambiguously determined by \(\delta_{\mathrm{B}}\) .
+
+<--- Page Split --->
+
+Due to the asymmetry between \(|\uparrow \rangle\) and \(|\downarrow \rangle\) , there exists a range of values of \(\delta_{\mathrm{B}}\) where the sign of the \(Z\) at the energy minima in the center \((- )\) and at the tails \((+)\) is opposite, but the system can still maintain a homogeneous positively- magnetized profile being metastable in the center. When the detuning is decreased below the critical value \(\delta_{c}\) (see main text), the metastable minimum disappears resulting in a unique steady magnetic profile with negative \(Z\) in the center and positive \(Z\) in the tails.  
+
+While the spin energy profiles of Eq. (4) are useful to explain the presence of two minima separated, this LDA representation only shows the LDA energy landscape per particle and not the total energy of the system. For instance, the LDA energy profiles don't include the contribution coming from the interface between opposite \(Z\) , whose kinetic energy represents a further contribution to the total energy barrier, as intended to be shown in Fig. 1 in the main text.  
+
+## II. CALIBRATION AND ANALYSIS PROCEDURE  
+
+An important calibration concerns the determination of the critical detuning at which the double well energy landscape is expected to disappear. We determine \(\delta_{c}\) by performing the same protocols used in [27] to measure the hysteresis width of the ferromagnetic regime. This consists in the same ramp shown Fig. 2(a) of the main text, applied with a null waiting time.  
+
+The data used in the main text are obtained in the range of \(\delta\) directly above the critical one. Thanks to the appearing of the bubble in the center of the cloud, we first determine the presence of the bubble by fixing a threshold \(Z_{\mathrm{bubble}} = 0.2\) . If the average magnetization in the central 40 pixels is below \(Z_{\mathrm{bubble}}\) , one bubble is counted. The total bubble counts at fixed waiting time determines the probability \(P\) , as plotted in Fig. 2(c) of the main text. We verify that the choice of the threshold \(Z_{\mathrm{bubble}}\) and the averaging area do not critically impact on the outcomes presented here. Once the bubble is detected, the full magnetization profile is initially fitted by using a double sigmoidal function,  
+
+\[A\left[\arctan \left(\frac{x - x_{r}}{s_{r}}\right) - \arctan \left(\frac{x - x_{l}}{s_{l}}\right)\right] \quad (7)\]  
+
+where \(A\) is the amplitude and \(x_{(r),[l]}\) and \(s_{(r),[l]}\) are the (right) [left] centers and sigmas of the two sigmoids. The positions \(x_{(l),[r]}\) are then used as starting values for a second fitting routine that independently analyses the left and right bubble interfaces. This second step is used to better determine the exact positions of the interfaces without the effects of cloud asymmetry and offsets. The obtained values \(x_{(l),[r]}\) allow to determine the bubble size as \(\sigma_{x} = x_{r} - x_{l}\)
+
+<--- Page Split --->
+
+## III. DETERMINATION OF \(\tau\) AND ALTERNATIVE \(\tau_{50\%}\)  
+
+In the main text we explain how we determine the characteristic decay time \(\tau\) by fitting \(F_{t}\) to \((1 - \epsilon) / \sqrt{1 + (e^{t / \tau} - 1)^{2}} + \epsilon\) . This formula allows us to extract \(\tau\) even for experimental sequences with limited statistics and it results to be robust against the initialisation of the fitting parameters.  
+
+To verify the solidity of our approach we also considered a different characteristic time \(\tau_{50\%}\) defined as the time at which the probability \(P\) to observe a bubble is \(50\%\) . This approach is a valid alternative for measurements featuring a limited statistics. To determine \(\tau_{50\%}\) we fit \(P\) with the following function:  
+
+\[P(t) = \mathrm{Min}[a_{1}*(e^{t / a_{2}} - 1),1] \quad (8)\]  
+
+with \(a_{1}\) and \(a_{2}\) as free parameters. These two are then used to determine \(\tau_{50\%}\) from  
+
+\[\frac{1}{2} = a_{1}*(e^{t_{50\%} / a_{2}} - 1) \quad (9)\]  
+
+We check, within the statistical uncertainties, that the value of \(\tau_{50\%}\) does not change by using different fitting functions (linear, exponential with offsets in time and \(P\) ). Figure M1 shows that \(\tau\) and \(\tau_{50\%}\) are compatible both for the experimental measurements and numerical simulations. In particular, simulation results allow us to conclude that, while \(\tau_{50\%}\) is expected to be influenced by the delay time before the bubble decays, \(\tau_{50\%}\) is still a good approximation of \(\tau\) . This suggests that the delay time and \(\tau\) are related and further investigations are necessary to understand how.  
+
+In general, we conclude that the determination of \(\tau\) used in the main text is solid. In particular, one notes that the two methods rely on two very different observables, the mean magnetization  
+
+![PLACEHOLDER_14_0]
+
+<center>FIG. M1. \(\tau\) vs \(\tau_{50\%}\) for experimental (a) and numerical (b) results. The two quantity are compatible to each other within error bars in experimental results and show only small deviation in simulation data. Color code for the points is the same used in the main text and the blue line marks \(\tau = \tau_{50\%}\) . </center>
+
+<--- Page Split --->
+
+in the center, averaged over all experimental shots ( \(\tau\) ), and the probabilistic presence of a bubble \((\tau_{50\%})\) .  
+
+## IV. NUMERICAL SIMULATIONS  
+
+The numerical results presented in the main text are based on one- dimensional Gross- Pitaevskii simulations. The parameters are chosen to faithfully reproduce the experimental conditions: in particular, the system trapped by a harmonic potential with frequency \(\omega_{0} \simeq 2\pi \times 16 \mathrm{Hz}\) , so that the Thomas- Fermi radius is \(L \simeq 200 \mu \mathrm{m}\) ; moreover, interactions are chosen to obtain \(|\kappa |n_{0} = |\Delta |n_{0} \simeq 2\pi \times 1.1 \mathrm{kHz}\) , \(n_{0}\) being the total density in the center of the cloud. The system is first prepared, through imaginary- time evolution, in the ground state corresponding to \(\delta_{f} = 2\pi \times 1 \mathrm{kHz}\) , thus, regardless of the value of \(\Omega_{R}\) , it is almost fully polarized in the \(|\uparrow \rangle\) state.  
+
+A white noise of amplitude equal to \(3\%\) of the central density is added on top of the ground state: this corresponds to an injected energy of roughly \(\epsilon /k_{B} = 215 \mathrm{nK}\) . We then let the system evolve in real time, without changing any parameter and we observe that, after a transient, the noise distribution becomes stationary; we interpret this result as thermalization of the mixture to a temperature \(T \propto \epsilon\) . Under an ergodicity assumption, we can determine the dynamics of the system by averaging over many repetitions of the same time- evolution, each one obtained starting from a different noisy sample. To summarize, we perform mean- field simulations in which noise plays the role of an effective temperature. Of course, these do not allow to investigate the role of quantum fluctuations: however, since the estimated experimental temperature is much higher than \(|\kappa |n_{0} / k_{B} \sim 50 \mathrm{nK}\) , the dynamics is likely to be dominated by thermal noise and a comparison with classical field simulations is justified.  
+
+The real- time dynamics after thermalization reproduces, once again, the experimental protocol: a detuning ramp with speed \(\sim 50 \mathrm{Hz / ms}\) is applied in order to reach the false vacuum state corresponding to some final \(\delta_{f} < 0\) ; the magnetization of the system is then monitored for a waiting time in the range \([10, 300] \mathrm{ms}\) , depending on the simulation parameters.  
+
+In order to extract the characteristic decay time \(\tau\) and \(\tau_{50}\) , we compute:  
+
+\[F(t) = \frac{\langle Z(x \sim 0, t) \rangle - Z_{TV}}{Z_{FV} - Z_{TV}} \quad (10)\]  
+
+where \(\langle Z(x \sim 0, t) \rangle\) is the statistical average of magnetization over the central \(10 \mu \mathrm{m}\) of the cloud. If the number of samples is sufficiently high (we use 1000), this function represents the probability of not observing a bubble at time \(t\) . Therefore, \(\tau_{50}\) is computed, by definition, by solving \(F(\tau_{50}) = 0.5\) .
+
+<--- Page Split --->
+
+The FVD rates are obtained instead via a linear fit of \(\log F(t)\) : in most cases the predicted exponential behaviour is found within a time interval corresponding to \(F(t) \in [0.3, 0.7]\) ; small adjustments of this window are necessary for the simulations associated to the smallest and longest tunnelling times.  
+
+## V. ISTANTONS  
+
+The theoretical description of vacuum decay is non- perturbative and based on instanton solutions to the equations of motion using an imaginary time coordinate. The classical field theory for this system reduces down to a field theory for the magnetisation \(Z\) . For thermal instantons, bubbles nucleate at a rate (see e.g.[14])  
+
+\[\Gamma = 1 / \tau = A(\beta E_{c})^{j / 2}e^{-\beta E_{c}}. \quad (11)\]  
+
+where \(\beta = 1 / (k_{B}T)\) and \(E_{c}\) is the energy of the instanton. The factor \(A\) depends on fluctuations about the instanton and \(j\) is the number of translational symmetries. There should be one zero mode \(j = 1\) if there is translational invariance in the system. (The bubbles in the experiment always nucleate near the centre, so translational invariance is suspect. Fortunately, the power law dependence has only a small effect on the results). There are a very limited number of models for which the pre- factor \(A\) is calculable at present, and we will therefore regard \(A\) as a fitting parameter in the subsequent analysis. Note that the non- perturbative approach is valid when the exponent is larger than one, i.e. for temperatures \(k_{B}T < E_{c}\) . At even lower temperatures, vacuum fluctuations become the dominant seeding mechanism. In our system this happens for \(k_{B}T < \hbar |\kappa |n \sim 50 \mathrm{nK}\) , and the resulting vacuum decay rate would be far less than the rate seen in the experiment.  
+
+The energy for a thermal instanton includes a gradient contribution  
+
+\[E_{c} = \frac{\hbar n}{4}\int \left\{\frac{\hbar}{2m}\frac{(\nabla Z)^{2}}{1 - Z^{2}} + V\right\} dx, \quad (12)\]  
+
+where the potential  
+
+\[V = \kappa nZ^{2} - 2\Omega_{R}(1 - Z^{2})^{1 / 2} - 2\delta_{\mathrm{f}}Z. \quad (13)\]  
+
+We can scale out the dependence on the density so that \(\hat{E}_{c} = E_{c} / (\hbar n^{2}\xi |\kappa |)\) for the length scale \(\xi = \hbar /(m|\kappa |n)^{1 / 2}\) . For thermal bubbles in one dimension, the instanton calculation is equivalent to a WKB approximation to the action, with the familiar WKB form  
+
+\[\hat{E}_{c} = \frac{1}{2}\int_{Z_{TP}}^{Z_{FV}}\left(\frac{2(V - V_{FV})}{|\kappa|n}\right)^{1 / 2}\frac{dZ}{\sqrt{1 - Z^{2}}}, \quad (14)\]
+
+<--- Page Split --->
+
+
+TABLE I. Fitting coefficients for the thermal instanton model of vacuum decay with \(j = 1\) . The fit is limited to \((\delta_{f} - \delta_{c}) / \Omega_{R} > 0.05\) to ensure that \(b\hat{E}_{c} > 1\)   
+
+<table><tr><td>ΩR/2π</td><td>aexp(σa)</td><td>bexp(σb)</td><td>asim(σa)</td><td>bsim(σb)</td></tr><tr><td>300</td><td>0.54(0.09)</td><td>56.5(1.9)</td><td>0.93(0.06)</td><td>55.0(1.9)</td></tr><tr><td>400</td><td>0.83(0.42)</td><td>44.4(6.1)</td><td>0.70(0.07)</td><td>41.3(0.87)</td></tr><tr><td>600</td><td>0.02(0.43)</td><td>30.3(3.7)</td><td>0.01(0.14)</td><td>29.8(1.3)</td></tr><tr><td>800</td><td>0.30(0.75)</td><td>25.8(5.7)</td><td>-0.44(0.11)</td><td>25.3(0.9)</td></tr></table>  
+
+The integral extends from the turning point \(Z_{TP}\) to the false vacuum \(Z_{FV}\) . The extra factor \((1 - Z^{2})^{- 1 / 2}\) is due to the form of the derivative terms in the energy (12).  
+
+The experimental data has been used to determine the best parameters in a fit for \(\ln \tau = \ln A + b\hat{E}_{c} - \ln (b\hat{E}_{c}) / 2\) . The results are given in Table I. The condensate number density is given by \(n = (k_{B}T / \hbar |\kappa |n)b / \xi\) . For the temperature \(T = 1\mu \mathrm{K}\) , the values of \(n\) at lower \(\Omega\) are around half of the value expected for the system, but not unreasonable given the limitations of the one dimensional treatment. If the bubble only fills a fraction of the cross- section, it effectively feels only part of the integrated density.  
+
+In the case of small potential barriers, the potential can be expanded to cubic order about an inflection point at \(Z_{c}\) and \(\delta = \delta_{c}\) , where  
+
+\[\delta_{c} = \kappa n(1 - Z_{c}^{3}),\qquad Z_{c} = \left(1 - \left(\frac{\Omega_{R}}{|\kappa|n}\right)^{\frac{2}{3}}\right)^{\frac{1}{2}}. \quad (15)\]  
+
+The integral in this case can be performed exactly,  
+
+\[\hat{E}_{c}\approx 1.77\left(\frac{\delta_{f} - \delta_{c}}{|\kappa|n}\right)^{\frac{5}{4}}\left(\frac{\Omega_{R}}{|\kappa|n}\right)^{\frac{1}{6}}\left(\frac{|\delta_{c}|}{|\kappa|n}\right)^{-\frac{1}{4}} \quad (16)\]  
+
+To verify that the instanton prediction and simulation are consistent, we repeat numerical simulations at fixed \(\delta_{f}\) and variable \(\epsilon\) . We observe that the extracted \(\tau\) results proportional to \(e^{(1 / \epsilon)}\) and this well justifies the association between the injected noise parameter \(\epsilon\) and the temperature \(T\) .
+
+<--- Page Split --->
+
+[2] K. C. Kulander, K. J. Schafer, and J. L. Krause, Atoms in Intense Laser Fields (Academic Press, New York, 1992) p. 247.  
+
+[3] G. Lagnese, F. M. Surace, M. Kormos, and P. Calabrese, False vacuum decay in quantum spin chains, Phys. Rev. B 104, L201106 (2021).  
+
+[4] A. Milsted, J. Liu, J. Preskill, and G. Vidal, Collisions of false- vacuum bubble walls in a quantum spin chain, PRX Quantum 3, 020316 (2022).  
+
+[5] A. J. Baldwin, T. P. J. Knowles, G. G. Tartaglia, A. W. Fitzpatrick, G. L. Devlin, S. L. Shammas, C. A. Waudby, M. F. Mossuto, S. Meehan, S. L. Gras, J. Christodoulou, S. J. Anthony- Cahill, P. D. Barker, M. Vendruscolo, and C. M. Dobson, Metastability of native proteins and the phenomenon of amyloid formation, Journal of the American Chemical Society 133, 14160 (2011), pMID: 21650202, https://doi.org/10.1021/ja2017703.  
+
+[6] D. Ghosh and A. Ranjan, The metastable states of protein, Protein Science 29, 1559 (2020).  
+
+[7] C. Hogan, Gravitational radiation from cosmological phase transitions, Monthly Notices of the Royal Astronomical Society 218, 629 (1986).  
+
+[8] M. E. Shaposhnikov, Baryon Asymmetry of the Universe in Standard Electroweak Theory, Nucl. Phys. B 287, 757 (1987).  
+
+[9] S. M. Feeney, M. C. Johnson, D. J. Mortlock, and H. V. Peiris, First observational tests of eternal inflation: Analysis methods and wmap 7- year results, Phys. Rev. D 84, 043507 (2011), arXiv:1012.3667 [astro- ph.CO].  
+
+[10] C. G. Callan and S. R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16, 1762 (1977).  
+
+[11] S. R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15, 2929 (1977), [Erratum: Phys. Rev. D 16, 1248 (1977)].  
+
+[12] A. D. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Phys. B 216, 421 (1983), [Erratum: Nucl.Phys.B 223, 544 (1983)].  
+
+[13] A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and experimental signatures, Rept. Prog. Phys. 82, 076901 (2019), arXiv:1811.01948 [hep- ph].  
+
+[14] M. Hindmarsh, M. Luben, J. Lumma, and M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes, 24 (2021).  
+
+[15] O. Fialko, B. Opanchuk, A. I. Sidorov, P. D. Drummond, and J. Brand, Fate of the false vacuum: Towards realization with ultra- cold atoms, Europhysics Letters 110, 56001 (2015).  
+
+[16] J. Braden, M. C. Johnson, H. V. Peiris, and S. Weinfurtner, Towards the cold atom analog false vacuum, Journal of High Energy Physics 2018, 2018 (2019).  
+
+[17] T. P. Billam, R. Gregory, F. Michel, and I. G. Moss, Simulating seeded vacuum decay in a cold atom system, Phys. Rev. D 100, 065016 (2019).  
+
+[18] Z. Davoudi, M. Hafezi, C. Monroe, G. Pagano, A. Seif, and A. Shaw, Towards analog quantum simulations of lattice gauge theories with trapped ions, Phys. Rev. Res. 2, 023015 (2020).
+
+<--- Page Split --->
+
+[19] T. P. Billam, K. Brown, and I. G. Moss, Simulating cosmological supercooling with a cold- atom system, Phys. Rev. A 102, 043324 (2020).  
+
+[20] T. P. Billam, K. Brown, A. J. Groszek, and I. G. Moss, Simulating cosmological supercooling with a cold atom system. ii. thermal damping and parametric instability, Phys. Rev. A 104, 053309 (2021).  
+
+[21] K. L. Ng, B. Opanchuk, M. Thenabadu, M. Reid, and P. D. Drummond, Fate of the false vacuum: Finite temperature, entropy, and topological phase in quantum simulations of the early universe, PRX Quantum 2, 010350 (2021).  
+
+[22] B. Song, S. Dutta, S. Bhave, J.- C. Yu, E. Carter, N. Cooper, and U. Schneider, Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice, Nature Physics 18, 259- 264 (2022).  
+
+[23] J. Preskill, Simulating quantum field theory with a quantum computer, PoS LATTICE2018, 024 (2019).  
+
+[24] S. Abel and M. Spannowsky, Quantum- field- theoretic simulation platform for observing the fate of the false vacuum, PRX Quantum 2, 010349 (2021).  
+
+[25] H. Grabert and U. Weiss, Crossover from thermal hopping to quantum tunneling, Phys. Rev. Lett. 53, 1787 (1984).  
+
+[26] H. Grabert, U. Weiss, and P. Hanggi, Quantum tunneling in dissipative systems at finite temperatures, Phys. Rev. Lett. 52, 2193 (1984).  
+
+[27] R. Cominotti, A. Berti, C. Dulin, C. Rogora, G. Lamporesi, I. Carusotto, A. Recati, A. Zenesini, and G. Ferrari, Ferromagnetism in an extended coherently- coupled atomic superfluid. (to be published in Phys. Rev. X, 2023), arXiv:2209.13235 [cond- mat.quant- gas].  
+
+[28] A. Farolfi, D. Trypogeorgos, G. Colzi, E. Fava, G. Lamporesi, and G. Ferrari, Design and characterization of a compact magnetic shield for ultracold atomic gas experiments, Review of Scientific Instruments 90, 115114 (2019).  
+
+[29] D. Guéry- Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez- Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).  
+
+[30] E. Torrontegui, S. Ibáñez, S. Martínez- Garaot, M. Modugno, A. del Campo, D. Guéry- Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, Chapter 2 - shortcuts to adiabaticity, in Advances in Atomic, Molecular, and Optical Physics, Advances In Atomic, Molecular, and Optical Physics, Vol. 62, edited by E. Arimondo, P. R. Berman, and C. C. Lin (Academic Press, 2013) pp. 117- 169.  
+
+[31] W. L. Tan, P. Becker, F. Liu, G. Pagano, K. S. Collins, A. De, L. Feng, H. B. Kaplan, A. Kyprianidis, R. Lundgren, W. Morong, S. Whitsitt, A. V. Gorshkov, and C. Monroe, Domain- wall confinement and dynamics in a quantum simulator, Nature Physics 17, 742- (2021).
+
+<--- Page Split --->

preprint/preprint__00d7abe0a4b5c990501df86cac16b26584184537e4e60f6f33e33b81c4a5b14a/preprint__00d7abe0a4b5c990501df86cac16b26584184537e4e60f6f33e33b81c4a5b14a_det.mmd

@@ -0,0 +1,472 @@
+<|ref|>title<|/ref|><|det|>[[44, 107, 852, 175]]<|/det|>
+# Observation of false vacuum decay via bubble formation in ferromagnetic superfluids  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 857, 236]]<|/det|>
+Anna Berti  CNR- INO, Pitaevskii BEC Center, Università di Trento  https://orcid.org/0000- 0003- 3073- 9554  
+
+<|ref|>text<|/ref|><|det|>[[44, 241, 500, 283]]<|/det|>
+Riccardo Cominotti  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+<|ref|>text<|/ref|><|det|>[[44, 289, 500, 330]]<|/det|>
+Chiara Rogora  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+<|ref|>text<|/ref|><|det|>[[44, 336, 648, 377]]<|/det|>
+Ian Moss  School of Mathematics, Statistics and Physics, Newcastle University  
+
+<|ref|>text<|/ref|><|det|>[[44, 382, 238, 423]]<|/det|>
+Thomas Billam  Newcastle University  
+
+<|ref|>text<|/ref|><|det|>[[44, 429, 500, 470]]<|/det|>
+Iacopo Carusotto  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+<|ref|>text<|/ref|><|det|>[[44, 475, 500, 516]]<|/det|>
+Giacomo Lamporesi  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+<|ref|>text<|/ref|><|det|>[[44, 521, 500, 562]]<|/det|>
+Alessio Recati  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+<|ref|>text<|/ref|><|det|>[[44, 568, 803, 609]]<|/det|>
+Gabriele Ferrari  Universita' di Trento and INO- CNR BEC Center  https://orcid.org/0000- 0003- 1827- 5048  
+
+<|ref|>text<|/ref|><|det|>[[44, 614, 512, 655]]<|/det|>
+Alessandro Zenesini ( \(\boxed{ \begin{array}{r l} \end{array} }\) alessandro.zenesini@ino.it)  CNR- INO, Pitaevskii BEC Center, Università di Trento  
+
+<|ref|>text<|/ref|><|det|>[[44, 694, 102, 712]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 732, 137, 751]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 770, 291, 789]]<|/det|>
+Posted Date: June 8th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 809, 475, 828]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 2923763/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 846, 910, 890]]<|/det|>
+License: © \(\circledast\) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 907, 530, 927]]<|/det|>
+Additional Declarations: There is NO Competing Interest.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 955, 88]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Physics on January 22nd, 2024. See the published version at https://doi.org/10.1038/s41567-023-02345-4.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[255, 88, 740, 135]]<|/det|>
+# Observation of false vacuum decay via bubble formation in ferromagnetic superfluids  
+
+<|ref|>text<|/ref|><|det|>[[178, 153, 820, 408]]<|/det|>
+A. Zenesini \(^{1,2}\) , 
+A. Berti \(^{1}\) , 
+R. Cominotti \(^{1}\) , 
+C. Rogora \(^{1}\) , 
+I. 
+G. Moss \(^{3}\) , 
+T. 
+P. Billam \(^{4}\) , 
+I. Carusotto \(^{1}\) , 
+G. Lamporesi \(^{1,2}\) , 
+A. Recati \(^{1}\) , and 
+G. Ferrari \(^{1,2}\) \(^{1}\) Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, 38123 Trento, Italy \(^{2}\) Trento Institute for Fundamental Physics and Applications, INFN, 38123 Trento, Italy \(^{3}\) School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK and \(^{4}\) Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK (Dated: May 22, 2023)  
+
+<|ref|>text<|/ref|><|det|>[[169, 422, 828, 803]]<|/det|>
+Metastability is ubiquitous in nature and is observed through the crossing of an energy barrier toward a configuration of lower energy as, for example, in chemical processes [1] or electron field ionization [2]. In classical many- body systems, metastability naturally emerges in the presence of a first- order phase transition and finds a prototypical example in supercooled vapour. In the last decades, the extension to quantum field theory and quantum many- body systems has attracted significant interest in the context of statistical physics [3, 4], protein folding [5, 6], and cosmology [7- 9], where thermal and quantum fluctuations are expected to trigger the transition from the metastable state (false vacuum) to the ground state (real vacuum) via the probabilistic nucleation of spatially localized bubbles [10, 11]. However, the long- standing theoretical progress in estimating the relaxation rate of the metastable field via bubble nucleation has not yet found a counterpart in terms of experimental observations. Here we experimentally observe and characterize bubble nucleation in isolated and coherently- coupled atomic superfluids, and support our observations with numerical simulations. The agreement between our results and a novel analytic formula based on instanton theory confirms the quantum- field character of the observed decay, and promotes coherently- coupled atomic superfluids as emulators of out- of- equilibrium quantum field phenomena.  
+
+<|ref|>text<|/ref|><|det|>[[114, 834, 881, 931]]<|/det|>
+A supercooled gas is a classic example of a metastable state which exists just across a first order phase transition. The passage to the ground state (the liquid phase) is mediated by resonant bubble nucleation when the energy gain provided by the liquid bulk is compensated by the cost of the surface tension. This energy balance leads to a critical bubble size and a stochastic
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 882, 339]]<|/det|>
+formation of the bubble typically occurs around nucleation spots given by impurities in the gas or imperfections at the container. The extension of this idea to a quantum many- body or a quantum field system has attracted extensive attention in a wide range of scenarios and length scales, from the understanding of early universe [7- 9] to the characterization of spin chains [3, 4]. In all these models, the metastable state at the origin of the bubble nucleation, is identified as "false vacuum" and the role of surface tension is taken by a genuinely quantum term. In the purest form, the false vacuum decay into the ground state would take place through quantum vacuum fluctuations [10, 11] (similarly to impurities in the classical case). However, as for example in the early universe, the tunnelling is equally likely to be boosted by thermal fluctuations, and the process would be of the type styled "vacuum decay at finite temperature" [12] (see [13, 14] for a review).  
+
+<|ref|>text<|/ref|><|det|>[[113, 345, 882, 519]]<|/det|>
+In the cosmological case, the energy scales are well above any that are accessible to experiments, and the phenomenon of false vacuum decay remains one of the most important yet untested processes considered in theoretical high energy physics. Recently, the extreme flexibility of neutral and charged atoms tabletop experiments and the advances of classical and quantum computer algorithms have paved the way for the proposal of experimental environments [15- 22] and virtual simulators [23, 24]. Up to now only numerical results have been achieved and the experimental observation of an analogue to false vacuum decay would therefore be of high significance.  
+
+<|ref|>text<|/ref|><|det|>[[113, 526, 882, 880]]<|/det|>
+In tabletop experiments, the observation of bubble nucleation requires several ingredients which are difficult to arrange simultaneously. First, a mean- field interaction- induced energy landscape composed of an asymmetric double well represents the minimal requirement for the decay from the metastable state to the absolute ground state via macroscopic tunneling across the energy barrier, followed by relaxation; see sketch in Fig. 1. Second, unlike in the ordinary quantum tunneling of a single particle [1, 25, 26], it is an effective field describing the system that changes state. Third, the time resolution of the experiment should cover many orders of magnitude to allow for the investigation of the predicted exponential time- dependence on the tuning parameters. This must be associated to a high stability and accuracy of the tuning parameters. An extended ferromagnetic superfluid [27] possesses the ideal properties to act as a field simulator, in particular its first order phase transition character, the long range coherence and the flexibility to control its experimental parameters within a stable and isolated environment. In tight analogy with supercooling, in an extended quantum system the presence of a spatial region with different magnetization to the bulk carries a positive kinetic energy due to the winding of the field at the interface, see Fig. 1.  
+
+<|ref|>text<|/ref|><|det|>[[115, 886, 880, 932]]<|/det|>
+In this letter, we present the experimental observation of bubble formation via false vacuum decay in a quantum system. We observe that the bubble nucleation time scales exponentially with
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[275, 95, 710, 324]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[113, 357, 882, 561]]<|/det|>
+FIG. 1. Mean- field energy and bubble formation. The cloud is initially prepared with all the atoms in \(|\uparrow \rangle\) (A). While the single \(|\downarrow \rangle\) spin state is energetically lower ( \(E_{\downarrow} < E_{\uparrow}\) ) in the center of the cloud, in the low density tails the situation is opposite. The interface has a positive energy which adds up to the double minimum energy landscape emerging from the ferromagnetic interaction. Macroscopic quantum tunneling can take place resonantly to the bubble state (B) which has a \(|\downarrow \rangle\) bubble in the center, whose core energy gain compensates for the interface energy cost. The barrier crossing can be triggered by quantum fluctuations in the zero- temperature case (dashed arrow) or by thermal fluctuations at finite temperature (empty arrow). After the tunneling process, in the presence of dissipation, the bubble increases in size to reach the ground state (C), without coming back to (A).  
+
+<|ref|>text<|/ref|><|det|>[[114, 593, 880, 664]]<|/det|>
+an experimental parameter that is connected to the energy barrier properties. Theoretical and numerical simulations support our observations and allow us to confirm the quantum field origin of the decay and its thermal activation.  
+
+<|ref|>text<|/ref|><|det|>[[113, 675, 882, 850]]<|/det|>
+The experimental platform is composed of a bosonic gas of \(^{23}\mathrm{Na}\) atoms, optically trapped and cooled below the condensation temperature. The gas is initially prepared in the internal state \(|F,m_{F}\rangle = |1, - 1\rangle = |\downarrow \rangle\) , where \(F\) is the total angular momentum and \(m_{F}\) its projection on the quantization axis. A microwave radiation with amplitude \(\Omega_{R}\) coherently couples the \(|\downarrow \rangle\) state to \(|2, - 2\rangle = |\uparrow \rangle\) . The relevant scattering lengths for such a two- level system are \(a_{\downarrow \downarrow} = 54.5a_{0}\) , \(a_{\uparrow \uparrow} = 64.3a_{0}\) , and \(a_{\downarrow \uparrow} = 54.5a_{0}\) , and lead to the condition \(\Delta a = (a_{\uparrow \uparrow} + a_{\downarrow \downarrow}) / 2 - a_{\downarrow \uparrow} < 0\) , i.e., to a system with a ferromagnetic ground state [27].  
+
+<|ref|>text<|/ref|><|det|>[[114, 860, 880, 932]]<|/det|>
+The trapping potential is axially symmetric and harmonic in all three directions, but strongly asymmetric (axial and radial trapping frequencies \(\omega_{x} / 2\pi = 20\mathrm{Hz}\) and \(\omega_{\rho} / 2\pi = 2\mathrm{kHz}\) ), producing an elongated system with inhomogeneous density and spatial size given by the longitudinal and
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[272, 92, 720, 496]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 523, 882, 655]]<|/det|>
+<center>FIG. 2. Protocols and bubble observation. a) Experimental protocol. Ellipses illustrate the cloud magnetization at different \(t\) and the two sketches show the energy landscape for positive (up) and negative (down) \(\delta\) . b) Collection of integrated magnetization profiles \(Z(x)\) after different waiting times \(t\) . For each value of \(t\) , 7 different realizations are shown. c) Magnetization profiles for the realizations marked with arrows in panel (b). d) Measured probability \(P\) (empty circles) to observe a shot with a bubble at fixed time is shown. The probability is well fitted to an exponential curve (grey continuous line) until it saturates to 1. </center>  
+
+<|ref|>text<|/ref|><|det|>[[114, 679, 882, 830]]<|/det|>
+radial Thomas- Fermi radius \(R_{\mathrm{x}} = 200\mu \mathrm{m}\) and \(R_{\rho} = 2.5\mu \mathrm{m}\) . At the end of each experimental realization, we image the two spin states independently and extract their density distributions. The transverse confinement is tight enough to suppress the radial spin dynamics of the condensate. We therefore integrate each image along the transverse direction and obtain the integrated 1D density profiles \(n_{\uparrow}(x)\) and \(n_{\downarrow}(x)\) , from which we extract the profile of the relative magnetization \(Z(x) = [n_{\uparrow}(x) - n_{\downarrow}(x)] / [n_{\uparrow}(x) + n_{\downarrow}(x)]\) .  
+
+<|ref|>text<|/ref|><|det|>[[114, 835, 882, 932]]<|/det|>
+The coupled two- level system can be studied by separately treating the total density ( \(n = n_{\uparrow} + n_{\downarrow}\) ) and the spin ( \(n_{\uparrow} - n_{\downarrow} = nZ\) ) degrees of freedom. While the density is simply dominated by a continuity equation, the spin degree of freedom is ruled by a magnetic mean- field Hamiltonian, which shows a first- order phase transition in the central region of the cloud for \(\Omega_{R} < |\kappa |n\) , where
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 578, 107]]<|/det|>
+\(\kappa \propto \Delta a\) is the relevant interaction parameter; see Methods.  
+
+<|ref|>text<|/ref|><|det|>[[113, 113, 882, 392]]<|/det|>
+The first- order phase transition originates from a symmetry breaking when the energy landscape as a function of the magnetization \(Z\) goes from a single to a double minimum at \(\Omega_{R}< |\kappa |n =\) \(2\pi \times 1150\mathrm{Hz}\) . At fixed \(\Omega_{R}\) , the experimentally tunable parameter is the detuning \(\delta\) between the two- level system and the coupling radiation. For small enough \(|\delta |\) , the energy landscape \(E(Z)\) is represented by an asymmetric double well, that turns symmetric for \(\delta = 0\) . In particular, for positive \(\delta\) , the energy is minimized by positive values of \(Z\) , and viceversa The relevant parameter for the bubble nucleation is the shape (height and width) of the energy barrier separating the two wells that the system needs to overcome as a field, i.e., in a macroscopic manner. This depends on \(\delta\) , \(n\) and \(\Omega_{R}\) . When \(|\delta |\) exceeds a critical value \(\delta_{c}\) , the metastable well disappears [27]. Borrowing the nomenclature from ferromagnetism, \(\pm \delta_{c}\) correspond to the edges of the hysteresis region and their value depends both on \(\Omega_{R}\) and \(|\kappa |n\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 397, 882, 546]]<|/det|>
+Figure 2(a) illustrates the experimental protocol. We first transfer the whole system from \(|\downarrow \rangle\) to \(|\uparrow \rangle\) with a \(\pi\) pulse. While keeping \(\Omega_{R}\) constant, \(\delta\) is linearly ramped down from \(\delta_{i} / 2\pi = 5.5\mathrm{kHz}\) to a variable \(\delta_{f}\) on a timescale between 20 and 60 ms. Since the ramp starts with \(\delta \gg \Omega_{R}\) , the system follows the spin rotation remaining in the local ground state until \(\delta < 0\) when such a local ground state becomes a metastable state; see inset in Fig. 2(a). Once \(\delta_{f}\) is reached, the states are independently imaged after a variable waiting time \(t\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 552, 882, 752]]<|/det|>
+If \(\delta_{f} > 0\) , the whole system is and remains in the absolute ground state \(|\uparrow \rangle\) , whereas for \(\delta_{f}< 0\) , after a variable time, a macroscopic region in the central part of the system flips to \(|\downarrow \rangle\) , generating a bubble; see examples in Fig. 2(b) and magnetization profiles in (c). On average the bubble occurrence probability is larger if the waiting time is longer [see Fig. 2(b) and (d)]. For a quantitative analysis, at each \(t\) , we repeat the measurement up to 10 times in order to investigate the statistical formation of bubbles. Note that, while in uniform systems the bubbles would stochastically nucleate in random spatial positions, our nonuniform density profile of the atomic sample strongly favors the nucleation at the center of the cloud, where \(\delta_{f}\) is closest to \(\delta_{c}\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 757, 882, 932]]<|/det|>
+A useful quantity to characterize the bubble nucleation in time is \(F_{t} = (1 + \langle Z\rangle_{t} / \langle Z\rangle_{t = 0}) / 2\) , which was used in Ref. [3] to compare an exact diagonalization approach in a zero- temperature spin chain to instanton predictions. Here \(\langle \cdot \rangle_{t}\) stands for \(Z\) measured at time \(t\) and averaged over many realizations. In Fig. 3(a) and (b), we show the average magnetization \(\langle Z\rangle_{t}\) profile as a function of waiting time for two values of detuning. Since the bubble appears always in the center of the system, to compute \(F_{t}\) , we extract the mean magnetization \(\langle Z\rangle_{t}\) in the central 20- \(\mu \mathrm{m}\) - wide region \((\approx R_{x} / 10)\) . The resulting \(F_{t}\) , plotted in panel (c), initially remains flat, and then it exponentially
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 883, 313]]<|/det|>
+decays because of the bubble nucleation. Both features were also observed in Ref. [3] and the understanding of the starting plateau is still an open question from the theoretical point of view. We find that the measured \(F_{t}\) is well described by the empirical function \((1 - \epsilon) / \sqrt{1 + (e^{t / \tau} - 1)^{2}} + \epsilon\) , which is 1 for \(t = 0\) , scales as \(t^{2}\) for small \(t\) and is exponentially decaying to \(\epsilon\) for large \(t\) . The two fitting parameters are \(\tau\) , that describes the characteristic timescale for the bubble formation, and \(\epsilon\) , that takes into account that the asymptotic magnetization \(Z_{t = \infty}\) can be different from the one of the ground state, \(Z_{TV}\) ( \(F = 0\) ). Note that the timescale \(\tau\) is related to the exponential decay, while the empirical formula takes into account an initial plateau present in the averaged magnetisation \(F_{t}\) . (in Methods we show that the plateau length and \(\tau\) are strictly connected).  
+
+<|ref|>text<|/ref|><|det|>[[113, 319, 882, 469]]<|/det|>
+Numerical simulations based on 1D Gross- Pitaevskii equations, reported in Fig. 3(d) and (e), qualitatively reproduce the experimental observations. In the numerics, classical noise is included to simulate the effect of a finite temperature (more details can be found in Methods). Data in Fig. 3(d) and (e) are obtained by averaging over 1000 different noisy realizations of the real- time dynamics: the large statistics allows us to directly extract the exponential decay time \(\tau_{\mathrm{sim}}\) through a linear fit of \(\ln (F_{t})\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 475, 882, 650]]<|/det|>
+In Fig. 3(g), we report six experimental values of \(\tau\) obtained for \(\Omega_{R} = 2\pi \times 300 \mathrm{Hz}\) , plotted as a function of the distance from the critical detuning, \((\delta_{f} - \delta_{c}) / |\kappa |n\) . The results show an exponential dependence on the tuning parameter over two orders of magnitude, from a few to hundreds of ms. Such a sensitivity to a parameter is remarkable for ultracold atoms experiments. In particular, the experimental observation of the quasi- exponential dependence of \(\tau\) with respect to \(\delta_{f}\) in an interval of the order of \(100 \mathrm{Hz}\) critically relies on the magnetic field stability better than a few tens of \(\mu \mathrm{G}\) [28].  
+
+<|ref|>text<|/ref|><|det|>[[113, 655, 882, 802]]<|/det|>
+The values of \(\tau_{\mathrm{sim}}\) for the simulations [light symbols in Fig. 3(g)] qualitatively show the same behaviour of the experimental data. The agreement becomes even quantitative [dark symbols in Fig. 3(g)], by using a rescaling of \(|\kappa |n\) and a small shift of \(\delta\) . The need for such a rescaling was demonstrated in Ref. [27], as a consequence of dimensionality, noise and non complete adiabaticity of the preparation protocol. In Fig. 4, we compare experimental \(\tau\) and rescaled numerical \(\tau_{\mathrm{sim}}\) , for four different values of \(\Omega_{R}\) , by using the same rescaling for all four panels.  
+
+<|ref|>text<|/ref|><|det|>[[113, 809, 882, 932]]<|/det|>
+Our observations are consistent with the scenario of a condensate spinor field initially in a ferromagnetic metastable state, which decays via macroscopic tunneling to bubbles (domains) of the ferromagnetic ground state. The escape of a quantum field from the false vacuum, occurring via macroscopic tunneling, and the bubble formation finds a suitable description in terms of an instanton, or critical solution to the field equations in imaginary time [10–12]. Such a theory
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[270, 92, 710, 500]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 525, 883, 794]]<|/det|>
+<center>FIG. 3. Measurement of the evolution of \(Z(x)\) in time after the ramp on \(\delta\) for \(\Omega_{R} / 2\pi = 300\mathrm{Hz}\) , for \(\delta_{f} / \Omega_{R} = -1.70\) in (a) and \(-1.79\) in (b). c) Value of \(F_{\mathrm{t}}\) evaluated in the \(20\mu \mathrm{m}\) central region of the cloud are fitted by the empirical expression reported in the text (squares for data in (a) and pentagons for (b)). Error bars are the standard deviation over up to ten repetitions. d-e) Numerical simulations for \(\delta_{f} / \Omega_{R} = -1.52\) in (d) and \(-1.585\) in (e). Value of \(F_{\mathrm{t}}\) for the simulations (triangles for data in (d) and stars for (e)). The red dashed lined are linear fits in the exponentially decaying part. g) Experimental \(\tau\) and numerical \(\tau_{\mathrm{sim}}\) timescale of the bubble formation as a function of \((\delta_{f} - \delta_{c}) / |\kappa |n\) . Error bars include statistical uncertainties on the fit and uncertainty on the \(\delta_{f} - \delta_{c}\) coming from magnetic field stability and calibration. Numerical timescale of the bubble formation \(\tau_{\mathrm{sim}}\) is shown before (light symbols) and after (dark symbol) rescaling. The empty triangle is an experimental point taken with a preparation ramp twice slower than the others, to verify the impact on the nucleation time resulting from a residual non-adiabaticity in the preparation of the sample. </center>  
+
+<|ref|>text<|/ref|><|det|>[[114, 834, 882, 930]]<|/det|>
+provides a threshold energy scale, below (above) which quantum (thermal) fluctuations dominate: zero- \(T\) quantum tunneling is expected to be dominant when \(T\) is below the critical temperature \(T^{*} = \hbar |\kappa |n / k_{B}\) . Considering the peak density in our system, we estimate \(T^{*} \simeq 50 \mathrm{nK}\) . Although the temperature of our condensates is \(T = 1.5 \mu \mathrm{K} \gg T^{*}\) , given the harmonic confinement and the
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[272, 92, 720, 422]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 448, 881, 581]]<|/det|>
+<center>FIG. 4. Decay time \(\tau\) and \(\tau_{\mathrm{sim}}\) and instanton theory. Experimental \(\tau\) and simulations \(\tau_{\mathrm{sim}}\) are obtained as explained in the text for \(\Omega_{R} / 2\pi = 300,400,600\) and \(800\mathrm{Hz}\) . A rescaling common to all \(\Omega_{R}\) is applied to the horizontal axes of the simulation; see text. Dashed and full curves are fits of the experimental and simulation data according to the instanton formula. Full markers stand for simulation results while empty markers for experimental data. Error bars include statistical uncertainties on the fit and uncertainty on the \(\delta_{f}\) due to on the magnetic field stability. </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 620, 881, 718]]<|/det|>
+exchange interaction which pushes the thermal component away from the condensate, we estimate an effective local temperature of about \(250\mathrm{nK}\) in the condensate region which is still larger than \(T^{*}\) in the region where the bubbles appear. Therefore we expect the macroscopic tunneling to be in the thermally activated regime.  
+
+<|ref|>text<|/ref|><|det|>[[113, 731, 882, 932]]<|/det|>
+Within the instanton approach, the bubble nucleation probability has the characteristic timescale \(\tau\) , which has an exponential dependence \(A(E_{c} / k_{B}T)^{- 1 / 2}e^{E_{c} / k_{B}T}\) . \(E_{c}(\delta ,\kappa n,\Omega_{R})\) is the energy of the critical solution and strongly depends on the shape of the many- body potential and in particular on the barrier height (Fig. 1). The pre- factor \(A\) depends on fluctuations about the critical solution, but there are very few models for which this factor is calculable, at present. We therefore regard the pre- factor \(A\) as a fitting parameter in the following analysis. We can estimate \(E_{c}\) , and provide an analytical expression in the limit of vanishing metastable well (small \(\delta_{f} - \delta_{c}\) ), by considering a homogeneous 1D system. The potential for the magnetization field \(Z\) can be
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 353, 106]]<|/det|>
+written as (see, e.g., Ref.[27] )  
+
+<|ref|>equation<|/ref|><|det|>[[345, 125, 877, 146]]<|/det|>
+\[V(Z) = \kappa n Z^{2} - 2\Omega (1 - Z^{2})^{1 / 2} - 2\delta_{f}Z \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 167, 361, 185]]<|/det|>
+and the instanton energy reads  
+
+<|ref|>equation<|/ref|><|det|>[[300, 194, 877, 240]]<|/det|>
+\[\frac{E_{c}}{\hbar|\kappa|n} = \sqrt{\frac{\hbar n}{2m|\kappa|}}\int_{Z_{T P}}^{Z_{F V}}\left[\frac{V(Z) - V(Z_{F V})}{|\kappa|n(1 - Z^{2})}\right]^{1 / 2}d Z, \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 251, 881, 348]]<|/det|>
+where \(Z_{T P}\) is the classical turning point (in the inverted potential \(V\) ) and \(Z_{F(alse)V(acuum)}\) the value of the magnetization of the metastable state. Most of our data are taken in a regime where the barrier is much smaller than the depth of the ground state well. In this limiting case the instanton energy reads  
+
+<|ref|>equation<|/ref|><|det|>[[291, 355, 877, 406]]<|/det|>
+\[\frac{E_{c}}{\hbar|\kappa|n}\propto \sqrt{\frac{\hbar n}{2m|\kappa|}}\left(\frac{\delta_{f} - \delta_{c}}{|\kappa|n}\right)^{\frac{5}{4}}\left(\frac{\Omega_{R}}{|\kappa|n}\right)^{\frac{1}{6}}\left(\frac{|\delta_{c}|}{|\kappa|n}\right)^{-\frac{1}{4}}, \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 417, 881, 599]]<|/det|>
+where \(\delta_{c} = \kappa n[1 - (\Omega /(|\kappa |n))^{\frac{2}{3}}]^{\frac{3}{2}}\) : see Methods. We compare the previous expression to the experimental data and numerical simulations using a two- parameter fit \(\ln \tau = \ln A + b\hat{E}_{c} + \ln (b\hat{E}_{c}) / 2\) , where \(\hat{E}_{c} = \sqrt{2m|\kappa| / (\hbar n)} E_{c} / \hbar |\kappa |n\) is the rescaled energy. The results are shown in Fig. 4. Considering the approximations used to derive Eq. (3) – in particular the absence of the trapping potential, no phase fluctuations and small barrier – the agreement is remarkable and the instanton theory appears to capture the main dependence of the false vacuum decay rate on the microscopic parameter \(\delta_{f}\) which is responsible for the broken \(\mathbb{Z}_{2}\) symmetry.  
+
+<|ref|>text<|/ref|><|det|>[[113, 603, 882, 932]]<|/det|>
+In this paper, we present solid evidence of the thermally- induced macroscopic tunneling of a coherent quantum field, manifested by bubbles of true vacuum phase nucleating in a false vacuum state. The true and false vacua are the local and global energy minimum of a ferromagnetic atomic Bose- Einstein condensate, respectively. The experimental results clearly show an exponential dependence of the decay rate on the microscopic parameters and the hysteric region width. Such a dependence is successfully captured by numerical simulations and more remarkably by a simple instanton theory based on a reduced energy functional for the magnetisation. Our platform paves the way to explore the process of bubble formation and growth in intricate detail, and to build a new bridge between low energy and high energy phenomena characterized by metastability within a first order phase transition. In this spirit our work opens up new avenues in the understanding of early universe, as well as ferromagnetic quantum phase transitions. The possibility of engineering the barrier properties via injection of tailored noise and of deterministically seeding bubbles are promising future directions for experimental investigations with focus on the role of dissipation,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 87, 881, 210]]<|/det|>
+the existence of shortcut- to- adiabaticity [29, 30], the creation of entanglement, of domain wall confinement [31], and relativistic and non relativistic aspects of the bubble nucleation and dynamics. Furthermore an experimental effort towards colder systems would allow us to reach the tunneling regime dominated by quantum fluctuations. A natural extension of the present work goes to dimensionality larger than one, where the theoretical treatment is challenging.  
+
+<|ref|>text<|/ref|><|det|>[[113, 227, 882, 502]]<|/det|>
+Acknowledgements - We thank A. Biella and P. Hauke for fruitful discussions. We acknowledge funding from Provincia Autonoma di Trento, from INFN through the FISH project, from the Italian MIUR under the PRIN2017 project CEnTraL (Protocol Number 20172H2SC4), from the European Union's Horizon 2020 research and innovation Programme through the STAQS project of QuantERA II (Grant Agreement No. 101017733), from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 804305), from the UK Quantum Technologies for Fundamental Physics programme (grants ST/T00584X/1 and ST/W006162/1) and from PNRR MUR project PE0000023- NQSTI. This work was supported by Q@TN, the joint lab between University of Trento, FBK - Fondazione Bruno Kessler, INFN - National Institute for Nuclear Physics and CNR - National Research Council.  
+
+<|ref|>text<|/ref|><|det|>[[114, 545, 882, 668]]<|/det|>
+Author contribution - G.F., G.L. and A.Z. conceived the project. R.C., C.R., and A.Z. performed the experiments and analyzed the data. A.B., I.C., I.M., T.B., and A.R. performed the theoretical analysis. A.B. developed the numerical code and performed the simulations. G.F. supervised the project. All authors contributed to the discussion and interpretation of the results and paper writing.  
+
+<|ref|>text<|/ref|><|det|>[[114, 711, 881, 780]]<|/det|>
+Data availability - Data in paper figures are available in Extended data. Two dimensional raw atomic cloud pictures from all experimental runs and analysis code are available upon request to A.Z.  
+
+<|ref|>text<|/ref|><|det|>[[140, 825, 647, 844]]<|/det|>
+Corresponding author - Correspondence to A.Z., G.L. and A.R.  
+
+<|ref|>text<|/ref|><|det|>[[140, 888, 827, 905]]<|/det|>
+Ethics declarations: Competing interests - The authors declare no competing interests.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[446, 89, 546, 105]]<|/det|>
+## METHODS  
+
+<|ref|>sub_title<|/ref|><|det|>[[253, 128, 739, 147]]<|/det|>
+### I. FERROMAGNETISM IN ELONGATED MIXTURES  
+
+<|ref|>text<|/ref|><|det|>[[113, 171, 880, 242]]<|/det|>
+The ferromagnetic properties of atomic superfluid coupled mixtures are experimentally measured and discussed in [27]. Here we summarize the key ingredients which help understanding the results presented in the main text of the article.  
+
+<|ref|>text<|/ref|><|det|>[[113, 247, 882, 448]]<|/det|>
+Our system is composed of two sodium hyperfine states \(|F,m_{F}\rangle = |2, - 2\rangle \equiv |\uparrow \rangle\) and \(|1, - 1\rangle \equiv\) \(|\downarrow \rangle\) , where \(F\) is the total angular momentum and \(m_{F}\) its projection. The two populations \(n_{\uparrow}(x,y)\) and \(n_{\downarrow}(x,y)\) are independently measured by shadow imaging. Starting from the two two- dimensional pictures of the cloud, we determine the relative magnetization \(Z(x)\) as \(Z(x) =\) \((n_{\uparrow}(x) - n_{\downarrow}(x)) / n(x)\) , where \(n_{\uparrow ,(\downarrow)}(x) = \int n_{\uparrow ,(\downarrow)}(x,y)dy\) and \(n(x) = \int (n_{\uparrow}(x,y) + n_{\downarrow}(x,y))dy\) are the 1D integrated densities. The integration along \(y\) takes advantage of the suppressed radial dynamics. In local density approximation (LDA), the energy per particle associated to the spin channel of the mixture is  
+
+<|ref|>equation<|/ref|><|det|>[[317, 454, 877, 489]]<|/det|>
+\[E(Z,\phi)\propto -\frac{\delta_{f}}{2} Z + \frac{\kappa n}{2} Z^{2} - \Omega_{\mathrm{R}}\sqrt{1 - Z^{2}}\cos \phi \quad (4)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 499, 881, 571]]<|/det|>
+where the phase \(\phi\) is the relative phase between \(|\uparrow \rangle\) and \(|\downarrow \rangle\) . The detuning \(\delta_{f}\) used in the text is equal to \(\delta_{\mathrm{B}} + n\Delta\) where \(\delta_{\mathrm{B}}\) is the experimental controllable detuning. The quantity \(\kappa\) and \(\Delta\) are associated to the collisional proprieties of the mixture and are  
+
+<|ref|>equation<|/ref|><|det|>[[398, 581, 877, 647]]<|/det|>
+\[\begin{array}{l}\Delta \equiv \frac{g_{\downarrow\downarrow} - g_{\uparrow\uparrow}}{2\hbar} < 0\\ \kappa \equiv \frac{g_{\downarrow\downarrow} + g_{\uparrow\uparrow}}{2\hbar} -\frac{g_{\downarrow\uparrow}}{\hbar} < 0 \end{array} \quad (6)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 655, 880, 701]]<|/det|>
+where \(g_{\downarrow \downarrow},g_{\uparrow \uparrow}\) and \(g_{\downarrow \uparrow}\) are the two intra species and the inter species coupling constants. Note that \(n\Delta\) derives from the \(|\uparrow \rangle\) and \(|\downarrow \rangle\) self interaction asymmetry.  
+
+<|ref|>text<|/ref|><|det|>[[113, 707, 882, 932]]<|/det|>
+In an elongated cloud having a parabolic Thomas Fermi density profile, the ferromagnetic phase is located in the center of the cloud where the non liner term \(|\kappa |nZ^{2} / 2\) is maximal. Under the condition \(|\kappa |n< \Omega\) , in fact, the energy per particle is characterized by a symmetric double minimum structures a signature of the symmetry breaking typical of the ferromagnetic phase. At non zero detuning, the symmetry of the two wells is broken. Thanks to the tuning knob \(\delta_{B}\) , which is linearly proportional to the applied magnetic field, one can change the relative energy difference between the two energy minima, converting one or the other state into the absolute ground state or the metastable state. The tails of the cloud remain in the paramagnetic regime, having smaller density, and \(Z\) of the only energy minimum is unambiguously determined by \(\delta_{\mathrm{B}}\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 882, 234]]<|/det|>
+Due to the asymmetry between \(|\uparrow \rangle\) and \(|\downarrow \rangle\) , there exists a range of values of \(\delta_{\mathrm{B}}\) where the sign of the \(Z\) at the energy minima in the center \((- )\) and at the tails \((+)\) is opposite, but the system can still maintain a homogeneous positively- magnetized profile being metastable in the center. When the detuning is decreased below the critical value \(\delta_{c}\) (see main text), the metastable minimum disappears resulting in a unique steady magnetic profile with negative \(Z\) in the center and positive \(Z\) in the tails.  
+
+<|ref|>text<|/ref|><|det|>[[113, 243, 882, 365]]<|/det|>
+While the spin energy profiles of Eq. (4) are useful to explain the presence of two minima separated, this LDA representation only shows the LDA energy landscape per particle and not the total energy of the system. For instance, the LDA energy profiles don't include the contribution coming from the interface between opposite \(Z\) , whose kinetic energy represents a further contribution to the total energy barrier, as intended to be shown in Fig. 1 in the main text.  
+
+<|ref|>sub_title<|/ref|><|det|>[[267, 400, 725, 419]]<|/det|>
+## II. CALIBRATION AND ANALYSIS PROCEDURE  
+
+<|ref|>text<|/ref|><|det|>[[113, 443, 882, 540]]<|/det|>
+An important calibration concerns the determination of the critical detuning at which the double well energy landscape is expected to disappear. We determine \(\delta_{c}\) by performing the same protocols used in [27] to measure the hysteresis width of the ferromagnetic regime. This consists in the same ramp shown Fig. 2(a) of the main text, applied with a null waiting time.  
+
+<|ref|>text<|/ref|><|det|>[[113, 547, 882, 745]]<|/det|>
+The data used in the main text are obtained in the range of \(\delta\) directly above the critical one. Thanks to the appearing of the bubble in the center of the cloud, we first determine the presence of the bubble by fixing a threshold \(Z_{\mathrm{bubble}} = 0.2\) . If the average magnetization in the central 40 pixels is below \(Z_{\mathrm{bubble}}\) , one bubble is counted. The total bubble counts at fixed waiting time determines the probability \(P\) , as plotted in Fig. 2(c) of the main text. We verify that the choice of the threshold \(Z_{\mathrm{bubble}}\) and the averaging area do not critically impact on the outcomes presented here. Once the bubble is detected, the full magnetization profile is initially fitted by using a double sigmoidal function,  
+
+<|ref|>equation<|/ref|><|det|>[[335, 758, 877, 799]]<|/det|>
+\[A\left[\arctan \left(\frac{x - x_{r}}{s_{r}}\right) - \arctan \left(\frac{x - x_{l}}{s_{l}}\right)\right] \quad (7)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 809, 882, 932]]<|/det|>
+where \(A\) is the amplitude and \(x_{(r),[l]}\) and \(s_{(r),[l]}\) are the (right) [left] centers and sigmas of the two sigmoids. The positions \(x_{(l),[r]}\) are then used as starting values for a second fitting routine that independently analyses the left and right bubble interfaces. This second step is used to better determine the exact positions of the interfaces without the effects of cloud asymmetry and offsets. The obtained values \(x_{(l),[r]}\) allow to determine the bubble size as \(\sigma_{x} = x_{r} - x_{l}\)
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[248, 88, 744, 108]]<|/det|>
+## III. DETERMINATION OF \(\tau\) AND ALTERNATIVE \(\tau_{50\%}\)  
+
+<|ref|>text<|/ref|><|det|>[[114, 130, 881, 202]]<|/det|>
+In the main text we explain how we determine the characteristic decay time \(\tau\) by fitting \(F_{t}\) to \((1 - \epsilon) / \sqrt{1 + (e^{t / \tau} - 1)^{2}} + \epsilon\) . This formula allows us to extract \(\tau\) even for experimental sequences with limited statistics and it results to be robust against the initialisation of the fitting parameters.  
+
+<|ref|>text<|/ref|><|det|>[[114, 208, 881, 305]]<|/det|>
+To verify the solidity of our approach we also considered a different characteristic time \(\tau_{50\%}\) defined as the time at which the probability \(P\) to observe a bubble is \(50\%\) . This approach is a valid alternative for measurements featuring a limited statistics. To determine \(\tau_{50\%}\) we fit \(P\) with the following function:  
+
+<|ref|>equation<|/ref|><|det|>[[380, 323, 877, 344]]<|/det|>
+\[P(t) = \mathrm{Min}[a_{1}*(e^{t / a_{2}} - 1),1] \quad (8)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 364, 772, 384]]<|/det|>
+with \(a_{1}\) and \(a_{2}\) as free parameters. These two are then used to determine \(\tau_{50\%}\) from  
+
+<|ref|>equation<|/ref|><|det|>[[408, 394, 877, 428]]<|/det|>
+\[\frac{1}{2} = a_{1}*(e^{t_{50\%} / a_{2}} - 1) \quad (9)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 440, 881, 592]]<|/det|>
+We check, within the statistical uncertainties, that the value of \(\tau_{50\%}\) does not change by using different fitting functions (linear, exponential with offsets in time and \(P\) ). Figure M1 shows that \(\tau\) and \(\tau_{50\%}\) are compatible both for the experimental measurements and numerical simulations. In particular, simulation results allow us to conclude that, while \(\tau_{50\%}\) is expected to be influenced by the delay time before the bubble decays, \(\tau_{50\%}\) is still a good approximation of \(\tau\) . This suggests that the delay time and \(\tau\) are related and further investigations are necessary to understand how.  
+
+<|ref|>text<|/ref|><|det|>[[114, 596, 881, 642]]<|/det|>
+In general, we conclude that the determination of \(\tau\) used in the main text is solid. In particular, one notes that the two methods rely on two very different observables, the mean magnetization  
+
+<|ref|>image<|/ref|><|det|>[[270, 663, 725, 840]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 862, 881, 928]]<|/det|>
+<center>FIG. M1. \(\tau\) vs \(\tau_{50\%}\) for experimental (a) and numerical (b) results. The two quantity are compatible to each other within error bars in experimental results and show only small deviation in simulation data. Color code for the points is the same used in the main text and the blue line marks \(\tau = \tau_{50\%}\) . </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 880, 135]]<|/det|>
+in the center, averaged over all experimental shots ( \(\tau\) ), and the probabilistic presence of a bubble \((\tau_{50\%})\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[342, 169, 650, 187]]<|/det|>
+## IV. NUMERICAL SIMULATIONS  
+
+<|ref|>text<|/ref|><|det|>[[113, 211, 882, 386]]<|/det|>
+The numerical results presented in the main text are based on one- dimensional Gross- Pitaevskii simulations. The parameters are chosen to faithfully reproduce the experimental conditions: in particular, the system trapped by a harmonic potential with frequency \(\omega_{0} \simeq 2\pi \times 16 \mathrm{Hz}\) , so that the Thomas- Fermi radius is \(L \simeq 200 \mu \mathrm{m}\) ; moreover, interactions are chosen to obtain \(|\kappa |n_{0} = |\Delta |n_{0} \simeq 2\pi \times 1.1 \mathrm{kHz}\) , \(n_{0}\) being the total density in the center of the cloud. The system is first prepared, through imaginary- time evolution, in the ground state corresponding to \(\delta_{f} = 2\pi \times 1 \mathrm{kHz}\) , thus, regardless of the value of \(\Omega_{R}\) , it is almost fully polarized in the \(|\uparrow \rangle\) state.  
+
+<|ref|>text<|/ref|><|det|>[[113, 392, 882, 667]]<|/det|>
+A white noise of amplitude equal to \(3\%\) of the central density is added on top of the ground state: this corresponds to an injected energy of roughly \(\epsilon /k_{B} = 215 \mathrm{nK}\) . We then let the system evolve in real time, without changing any parameter and we observe that, after a transient, the noise distribution becomes stationary; we interpret this result as thermalization of the mixture to a temperature \(T \propto \epsilon\) . Under an ergodicity assumption, we can determine the dynamics of the system by averaging over many repetitions of the same time- evolution, each one obtained starting from a different noisy sample. To summarize, we perform mean- field simulations in which noise plays the role of an effective temperature. Of course, these do not allow to investigate the role of quantum fluctuations: however, since the estimated experimental temperature is much higher than \(|\kappa |n_{0} / k_{B} \sim 50 \mathrm{nK}\) , the dynamics is likely to be dominated by thermal noise and a comparison with classical field simulations is justified.  
+
+<|ref|>text<|/ref|><|det|>[[113, 675, 881, 771]]<|/det|>
+The real- time dynamics after thermalization reproduces, once again, the experimental protocol: a detuning ramp with speed \(\sim 50 \mathrm{Hz / ms}\) is applied in order to reach the false vacuum state corresponding to some final \(\delta_{f} < 0\) ; the magnetization of the system is then monitored for a waiting time in the range \([10, 300] \mathrm{ms}\) , depending on the simulation parameters.  
+
+<|ref|>text<|/ref|><|det|>[[137, 778, 707, 797]]<|/det|>
+In order to extract the characteristic decay time \(\tau\) and \(\tau_{50}\) , we compute:  
+
+<|ref|>equation<|/ref|><|det|>[[386, 809, 877, 846]]<|/det|>
+\[F(t) = \frac{\langle Z(x \sim 0, t) \rangle - Z_{TV}}{Z_{FV} - Z_{TV}} \quad (10)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 860, 882, 932]]<|/det|>
+where \(\langle Z(x \sim 0, t) \rangle\) is the statistical average of magnetization over the central \(10 \mu \mathrm{m}\) of the cloud. If the number of samples is sufficiently high (we use 1000), this function represents the probability of not observing a bubble at time \(t\) . Therefore, \(\tau_{50}\) is computed, by definition, by solving \(F(\tau_{50}) = 0.5\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 881, 185]]<|/det|>
+The FVD rates are obtained instead via a linear fit of \(\log F(t)\) : in most cases the predicted exponential behaviour is found within a time interval corresponding to \(F(t) \in [0.3, 0.7]\) ; small adjustments of this window are necessary for the simulations associated to the smallest and longest tunnelling times.  
+
+<|ref|>sub_title<|/ref|><|det|>[[421, 216, 572, 234]]<|/det|>
+## V. ISTANTONS  
+
+<|ref|>text<|/ref|><|det|>[[113, 258, 881, 355]]<|/det|>
+The theoretical description of vacuum decay is non- perturbative and based on instanton solutions to the equations of motion using an imaginary time coordinate. The classical field theory for this system reduces down to a field theory for the magnetisation \(Z\) . For thermal instantons, bubbles nucleate at a rate (see e.g.[14])  
+
+<|ref|>equation<|/ref|><|det|>[[384, 370, 877, 392]]<|/det|>
+\[\Gamma = 1 / \tau = A(\beta E_{c})^{j / 2}e^{-\beta E_{c}}. \quad (11)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 408, 882, 660]]<|/det|>
+where \(\beta = 1 / (k_{B}T)\) and \(E_{c}\) is the energy of the instanton. The factor \(A\) depends on fluctuations about the instanton and \(j\) is the number of translational symmetries. There should be one zero mode \(j = 1\) if there is translational invariance in the system. (The bubbles in the experiment always nucleate near the centre, so translational invariance is suspect. Fortunately, the power law dependence has only a small effect on the results). There are a very limited number of models for which the pre- factor \(A\) is calculable at present, and we will therefore regard \(A\) as a fitting parameter in the subsequent analysis. Note that the non- perturbative approach is valid when the exponent is larger than one, i.e. for temperatures \(k_{B}T < E_{c}\) . At even lower temperatures, vacuum fluctuations become the dominant seeding mechanism. In our system this happens for \(k_{B}T < \hbar |\kappa |n \sim 50 \mathrm{nK}\) , and the resulting vacuum decay rate would be far less than the rate seen in the experiment.  
+
+<|ref|>text<|/ref|><|det|>[[138, 666, 673, 685]]<|/det|>
+The energy for a thermal instanton includes a gradient contribution  
+
+<|ref|>equation<|/ref|><|det|>[[361, 693, 877, 732]]<|/det|>
+\[E_{c} = \frac{\hbar n}{4}\int \left\{\frac{\hbar}{2m}\frac{(\nabla Z)^{2}}{1 - Z^{2}} + V\right\} dx, \quad (12)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 741, 270, 758]]<|/det|>
+where the potential  
+
+<|ref|>equation<|/ref|><|det|>[[352, 774, 877, 795]]<|/det|>
+\[V = \kappa nZ^{2} - 2\Omega_{R}(1 - Z^{2})^{1 / 2} - 2\delta_{\mathrm{f}}Z. \quad (13)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 811, 881, 881]]<|/det|>
+We can scale out the dependence on the density so that \(\hat{E}_{c} = E_{c} / (\hbar n^{2}\xi |\kappa |)\) for the length scale \(\xi = \hbar /(m|\kappa |n)^{1 / 2}\) . For thermal bubbles in one dimension, the instanton calculation is equivalent to a WKB approximation to the action, with the familiar WKB form  
+
+<|ref|>equation<|/ref|><|det|>[[328, 890, 877, 932]]<|/det|>
+\[\hat{E}_{c} = \frac{1}{2}\int_{Z_{TP}}^{Z_{FV}}\left(\frac{2(V - V_{FV})}{|\kappa|n}\right)^{1 / 2}\frac{dZ}{\sqrt{1 - Z^{2}}}, \quad (14)\]
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[113, 140, 880, 283]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[113, 97, 880, 138]]<|/det|>
+TABLE I. Fitting coefficients for the thermal instanton model of vacuum decay with \(j = 1\) . The fit is limited to \((\delta_{f} - \delta_{c}) / \Omega_{R} > 0.05\) to ensure that \(b\hat{E}_{c} > 1\)   
+
+<table><tr><td>ΩR/2π</td><td>aexp(σa)</td><td>bexp(σb)</td><td>asim(σa)</td><td>bsim(σb)</td></tr><tr><td>300</td><td>0.54(0.09)</td><td>56.5(1.9)</td><td>0.93(0.06)</td><td>55.0(1.9)</td></tr><tr><td>400</td><td>0.83(0.42)</td><td>44.4(6.1)</td><td>0.70(0.07)</td><td>41.3(0.87)</td></tr><tr><td>600</td><td>0.02(0.43)</td><td>30.3(3.7)</td><td>0.01(0.14)</td><td>29.8(1.3)</td></tr><tr><td>800</td><td>0.30(0.75)</td><td>25.8(5.7)</td><td>-0.44(0.11)</td><td>25.3(0.9)</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[114, 307, 880, 352]]<|/det|>
+The integral extends from the turning point \(Z_{TP}\) to the false vacuum \(Z_{FV}\) . The extra factor \((1 - Z^{2})^{- 1 / 2}\) is due to the form of the derivative terms in the energy (12).  
+
+<|ref|>text<|/ref|><|det|>[[113, 360, 882, 507]]<|/det|>
+The experimental data has been used to determine the best parameters in a fit for \(\ln \tau = \ln A + b\hat{E}_{c} - \ln (b\hat{E}_{c}) / 2\) . The results are given in Table I. The condensate number density is given by \(n = (k_{B}T / \hbar |\kappa |n)b / \xi\) . For the temperature \(T = 1\mu \mathrm{K}\) , the values of \(n\) at lower \(\Omega\) are around half of the value expected for the system, but not unreasonable given the limitations of the one dimensional treatment. If the bubble only fills a fraction of the cross- section, it effectively feels only part of the integrated density.  
+
+<|ref|>text<|/ref|><|det|>[[114, 514, 880, 558]]<|/det|>
+In the case of small potential barriers, the potential can be expanded to cubic order about an inflection point at \(Z_{c}\) and \(\delta = \delta_{c}\) , where  
+
+<|ref|>equation<|/ref|><|det|>[[311, 572, 878, 630]]<|/det|>
+\[\delta_{c} = \kappa n(1 - Z_{c}^{3}),\qquad Z_{c} = \left(1 - \left(\frac{\Omega_{R}}{|\kappa|n}\right)^{\frac{2}{3}}\right)^{\frac{1}{2}}. \quad (15)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 644, 514, 662]]<|/det|>
+The integral in this case can be performed exactly,  
+
+<|ref|>equation<|/ref|><|det|>[[325, 672, 878, 720]]<|/det|>
+\[\hat{E}_{c}\approx 1.77\left(\frac{\delta_{f} - \delta_{c}}{|\kappa|n}\right)^{\frac{5}{4}}\left(\frac{\Omega_{R}}{|\kappa|n}\right)^{\frac{1}{6}}\left(\frac{|\delta_{c}|}{|\kappa|n}\right)^{-\frac{1}{4}} \quad (16)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 733, 881, 826]]<|/det|>
+To verify that the instanton prediction and simulation are consistent, we repeat numerical simulations at fixed \(\delta_{f}\) and variable \(\epsilon\) . We observe that the extracted \(\tau\) results proportional to \(e^{(1 / \epsilon)}\) and this well justifies the association between the injected noise parameter \(\epsilon\) and the temperature \(T\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 883, 130]]<|/det|>
+[2] K. C. Kulander, K. J. Schafer, and J. L. Krause, Atoms in Intense Laser Fields (Academic Press, New York, 1992) p. 247.  
+
+<|ref|>text<|/ref|><|det|>[[115, 134, 883, 175]]<|/det|>
+[3] G. Lagnese, F. M. Surace, M. Kormos, and P. Calabrese, False vacuum decay in quantum spin chains, Phys. Rev. B 104, L201106 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[115, 180, 882, 220]]<|/det|>
+[4] A. Milsted, J. Liu, J. Preskill, and G. Vidal, Collisions of false- vacuum bubble walls in a quantum spin chain, PRX Quantum 3, 020316 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[115, 225, 883, 333]]<|/det|>
+[5] A. J. Baldwin, T. P. J. Knowles, G. G. Tartaglia, A. W. Fitzpatrick, G. L. Devlin, S. L. Shammas, C. A. Waudby, M. F. Mossuto, S. Meehan, S. L. Gras, J. Christodoulou, S. J. Anthony- Cahill, P. D. Barker, M. Vendruscolo, and C. M. Dobson, Metastability of native proteins and the phenomenon of amyloid formation, Journal of the American Chemical Society 133, 14160 (2011), pMID: 21650202, https://doi.org/10.1021/ja2017703.  
+
+<|ref|>text<|/ref|><|det|>[[115, 338, 814, 356]]<|/det|>
+[6] D. Ghosh and A. Ranjan, The metastable states of protein, Protein Science 29, 1559 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[115, 360, 883, 401]]<|/det|>
+[7] C. Hogan, Gravitational radiation from cosmological phase transitions, Monthly Notices of the Royal Astronomical Society 218, 629 (1986).  
+
+<|ref|>text<|/ref|><|det|>[[115, 405, 881, 446]]<|/det|>
+[8] M. E. Shaposhnikov, Baryon Asymmetry of the Universe in Standard Electroweak Theory, Nucl. Phys. B 287, 757 (1987).  
+
+<|ref|>text<|/ref|><|det|>[[115, 450, 882, 514]]<|/det|>
+[9] S. M. Feeney, M. C. Johnson, D. J. Mortlock, and H. V. Peiris, First observational tests of eternal inflation: Analysis methods and wmap 7- year results, Phys. Rev. D 84, 043507 (2011), arXiv:1012.3667 [astro- ph.CO].  
+
+<|ref|>text<|/ref|><|det|>[[115, 518, 881, 559]]<|/det|>
+[10] C. G. Callan and S. R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16, 1762 (1977).  
+
+<|ref|>text<|/ref|><|det|>[[115, 563, 881, 605]]<|/det|>
+[11] S. R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15, 2929 (1977), [Erratum: Phys. Rev. D 16, 1248 (1977)].  
+
+<|ref|>text<|/ref|><|det|>[[115, 609, 881, 650]]<|/det|>
+[12] A. D. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Phys. B 216, 421 (1983), [Erratum: Nucl.Phys.B 223, 544 (1983)].  
+
+<|ref|>text<|/ref|><|det|>[[115, 655, 881, 696]]<|/det|>
+[13] A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and experimental signatures, Rept. Prog. Phys. 82, 076901 (2019), arXiv:1811.01948 [hep- ph].  
+
+<|ref|>text<|/ref|><|det|>[[115, 700, 881, 741]]<|/det|>
+[14] M. Hindmarsh, M. Luben, J. Lumma, and M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes, 24 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[115, 745, 881, 787]]<|/det|>
+[15] O. Fialko, B. Opanchuk, A. I. Sidorov, P. D. Drummond, and J. Brand, Fate of the false vacuum: Towards realization with ultra- cold atoms, Europhysics Letters 110, 56001 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[115, 791, 881, 832]]<|/det|>
+[16] J. Braden, M. C. Johnson, H. V. Peiris, and S. Weinfurtner, Towards the cold atom analog false vacuum, Journal of High Energy Physics 2018, 2018 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[115, 836, 881, 877]]<|/det|>
+[17] T. P. Billam, R. Gregory, F. Michel, and I. G. Moss, Simulating seeded vacuum decay in a cold atom system, Phys. Rev. D 100, 065016 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[115, 882, 881, 923]]<|/det|>
+[18] Z. Davoudi, M. Hafezi, C. Monroe, G. Pagano, A. Seif, and A. Shaw, Towards analog quantum simulations of lattice gauge theories with trapped ions, Phys. Rev. Res. 2, 023015 (2020).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 883, 130]]<|/det|>
+[19] T. P. Billam, K. Brown, and I. G. Moss, Simulating cosmological supercooling with a cold- atom system, Phys. Rev. A 102, 043324 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[112, 133, 883, 175]]<|/det|>
+[20] T. P. Billam, K. Brown, A. J. Groszek, and I. G. Moss, Simulating cosmological supercooling with a cold atom system. ii. thermal damping and parametric instability, Phys. Rev. A 104, 053309 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[113, 179, 882, 242]]<|/det|>
+[21] K. L. Ng, B. Opanchuk, M. Thenabadu, M. Reid, and P. D. Drummond, Fate of the false vacuum: Finite temperature, entropy, and topological phase in quantum simulations of the early universe, PRX Quantum 2, 010350 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[113, 246, 882, 310]]<|/det|>
+[22] B. Song, S. Dutta, S. Bhave, J.- C. Yu, E. Carter, N. Cooper, and U. Schneider, Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice, Nature Physics 18, 259- 264 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[113, 314, 882, 355]]<|/det|>
+[23] J. Preskill, Simulating quantum field theory with a quantum computer, PoS LATTICE2018, 024 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[113, 359, 882, 401]]<|/det|>
+[24] S. Abel and M. Spannowsky, Quantum- field- theoretic simulation platform for observing the fate of the false vacuum, PRX Quantum 2, 010349 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[113, 405, 882, 446]]<|/det|>
+[25] H. Grabert and U. Weiss, Crossover from thermal hopping to quantum tunneling, Phys. Rev. Lett. 53, 1787 (1984).  
+
+<|ref|>text<|/ref|><|det|>[[113, 450, 882, 492]]<|/det|>
+[26] H. Grabert, U. Weiss, and P. Hanggi, Quantum tunneling in dissipative systems at finite temperatures, Phys. Rev. Lett. 52, 2193 (1984).  
+
+<|ref|>text<|/ref|><|det|>[[113, 495, 882, 560]]<|/det|>
+[27] R. Cominotti, A. Berti, C. Dulin, C. Rogora, G. Lamporesi, I. Carusotto, A. Recati, A. Zenesini, and G. Ferrari, Ferromagnetism in an extended coherently- coupled atomic superfluid. (to be published in Phys. Rev. X, 2023), arXiv:2209.13235 [cond- mat.quant- gas].  
+
+<|ref|>text<|/ref|><|det|>[[113, 563, 882, 627]]<|/det|>
+[28] A. Farolfi, D. Trypogeorgos, G. Colzi, E. Fava, G. Lamporesi, and G. Ferrari, Design and characterization of a compact magnetic shield for ultracold atomic gas experiments, Review of Scientific Instruments 90, 115114 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[113, 631, 882, 673]]<|/det|>
+[29] D. Guéry- Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez- Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[113, 677, 882, 764]]<|/det|>
+[30] E. Torrontegui, S. Ibáñez, S. Martínez- Garaot, M. Modugno, A. del Campo, D. Guéry- Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, Chapter 2 - shortcuts to adiabaticity, in Advances in Atomic, Molecular, and Optical Physics, Advances In Atomic, Molecular, and Optical Physics, Vol. 62, edited by E. Arimondo, P. R. Berman, and C. C. Lin (Academic Press, 2013) pp. 117- 169.  
+
+<|ref|>text<|/ref|><|det|>[[113, 768, 882, 831]]<|/det|>
+[31] W. L. Tan, P. Becker, F. Liu, G. Pagano, K. S. Collins, A. De, L. Feng, H. B. Kaplan, A. Kyprianidis, R. Lundgren, W. Morong, S. Whitsitt, A. V. Gorshkov, and C. Monroe, Domain- wall confinement and dynamics in a quantum simulator, Nature Physics 17, 742- (2021).
+
+<--- Page Split --->

preprint/preprint__00eb7cf6559fe9e55f1f5595a3abcbbf42befb8fdab5e70d9108735caa725b65/images_list.json

@@ -0,0 +1,100 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Experimental scheme and properties of MAPbI3 perovskite (a) THz pulse geometry with a tetragonal unit cell (black rectangular cuboid) of MAPbI3. (dark grey: Pb, purple: I, brown: C, light blue: N, light pink: H) The THz biasing along the \\(c\\) axis of a crystallite is depicted. (b) Simplified electronic band structure of MAPbI3 in the tetragonal phase along the directions \\(\\Gamma (0,0,0)\\rightarrow \\mathrm{Z}(0,0,0.5)\\) and \\(\\Gamma (0,0,0)\\rightarrow \\mathrm{A}(0.5,0.5,0.5)\\) . The bandwidths and the lattice parameters are used from [Ref \\(^{12}\\) ]. (c) Optical absorption spectrum of MAPbI3 in the spectral range of the probe pulses.",
+    "footnote": [],
+    "bbox": [
+      [
+        201,
+        92,
+        820,
+        388
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Experimental observation of the transient Wannier Stark localization and the visualized diagram (a) Experimental differential transmission spectra on a polycrystalline film of",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        658,
+        866,
+        820
+      ]
+    ],
+    "page_idx": 7
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Numerical simulation of differential absorption spectra (a) Negative change of the optical interband absorption \\(- \\Delta \\alpha_{\\overline{\\Gamma Z}}\\) for static fields from a cosine band modeling along \\(\\overline{\\Gamma Z}\\) direction. The region of electric field strengths up to \\(1\\mathrm{MV / cm}\\) is enlarged to show Franz-Keldysh oscillations and the transition to the Wannier-Stark regime. (b) Calculated \\(- \\Delta \\alpha_{\\overline{\\Gamma Z}}\\) spectra for the excitation with a THz pulse with a peak field strength of \\(E_{0} = 6\\mathrm{MV / cm}\\) , where the delay \\(\\tau\\) between the THz and the optical pulse is varied. (c) Simulated temporal profile of the applied THz bias transient. The pulse duration \\(\\overline{T}\\) is \\(240\\mathrm{fs}\\) , the THz frequency is \\(20\\mathrm{THz}\\) , and the dephasing time is \\(T_{2} = 20\\mathrm{fs}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        92,
+        888,
+        333
+      ]
+    ],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Experiments on polycrystalline system and simulations with averaging of cosine band model from \\(\\Gamma Z\\) to \\(\\Gamma A\\) direction. (a) Illustration for the averaging process over the interpolation parameter \\(f\\) from the \\(\\overline{\\Gamma Z}\\) direction \\((f = 0)\\) to \\(\\overline{\\Gamma A}\\) direction \\((f = 1)\\) . The negative absorption changes \\(-\\Delta \\alpha_{f}\\) are calculated for different one-dimensional systems using a THz pulse centered at \\(t = 0\\) , with an amplitude of \\(E_{0} = 4 \\mathrm{MV / cm}\\) , a pulse duration of \\(\\overline{T} = 240 \\mathrm{fs}\\) , and a THz center frequency of \\(20 \\mathrm{THz}\\) . (b) Temporal slices of \\(\\Delta T / T\\) as a function of probe photon energy (Fig. 2(a)), at a delay time corresponding to the contour with constant electric field amplitudes \\(E\\) (Fig. 2(b)). (c) averaged absorption change, \\(-\\Delta \\alpha_{\\mathrm{avg}}\\) , for static fields of various strengths. (d) averaged absorption change, \\(-\\Delta \\alpha_{\\mathrm{avg}}\\) , for a THz pulse centered at \\(t = 0\\) and various field strengths.",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
+        92,
+        881,
+        576
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
+    "footnote": [],
+    "bbox": [
+      [
+        60,
+        100,
+        940,
+        536
+      ]
+    ],
+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
+    "bbox": [
+      [
+        55,
+        52,
+        485,
+        614
+      ]
+    ],
+    "page_idx": 31
+  }
+]

preprint/preprint__00eb7cf6559fe9e55f1f5595a3abcbbf42befb8fdab5e70d9108735caa725b65/preprint__00eb7cf6559fe9e55f1f5595a3abcbbf42befb8fdab5e70d9108735caa725b65.mmd

@@ -0,0 +1,424 @@
+
+# Low-field Onset of Wannier-Stark Localization in a Polycrystalline Hybrid Organic Inorganic Perovskite  
+
+Daniel Berghoff  Paderborn University  Johannes Bühler  University of Konstanz  
+
+Mischa Bonn  Max Planck Institute for Polymer Research  
+
+Alfred Leitenstorfer  University of Konstanz  
+
+Torsten Meier  University of Paderborn  https://orcid.org/0000- 0001- 8864- 2072  
+
+Heejae Kim ( kim@mpip-mainz.mpg.de)  Max Planck Institute for Polymer Research  
+
+## Article  
+
+Keywords: Wannier- Stark localization, Electron confinement, Ultrafast Biasing, Optical modulation, Hybrid perovskites  
+
+Posted Date: April 8th, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 386040/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Version of Record: A version of this preprint was published at Nature Communications on September 29th, 2021. See the published version at https://doi.org/10.1038/s41467- 021- 26021- 4.
+
+<--- Page Split --->
+
+# Low-field Onset of Wannier-Stark Localization in a Polycrystalline Hybrid Organic Inorganic Perovskite  
+
+Daniel Berghoff \(^{1}\) , Johannes Bühler \(^{2}\) , Mischa Bonn \(^{3}\) , Alfred Leitenstorfer \(^{2}\) , Torsten Meier \(^{*1}\) , Heejae Kim \(^{*3}\)  
+
+\(^{1}\) Department of Physics, Paderborn University, D- 33098 Paderborn, Germany  
+
+\(^{2}\) Department of Physics and Center for Applied Photonics, University of Konstanz, D- 78457 Konstanz, Germany  
+
+\(^{3}\) Department of Molecular Spectroscopy, Max Planck Institute for Polymer Research, D- 55128 Mainz, Germany  
+
+## KEYWORDS  
+
+Wannier- Stark localization, Electron confinement, Ultrafast Biasing, Optical modulation, Hybrid perovskites
+
+<--- Page Split --->
+
+## ABSTRACT  
+
+Control over light propagation in a material by applying external fields is at the heart of photonic applications. Here, we demonstrate ultrafast modulation of the optical properties in the room temperature polycrystalline MAPbI₃ perovskite using phase- stable terahertz pulses, centered at 20 THz. The biasing field from the THz pulse creates extreme localization of electronic states in the ab plane – Wannier- Stark localization. This quasi- instantaneous reduction of dimensionality (from 3D to 2D) causes a marked change in the absorption shape, enabling the modulation depth to be tens of percent at moderate field strengths (3 MV/cm). The notably low- field onset results from a narrow electronic bandwidth, a large relevant lattice constant, and the coincidence of the two along the same direction in this tetragonal perovskite. We show that the transient optical response is in fact dominated by the least dispersive direction of the electronic band structure, facilitating a substantial modulation despite the arbitrary arrangement of the individual crystallites. The demonstration of THz- field- induced optical modulation in a solution- processed, disordered, and polycrystalline material is of substantial potential significance for novel photonic applications.  
+
+## Introduction  
+
+The intriguing properties of electrons in periodic potentials in the presence of strong external electric fields are highly relevant for photonic applications, including optical modulators, optical switches, and optical signal processing. Drastic changes in optical properties can be achieved via localization of electronic states using externally applied fields. In the presence of strong external electric fields \(E\) , the continuum of electronic energy bands splits into a series of discrete levels in the direction of the field<sup>1</sup>, and the corresponding wave functions are confined on a length scale given by \(\Delta /(eE)\) , where \(\Delta\) is the energetic width of the electronic band in the absence of biasing.
+
+<--- Page Split --->
+
+These localized states, the Wannier- Stark states \(^{2,3}\) , are equally spaced both in energy by an amount \(eED\) , and in space by the lattice period \(D\) . Since a spatial separation of \(nD\) lattice periods results in an energy shift of \(neED\) with respect to the central spatially- direct \((n = 0)\) transition, this Wannier- Stark localization leads to strong spectral modulation of the interband absorption continuum below and above the optical band gap.  
+
+The quantum confinement induced by external fields is an extreme state of matter and has never been achieved under static biasing in natural solids but only in artificial superlattices \(^{4 - 8}\) . So far, only one natural solid, a single crystal GaAs \(^{8}\) has allowed for achieving the Wannier- Stark localization transiently by virtue of the recent availability of extremely intense and phase- stable pulses of multi- terahertz radiation \(^{9,10}\) . The ultrafast biasing fields could reach amplitudes up to several tens of MV/cm \(^{9,10}\) , i.e., field strengths comparable to the interatomic fields. For GaAs, an optimally oriented single crystal was required to observe Wannier- Stark localization with the required field strengths exceeding 10 MV/cm \(^{8}\) .  
+
+Here, we demonstrate the transient Wannier- Stark localization at a substantially lower field strength in a disordered, solution- processed, polycrystalline film of methylammonium lead iodide perovskite (MAPbI \(_{3}\) , Fig. 1(a)). Already at relatively modest field strengths, the thin film's optical transmission is modified by tens of percent. To resolve optical transitions to individual Wannier- Stark states in, e.g., absorption spectra, their energetic spacing needs to be larger than the (total) linewidth \(\Gamma\) , i.e., \(eED > \Gamma\) \(^{4,5,11}\) Due to the small lattice constant of bulk crystals and the large linewidth which results from the scattering of electrons with lattice vibrations and other electrons, the requirement \(eED > \Gamma\) can typically not be fulfilled under stationary external fields below the strength where the dielectric breakdown occurs \(^{6,7}\) . At room temperature, however, this material exhibits a tetragonal structure with lattice parameters of \(a = 8.8 \mathring{\mathrm{A}}\) and \(c = 12.5 \mathring{\mathrm{A}}\) by the expansion
+
+<--- Page Split --->
+
+of the cubic perovskite unit cell \(^{12,13}\) . The periodicities are nearly twice as large as the lattice parameter \(a = 5.6 \text{Å}\) of cubic GaAs \(^{8}\) .  
+
+We will show that the large relevant lattice constant (Fig. 1(a)), the small width of electronic energy bands (Fig. 1(b)), and the coincidence of these two along the same high- symmetry direction lead to Stark localization in this organic perovskite at field amplitudes as low as \(3 \text{MV/cm}\) , i.e., at a fraction of the field strength required to enter this regime in optimally oriented, single- crystalline GaAs. Moreover, the measured differential spectra containing the overall effects from arbitrarily oriented microcrystals are qualitatively well- described by a two- band model with a cosine band structure. By considering different orientations of the microcrystals in our simulations, we demonstrate that the contribution from the direction with the largest periodicity, i.e., the \(\overline{\Gamma Z}\) direction \(c = 12.5 \text{Å}\) , strongly dominates the transient changes of the optical response. These findings, together with its renowned characteristics, make MAPbI \(_3\) a strong candidate for cost- effective, efficient, fast, and sensitive optical modulator materials.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Experimental scheme and properties of MAPbI3 perovskite (a) THz pulse geometry with a tetragonal unit cell (black rectangular cuboid) of MAPbI3. (dark grey: Pb, purple: I, brown: C, light blue: N, light pink: H) The THz biasing along the \(c\) axis of a crystallite is depicted. (b) Simplified electronic band structure of MAPbI3 in the tetragonal phase along the directions \(\Gamma (0,0,0)\rightarrow \mathrm{Z}(0,0,0.5)\) and \(\Gamma (0,0,0)\rightarrow \mathrm{A}(0.5,0.5,0.5)\) . The bandwidths and the lattice parameters are used from [Ref \(^{12}\) ]. (c) Optical absorption spectrum of MAPbI3 in the spectral range of the probe pulses. </center>  
+
+## Results and Discussion  
+
+## Experimental observation of Wannier-Stark Localization  
+
+For applying the strong transient bias, non- resonant in energy with any of the optical phonons and electronic transitions, we employ phase- stable multi- cycle optical pulses with a center frequency of 20 THz. The pump pulse is generated using a difference- frequency generation
+
+<--- Page Split --->
+
+scheme in GaSe \(^{9,10}\) . For comparison, the MAPbI \(_3\) perovskite has a direct bandgap of \(E_{gap} = 1.62 \mathrm{eV}\) (390 THz, Fig. 1(c)) at room temperature. The phonon modes of Pb- I inorganic sublattice are below 10 THz and methylammonium organic molecular vibrations above 26 THz \(^{14}\) . Due to the presence of the organic cation with a low rotational barrier \(^{15}\) , the crystal shows some degree of disorder at elevated temperature and a less pronounced periodicity compared to all- inorganic perovskites \(^{15,16}\) . The sample is a polycrystalline film with a thickness of \(\sim 300 \mathrm{nm}\) spin- coated \(^{17,18}\) on a cyclic olefin/ethylene copolymer substrate (TOPAS \(^{8}\) ) \(^{19}\) . The differential transmission induced by the external electric field transient is probed by near- IR and visible probe pulses, with spectra covering broad interband electronic transition energies between \(1.4 \mathrm{eV}\) and \(2.4 \mathrm{eV}\) (see Fig. S1). The duration of these probe laser pulses is 7 fs, which is significantly shorter than the half- cycle period of the THz pump transients of 25 fs. Details of the experimental settings are described in the Method section and Ref \(^{8}\) .  
+
+Fig. 2(a) shows the differential transmission \(\Delta T / T\) upon applying the THz biasing as a function of delay time between the pump and probe pulses. The peak field strength of the THz pump pulses is \(6.1 \mathrm{MV / cm}\) . As expected for the non- resonant THz pulse, the optical response of the material is instantaneous and peaks when the THz field strength is maximal. The modulation occurs at twice the frequency of the THz pulse (Fig. 2(b)), since the measured differential transmission is at least a third- order nonlinear process \(^{20}\) . In such a centrosymmetric crystal as the room- temperature tetragonal phase of perovskite MAPbI \(_3\) \(^{21}\) , no contribution from the electro- optic effect is expected which is linear in the electric bias field. The clear temporal modulation of differential transmission appears at high fields, \(- 100 < \tau < 100 \mathrm{fs}\) , as the strong \(E\) field shortens the interband dephasing time in the vicinity of the bandgap to be comparable to the half- cycle period of 25 fs of the THz
+
+<--- Page Split --->
+
+transient. Thus, the precise arrival time of the probe pulse exciting the interband polarization was resolved within the dephasing time.  
+
+More importantly, two distinct regimes can be identified in the time- resolved transient spectrum (Fig. 2(a)). For relatively weak fields, \(E < 3 \mathrm{MV}\) , for \(\tau < - 100 \mathrm{fs}\) , an induced absorption (blue, \(\Delta T / T < 0\) ) right below and an induced transmission (red, \(\Delta T / T > 0\) ) right above the bandgap of \(E_{gap} = 1.62 \mathrm{eV}\) are observed. The second regime is apparent for field strengths \(\mathrm{E} > 3 \mathrm{MV / cm}\) , occurring between delay times \(- 100 < \tau < 100 \mathrm{fs}\) (Fig. 2(b)). Here, the maximum modulation depth becomes as large as \(38 \%\) at the probe energy of \(E_{pr} = 1.7 \mathrm{eV}\) (Fig. 2(a) and Fig. S2). Also, the transient response covers a significantly extended spectral range, compared to the moderate field regime. The induced transmission (red) above the bandgap now reaches up to \(E_{pr} = 1.9 \mathrm{eV}\) , where it abruptly switches to induced absorption (blue, \(\Delta T / T < 0\) ). This negative region of \(\Delta T / T < 0\) persists at probe energies all the way up to \(E_{pr} = 2.4 \mathrm{eV}\) . This one central step from reduced to increased absorption near the center of the band \(E_{pr} = 2 \mathrm{eV}\) , is a noticeable signature of Stark localization, where the Wannier- Stark states are localized onto one unit cell.  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Experimental observation of the transient Wannier Stark localization and the visualized diagram (a) Experimental differential transmission spectra on a polycrystalline film of </center>
+
+<--- Page Split --->
+
+MAPbI3 perovskite at room temperature, as a function of delay time of probe pulses after THz pump pulses. The THz pulses have a peak field strength of 6.1 MV/cm and a center frequency of 20 THz; the probe pulses have photon energy of \(1.4 \sim 2.4 \mathrm{eV}\) . (b) Temporal profile of the applied THz bias transient. (c) Schematic picture of Wannier Stark localization. In the presence of strong external fields along the \(c\) axis, electronic states (orange: conduction band, blue: valence band) are localized to a few layers of \(ab\) plane, and energetically separated by \(\Delta E_{WSL} = eE_{THzC}\) between adjacent lattice sites. Black arrows depict the interband transitions within the same site \((n = 0)\) and between different sites \((n = \pm 1)\) . (d) The absorbance with and without the external transient biasing. The Wannier- Stark localization effectively reduces the 3D electronic structure into 2D layered structure along the \(ab\) plane, as depicted in blue together with the simplified 3D structure.  
+
+By driving the 3- dimensional (3D) system into Wannier- Stark localization, i.e., localizing it in the field direction, we transiently create an effectively 2D electronic system (Fig. 2(c, d)). Given the unit cell doubling, this optically prepared transient 2D system perpendicular to the \(c\) axis may be directly compared to the physically isolated double- layer structure of PbI6 octahedra. In such 2D perovskites as (BA)2(MA)1-1PbI13+1 perovskites22, the inorganic layers (perpendicular to the \(c\) axis in 3D equivalence) are separated by bulky organic layers23. The bandgap of the 2D quantum well perovskites is widened due to the bandwidth narrowing (mainly due to the zero dispersion along the vertical direction) compared to 3D perovskite24. In the case of (BA)2(MA)1-1PbI13+1 perovskites, where the PbI6 octahedral network forms a double layer \((l = 2)\) , the optical band gap is \(\sim 2.1 \mathrm{eV}\) , which is comparable to the observed \(1.9 \mathrm{eV}^{25}\) . It is noteworthy that the observed Wannier- Stark step at \(E_{pr} = 1.9 \mathrm{eV}\) under THz fields is slightly lower than the expected value under static fields due to the spectral broadening induced by the THz modulation, as will be discussed
+
+<--- Page Split --->
+
+below. Therefore, the abrupt shift of the absorption edge from \(E_{pr} = 1.6 \mathrm{eV}\) to \(1.9 \mathrm{eV}\) at high transient fields (Fig. 2(d)) could be attributed to the transfer of spectral weight from \(\alpha (E_{g,3D} < E_{pr} < E_{g,2D})\) to \(\alpha (E_{g,2D} < E_{pr})\) . Such a THz- induced reduction of dimensionality from a 3D to a 2D system could enable new applications in both transport and optoelectronics due to the relatively easy access to that regime in these hybrid perovskite materials.  
+
+## Simulations considering one orientation  
+
+To capture the essential ingredients responsible for the experimental observations, we carry out theoretical calculations based on different models of increasing complexity. We start with considering perfect alignment of the THz field with the direction along which the joint bandwidth of the highest valence and the lowest conduction band is narrowest. For the case of the tetragonal MAPbI₃ perovskite, the narrowest joint bandwidth, \(\Delta_{\overline{\mathrm{FZ}}} = 0.75 \mathrm{eV}\) , is along the \(\overline{\Gamma Z}\) direction (Fig. 1(b))¹². We thus take into account two one- dimensional bands, i.e., one valence and one conduction band with a cosine- like (tight- binding) band structure and the bandgap of \(1.62 \mathrm{eV}\) . Thus, the energy difference for interband transitions is taken as \(E_{cv}(k) = 1.62 \mathrm{eV} + (\Delta_{\overline{\mathrm{FZ}}} / 2)(1 - \cos (g(k, a) *))\) (see Methods section for details of the function \(g(k, a *)\) ). For this model, the spectra are obtained by numerically solving the semiconductor Bloch equations ²⁶- ²⁸, as described in the Methods section.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. Numerical simulation of differential absorption spectra (a) Negative change of the optical interband absorption \(- \Delta \alpha_{\overline{\Gamma Z}}\) for static fields from a cosine band modeling along \(\overline{\Gamma Z}\) direction. The region of electric field strengths up to \(1\mathrm{MV / cm}\) is enlarged to show Franz-Keldysh oscillations and the transition to the Wannier-Stark regime. (b) Calculated \(- \Delta \alpha_{\overline{\Gamma Z}}\) spectra for the excitation with a THz pulse with a peak field strength of \(E_{0} = 6\mathrm{MV / cm}\) , where the delay \(\tau\) between the THz and the optical pulse is varied. (c) Simulated temporal profile of the applied THz bias transient. The pulse duration \(\overline{T}\) is \(240\mathrm{fs}\) , the THz frequency is \(20\mathrm{THz}\) , and the dephasing time is \(T_{2} = 20\mathrm{fs}\) . </center>  
+
+Already when considering static fields (Fig. 3(a)), the simulation results obtained by this simple model exhibits substantial qualitative similarities with the transient experimental results shown in Fig. 2(a). For all field strengths, increased absorption is present below the bandgap and reduced absorption directly above the band gap. For rather weak field strengths of up to about \(0.5\mathrm{MV / cm}\) , oscillations arising from the Franz- Keldysh effect are visible, shifting towards the band center with
+
+<--- Page Split --->
+
+increasing field. For fields exceeding \(\sim 3 \mathrm{MV / cm}\) , signatures of Wannier- Stark localization become noticeable, as the field- dependent interband transition energies shift to higher and lower energies by \(neED\) with increasing \(E\) (Fig. 2(c)). Starting at around \(3 \mathrm{MV / cm}\) , the condition for Stark localization is fulfilled, i.e., \(eED > \Delta /2\) (meaning that the energy of the \((n = - 1)\) Wannier- Stark state is in the bandgap region, see Fig. 2(c, d)), and therefore, the dominant feature is the step- like change from reduced absorption to induced absorption in the center of the band at \(1.974 \mathrm{eV}\) (this value is the average transition frequency within our model). This step- like change is, in fact, also the main feature visible in the experimental results for sufficiently high fields, i.e., between about \(- 100 < \tau < 100\) fs as shown in Figs. 2 (a).  
+
+Besides, by considering pulsed THz fields, the simulated differential spectra with the same model (Fig. 3(b, c)) well describe both spectral and temporal features in the observed transient modulation of differential transmission spectra (Fig. 2(a)). Fig. 3(b) shows the negative change of the transient absorption, \(- \Delta \alpha_{\mathrm{TFZ}}\) , upon non- resonant biasing with a THz pulse with a peak field strength of \(E_{\theta} = 6 \mathrm{MV / cm}\) and a center frequency of \(20 \mathrm{THz}\) , as shown in Fig. 3(c). Besides temporal modulation of the entire transient spectra at twice the carrier frequency of the THz transient, the dominant feature at sufficiently large field strengths \((- 100 < \tau < 100 \mathrm{fs})\) is the rapid change from increased to reduced transmission in the center of the band \(E_{pr} = 2 \mathrm{eV}\) , which originates from Stark localization. The slightly lower value of the observed central step at \(E_{pr} = 1.9 \mathrm{eV}\) and the asymmetric nature of the spectral shape with respect to the central step (Fig. 2(a)) compared to this simplified model (Fig. 3 (b)) can be explained by the polycrystallinity of the system as discussed below. Given the complexity, disorder, and polycrystallinity of the investigated sample, the required field strength at which this step starts to appear is in surprisingly good agreement with the experiment which confirms that the observed response constitutes a clear
+
+<--- Page Split --->
+
+sign of Wannier- Stark localization. Our interpretations are further supported by Fig. S6, which shows how the results of Fig. 3 change if we consider that the THz field is aligned with the \(\overline{\Gamma}\overline{\mathrm{A}}\) direction instead of the \(\overline{\Gamma}\overline{\mathrm{Z}}\) direction. Comparing those two figures clearly shows that due to the larger bandwidth in the \(\overline{\Gamma}\overline{\mathrm{A}}\) direction the Wannier- Stark localization requires higher field amplitudes to develop and furthermore would lead to a transition from reduced to induced absorption at significantly higher energies as observed in experiment. The effects of different field directions and the averaging over them is discussed in more detail below (see Fig. 4).  
+
+As demonstrated so far, Wannier- Stark localization starts to occur at the field amplitude as low as \(3\mathrm{MV / cm}\) in the MAPBI \(_3\) perovskite, due to the relatively large periodicity, the narrow joint bandwidth, and the coincidence of the two along the same direction. The largest lattice constant of tetragonal MAPBI \(_3\) perovskite, along the \(c\) axis, \(c = 12.5\mathrm{\AA}\) , is more than twice as large as those of conventional all- inorganic semiconductors crystallizing with strong covalent bonds in the diamond, wurtzite, or zincblende forms \((3.5\sim 6.5\mathrm{\AA}\) at \(300\mathrm{K}\) ). This finding arises because (i) the cubic perovskite unit cell is expanded through rotation of ab plane by \(45^{\circ}\) and cell doubling along c axis in the tetragonal phase; and (ii) the pseudocubic lattice parameter formed by relatively large \(\mathrm{Pb^{2 + }}\) and \(\Gamma\) ions is \(6.3\mathrm{\AA}^{13}\) , which is at the larger side of the distribution of parameters for cubic lattice parameters. The pseudocubic lattice parameter is large enough to accommodate large organic molecular cations within the void of their network.  
+
+The direction of the narrowest joint bandwidth of the conduction and valence bands, \(\overline{\Gamma}\overline{\mathrm{Z}}\) , coincides with the \(c\) axis. The conduction band is composed of the overlap of \(\mathrm{Pb(6p) - I(5p)}\) atomic orbitals and the valence band is of that of \(\mathrm{Pb(6s) - I(5p)}\) orbitals \(^{29}\) . Thus, the \(\mathrm{Pb - I}\) bond length as well as the \(\mathrm{Pb - I - Pb}\) angle could determine the widths of both bands and the magnitude of the band
+
+<--- Page Split --->
+
+gap. In the tetragonal MAPbI₃ perovskite, the corner- shared PbI₆ octahedra in cubic phase are tilted about the \(c\) axis in the opposite direction between successive tilts, which reduces the Pb- I- Pb angle from 180° along the diagonal direction of the a and b axis. The smaller Pb- I- Pb bond angle indicates weaker orbital overlap between Pb and I atoms and thus smaller band dispersion along \(\overline{\Gamma}\overline{\mathrm{M}}\) than \(\overline{\Gamma}\overline{\mathrm{Z}}\) . However, the Pb- I bond lengths along the \(c\) axis is known to be longer on average³⁰ and has greater effect on the dispersion than the angle due to the \(\sigma\) bonding nature, which leads to the coincidence of the direction of the largest lattice constant and the narrowest bandwidth. We note that unlike GaAs, the body diagonal direction exhibits the strongest dispersion (\(\overline{\Gamma}\overline{\mathrm{A}}\) ). Overall, the large ionic diameter and the geometric distortion result in the unusually narrow joint bandwidth, lower than 1 eV.  
+
+## Including polycrystallinity by averaging over orientations  
+
+We now account for the system's polycrystallinity by considering contributions to the differential transmittance spectra from crystallites with orientations different from those with the \(c\) axis parallel to the THz field polarization. To include arbitrary orientations of the crystallites into our simulations, we take the \(\overline{\Gamma}\overline{\mathrm{Z}}\) and the \(\overline{\Gamma}\overline{\mathrm{A}}\) directions, i.e., the two extreme directions with the narrowest/broadest bandwidth and simultaneously the smallest/largest distance in k- space (see Fig. 1(b)) and perform an average overall in between bandwidths and extensions of the first Brillouin zone (see Method section), by interpolating between the two limiting cases with a parameter \(f\) . The simulated absorption changes at a field amplitude of \(E_{0} = 4 \mathrm{MV / cm}\) with various interpolation parameters \(f\) 's are shown in Fig. 4 (a) together with the measured differential spectra at different instantaneous field amplitudes of the THz pulse (Fig. 4 (b)). Here, \(f = 0\) denotes the response along the \(\overline{\Gamma}\overline{\mathrm{Z}}\) direction (i.e., the \(c\) - axis), and \(f = 1\) along the \(\overline{\Gamma}\overline{\mathrm{A}}\) direction.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Experiments on polycrystalline system and simulations with averaging of cosine band model from \(\Gamma Z\) to \(\Gamma A\) direction. (a) Illustration for the averaging process over the interpolation parameter \(f\) from the \(\overline{\Gamma Z}\) direction \((f = 0)\) to \(\overline{\Gamma A}\) direction \((f = 1)\) . The negative absorption changes \(-\Delta \alpha_{f}\) are calculated for different one-dimensional systems using a THz pulse centered at \(t = 0\) , with an amplitude of \(E_{0} = 4 \mathrm{MV / cm}\) , a pulse duration of \(\overline{T} = 240 \mathrm{fs}\) , and a THz center frequency of \(20 \mathrm{THz}\) . (b) Temporal slices of \(\Delta T / T\) as a function of probe photon energy (Fig. 2(a)), at a delay time corresponding to the contour with constant electric field amplitudes \(E\) (Fig. 2(b)). (c) averaged absorption change, \(-\Delta \alpha_{\mathrm{avg}}\) , for static fields of various strengths. (d) averaged absorption change, \(-\Delta \alpha_{\mathrm{avg}}\) , for a THz pulse centered at \(t = 0\) and various field strengths. </center>
+
+<--- Page Split --->
+
+As shown in Fig. 4(a), the absorption changes depend strongly on the interpolation parameter \(f\) , i.e., on the bandwidth and the distance to the border of the first Brillouin zone. For \(f = 0\) , which corresponds to the \(\overline{\Gamma Z}\) direction, the field amplitude of \(E_{0} = 4 \mathrm{MV / cm}\) drives the system into the region of Stark localization. Therefore, for a static field of such an amplitude, one would see a strong induced absorption in the band center at \(1.974 \mathrm{eV}\) , which corresponds to an optical transition to the Stark localized state. The transient nature of the THz pulse causes the single negative peak to be split into two peaks and the spectral region of induced absorption to be slightly broadened. With increasing \(f\) , both the bandwidth and the distance to the border of the first Brillouin zone increase. As a result, the minimum field strength for which Stark localization is realized increases significantly by approximately a factor \((c / a_{\overline{\Gamma Z}}^{*})(\Delta_{\overline{\Gamma A}} / \Delta_{\overline{\Gamma Z}})\) , equaling about 4.7. Consequently, already for \(f = 0.25\) , the absorption changes show no sign of Stark localization, with several oscillations emerging owing to the THz driving. This trend of overall weaker absorption changes with some oscillatory structure is also present for even larger \(f\) . The only feature present in all spectra shown in Fig. 4 (a) is some induced absorption below the bandgap and reduced absorption directly above the bandgap.  
+
+However, when averaging over the interpolation parameter \(f\) , i.e., over the orientations considered by our modeling, the result (black curve in Fig. 4(a)) reproduces the main features present for \(f = 0\) , with somewhat fewer oscillations. Most importantly, the change from bleaching to induced absorption in the center of the band structure for the \(\overline{\Gamma Z}\) direction at about \(1.9 \mathrm{eV}\) is still present. The averaged graph is in good agreement with the differential spectra at high field amplitudes (upper curves in Fig. 4(b)). Thus, in the averaged results, the spectra for small \(f\)
+
+<--- Page Split --->
+
+dominate strongly since (i) the absorption changes are spectrally concentrated in the monitored region due to the small bandwidth, (ii) one is in the regime of Stark localization due to the small extent of the first Brillouin zone, and (iii) for larger \(f\) the rather weak and oscillatory results partly cancel each other. For these reasons, the contribution from the \(\overline{\Gamma Z}\) direction, corresponding to small \(f\) , is enhanced for energies far above the bandgap and dominates the entire phenomenon.  
+
+The results of Fig. 4(a, b) suggest that, for the randomly oriented crystallites in the film, the overall response is dominated by the response originating from the band dispersion in the \(\overline{\Gamma Z}\) direction. This reasoning is substantiated by the averaged field- dependent absorption changes calculated for both a static and a THz field shown in Figs. 4(c) and (d), respectively. As expected, the \(\overline{\Gamma Z}\) direction dominates the averaged results, which include the contributions from the dispersion in all the other directions. In both cases for strong fields, the dominant feature is a rapid change from reduced to increased absorption, which takes place near the center of the interband absorption that corresponds to the dispersion in the \(\overline{\Gamma Z}\) direction. Due to the spectral broadening induced by the THz modulation, this transition appears at slightly lower photon energies for the THz field, Fig. 4(c), than for the static field, Fig. 4(d). Thus, Fig. 4(c, d) is consistent with the notion that the step- like sign change in the center of the band for sufficiently strong field amplitudes is a signature of Stark localization for the polycrystalline perovskite sample.  
+
+In conclusion, we have demonstrated the onset of transient Wannier- Stark localization in the polycrystalline form of methylammonium lead iodide perovskite at surprisingly low electric field amplitudes. Despite the static and dynamic disorder of the methylammonium molecular cations at room temperature and the arbitrary distribution of crystal domains with respect to the THz field direction, the dominant contribution from the \(\overline{\Gamma Z}\) direction of the band structure allows for the clear
+
+<--- Page Split --->
+
+signature of Wannier- Stark localization. The ultrafast field- induced transition from 3D to effectively 2D electronic states leads to substantial spectral transfer from the central spatially- direct \((n = 0)\) transition (around the optical band gap of 3D) to 0.3 eV red- (blue- )shifted spatially adjacent transitions \(n = +1\) \((n = - 1)\) , with up to \(38\%\) maximum modulation depth. Instead of semiconductor superlattices, which need expensive high- vacuum manufacturing processes, the solution- processed hybrid perovskites could meet the growing need for cost- effective \(^{31}\) , efficient, fast, and sensitive characteristics as optical modulators \(^{32}\) . Together with the renowned photophysical properties of MAPbI \(_3\) , such as the long carrier diffusion length \(^{33,34}\) , low mid- gap trap density \(^{29,34}\) , and large absorption coefficient \(^{35}\) , this finding of high modulation depth, fast response, and low onset field for Wannier- Stark localization highlights the potential of this material in photonic applications \(^{36,37}\) .  
+
+## Materials and Methods  
+
+## Experimental details  
+
+The phase- stable multi- cycle mid- IR pulses with a peak field strength of \(\sim 10\mathrm{MV / cm}\) are generated using difference frequency mixing (DFG) in GaSe \(^{9,10}\) . The regeneratively amplified pulses with 780 nm and 130 fs are used to pump two parallel optical parametric amplifier stages to provide tunable near- infrared pulses with minimum relative phase fluctuation. The two near- IR pulses are then combined and sent to the GaSe nonlinear crystal for the DFG. The thus generated mid- IR pulses are focused onto the sample with off- axis parabolic mirrors of focal length \(\tilde{f} = 15\mathrm{mm}\) and effective \(\mathrm{NA} = 0.2\) . The electric field transient is characterized by ultrabroadband electro- optic sampling \(^{38}\) at a 30- \(\mu \mathrm{m}\) - thick GaSe crystal using balanced detection of an 8- fs probe pulse centered at a wavelength of \(1.2\mu \mathrm{m}\) as the gating pulse. The quantitative value of the field
+
+<--- Page Split --->
+
+amplitude is obtained by measuring the mid- IR average power and focal spot size. Then, the value at the interior of the MAPbI₃ perovskite sample are estimated using the Fresnel transmission coefficient for the mid- IR field at the air- MAPbI₃ interface.  
+
+For detection of the field- induced differential optical transmittance in broad spectral range, we generate near- IR and visible pulses with the duration of 7 fs by non- collinear optical parametric amplification (Fig. S1)³⁹. The probe pulses are combined with the mid- IR pump pulses at a germanium beam splitter so that both pulses co- propagate through the sample. The probe pulses are then dispersed onto a spectrometer coupled to a CCD camera for the spectral resolution. The relative timing between the pump and probe pulses was controlled using an optical delay stage. To detect the differential optical transmission spectra, we modulate the mid- IR pump pulses by an optical chopper operating at 125 Hz, which is synchronized with the 1 kHz laser repetition rate and the readout of the CCD camera. Two subsequent spectra taken from the CCD camera are subtracted by each other and normalized by one spectrum without the pump. The sample compartment in the experimental setup was purged with dry nitrogen in order to avoid degradation. The complete experimental setup and the laser system have been fully illustrated in Ref [⁸].  
+
+## Theoretical approach  
+
+For calculating the linear optical interband absorption spectra, we numerically solve the semiconductor Bloch equations (SBE), including the intraband acceleration induced by the strong THz field²⁶-²⁸. We use here a one- dimensional trajectory in k- space, denoted as the \(\overline{\Gamma x}\) direction where x is an arbitrary point in the 1. Brillouin zone, which is parallel to the polarization direction
+
+<--- Page Split --->
+
+of the incident THz field and goes through the \(\Gamma\) - point of the Brillouin zone. In the linear optical regime, the SBE reduce to the equations of motion for the microscopic polarizations \(p_{k}^{c\nu}\) and read  
+
+\[\frac{\partial}{\partial t} p_{k}^{c\nu} = \frac{i}{\hbar} E_{c\nu}(k)p_{k}^{c\nu} + \frac{e}{\hbar} E_{\mathrm{THz}}(t)\nabla_{k}p_{k}^{c\nu} - \frac{i}{\hbar} E_{\mathrm{opt}}(t)\mu_{k}^{c\nu} - \frac{p_{k}^{c\nu}}{T_{2}}\]  
+
+Dephasing processes are treated phenomenologically by adding the dephasing time \(T_{2}\) .  
+
+For all calculations presented in this paper, we include the intraband dynamics induced by the static or pulsed THz fields to infinite order, whereas the weak optical probe of the interband absorption is considered only to the first order. In this linear- optical regime, we thus neglect carrier generation by multi- photon processes and impact ionization, which does not seem to play a dominant role in the measured transient spectra. Interband tunneling by the THz field could lead to bleaching at later delay times and the slightly asymmetric spectral evolution with respect to \(\tau = 0\) (Fig. 2(A)) (corresponding to the trailing edge of the THz transient in the Supplementary Material of ref [8]). However, significant carrier multiplication does not occur within this experimental window, as shown in Fig. S3.  
+
+For the interband dipole matrix element, we use the usual decay with increasing transition frequency<sup>40</sup>  
+
+\[\mu_{k} = \mu_{0}\frac{1.62\mathrm{eV}}{E_{\mathrm{cv}}(k)}\]  
+
+where the choice of \(\mu_{0}\) is not relevant here, as it contributes only as a prefactor to the absorption spectra.  
+
+For the THz pulses, we use a Gaussian envelope
+
+<--- Page Split --->
+
+\[E_{\mathrm{THz}}(t) = E_{0}e^{-4\ln (2)\left(\frac{t - \tau}{\bar{T}}\right)^{2}}\cos \left(\omega_{\mathrm{THz}}(t - \tau)\right)\]  
+
+with the electric- field amplitude \(E_{0}\) , the pulse duration \(\bar{T}\) (FWHM of the intensity), the time delay \(\tau\) , and the THz frequency \(\omega_{\mathrm{THz}}\) . The optical probe pulse is modeled as a weak ultrashort delta- like pulse.  
+
+The total optical polarization is obtained by summing over the microscopic polarizations \(p_{k}^{\mathrm{cv}}\)  
+
+\[P(t) = \sum_{k}\mu_{k}^{\mathrm{c}}p_{k}^{\mathrm{cv}}(t) + c.c.\]  
+
+By Fourier transforming the macroscopic polarization \(P(t)\) the linear absorption can be obtained by  
+
+\[\alpha_{1\mathrm{D},\overline{\mathrm{1x}}}(\omega)\propto \omega \mathrm{Im}\big(P(\omega)\big)\]  
+
+To be able to compare the numerical results for the one- dimensional k- space trajectory to the measured \(\Delta T / T\) spectra, the negative change of the optical absorption in three dimensions - \(\Delta \alpha_{3\mathrm{D}}\) is calculated assuming a parabolic electronic dispersion perpendicular to the considered one- dimensional direction. Due to the constant two- dimensional density of states for a parabolic dispersion, the absorption of the corresponding three- dimensional system is easily obtained as Ref [8]  
+
+\[\alpha_{\overline{\mathrm{1x}}}(\omega)\propto \int_{0}^{\omega}\alpha_{1\mathrm{D},\overline{\mathrm{1x}}}(\omega^{\prime})d\omega^{\prime}.\]
+
+<--- Page Split --->
+
+## Band structure model and averaging over crystallographic directions  
+
+To incorporate both the bandwidth and the effective mass \(m^{*}\) at the band gap as obtained from abinitio calculation in Ref [12] into our model, we use an interband energy difference of  
+
+\[E_{c v}(k) = E_{0} + \frac{\Delta}{2} (1 - \cos (g(k a^{*})k a^{*}))\]  
+
+Here, \(\pi /a^{*}\) is the distance from the \(\Gamma\) - point to the border of the first Brillouin zone  
+
+and the interpolation function  
+
+\[g(k a^{*}) = f + (1 - f)\frac{k a^{*}}{\pi}\]  
+
+guarantees that \(E_{c v}(0) = E_{0}\) and \(E_{c v}(\pm \pi /a^{*}) = E_{0} + \Delta\) , meaning the bandgap energy \(E_{0}\) and the bandwidth \(\Delta\) are preserved.  
+
+The parameter \(f\) is adjusted to obtain the effective mass which corresponds to the second derivative of the band structure at the \(\Gamma\) point:  
+
+\[m^{*} = \hbar^{2}\left[\frac{d^{2}E_{c v}(k)}{d k^{2}}\right]\left|0\right|^{1}\]  
+
+as given in Ref [12].  
+
+As mentioned before, the polycrystallinity of the system is included by averaging over several differential transmittance spectra.  
+
+The transition from the \(\overline{\Gamma Z}\) to the \(\overline{\Gamma A}\) direction is carried out by varying the bandwidth \(\Delta\) from \(\Delta_{\overline{\Gamma Z}} = 0.75 \mathrm{eV}\) to \(\Delta_{\overline{\Gamma A}} = 1.55 \mathrm{eV}\) , the extent of the first Brillouin zone \(\frac{\pi}{a^{*}}\) from \(\frac{\pi}{a_{\overline{\Gamma Z}}^{*}} = \frac{\pi}{c} = \frac{\pi}{1.27} \mathrm{nm}^{- 1}\)
+
+<--- Page Split --->
+
+to \(\frac{\pi}{a_{\Gamma A}^{*}} = \frac{\pi}{a c}\sqrt{2c^{2} + a^{2}} = \frac{\pi}{0.56}\mathrm{nm}^{- 1}\) and the effective mass \(\mathrm{m}^{*}\) from \(\mathrm{m}_{\Gamma Z}^{*} = 0.17\mathrm{m}_{0}\) to \(\mathrm{m}_{\Gamma A}^{*}\) \(= 0.09\mathrm{m}_{0}\) via a parameter \(f\) which varies from 0 (i.e. the \(\overline{\Gamma Z}\) - direction) to 1 (i.e. the \(\overline{\Gamma A}\) - direction) 12. The interpolation is performed as:  
+
+\[\Delta (\mathrm{f}) = \Delta_{\overline{\Gamma Z}} + \mathrm{f}\big(\Delta_{\overline{\Gamma A}} - \Delta_{\overline{\Gamma Z}}\big)\]  
+
+\[\frac{\pi}{a^{*}(f)} = \frac{\pi}{a_{\Gamma Z}^{*}} +f\left(\frac{\pi}{a_{\Gamma A}^{*}} -\frac{\pi}{a_{\Gamma Z}^{*}}\right)\]  
+
+\[m^{*}(f) = m_{\Gamma Z}^{*} + f\big(m_{\Gamma A}^{*} - m_{\Gamma Z}^{*}\big)\]  
+
+where \(f = 0\) describes the \(\overline{\Gamma Z}\) - direction and \(f = 1\) the \(\overline{\Gamma A}\) - direction, respectively.  
+
+The above described averaging of several spectra for the discretized parameter \(f\) is performed via evaluating  
+
+\[\alpha_{\mathrm{avg}}(\omega) = \frac{1}{n}\sum_{f_{i}}\alpha_{f_{i}}(\omega),i\in [1,n]\]  
+
+With the respective absorption \(\alpha_{f = 0} = \alpha_{1D,\overline{\Gamma Z}}\) and \(\alpha_{f = 1} = \alpha_{1D,\overline{\Gamma A}}\) where for convergence \(n\) is typically chosen as 51.  
+
+## Supporting Information  
+
+Fig. S1. Normalized spectra of near- IR (red) and visible (blue) probe pulses.  
+
+Fig. S2. Differential transmission changes measured at probe photon energies of 1.7 eV (red line) and 2.0 eV (blue) together with the \(\mathrm{E}^{2}(\mathrm{t})\) of THz pulse profile.
+
+<--- Page Split --->
+
+Fig. S3. Contributions from free carriers generated via interband tunneling.  
+
+Fig. S4. Simulations with averaging from the \(\overline{\Gamma Z}\) to the \(\overline{\Gamma A}\) direction for a THz pulse centered at \(t = 0\) and various field strengths.  
+
+Fig. S5. Simulated absorption change, \(- \Delta \alpha_{\mathrm{avg}}\) , averaged for a pure cosine model band structure (without the function g, see methods, which was introduced to fit the effective mass) from \(\overline{\Gamma Z}\) to \(\overline{\Gamma A}\) direction for a THz pulse centered at \(t = 0\) and various field strengths.  
+
+Figure S6. Simulated change of the optical interband absorption \(- \Delta \alpha_{\overline{\Gamma A}}\) from a cosine band modeling along \(\overline{\Gamma A}\) direction for static fields and a pulsed THz field.  
+
+## AUTHOR INFORMATION  
+
+## Corresponding Author  
+
+\*Corresponding author. torsten.meier@upb.de; kim@mpip-mainz.mpg.de  
+
+## Author Contributions  
+
+The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. \(\ddagger\) These authors contributed equally.  
+
+## Notes  
+
+The authors declare no competing financial interest.
+
+<--- Page Split --->
+
+## ACKNOWLEDGMENT  
+
+The authors thank Keno Krewer and Johannes Hunger for helpful discussions. T. M. and D. B. acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Research Center TRR 142 (project number 231447078, project A02). M. B. and H. K. thank the DFG for financial support through the Collaborative Research Center TRR 288 (project number 422213477, project B07), the European Union's Horizon 2020 research and innovation program under grant agreement No.658467, and the Max Planck Society for financial support. A. L. and J. B. acknowledge financial support from the European Research Council through ERC Advanced Grant 290876 (UltraPhase) and the Carl Zeiss Foundation through the fellowship program.  
+
+## REFERENCES  
+
+1. Wannier, G. H. Wave Functions and Effective Hamiltonian for Bloch Electrons in an Electric Field. Phys. Rev. 117, 432–439 (1960).  
+2. Bloch, F. Über die Quantenmechanik der Elektronen in Kristallgittern. Zeitschrift für Phys. 52, 555–600 (1929).  
+3. Zener, C. A theory of the electrical breakdown of solid dielectrics. Proc. R. Soc. London. Ser. A 145, 523–529 (1934).  
+4. Mendez, E. E., Agulló-Rueda, F. & Hong, J. M. Stark Localization in GaAs-GaAlAs Superlattices under an Electric Field. Phys. Rev. Lett. 60, 2426–2429 (1988).  
+5. Voisin, P. et al. Observation of the Wannier-Stark Quantization in a Semiconductor
+
+<--- Page Split --->
+
+Superlattice. Phys. Rev. Lett. 61, 1639–1642 (1988).  
+
+6. Feldmann, J. et al. Optical investigation of Bloch oscillations in a semiconductor superlattice. Phys. Rev. B 46, 7252–7255 (1992).  
+
+7. Waschke, C. et al. Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice. Phys. Rev. Lett. 70, 3319–3322 (1993).  
+
+8. Schmidt, C. et al. Signatures of transient Wannier-Stark localization in bulk gallium arsenide. Nat. Commun. 9, (2018).  
+
+9. Sell, A., Leitenstorfer, A. & Huber, R. Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm. Opt. Lett. 33, 2767 (2008).  
+
+10. Junginger, F. et al. Single-cycle multiterahertz transients with peak fields above 10 MV/cm. Opt. Lett. 35, 2645 (2010).  
+
+11. von Plessen, G. et al. Influence of scattering on the formation of Wannier-Stark ladders and Bloch oscillations in semiconductor superlattices. Phys. Rev. B 49, 14058–14061 (1994).  
+
+12. Umari, P., Mosconi, E. & De Angelis, F. Relativistic GW calculations on CH3 NH3 PbI 3 and CH3 NH3 SnI3 Perovskites for Solar Cell Applications. Sci. Rep. 4, 1–7 (2014).  
+
+13. Whitfield, P. S. et al. Structures, Phase Transitions and Tricritical Behavior of the Hybrid Perovskite Methyl Ammonium Lead Iodide. Sci. Rep. 6, 1–16 (2016).  
+
+14. Brivio, F. et al. Lattice dynamics and vibrational spectra of the orthorhombic, tetragonal, and cubic phases of methylammonium lead iodide. Phys. Rev. B 92, 1–8 (2015).
+
+<--- Page Split --->
+
+15. Quarti, C., Mosconi, E. & De Angelis, F. Interplay of orientational order and electronic structure in methylammonium lead iodide: Implications for solar cell operation. Chem. Mater. 26, 6557–6569 (2014).  
+
+16. Leguy, A. M. A. et al. Dynamic disorder, phonon lifetimes, and the assignment of modes to the vibrational spectra of methylammonium lead halide perovskites. Phys. Chem. Chem. Phys. 18, 27051–27066 (2016).  
+
+17. Kim, H. et al. Direct observation of mode-specific phonon-band gap coupling in methylammonium lead halide perovskites. Nat. Commun. 8, 687 (2017).  
+
+18. Karakus, M. et al. Phonon-Electron Scattering Limits Free Charge Mobility in Methylammonium Lead Iodide Perovskites. J. Phys. Chem. Lett. 6, 4991–4996 (2015).  
+
+19. D'Angelo, F., Mics, Z., Bonn, M. & Turchinovich, D. Ultra-broadband THz time-domain spectroscopy of common polymers using THz air photonics. Opt. Express 22, 12475–12485 (2014).  
+
+20. Yan, W. X., Zhao, X. G. & Wang, H. Coherent effects induced by dc-ac fields in semiconductor superlattices: The signature of fractional Wannier-Stark ladders. J. Phys. Condens. Matter 10, L11 (1998).  
+
+21. Frohna, K. et al. Inversion symmetry and bulk Rashba effect in methylammonium lead iodide perovskite single crystals. Nat. Commun. 9, (2018).  
+
+22. Blancon, J. C. et al. Unusual thickness dependence of exciton characteristics in 2D perovskite quantum wells. arXiv:1710.07653v2
+
+<--- Page Split --->
+
+23. Ishihara, T. & Goto, T. Exciton Features in 0-, 2-, and 3-Dimensional Networks of [Pbl6]4-Octahedra. Journal of the Physical Society of Japan 63, 3870-3879 (1994).  
+
+24. Umebayashi, T. et al. Electronic structures of lead iodide based low-dimensional crystals. Phys. Rev. B 67, 2-7 (2003).  
+
+25. Blancon, J. C. et al. Unusual thickness dependence of exciton characteristics in 2D perovskite quantum wells. arXiv 1-21 (2017).  
+
+26. Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photonics 8, 119-123 (2014).  
+
+27. Meier, T., Von Plessen, G., Thomas, P. & Koch, S. W. Coherent electric-field effects in semiconductors. Phys. Rev. Lett. 73, 902-905 (1994).  
+
+28. Golde, D., Meier, T. & Koch, S. W. High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations. Phys. Rev. B 77, 1-6 (2008).  
+
+29. Brandt, R. E., Stevanović, V., Ginley, D. S. & Buonassisi, T. Identifying defect-tolerant semiconductors with high minority-carrier lifetimes: Beyond hybrid lead halide perovskites. MRS Commun. 5, 265-275 (2015).  
+
+30. Guo, L., Xu, G., Tang, G., Fang, D. & Hong, J. Structural stability and optoelectronic properties of tetragonal {MAPbI}3 under strain. Nanotechnology 31, 225204 (2020).  
+
+31. Ball, J. M., Lee, M. M., Hey, A. & Snaith, H. J. Low-temperature processed meso-superstructured to thin-film perovskite solar cells. Energy Environ. Sci. 6, 1739 (2013).
+
+<--- Page Split --->
+
+32. Grinblat, G. et al. Ultrafast All-Optical Modulation in 2D Hybrid Perovskites. ACS Nano 13, 9504–9510 (2019).  
+
+33. Stranks, S. D. et al. Electron-hole diffusion lengths exceeding 1 micrometer in an organometal trihalide perovskite absorber. Science 342, 341–4 (2013).  
+
+34. Shi, D. et al. Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals. Science 347, 519–522 (2015).  
+
+35. Lee, M. M., Teuscher, J., Miyasaka, T., Murakami, T. N. & Snaith, H. J. Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites. Science 338, 643–7 (2012).  
+
+36. Bar-Joseph, I. et al. Room-temperature electroabsorption and switching in a GaAs/AlGaAs superlattice. Appl. Phys. Lett. 55, 340–342 (1989).  
+
+37. Bigan, E. et al. Optimization of optical waveguide modulators based on Wannier-Stark localization: an experimental study. IEEE J. Quantum Electron. 28, 214–223 (1992).  
+
+38. Riek, C., Seletskiy, D. V & Leitenstorfer, A. Femtosecond measurements of electric fields: from classical amplitudes to quantum fluctuations. Eur. J. Phys. 38, 24003 (2017).  
+
+39. Brida, D. et al. Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers. J. Opt. 12, 13001 (2009).  
+
+40. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors. (WORLD SCIENTIFIC, 2009).
+
+<--- Page Split --->
+
+29
+
+<--- Page Split --->
+
+## Figures  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+Experimental scheme and properties of MAPbI3 perovskite (a) THz pulse geometry with a tetragonal unit cell (black rectangular cuboid) of MAPbI3. (dark grey: Pb, purple: I, brown: C, light blue: N, light pink: H) The THz biasing along the c axis of a crystallite is depicted. (b) Simplified electronic band structure of MAPbI3 in the tetragonal phase along the directions \(\Gamma (0,0,0) \cong \mathrm{Z}(0,0,0.5)\) and \(\Gamma (0,0,0) \cong \mathrm{A}(0.5,0.5,0.5)\) . The bandwidths and the lattice parameters are used from [Ref 12]. (c) Optical absorption spectrum of MAPbI3 in the spectral range of the probe pulses.  
+
+![](images/Figure_3.jpg)
+
+
+<--- Page Split --->
+
+## Figure 2  
+
+Experimental observation of the transient Wannier Stark localization and the visualized diagram (a) Experimental differential transmission spectra on a polycrystalline film of MAPbI3 perovskite at room temperature, as a function of delay time of probe pulses after THz pump pulses. The THz pulses have a peak field strength of 6.1 MV/cm and a center frequency of 20 THz; the probe pulses have photon energy of \(1.4 \sim 2.4 \text{eV}\) . (b) Temporal profile of the applied THz bias transient. (c) Schematic picture of Wannier Stark localization. In the presence of strong external fields along the c axis, electronic states (orange: conduction band, blue: valence band) are localized to a few layers of ab plane, and energetically separated by \(\Delta \text{EWSL} = \text{eETHzc}\) between adjacent lattice sites. Black arrows depict the interband transitions within the same site (n = 0) and between different sites (n = ±1). (d) The absorbance with and without the external transient biasing. The Wannier- Stark localization effectively reduces the 3D electronic structure into 2D layered structure along the ab plane, as depicted in blue together with the simplified 3D structure.  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 3 </center>  
+
+Numerical simulation of differential absorption spectra. Please see .pdf file for full caption
+
+<--- Page Split --->
+![PLACEHOLDER_32_0]
+
+<center>Figure 4 </center>  
+
+![PLACEHOLDER_32_1]
+  
+
+. Experiments on polycrystalline system and simulations with averaging of cosine band model from \(\mathbb{W}\mathbb{W}\) to \(\mathbb{W}\mathbb{W}\) direction. Please see .pdf file for full caption  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- SlfinalNatComm.pdf
+
+<--- Page Split --->

preprint/preprint__00eb7cf6559fe9e55f1f5595a3abcbbf42befb8fdab5e70d9108735caa725b65/preprint__00eb7cf6559fe9e55f1f5595a3abcbbf42befb8fdab5e70d9108735caa725b65_det.mmd

@@ -0,0 +1,555 @@
+<|ref|>title<|/ref|><|det|>[[45, 108, 940, 177]]<|/det|>
+# Low-field Onset of Wannier-Stark Localization in a Polycrystalline Hybrid Organic Inorganic Perovskite  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 352, 281]]<|/det|>
+Daniel Berghoff  Paderborn University  Johannes Bühler  University of Konstanz  
+
+<|ref|>text<|/ref|><|det|>[[44, 289, 426, 330]]<|/det|>
+Mischa Bonn  Max Planck Institute for Polymer Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 336, 253, 376]]<|/det|>
+Alfred Leitenstorfer  University of Konstanz  
+
+<|ref|>text<|/ref|><|det|>[[44, 383, 618, 424]]<|/det|>
+Torsten Meier  University of Paderborn  https://orcid.org/0000- 0001- 8864- 2072  
+
+<|ref|>text<|/ref|><|det|>[[44, 428, 426, 469]]<|/det|>
+Heejae Kim ( kim@mpip-mainz.mpg.de)  Max Planck Institute for Polymer Research  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 510, 102, 528]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 548, 951, 590]]<|/det|>
+Keywords: Wannier- Stark localization, Electron confinement, Ultrafast Biasing, Optical modulation, Hybrid perovskites  
+
+<|ref|>text<|/ref|><|det|>[[44, 609, 285, 628]]<|/det|>
+Posted Date: April 8th, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 647, 463, 666]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 386040/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 684, 911, 726]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 763, 914, 805]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on September 29th, 2021. See the published version at https://doi.org/10.1038/s41467- 021- 26021- 4.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[117, 136, 876, 234]]<|/det|>
+# Low-field Onset of Wannier-Stark Localization in a Polycrystalline Hybrid Organic Inorganic Perovskite  
+
+<|ref|>text<|/ref|><|det|>[[114, 283, 844, 340]]<|/det|>
+Daniel Berghoff \(^{1}\) , Johannes Bühler \(^{2}\) , Mischa Bonn \(^{3}\) , Alfred Leitenstorfer \(^{2}\) , Torsten Meier \(^{*1}\) , Heejae Kim \(^{*3}\)  
+
+<|ref|>text<|/ref|><|det|>[[114, 369, 732, 390]]<|/det|>
+\(^{1}\) Department of Physics, Paderborn University, D- 33098 Paderborn, Germany  
+
+<|ref|>text<|/ref|><|det|>[[114, 418, 845, 475]]<|/det|>
+\(^{2}\) Department of Physics and Center for Applied Photonics, University of Konstanz, D- 78457 Konstanz, Germany  
+
+<|ref|>text<|/ref|><|det|>[[114, 504, 864, 560]]<|/det|>
+\(^{3}\) Department of Molecular Spectroscopy, Max Planck Institute for Polymer Research, D- 55128 Mainz, Germany  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 640, 230, 658]]<|/det|>
+## KEYWORDS  
+
+<|ref|>text<|/ref|><|det|>[[114, 674, 880, 730]]<|/det|>
+Wannier- Stark localization, Electron confinement, Ultrafast Biasing, Optical modulation, Hybrid perovskites
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 220, 108]]<|/det|>
+## ABSTRACT  
+
+<|ref|>text<|/ref|><|det|>[[112, 145, 886, 586]]<|/det|>
+Control over light propagation in a material by applying external fields is at the heart of photonic applications. Here, we demonstrate ultrafast modulation of the optical properties in the room temperature polycrystalline MAPbI₃ perovskite using phase- stable terahertz pulses, centered at 20 THz. The biasing field from the THz pulse creates extreme localization of electronic states in the ab plane – Wannier- Stark localization. This quasi- instantaneous reduction of dimensionality (from 3D to 2D) causes a marked change in the absorption shape, enabling the modulation depth to be tens of percent at moderate field strengths (3 MV/cm). The notably low- field onset results from a narrow electronic bandwidth, a large relevant lattice constant, and the coincidence of the two along the same direction in this tetragonal perovskite. We show that the transient optical response is in fact dominated by the least dispersive direction of the electronic band structure, facilitating a substantial modulation despite the arbitrary arrangement of the individual crystallites. The demonstration of THz- field- induced optical modulation in a solution- processed, disordered, and polycrystalline material is of substantial potential significance for novel photonic applications.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 615, 224, 633]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[113, 662, 886, 895]]<|/det|>
+The intriguing properties of electrons in periodic potentials in the presence of strong external electric fields are highly relevant for photonic applications, including optical modulators, optical switches, and optical signal processing. Drastic changes in optical properties can be achieved via localization of electronic states using externally applied fields. In the presence of strong external electric fields \(E\) , the continuum of electronic energy bands splits into a series of discrete levels in the direction of the field<sup>1</sup>, and the corresponding wave functions are confined on a length scale given by \(\Delta /(eE)\) , where \(\Delta\) is the energetic width of the electronic band in the absence of biasing.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 249]]<|/det|>
+These localized states, the Wannier- Stark states \(^{2,3}\) , are equally spaced both in energy by an amount \(eED\) , and in space by the lattice period \(D\) . Since a spatial separation of \(nD\) lattice periods results in an energy shift of \(neED\) with respect to the central spatially- direct \((n = 0)\) transition, this Wannier- Stark localization leads to strong spectral modulation of the interband absorption continuum below and above the optical band gap.  
+
+<|ref|>text<|/ref|><|det|>[[112, 277, 885, 543]]<|/det|>
+The quantum confinement induced by external fields is an extreme state of matter and has never been achieved under static biasing in natural solids but only in artificial superlattices \(^{4 - 8}\) . So far, only one natural solid, a single crystal GaAs \(^{8}\) has allowed for achieving the Wannier- Stark localization transiently by virtue of the recent availability of extremely intense and phase- stable pulses of multi- terahertz radiation \(^{9,10}\) . The ultrafast biasing fields could reach amplitudes up to several tens of MV/cm \(^{9,10}\) , i.e., field strengths comparable to the interatomic fields. For GaAs, an optimally oriented single crystal was required to observe Wannier- Stark localization with the required field strengths exceeding 10 MV/cm \(^{8}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 571, 885, 907]]<|/det|>
+Here, we demonstrate the transient Wannier- Stark localization at a substantially lower field strength in a disordered, solution- processed, polycrystalline film of methylammonium lead iodide perovskite (MAPbI \(_{3}\) , Fig. 1(a)). Already at relatively modest field strengths, the thin film's optical transmission is modified by tens of percent. To resolve optical transitions to individual Wannier- Stark states in, e.g., absorption spectra, their energetic spacing needs to be larger than the (total) linewidth \(\Gamma\) , i.e., \(eED > \Gamma\) \(^{4,5,11}\) Due to the small lattice constant of bulk crystals and the large linewidth which results from the scattering of electrons with lattice vibrations and other electrons, the requirement \(eED > \Gamma\) can typically not be fulfilled under stationary external fields below the strength where the dielectric breakdown occurs \(^{6,7}\) . At room temperature, however, this material exhibits a tetragonal structure with lattice parameters of \(a = 8.8 \mathring{\mathrm{A}}\) and \(c = 12.5 \mathring{\mathrm{A}}\) by the expansion
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 883, 144]]<|/det|>
+of the cubic perovskite unit cell \(^{12,13}\) . The periodicities are nearly twice as large as the lattice parameter \(a = 5.6 \text{Å}\) of cubic GaAs \(^{8}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 173, 886, 544]]<|/det|>
+We will show that the large relevant lattice constant (Fig. 1(a)), the small width of electronic energy bands (Fig. 1(b)), and the coincidence of these two along the same high- symmetry direction lead to Stark localization in this organic perovskite at field amplitudes as low as \(3 \text{MV/cm}\) , i.e., at a fraction of the field strength required to enter this regime in optimally oriented, single- crystalline GaAs. Moreover, the measured differential spectra containing the overall effects from arbitrarily oriented microcrystals are qualitatively well- described by a two- band model with a cosine band structure. By considering different orientations of the microcrystals in our simulations, we demonstrate that the contribution from the direction with the largest periodicity, i.e., the \(\overline{\Gamma Z}\) direction \(c = 12.5 \text{Å}\) , strongly dominates the transient changes of the optical response. These findings, together with its renowned characteristics, make MAPbI \(_3\) a strong candidate for cost- effective, efficient, fast, and sensitive optical modulator materials.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[201, 92, 820, 388]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 414, 884, 644]]<|/det|>
+<center>Figure 1. Experimental scheme and properties of MAPbI3 perovskite (a) THz pulse geometry with a tetragonal unit cell (black rectangular cuboid) of MAPbI3. (dark grey: Pb, purple: I, brown: C, light blue: N, light pink: H) The THz biasing along the \(c\) axis of a crystallite is depicted. (b) Simplified electronic band structure of MAPbI3 in the tetragonal phase along the directions \(\Gamma (0,0,0)\rightarrow \mathrm{Z}(0,0,0.5)\) and \(\Gamma (0,0,0)\rightarrow \mathrm{A}(0.5,0.5,0.5)\) . The bandwidths and the lattice parameters are used from [Ref \(^{12}\) ]. (c) Optical absorption spectrum of MAPbI3 in the spectral range of the probe pulses. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 710, 308, 728]]<|/det|>
+## Results and Discussion  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 760, 578, 780]]<|/det|>
+## Experimental observation of Wannier-Stark Localization  
+
+<|ref|>text<|/ref|><|det|>[[113, 809, 884, 900]]<|/det|>
+For applying the strong transient bias, non- resonant in energy with any of the optical phonons and electronic transitions, we employ phase- stable multi- cycle optical pulses with a center frequency of 20 THz. The pump pulse is generated using a difference- frequency generation
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 85, 886, 498]]<|/det|>
+scheme in GaSe \(^{9,10}\) . For comparison, the MAPbI \(_3\) perovskite has a direct bandgap of \(E_{gap} = 1.62 \mathrm{eV}\) (390 THz, Fig. 1(c)) at room temperature. The phonon modes of Pb- I inorganic sublattice are below 10 THz and methylammonium organic molecular vibrations above 26 THz \(^{14}\) . Due to the presence of the organic cation with a low rotational barrier \(^{15}\) , the crystal shows some degree of disorder at elevated temperature and a less pronounced periodicity compared to all- inorganic perovskites \(^{15,16}\) . The sample is a polycrystalline film with a thickness of \(\sim 300 \mathrm{nm}\) spin- coated \(^{17,18}\) on a cyclic olefin/ethylene copolymer substrate (TOPAS \(^{8}\) ) \(^{19}\) . The differential transmission induced by the external electric field transient is probed by near- IR and visible probe pulses, with spectra covering broad interband electronic transition energies between \(1.4 \mathrm{eV}\) and \(2.4 \mathrm{eV}\) (see Fig. S1). The duration of these probe laser pulses is 7 fs, which is significantly shorter than the half- cycle period of the THz pump transients of 25 fs. Details of the experimental settings are described in the Method section and Ref \(^{8}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 523, 886, 860]]<|/det|>
+Fig. 2(a) shows the differential transmission \(\Delta T / T\) upon applying the THz biasing as a function of delay time between the pump and probe pulses. The peak field strength of the THz pump pulses is \(6.1 \mathrm{MV / cm}\) . As expected for the non- resonant THz pulse, the optical response of the material is instantaneous and peaks when the THz field strength is maximal. The modulation occurs at twice the frequency of the THz pulse (Fig. 2(b)), since the measured differential transmission is at least a third- order nonlinear process \(^{20}\) . In such a centrosymmetric crystal as the room- temperature tetragonal phase of perovskite MAPbI \(_3\) \(^{21}\) , no contribution from the electro- optic effect is expected which is linear in the electric bias field. The clear temporal modulation of differential transmission appears at high fields, \(- 100 < \tau < 100 \mathrm{fs}\) , as the strong \(E\) field shortens the interband dephasing time in the vicinity of the bandgap to be comparable to the half- cycle period of 25 fs of the THz
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 144]]<|/det|>
+transient. Thus, the precise arrival time of the probe pulse exciting the interband polarization was resolved within the dephasing time.  
+
+<|ref|>text<|/ref|><|det|>[[112, 173, 886, 578]]<|/det|>
+More importantly, two distinct regimes can be identified in the time- resolved transient spectrum (Fig. 2(a)). For relatively weak fields, \(E < 3 \mathrm{MV}\) , for \(\tau < - 100 \mathrm{fs}\) , an induced absorption (blue, \(\Delta T / T < 0\) ) right below and an induced transmission (red, \(\Delta T / T > 0\) ) right above the bandgap of \(E_{gap} = 1.62 \mathrm{eV}\) are observed. The second regime is apparent for field strengths \(\mathrm{E} > 3 \mathrm{MV / cm}\) , occurring between delay times \(- 100 < \tau < 100 \mathrm{fs}\) (Fig. 2(b)). Here, the maximum modulation depth becomes as large as \(38 \%\) at the probe energy of \(E_{pr} = 1.7 \mathrm{eV}\) (Fig. 2(a) and Fig. S2). Also, the transient response covers a significantly extended spectral range, compared to the moderate field regime. The induced transmission (red) above the bandgap now reaches up to \(E_{pr} = 1.9 \mathrm{eV}\) , where it abruptly switches to induced absorption (blue, \(\Delta T / T < 0\) ). This negative region of \(\Delta T / T < 0\) persists at probe energies all the way up to \(E_{pr} = 2.4 \mathrm{eV}\) . This one central step from reduced to increased absorption near the center of the band \(E_{pr} = 2 \mathrm{eV}\) , is a noticeable signature of Stark localization, where the Wannier- Stark states are localized onto one unit cell.  
+
+<|ref|>image<|/ref|><|det|>[[120, 658, 866, 820]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 838, 886, 893]]<|/det|>
+<center>Figure 2. Experimental observation of the transient Wannier Stark localization and the visualized diagram (a) Experimental differential transmission spectra on a polycrystalline film of </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 424]]<|/det|>
+MAPbI3 perovskite at room temperature, as a function of delay time of probe pulses after THz pump pulses. The THz pulses have a peak field strength of 6.1 MV/cm and a center frequency of 20 THz; the probe pulses have photon energy of \(1.4 \sim 2.4 \mathrm{eV}\) . (b) Temporal profile of the applied THz bias transient. (c) Schematic picture of Wannier Stark localization. In the presence of strong external fields along the \(c\) axis, electronic states (orange: conduction band, blue: valence band) are localized to a few layers of \(ab\) plane, and energetically separated by \(\Delta E_{WSL} = eE_{THzC}\) between adjacent lattice sites. Black arrows depict the interband transitions within the same site \((n = 0)\) and between different sites \((n = \pm 1)\) . (d) The absorbance with and without the external transient biasing. The Wannier- Stark localization effectively reduces the 3D electronic structure into 2D layered structure along the \(ab\) plane, as depicted in blue together with the simplified 3D structure.  
+
+<|ref|>text<|/ref|><|det|>[[112, 502, 886, 907]]<|/det|>
+By driving the 3- dimensional (3D) system into Wannier- Stark localization, i.e., localizing it in the field direction, we transiently create an effectively 2D electronic system (Fig. 2(c, d)). Given the unit cell doubling, this optically prepared transient 2D system perpendicular to the \(c\) axis may be directly compared to the physically isolated double- layer structure of PbI6 octahedra. In such 2D perovskites as (BA)2(MA)1-1PbI13+1 perovskites22, the inorganic layers (perpendicular to the \(c\) axis in 3D equivalence) are separated by bulky organic layers23. The bandgap of the 2D quantum well perovskites is widened due to the bandwidth narrowing (mainly due to the zero dispersion along the vertical direction) compared to 3D perovskite24. In the case of (BA)2(MA)1-1PbI13+1 perovskites, where the PbI6 octahedral network forms a double layer \((l = 2)\) , the optical band gap is \(\sim 2.1 \mathrm{eV}\) , which is comparable to the observed \(1.9 \mathrm{eV}^{25}\) . It is noteworthy that the observed Wannier- Stark step at \(E_{pr} = 1.9 \mathrm{eV}\) under THz fields is slightly lower than the expected value under static fields due to the spectral broadening induced by the THz modulation, as will be discussed
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 249]]<|/det|>
+below. Therefore, the abrupt shift of the absorption edge from \(E_{pr} = 1.6 \mathrm{eV}\) to \(1.9 \mathrm{eV}\) at high transient fields (Fig. 2(d)) could be attributed to the transfer of spectral weight from \(\alpha (E_{g,3D} < E_{pr} < E_{g,2D})\) to \(\alpha (E_{g,2D} < E_{pr})\) . Such a THz- induced reduction of dimensionality from a 3D to a 2D system could enable new applications in both transport and optoelectronics due to the relatively easy access to that regime in these hybrid perovskite materials.  
+
+<|ref|>sub_title<|/ref|><|det|>[[130, 299, 460, 317]]<|/det|>
+## Simulations considering one orientation  
+
+<|ref|>text<|/ref|><|det|>[[112, 346, 886, 718]]<|/det|>
+To capture the essential ingredients responsible for the experimental observations, we carry out theoretical calculations based on different models of increasing complexity. We start with considering perfect alignment of the THz field with the direction along which the joint bandwidth of the highest valence and the lowest conduction band is narrowest. For the case of the tetragonal MAPbI₃ perovskite, the narrowest joint bandwidth, \(\Delta_{\overline{\mathrm{FZ}}} = 0.75 \mathrm{eV}\) , is along the \(\overline{\Gamma Z}\) direction (Fig. 1(b))¹². We thus take into account two one- dimensional bands, i.e., one valence and one conduction band with a cosine- like (tight- binding) band structure and the bandgap of \(1.62 \mathrm{eV}\) . Thus, the energy difference for interband transitions is taken as \(E_{cv}(k) = 1.62 \mathrm{eV} + (\Delta_{\overline{\mathrm{FZ}}} / 2)(1 - \cos (g(k, a) *))\) (see Methods section for details of the function \(g(k, a *)\) ). For this model, the spectra are obtained by numerically solving the semiconductor Bloch equations ²⁶- ²⁸, as described in the Methods section.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 92, 888, 333]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 343, 886, 608]]<|/det|>
+<center>Figure 3. Numerical simulation of differential absorption spectra (a) Negative change of the optical interband absorption \(- \Delta \alpha_{\overline{\Gamma Z}}\) for static fields from a cosine band modeling along \(\overline{\Gamma Z}\) direction. The region of electric field strengths up to \(1\mathrm{MV / cm}\) is enlarged to show Franz-Keldysh oscillations and the transition to the Wannier-Stark regime. (b) Calculated \(- \Delta \alpha_{\overline{\Gamma Z}}\) spectra for the excitation with a THz pulse with a peak field strength of \(E_{0} = 6\mathrm{MV / cm}\) , where the delay \(\tau\) between the THz and the optical pulse is varied. (c) Simulated temporal profile of the applied THz bias transient. The pulse duration \(\overline{T}\) is \(240\mathrm{fs}\) , the THz frequency is \(20\mathrm{THz}\) , and the dephasing time is \(T_{2} = 20\mathrm{fs}\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 739, 886, 900]]<|/det|>
+Already when considering static fields (Fig. 3(a)), the simulation results obtained by this simple model exhibits substantial qualitative similarities with the transient experimental results shown in Fig. 2(a). For all field strengths, increased absorption is present below the bandgap and reduced absorption directly above the band gap. For rather weak field strengths of up to about \(0.5\mathrm{MV / cm}\) , oscillations arising from the Franz- Keldysh effect are visible, shifting towards the band center with
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 389]]<|/det|>
+increasing field. For fields exceeding \(\sim 3 \mathrm{MV / cm}\) , signatures of Wannier- Stark localization become noticeable, as the field- dependent interband transition energies shift to higher and lower energies by \(neED\) with increasing \(E\) (Fig. 2(c)). Starting at around \(3 \mathrm{MV / cm}\) , the condition for Stark localization is fulfilled, i.e., \(eED > \Delta /2\) (meaning that the energy of the \((n = - 1)\) Wannier- Stark state is in the bandgap region, see Fig. 2(c, d)), and therefore, the dominant feature is the step- like change from reduced absorption to induced absorption in the center of the band at \(1.974 \mathrm{eV}\) (this value is the average transition frequency within our model). This step- like change is, in fact, also the main feature visible in the experimental results for sufficiently high fields, i.e., between about \(- 100 < \tau < 100\) fs as shown in Figs. 2 (a).  
+
+<|ref|>text<|/ref|><|det|>[[112, 416, 886, 894]]<|/det|>
+Besides, by considering pulsed THz fields, the simulated differential spectra with the same model (Fig. 3(b, c)) well describe both spectral and temporal features in the observed transient modulation of differential transmission spectra (Fig. 2(a)). Fig. 3(b) shows the negative change of the transient absorption, \(- \Delta \alpha_{\mathrm{TFZ}}\) , upon non- resonant biasing with a THz pulse with a peak field strength of \(E_{\theta} = 6 \mathrm{MV / cm}\) and a center frequency of \(20 \mathrm{THz}\) , as shown in Fig. 3(c). Besides temporal modulation of the entire transient spectra at twice the carrier frequency of the THz transient, the dominant feature at sufficiently large field strengths \((- 100 < \tau < 100 \mathrm{fs})\) is the rapid change from increased to reduced transmission in the center of the band \(E_{pr} = 2 \mathrm{eV}\) , which originates from Stark localization. The slightly lower value of the observed central step at \(E_{pr} = 1.9 \mathrm{eV}\) and the asymmetric nature of the spectral shape with respect to the central step (Fig. 2(a)) compared to this simplified model (Fig. 3 (b)) can be explained by the polycrystallinity of the system as discussed below. Given the complexity, disorder, and polycrystallinity of the investigated sample, the required field strength at which this step starts to appear is in surprisingly good agreement with the experiment which confirms that the observed response constitutes a clear
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 885, 323]]<|/det|>
+sign of Wannier- Stark localization. Our interpretations are further supported by Fig. S6, which shows how the results of Fig. 3 change if we consider that the THz field is aligned with the \(\overline{\Gamma}\overline{\mathrm{A}}\) direction instead of the \(\overline{\Gamma}\overline{\mathrm{Z}}\) direction. Comparing those two figures clearly shows that due to the larger bandwidth in the \(\overline{\Gamma}\overline{\mathrm{A}}\) direction the Wannier- Stark localization requires higher field amplitudes to develop and furthermore would lead to a transition from reduced to induced absorption at significantly higher energies as observed in experiment. The effects of different field directions and the averaging over them is discussed in more detail below (see Fig. 4).  
+
+<|ref|>text<|/ref|><|det|>[[112, 350, 886, 721]]<|/det|>
+As demonstrated so far, Wannier- Stark localization starts to occur at the field amplitude as low as \(3\mathrm{MV / cm}\) in the MAPBI \(_3\) perovskite, due to the relatively large periodicity, the narrow joint bandwidth, and the coincidence of the two along the same direction. The largest lattice constant of tetragonal MAPBI \(_3\) perovskite, along the \(c\) axis, \(c = 12.5\mathrm{\AA}\) , is more than twice as large as those of conventional all- inorganic semiconductors crystallizing with strong covalent bonds in the diamond, wurtzite, or zincblende forms \((3.5\sim 6.5\mathrm{\AA}\) at \(300\mathrm{K}\) ). This finding arises because (i) the cubic perovskite unit cell is expanded through rotation of ab plane by \(45^{\circ}\) and cell doubling along c axis in the tetragonal phase; and (ii) the pseudocubic lattice parameter formed by relatively large \(\mathrm{Pb^{2 + }}\) and \(\Gamma\) ions is \(6.3\mathrm{\AA}^{13}\) , which is at the larger side of the distribution of parameters for cubic lattice parameters. The pseudocubic lattice parameter is large enough to accommodate large organic molecular cations within the void of their network.  
+
+<|ref|>text<|/ref|><|det|>[[113, 749, 885, 876]]<|/det|>
+The direction of the narrowest joint bandwidth of the conduction and valence bands, \(\overline{\Gamma}\overline{\mathrm{Z}}\) , coincides with the \(c\) axis. The conduction band is composed of the overlap of \(\mathrm{Pb(6p) - I(5p)}\) atomic orbitals and the valence band is of that of \(\mathrm{Pb(6s) - I(5p)}\) orbitals \(^{29}\) . Thus, the \(\mathrm{Pb - I}\) bond length as well as the \(\mathrm{Pb - I - Pb}\) angle could determine the widths of both bands and the magnitude of the band
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 425]]<|/det|>
+gap. In the tetragonal MAPbI₃ perovskite, the corner- shared PbI₆ octahedra in cubic phase are tilted about the \(c\) axis in the opposite direction between successive tilts, which reduces the Pb- I- Pb angle from 180° along the diagonal direction of the a and b axis. The smaller Pb- I- Pb bond angle indicates weaker orbital overlap between Pb and I atoms and thus smaller band dispersion along \(\overline{\Gamma}\overline{\mathrm{M}}\) than \(\overline{\Gamma}\overline{\mathrm{Z}}\) . However, the Pb- I bond lengths along the \(c\) axis is known to be longer on average³⁰ and has greater effect on the dispersion than the angle due to the \(\sigma\) bonding nature, which leads to the coincidence of the direction of the largest lattice constant and the narrowest bandwidth. We note that unlike GaAs, the body diagonal direction exhibits the strongest dispersion (\(\overline{\Gamma}\overline{\mathrm{A}}\) ). Overall, the large ionic diameter and the geometric distortion result in the unusually narrow joint bandwidth, lower than 1 eV.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 456, 580, 475]]<|/det|>
+## Including polycrystallinity by averaging over orientations  
+
+<|ref|>text<|/ref|><|det|>[[112, 504, 886, 876]]<|/det|>
+We now account for the system's polycrystallinity by considering contributions to the differential transmittance spectra from crystallites with orientations different from those with the \(c\) axis parallel to the THz field polarization. To include arbitrary orientations of the crystallites into our simulations, we take the \(\overline{\Gamma}\overline{\mathrm{Z}}\) and the \(\overline{\Gamma}\overline{\mathrm{A}}\) directions, i.e., the two extreme directions with the narrowest/broadest bandwidth and simultaneously the smallest/largest distance in k- space (see Fig. 1(b)) and perform an average overall in between bandwidths and extensions of the first Brillouin zone (see Method section), by interpolating between the two limiting cases with a parameter \(f\) . The simulated absorption changes at a field amplitude of \(E_{0} = 4 \mathrm{MV / cm}\) with various interpolation parameters \(f\) 's are shown in Fig. 4 (a) together with the measured differential spectra at different instantaneous field amplitudes of the THz pulse (Fig. 4 (b)). Here, \(f = 0\) denotes the response along the \(\overline{\Gamma}\overline{\mathrm{Z}}\) direction (i.e., the \(c\) - axis), and \(f = 1\) along the \(\overline{\Gamma}\overline{\mathrm{A}}\) direction.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[123, 92, 881, 576]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 601, 884, 907]]<|/det|>
+<center>Figure 4. Experiments on polycrystalline system and simulations with averaging of cosine band model from \(\Gamma Z\) to \(\Gamma A\) direction. (a) Illustration for the averaging process over the interpolation parameter \(f\) from the \(\overline{\Gamma Z}\) direction \((f = 0)\) to \(\overline{\Gamma A}\) direction \((f = 1)\) . The negative absorption changes \(-\Delta \alpha_{f}\) are calculated for different one-dimensional systems using a THz pulse centered at \(t = 0\) , with an amplitude of \(E_{0} = 4 \mathrm{MV / cm}\) , a pulse duration of \(\overline{T} = 240 \mathrm{fs}\) , and a THz center frequency of \(20 \mathrm{THz}\) . (b) Temporal slices of \(\Delta T / T\) as a function of probe photon energy (Fig. 2(a)), at a delay time corresponding to the contour with constant electric field amplitudes \(E\) (Fig. 2(b)). (c) averaged absorption change, \(-\Delta \alpha_{\mathrm{avg}}\) , for static fields of various strengths. (d) averaged absorption change, \(-\Delta \alpha_{\mathrm{avg}}\) , for a THz pulse centered at \(t = 0\) and various field strengths. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 137, 886, 655]]<|/det|>
+As shown in Fig. 4(a), the absorption changes depend strongly on the interpolation parameter \(f\) , i.e., on the bandwidth and the distance to the border of the first Brillouin zone. For \(f = 0\) , which corresponds to the \(\overline{\Gamma Z}\) direction, the field amplitude of \(E_{0} = 4 \mathrm{MV / cm}\) drives the system into the region of Stark localization. Therefore, for a static field of such an amplitude, one would see a strong induced absorption in the band center at \(1.974 \mathrm{eV}\) , which corresponds to an optical transition to the Stark localized state. The transient nature of the THz pulse causes the single negative peak to be split into two peaks and the spectral region of induced absorption to be slightly broadened. With increasing \(f\) , both the bandwidth and the distance to the border of the first Brillouin zone increase. As a result, the minimum field strength for which Stark localization is realized increases significantly by approximately a factor \((c / a_{\overline{\Gamma Z}}^{*})(\Delta_{\overline{\Gamma A}} / \Delta_{\overline{\Gamma Z}})\) , equaling about 4.7. Consequently, already for \(f = 0.25\) , the absorption changes show no sign of Stark localization, with several oscillations emerging owing to the THz driving. This trend of overall weaker absorption changes with some oscillatory structure is also present for even larger \(f\) . The only feature present in all spectra shown in Fig. 4 (a) is some induced absorption below the bandgap and reduced absorption directly above the bandgap.  
+
+<|ref|>text<|/ref|><|det|>[[113, 679, 886, 877]]<|/det|>
+However, when averaging over the interpolation parameter \(f\) , i.e., over the orientations considered by our modeling, the result (black curve in Fig. 4(a)) reproduces the main features present for \(f = 0\) , with somewhat fewer oscillations. Most importantly, the change from bleaching to induced absorption in the center of the band structure for the \(\overline{\Gamma Z}\) direction at about \(1.9 \mathrm{eV}\) is still present. The averaged graph is in good agreement with the differential spectra at high field amplitudes (upper curves in Fig. 4(b)). Thus, in the averaged results, the spectra for small \(f\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 251]]<|/det|>
+dominate strongly since (i) the absorption changes are spectrally concentrated in the monitored region due to the small bandwidth, (ii) one is in the regime of Stark localization due to the small extent of the first Brillouin zone, and (iii) for larger \(f\) the rather weak and oscillatory results partly cancel each other. For these reasons, the contribution from the \(\overline{\Gamma Z}\) direction, corresponding to small \(f\) , is enhanced for energies far above the bandgap and dominates the entire phenomenon.  
+
+<|ref|>text<|/ref|><|det|>[[112, 279, 885, 687]]<|/det|>
+The results of Fig. 4(a, b) suggest that, for the randomly oriented crystallites in the film, the overall response is dominated by the response originating from the band dispersion in the \(\overline{\Gamma Z}\) direction. This reasoning is substantiated by the averaged field- dependent absorption changes calculated for both a static and a THz field shown in Figs. 4(c) and (d), respectively. As expected, the \(\overline{\Gamma Z}\) direction dominates the averaged results, which include the contributions from the dispersion in all the other directions. In both cases for strong fields, the dominant feature is a rapid change from reduced to increased absorption, which takes place near the center of the interband absorption that corresponds to the dispersion in the \(\overline{\Gamma Z}\) direction. Due to the spectral broadening induced by the THz modulation, this transition appears at slightly lower photon energies for the THz field, Fig. 4(c), than for the static field, Fig. 4(d). Thus, Fig. 4(c, d) is consistent with the notion that the step- like sign change in the center of the band for sufficiently strong field amplitudes is a signature of Stark localization for the polycrystalline perovskite sample.  
+
+<|ref|>text<|/ref|><|det|>[[113, 714, 885, 876]]<|/det|>
+In conclusion, we have demonstrated the onset of transient Wannier- Stark localization in the polycrystalline form of methylammonium lead iodide perovskite at surprisingly low electric field amplitudes. Despite the static and dynamic disorder of the methylammonium molecular cations at room temperature and the arbitrary distribution of crystal domains with respect to the THz field direction, the dominant contribution from the \(\overline{\Gamma Z}\) direction of the band structure allows for the clear
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 458]]<|/det|>
+signature of Wannier- Stark localization. The ultrafast field- induced transition from 3D to effectively 2D electronic states leads to substantial spectral transfer from the central spatially- direct \((n = 0)\) transition (around the optical band gap of 3D) to 0.3 eV red- (blue- )shifted spatially adjacent transitions \(n = +1\) \((n = - 1)\) , with up to \(38\%\) maximum modulation depth. Instead of semiconductor superlattices, which need expensive high- vacuum manufacturing processes, the solution- processed hybrid perovskites could meet the growing need for cost- effective \(^{31}\) , efficient, fast, and sensitive characteristics as optical modulators \(^{32}\) . Together with the renowned photophysical properties of MAPbI \(_3\) , such as the long carrier diffusion length \(^{33,34}\) , low mid- gap trap density \(^{29,34}\) , and large absorption coefficient \(^{35}\) , this finding of high modulation depth, fast response, and low onset field for Wannier- Stark localization highlights the potential of this material in photonic applications \(^{36,37}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 488, 313, 506]]<|/det|>
+## Materials and Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 538, 291, 556]]<|/det|>
+## Experimental details  
+
+<|ref|>text<|/ref|><|det|>[[112, 586, 886, 890]]<|/det|>
+The phase- stable multi- cycle mid- IR pulses with a peak field strength of \(\sim 10\mathrm{MV / cm}\) are generated using difference frequency mixing (DFG) in GaSe \(^{9,10}\) . The regeneratively amplified pulses with 780 nm and 130 fs are used to pump two parallel optical parametric amplifier stages to provide tunable near- infrared pulses with minimum relative phase fluctuation. The two near- IR pulses are then combined and sent to the GaSe nonlinear crystal for the DFG. The thus generated mid- IR pulses are focused onto the sample with off- axis parabolic mirrors of focal length \(\tilde{f} = 15\mathrm{mm}\) and effective \(\mathrm{NA} = 0.2\) . The electric field transient is characterized by ultrabroadband electro- optic sampling \(^{38}\) at a 30- \(\mu \mathrm{m}\) - thick GaSe crystal using balanced detection of an 8- fs probe pulse centered at a wavelength of \(1.2\mu \mathrm{m}\) as the gating pulse. The quantitative value of the field
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 178]]<|/det|>
+amplitude is obtained by measuring the mid- IR average power and focal spot size. Then, the value at the interior of the MAPbI₃ perovskite sample are estimated using the Fresnel transmission coefficient for the mid- IR field at the air- MAPbI₃ interface.  
+
+<|ref|>text<|/ref|><|det|>[[112, 207, 886, 612]]<|/det|>
+For detection of the field- induced differential optical transmittance in broad spectral range, we generate near- IR and visible pulses with the duration of 7 fs by non- collinear optical parametric amplification (Fig. S1)³⁹. The probe pulses are combined with the mid- IR pump pulses at a germanium beam splitter so that both pulses co- propagate through the sample. The probe pulses are then dispersed onto a spectrometer coupled to a CCD camera for the spectral resolution. The relative timing between the pump and probe pulses was controlled using an optical delay stage. To detect the differential optical transmission spectra, we modulate the mid- IR pump pulses by an optical chopper operating at 125 Hz, which is synchronized with the 1 kHz laser repetition rate and the readout of the CCD camera. Two subsequent spectra taken from the CCD camera are subtracted by each other and normalized by one spectrum without the pump. The sample compartment in the experimental setup was purged with dry nitrogen in order to avoid degradation. The complete experimental setup and the laser system have been fully illustrated in Ref [⁸].  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 693, 297, 712]]<|/det|>
+## Theoretical approach  
+
+<|ref|>text<|/ref|><|det|>[[113, 741, 884, 866]]<|/det|>
+For calculating the linear optical interband absorption spectra, we numerically solve the semiconductor Bloch equations (SBE), including the intraband acceleration induced by the strong THz field²⁶-²⁸. We use here a one- dimensional trajectory in k- space, denoted as the \(\overline{\Gamma x}\) direction where x is an arbitrary point in the 1. Brillouin zone, which is parallel to the polarization direction
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 145]]<|/det|>
+of the incident THz field and goes through the \(\Gamma\) - point of the Brillouin zone. In the linear optical regime, the SBE reduce to the equations of motion for the microscopic polarizations \(p_{k}^{c\nu}\) and read  
+
+<|ref|>equation<|/ref|><|det|>[[250, 170, 747, 213]]<|/det|>
+\[\frac{\partial}{\partial t} p_{k}^{c\nu} = \frac{i}{\hbar} E_{c\nu}(k)p_{k}^{c\nu} + \frac{e}{\hbar} E_{\mathrm{THz}}(t)\nabla_{k}p_{k}^{c\nu} - \frac{i}{\hbar} E_{\mathrm{opt}}(t)\mu_{k}^{c\nu} - \frac{p_{k}^{c\nu}}{T_{2}}\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 244, 797, 265]]<|/det|>
+Dephasing processes are treated phenomenologically by adding the dephasing time \(T_{2}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 293, 886, 594]]<|/det|>
+For all calculations presented in this paper, we include the intraband dynamics induced by the static or pulsed THz fields to infinite order, whereas the weak optical probe of the interband absorption is considered only to the first order. In this linear- optical regime, we thus neglect carrier generation by multi- photon processes and impact ionization, which does not seem to play a dominant role in the measured transient spectra. Interband tunneling by the THz field could lead to bleaching at later delay times and the slightly asymmetric spectral evolution with respect to \(\tau = 0\) (Fig. 2(A)) (corresponding to the trailing edge of the THz transient in the Supplementary Material of ref [8]). However, significant carrier multiplication does not occur within this experimental window, as shown in Fig. S3.  
+
+<|ref|>text<|/ref|><|det|>[[113, 622, 883, 677]]<|/det|>
+For the interband dipole matrix element, we use the usual decay with increasing transition frequency<sup>40</sup>  
+
+<|ref|>equation<|/ref|><|det|>[[460, 707, 597, 747]]<|/det|>
+\[\mu_{k} = \mu_{0}\frac{1.62\mathrm{eV}}{E_{\mathrm{cv}}(k)}\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 758, 883, 812]]<|/det|>
+where the choice of \(\mu_{0}\) is not relevant here, as it contributes only as a prefactor to the absorption spectra.  
+
+<|ref|>text<|/ref|><|det|>[[113, 842, 499, 861]]<|/det|>
+For the THz pulses, we use a Gaussian envelope
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[315, 88, 682, 125]]<|/det|>
+\[E_{\mathrm{THz}}(t) = E_{0}e^{-4\ln (2)\left(\frac{t - \tau}{\bar{T}}\right)^{2}}\cos \left(\omega_{\mathrm{THz}}(t - \tau)\right)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 151, 884, 245]]<|/det|>
+with the electric- field amplitude \(E_{0}\) , the pulse duration \(\bar{T}\) (FWHM of the intensity), the time delay \(\tau\) , and the THz frequency \(\omega_{\mathrm{THz}}\) . The optical probe pulse is modeled as a weak ultrashort delta- like pulse.  
+
+<|ref|>text<|/ref|><|det|>[[113, 275, 850, 298]]<|/det|>
+The total optical polarization is obtained by summing over the microscopic polarizations \(p_{k}^{\mathrm{cv}}\)  
+
+<|ref|>equation<|/ref|><|det|>[[386, 327, 610, 370]]<|/det|>
+\[P(t) = \sum_{k}\mu_{k}^{\mathrm{c}}p_{k}^{\mathrm{cv}}(t) + c.c.\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 399, 884, 456]]<|/det|>
+By Fourier transforming the macroscopic polarization \(P(t)\) the linear absorption can be obtained by  
+
+<|ref|>equation<|/ref|><|det|>[[394, 485, 603, 508]]<|/det|>
+\[\alpha_{1\mathrm{D},\overline{\mathrm{1x}}}(\omega)\propto \omega \mathrm{Im}\big(P(\omega)\big)\]  
+
+<|ref|>text<|/ref|><|det|>[[112, 536, 886, 732]]<|/det|>
+To be able to compare the numerical results for the one- dimensional k- space trajectory to the measured \(\Delta T / T\) spectra, the negative change of the optical absorption in three dimensions - \(\Delta \alpha_{3\mathrm{D}}\) is calculated assuming a parabolic electronic dispersion perpendicular to the considered one- dimensional direction. Due to the constant two- dimensional density of states for a parabolic dispersion, the absorption of the corresponding three- dimensional system is easily obtained as Ref [8]  
+
+<|ref|>equation<|/ref|><|det|>[[379, 761, 617, 787]]<|/det|>
+\[\alpha_{\overline{\mathrm{1x}}}(\omega)\propto \int_{0}^{\omega}\alpha_{1\mathrm{D},\overline{\mathrm{1x}}}(\omega^{\prime})d\omega^{\prime}.\]
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[113, 88, 696, 110]]<|/det|>
+## Band structure model and averaging over crystallographic directions  
+
+<|ref|>text<|/ref|><|det|>[[113, 137, 883, 195]]<|/det|>
+To incorporate both the bandwidth and the effective mass \(m^{*}\) at the band gap as obtained from abinitio calculation in Ref [12] into our model, we use an interband energy difference of  
+
+<|ref|>equation<|/ref|><|det|>[[334, 223, 662, 262]]<|/det|>
+\[E_{c v}(k) = E_{0} + \frac{\Delta}{2} (1 - \cos (g(k a^{*})k a^{*}))\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 290, 760, 312]]<|/det|>
+Here, \(\pi /a^{*}\) is the distance from the \(\Gamma\) - point to the border of the first Brillouin zone  
+
+<|ref|>text<|/ref|><|det|>[[113, 342, 352, 361]]<|/det|>
+and the interpolation function  
+
+<|ref|>equation<|/ref|><|det|>[[388, 391, 610, 430]]<|/det|>
+\[g(k a^{*}) = f + (1 - f)\frac{k a^{*}}{\pi}\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 457, 883, 513]]<|/det|>
+guarantees that \(E_{c v}(0) = E_{0}\) and \(E_{c v}(\pm \pi /a^{*}) = E_{0} + \Delta\) , meaning the bandgap energy \(E_{0}\) and the bandwidth \(\Delta\) are preserved.  
+
+<|ref|>text<|/ref|><|det|>[[113, 543, 883, 599]]<|/det|>
+The parameter \(f\) is adjusted to obtain the effective mass which corresponds to the second derivative of the band structure at the \(\Gamma\) point:  
+
+<|ref|>equation<|/ref|><|det|>[[393, 628, 603, 677]]<|/det|>
+\[m^{*} = \hbar^{2}\left[\frac{d^{2}E_{c v}(k)}{d k^{2}}\right]\left|0\right|^{1}\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 685, 271, 705]]<|/det|>
+as given in Ref [12].  
+
+<|ref|>text<|/ref|><|det|>[[113, 714, 883, 770]]<|/det|>
+As mentioned before, the polycrystallinity of the system is included by averaging over several differential transmittance spectra.  
+
+<|ref|>text<|/ref|><|det|>[[113, 799, 883, 868]]<|/det|>
+The transition from the \(\overline{\Gamma Z}\) to the \(\overline{\Gamma A}\) direction is carried out by varying the bandwidth \(\Delta\) from \(\Delta_{\overline{\Gamma Z}} = 0.75 \mathrm{eV}\) to \(\Delta_{\overline{\Gamma A}} = 1.55 \mathrm{eV}\) , the extent of the first Brillouin zone \(\frac{\pi}{a^{*}}\) from \(\frac{\pi}{a_{\overline{\Gamma Z}}^{*}} = \frac{\pi}{c} = \frac{\pi}{1.27} \mathrm{nm}^{- 1}\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 85, 884, 193]]<|/det|>
+to \(\frac{\pi}{a_{\Gamma A}^{*}} = \frac{\pi}{a c}\sqrt{2c^{2} + a^{2}} = \frac{\pi}{0.56}\mathrm{nm}^{- 1}\) and the effective mass \(\mathrm{m}^{*}\) from \(\mathrm{m}_{\Gamma Z}^{*} = 0.17\mathrm{m}_{0}\) to \(\mathrm{m}_{\Gamma A}^{*}\) \(= 0.09\mathrm{m}_{0}\) via a parameter \(f\) which varies from 0 (i.e. the \(\overline{\Gamma Z}\) - direction) to 1 (i.e. the \(\overline{\Gamma A}\) - direction) 12. The interpolation is performed as:  
+
+<|ref|>equation<|/ref|><|det|>[[380, 222, 616, 245]]<|/det|>
+\[\Delta (\mathrm{f}) = \Delta_{\overline{\Gamma Z}} + \mathrm{f}\big(\Delta_{\overline{\Gamma A}} - \Delta_{\overline{\Gamma Z}}\big)\]  
+
+<|ref|>equation<|/ref|><|det|>[[371, 275, 625, 320]]<|/det|>
+\[\frac{\pi}{a^{*}(f)} = \frac{\pi}{a_{\Gamma Z}^{*}} +f\left(\frac{\pi}{a_{\Gamma A}^{*}} -\frac{\pi}{a_{\Gamma Z}^{*}}\right)\]  
+
+<|ref|>equation<|/ref|><|det|>[[365, 349, 630, 375]]<|/det|>
+\[m^{*}(f) = m_{\Gamma Z}^{*} + f\big(m_{\Gamma A}^{*} - m_{\Gamma Z}^{*}\big)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 404, 732, 425]]<|/det|>
+where \(f = 0\) describes the \(\overline{\Gamma Z}\) - direction and \(f = 1\) the \(\overline{\Gamma A}\) - direction, respectively.  
+
+<|ref|>text<|/ref|><|det|>[[113, 455, 884, 511]]<|/det|>
+The above described averaging of several spectra for the discretized parameter \(f\) is performed via evaluating  
+
+<|ref|>equation<|/ref|><|det|>[[360, 540, 637, 590]]<|/det|>
+\[\alpha_{\mathrm{avg}}(\omega) = \frac{1}{n}\sum_{f_{i}}\alpha_{f_{i}}(\omega),i\in [1,n]\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 599, 884, 639]]<|/det|>
+With the respective absorption \(\alpha_{f = 0} = \alpha_{1D,\overline{\Gamma Z}}\) and \(\alpha_{f = 1} = \alpha_{1D,\overline{\Gamma A}}\) where for convergence \(n\) is typically chosen as 51.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 750, 320, 768]]<|/det|>
+## Supporting Information  
+
+<|ref|>text<|/ref|><|det|>[[113, 798, 715, 819]]<|/det|>
+Fig. S1. Normalized spectra of near- IR (red) and visible (blue) probe pulses.  
+
+<|ref|>text<|/ref|><|det|>[[113, 848, 884, 904]]<|/det|>
+Fig. S2. Differential transmission changes measured at probe photon energies of 1.7 eV (red line) and 2.0 eV (blue) together with the \(\mathrm{E}^{2}(\mathrm{t})\) of THz pulse profile.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 706, 109]]<|/det|>
+Fig. S3. Contributions from free carriers generated via interband tunneling.  
+
+<|ref|>text<|/ref|><|det|>[[113, 139, 884, 195]]<|/det|>
+Fig. S4. Simulations with averaging from the \(\overline{\Gamma Z}\) to the \(\overline{\Gamma A}\) direction for a THz pulse centered at \(t = 0\) and various field strengths.  
+
+<|ref|>text<|/ref|><|det|>[[113, 224, 884, 316]]<|/det|>
+Fig. S5. Simulated absorption change, \(- \Delta \alpha_{\mathrm{avg}}\) , averaged for a pure cosine model band structure (without the function g, see methods, which was introduced to fit the effective mass) from \(\overline{\Gamma Z}\) to \(\overline{\Gamma A}\) direction for a THz pulse centered at \(t = 0\) and various field strengths.  
+
+<|ref|>text<|/ref|><|det|>[[113, 345, 884, 402]]<|/det|>
+Figure S6. Simulated change of the optical interband absorption \(- \Delta \alpha_{\overline{\Gamma A}}\) from a cosine band modeling along \(\overline{\Gamma A}\) direction for static fields and a pulsed THz field.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 491, 342, 509]]<|/det|>
+## AUTHOR INFORMATION  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 535, 310, 553]]<|/det|>
+## Corresponding Author  
+
+<|ref|>text<|/ref|><|det|>[[115, 572, 700, 592]]<|/det|>
+\*Corresponding author. torsten.meier@upb.de; kim@mpip-mainz.mpg.de  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 622, 301, 640]]<|/det|>
+## Author Contributions  
+
+<|ref|>text<|/ref|><|det|>[[115, 660, 883, 715]]<|/det|>
+The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. \(\ddagger\) These authors contributed equally.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 746, 165, 763]]<|/det|>
+## Notes  
+
+<|ref|>text<|/ref|><|det|>[[115, 784, 525, 803]]<|/det|>
+The authors declare no competing financial interest.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 313, 108]]<|/det|>
+## ACKNOWLEDGMENT  
+
+<|ref|>text<|/ref|><|det|>[[112, 135, 886, 436]]<|/det|>
+The authors thank Keno Krewer and Johannes Hunger for helpful discussions. T. M. and D. B. acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Research Center TRR 142 (project number 231447078, project A02). M. B. and H. K. thank the DFG for financial support through the Collaborative Research Center TRR 288 (project number 422213477, project B07), the European Union's Horizon 2020 research and innovation program under grant agreement No.658467, and the Max Planck Society for financial support. A. L. and J. B. acknowledge financial support from the European Research Council through ERC Advanced Grant 290876 (UltraPhase) and the Carl Zeiss Foundation through the fellowship program.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 492, 241, 510]]<|/det|>
+## REFERENCES  
+
+<|ref|>text<|/ref|><|det|>[[111, 525, 886, 884]]<|/det|>
+1. Wannier, G. H. Wave Functions and Effective Hamiltonian for Bloch Electrons in an Electric Field. Phys. Rev. 117, 432–439 (1960).  
+2. Bloch, F. Über die Quantenmechanik der Elektronen in Kristallgittern. Zeitschrift für Phys. 52, 555–600 (1929).  
+3. Zener, C. A theory of the electrical breakdown of solid dielectrics. Proc. R. Soc. London. Ser. A 145, 523–529 (1934).  
+4. Mendez, E. E., Agulló-Rueda, F. & Hong, J. M. Stark Localization in GaAs-GaAlAs Superlattices under an Electric Field. Phys. Rev. Lett. 60, 2426–2429 (1988).  
+5. Voisin, P. et al. Observation of the Wannier-Stark Quantization in a Semiconductor
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 89, 580, 108]]<|/det|>
+Superlattice. Phys. Rev. Lett. 61, 1639–1642 (1988).  
+
+<|ref|>text<|/ref|><|det|>[[113, 139, 883, 193]]<|/det|>
+6. Feldmann, J. et al. Optical investigation of Bloch oscillations in a semiconductor superlattice. Phys. Rev. B 46, 7252–7255 (1992).  
+
+<|ref|>text<|/ref|><|det|>[[113, 223, 884, 277]]<|/det|>
+7. Waschke, C. et al. Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice. Phys. Rev. Lett. 70, 3319–3322 (1993).  
+
+<|ref|>text<|/ref|><|det|>[[113, 308, 883, 362]]<|/det|>
+8. Schmidt, C. et al. Signatures of transient Wannier-Stark localization in bulk gallium arsenide. Nat. Commun. 9, (2018).  
+
+<|ref|>text<|/ref|><|det|>[[113, 393, 884, 483]]<|/det|>
+9. Sell, A., Leitenstorfer, A. & Huber, R. Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm. Opt. Lett. 33, 2767 (2008).  
+
+<|ref|>text<|/ref|><|det|>[[114, 512, 882, 566]]<|/det|>
+10. Junginger, F. et al. Single-cycle multiterahertz transients with peak fields above 10 MV/cm. Opt. Lett. 35, 2645 (2010).  
+
+<|ref|>text<|/ref|><|det|>[[114, 597, 884, 652]]<|/det|>
+11. von Plessen, G. et al. Influence of scattering on the formation of Wannier-Stark ladders and Bloch oscillations in semiconductor superlattices. Phys. Rev. B 49, 14058–14061 (1994).  
+
+<|ref|>text<|/ref|><|det|>[[114, 682, 883, 736]]<|/det|>
+12. Umari, P., Mosconi, E. & De Angelis, F. Relativistic GW calculations on CH3 NH3 PbI 3 and CH3 NH3 SnI3 Perovskites for Solar Cell Applications. Sci. Rep. 4, 1–7 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[114, 767, 884, 821]]<|/det|>
+13. Whitfield, P. S. et al. Structures, Phase Transitions and Tricritical Behavior of the Hybrid Perovskite Methyl Ammonium Lead Iodide. Sci. Rep. 6, 1–16 (2016).  
+
+<|ref|>text<|/ref|><|det|>[[114, 852, 883, 906]]<|/det|>
+14. Brivio, F. et al. Lattice dynamics and vibrational spectra of the orthorhombic, tetragonal, and cubic phases of methylammonium lead iodide. Phys. Rev. B 92, 1–8 (2015).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 884, 180]]<|/det|>
+15. Quarti, C., Mosconi, E. & De Angelis, F. Interplay of orientational order and electronic structure in methylammonium lead iodide: Implications for solar cell operation. Chem. Mater. 26, 6557–6569 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[115, 208, 884, 298]]<|/det|>
+16. Leguy, A. M. A. et al. Dynamic disorder, phonon lifetimes, and the assignment of modes to the vibrational spectra of methylammonium lead halide perovskites. Phys. Chem. Chem. Phys. 18, 27051–27066 (2016).  
+
+<|ref|>text<|/ref|><|det|>[[115, 328, 884, 383]]<|/det|>
+17. Kim, H. et al. Direct observation of mode-specific phonon-band gap coupling in methylammonium lead halide perovskites. Nat. Commun. 8, 687 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[115, 412, 884, 467]]<|/det|>
+18. Karakus, M. et al. Phonon-Electron Scattering Limits Free Charge Mobility in Methylammonium Lead Iodide Perovskites. J. Phys. Chem. Lett. 6, 4991–4996 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[115, 496, 884, 589]]<|/det|>
+19. D'Angelo, F., Mics, Z., Bonn, M. & Turchinovich, D. Ultra-broadband THz time-domain spectroscopy of common polymers using THz air photonics. Opt. Express 22, 12475–12485 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[113, 617, 884, 707]]<|/det|>
+20. Yan, W. X., Zhao, X. G. & Wang, H. Coherent effects induced by dc-ac fields in semiconductor superlattices: The signature of fractional Wannier-Stark ladders. J. Phys. Condens. Matter 10, L11 (1998).  
+
+<|ref|>text<|/ref|><|det|>[[113, 736, 884, 792]]<|/det|>
+21. Frohna, K. et al. Inversion symmetry and bulk Rashba effect in methylammonium lead iodide perovskite single crystals. Nat. Commun. 9, (2018).  
+
+<|ref|>text<|/ref|><|det|>[[113, 821, 884, 877]]<|/det|>
+22. Blancon, J. C. et al. Unusual thickness dependence of exciton characteristics in 2D perovskite quantum wells. arXiv:1710.07653v2
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 883, 145]]<|/det|>
+23. Ishihara, T. & Goto, T. Exciton Features in 0-, 2-, and 3-Dimensional Networks of [Pbl6]4-Octahedra. Journal of the Physical Society of Japan 63, 3870-3879 (1994).  
+
+<|ref|>text<|/ref|><|det|>[[113, 174, 882, 229]]<|/det|>
+24. Umebayashi, T. et al. Electronic structures of lead iodide based low-dimensional crystals. Phys. Rev. B 67, 2-7 (2003).  
+
+<|ref|>text<|/ref|><|det|>[[113, 258, 883, 314]]<|/det|>
+25. Blancon, J. C. et al. Unusual thickness dependence of exciton characteristics in 2D perovskite quantum wells. arXiv 1-21 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[113, 343, 883, 398]]<|/det|>
+26. Schubert, O. et al. Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations. Nat. Photonics 8, 119-123 (2014).  
+
+<|ref|>text<|/ref|><|det|>[[113, 428, 883, 483]]<|/det|>
+27. Meier, T., Von Plessen, G., Thomas, P. & Koch, S. W. Coherent electric-field effects in semiconductors. Phys. Rev. Lett. 73, 902-905 (1994).  
+
+<|ref|>text<|/ref|><|det|>[[113, 512, 883, 602]]<|/det|>
+28. Golde, D., Meier, T. & Koch, S. W. High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations. Phys. Rev. B 77, 1-6 (2008).  
+
+<|ref|>text<|/ref|><|det|>[[113, 631, 883, 722]]<|/det|>
+29. Brandt, R. E., Stevanović, V., Ginley, D. S. & Buonassisi, T. Identifying defect-tolerant semiconductors with high minority-carrier lifetimes: Beyond hybrid lead halide perovskites. MRS Commun. 5, 265-275 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[113, 752, 883, 807]]<|/det|>
+30. Guo, L., Xu, G., Tang, G., Fang, D. & Hong, J. Structural stability and optoelectronic properties of tetragonal {MAPbI}3 under strain. Nanotechnology 31, 225204 (2020).  
+
+<|ref|>text<|/ref|><|det|>[[113, 836, 883, 891]]<|/det|>
+31. Ball, J. M., Lee, M. M., Hey, A. & Snaith, H. J. Low-temperature processed meso-superstructured to thin-film perovskite solar cells. Energy Environ. Sci. 6, 1739 (2013).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 144]]<|/det|>
+32. Grinblat, G. et al. Ultrafast All-Optical Modulation in 2D Hybrid Perovskites. ACS Nano 13, 9504–9510 (2019).  
+
+<|ref|>text<|/ref|><|det|>[[113, 174, 884, 230]]<|/det|>
+33. Stranks, S. D. et al. Electron-hole diffusion lengths exceeding 1 micrometer in an organometal trihalide perovskite absorber. Science 342, 341–4 (2013).  
+
+<|ref|>text<|/ref|><|det|>[[113, 258, 884, 313]]<|/det|>
+34. Shi, D. et al. Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals. Science 347, 519–522 (2015).  
+
+<|ref|>text<|/ref|><|det|>[[113, 342, 884, 433]]<|/det|>
+35. Lee, M. M., Teuscher, J., Miyasaka, T., Murakami, T. N. & Snaith, H. J. Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites. Science 338, 643–7 (2012).  
+
+<|ref|>text<|/ref|><|det|>[[113, 463, 884, 519]]<|/det|>
+36. Bar-Joseph, I. et al. Room-temperature electroabsorption and switching in a GaAs/AlGaAs superlattice. Appl. Phys. Lett. 55, 340–342 (1989).  
+
+<|ref|>text<|/ref|><|det|>[[113, 548, 884, 604]]<|/det|>
+37. Bigan, E. et al. Optimization of optical waveguide modulators based on Wannier-Stark localization: an experimental study. IEEE J. Quantum Electron. 28, 214–223 (1992).  
+
+<|ref|>text<|/ref|><|det|>[[113, 633, 884, 688]]<|/det|>
+38. Riek, C., Seletskiy, D. V & Leitenstorfer, A. Femtosecond measurements of electric fields: from classical amplitudes to quantum fluctuations. Eur. J. Phys. 38, 24003 (2017).  
+
+<|ref|>text<|/ref|><|det|>[[113, 718, 884, 773]]<|/det|>
+39. Brida, D. et al. Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers. J. Opt. 12, 13001 (2009).  
+
+<|ref|>text<|/ref|><|det|>[[113, 803, 886, 858]]<|/det|>
+40. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors. (WORLD SCIENTIFIC, 2009).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[856, 968, 881, 984]]<|/det|>
+29
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 143, 68]]<|/det|>
+## Figures  
+
+<|ref|>image<|/ref|><|det|>[[60, 100, 940, 536]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 560, 115, 580]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[40, 601, 953, 738]]<|/det|>
+Experimental scheme and properties of MAPbI3 perovskite (a) THz pulse geometry with a tetragonal unit cell (black rectangular cuboid) of MAPbI3. (dark grey: Pb, purple: I, brown: C, light blue: N, light pink: H) The THz biasing along the c axis of a crystallite is depicted. (b) Simplified electronic band structure of MAPbI3 in the tetragonal phase along the directions \(\Gamma (0,0,0) \cong \mathrm{Z}(0,0,0.5)\) and \(\Gamma (0,0,0) \cong \mathrm{A}(0.5,0.5,0.5)\) . The bandwidths and the lattice parameters are used from [Ref 12]. (c) Optical absorption spectrum of MAPbI3 in the spectral range of the probe pulses.  
+
+<|ref|>image<|/ref|><|det|>[[50, 745, 945, 933]]<|/det|>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 117, 61]]<|/det|>
+## Figure 2  
+
+<|ref|>text<|/ref|><|det|>[[39, 82, 951, 355]]<|/det|>
+Experimental observation of the transient Wannier Stark localization and the visualized diagram (a) Experimental differential transmission spectra on a polycrystalline film of MAPbI3 perovskite at room temperature, as a function of delay time of probe pulses after THz pump pulses. The THz pulses have a peak field strength of 6.1 MV/cm and a center frequency of 20 THz; the probe pulses have photon energy of \(1.4 \sim 2.4 \text{eV}\) . (b) Temporal profile of the applied THz bias transient. (c) Schematic picture of Wannier Stark localization. In the presence of strong external fields along the c axis, electronic states (orange: conduction band, blue: valence band) are localized to a few layers of ab plane, and energetically separated by \(\Delta \text{EWSL} = \text{eETHzc}\) between adjacent lattice sites. Black arrows depict the interband transitions within the same site (n = 0) and between different sites (n = ±1). (d) The absorbance with and without the external transient biasing. The Wannier- Stark localization effectively reduces the 3D electronic structure into 2D layered structure along the ab plane, as depicted in blue together with the simplified 3D structure.  
+
+<|ref|>image<|/ref|><|det|>[[50, 365, 940, 644]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[43, 670, 117, 690]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[43, 712, 825, 733]]<|/det|>
+Numerical simulation of differential absorption spectra. Please see .pdf file for full caption
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[55, 52, 485, 614]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 641, 117, 660]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>image<|/ref|><|det|>[[520, 55, 940, 614]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[42, 683, 949, 725]]<|/det|>
+. Experiments on polycrystalline system and simulations with averaging of cosine band model from \(\mathbb{W}\mathbb{W}\) to \(\mathbb{W}\mathbb{W}\) direction. Please see .pdf file for full caption  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 749, 310, 776]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 800, 764, 820]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[61, 838, 264, 857]]<|/det|>
+- SlfinalNatComm.pdf
+
+<--- Page Split --->

preprint/preprint__011f1f7cdec2740845fc5c2f410ff02c63329260c767801a3ae4c3d8ae57e6f6/images_list.json

@@ -0,0 +1,55 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "C",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 55
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "Adipogenic",
+    "footnote": [],
+    "bbox": [
+      [
+        32,
+        404,
+        435,
+        630
+      ]
+    ],
+    "page_idx": 56
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "Alizarin Red (day 21)",
+    "footnote": [],
+    "bbox": [
+      [
+        471,
+        193,
+        707,
+        333
+      ]
+    ],
+    "page_idx": 57
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "Osteogenic",
+    "footnote": [],
+    "bbox": [
+      [
+        460,
+        245,
+        485,
+        255
+      ]
+    ],
+    "page_idx": 58
+  }
+]

preprint/preprint__0120cbbdf5abcce247bf35686d0d3fbc3c94f93c709d874b56ecf9271a6516aa/images_list.json

@@ -0,0 +1,107 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 | The synthesis steps of the PtNP-shell and the concept of mediating precise photothermal effects for cardioprotection. a, The synthesis steps of PtNP-shell and schematic diagram of photothermal effect. b, Schematic diagram of multifunctional autonomic modulation mediated by photothermal effect of PtNP-shell for precise cardioprotection against myocardial I/R injury and MI-induced VAs.",
+    "footnote": [],
+    "bbox": [
+      [
+        147,
+        85,
+        848,
+        444
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 | Characterization of PtNP-shell. a, TEM image of PtNP-shell (Right: element mapping). b, STEM images of PtNP-shell surface. c, XRD spectrum of PtNP-shell (Inset: SAED pattern). d, UV-vis-NIR absorption spectrum of PtNP-shell ( \\(75 \\mu \\mathrm{g} \\cdot \\mathrm{mL}^{-1}\\) ). e, Temperature elevation curves of PtNP-shell ( \\(50 \\mu \\mathrm{g} \\cdot \\mathrm{mL}^{-1}\\) ) under NIR-II laser irradiation ( \\(1 \\mathrm{W} \\cdot \\mathrm{cm}^{2}\\) ). f, Calculation of the PCE at \\(1064 \\mathrm{nm}\\) (PtNP-shell: \\(50 \\mu \\mathrm{g} \\cdot \\mathrm{mL}^{-1}\\) ).",
+    "footnote": [],
+    "bbox": [
+      [
+        144,
+        494,
+        850,
+        775
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 | PtNP-shell photothermal activation of different neuronal ion channels in vitro. a, Flowchart of calcium imaging assay performed on HT-22 cells. b, calcium imaging of HT-22 cells under different experimental conditions. c, Western blotting for TRPV1 and TREK1 from HT-22 and H9c2 cells. Percentage of d, TRPV1 and f, TREK1 groups of HT-22 cells within the field of view of the fluorescence microscope that responded to laser stimulation. Temporal dynamics of \\(\\mathrm{Ca}^{2 + }\\) signals in e, TRPV1 and g, TREK1 groups of cells. The solid lines indicate the mean, and shade represents the standard error of the mean (SEM). h, Cell viability of HT-22 treated with different concentrations of PtNP-shell for \\(24\\mathrm{h}\\) . i, Cell viability of HT-22 treated with NIR-II laser irradiation of different power densities and laser duration. The error bar indicates S.E.M. \\(***\\mathrm{P}< 0.001\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        145,
+        81,
+        850,
+        480
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 | Photothermal activation of the parasympathetic nervous system by PtNP-shell. a, Location of the canine NG. b, Schematic illustration of the process of photothermal modulation of NG. c, Temperature curves of NG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of NG. e, Representative images of HR reduction induced after stimulation of NG with different voltages. Maximal HR changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, \\(n = 6\\) . h, Quantification of the NG neural activity recordings, \\(n = 6\\) . i, Representative immunofluorescent images of Vacht (red), c-fos (green) and TRPV1 (pink) in the NG of beagles following different treatments. Data are shown as the mean \\(\\pm\\) S.E.M. \\(*P < 0.05\\) , \\(**P < 0.01\\) , \\(***P < 0.001\\) , ns means that the difference is not statistically significant.",
+    "footnote": [],
+    "bbox": [
+      [
+        144,
+        165,
+        850,
+        670
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 | PtNP-shell photothermal activation of the parasympathetic nervous system improves myocardial I/R injury. Modulation of NG to protect against myocardial I/R injury and associated VAs a, schematic diagram and b, flowchart. c, Representative visual depictions of VAs, including VPB, VT and VF. d, Quantitative analysis the ratio of sVT and VF incidence between different groups, \\(\\mathrm{n} = 6\\) . Quantitative analysis the number of e, VPBs, f, VTs and g, the duration of sVT of beagles. Effects on ventricular ERP at different sites in beagles treatment with PtNP-shell or control h, before and i, after myocardial I/R injury modelling. Levels of markers of myocardial injury, including j, MYO and k, c-TnI, after different treatments in beagles. Data are shown as the mean \\(\\pm\\) S.E.M. \\(^{*}\\mathrm{P}< 0.05\\) , \\(^{**}P< 0.01\\) , \\(^{***}\\mathrm{P}< 0.001\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        192,
+        425,
+        803,
+        720
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Fig. 6 | Photothermal inhibition of the sympathetic nervous system by PtNP-shell. a, Location of the canine LSG. b, Schematic illustration of the process of photothermal modulation of LSG. c, Temperature curves of LSG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of LSG. e, Representative images of BP elevation induced after stimulation of LSG with different voltages. Maximal SBP changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, \\(n = 6\\) . h, Quantification of the LSG neural activity recordings, \\(n = 6\\) . i, Representative immunofluorescent images of TH (red), c-fos (green) and TREK1 (pink) in the LSG of beagles following different treatments. Data are shown as the mean \\(\\pm\\) S.E.M. \\(*P< 0.05\\) , \\(**P< 0.01\\) , \\(***P< 0.001\\) , ns means that the difference is not statistically significant.",
+    "footnote": [],
+    "bbox": [
+      [
+        150,
+        80,
+        850,
+        592
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Fig. 7 | PtNP-shell photothermal inhibition of the sympathetic nervous system improves MI associated VAs. Modulation of LSG to protect against MI and associated VAs a, schematic diagram and b, flowchart. c, Quantitative analysis the ratio of sVT and VF incidence between different groups, \\(n = 6\\) . d, Quantitative analysis the number of VPBs of beagles. e, Typical images of VA induced by programmed electrical stimulation. f, Quantitative analysis of VAs score in different groups. Effects on ventricular ERP at different sites in Beagles treatment with PtNP-shell or control g, before and h, after MI modelling. i, Quantitative analysis of VF threshold in different groups. Data are shown as the mean \\(\\pm\\) S.E.M. \\(*P < 0.05\\) , \\(**P < 0.01\\) , \\(***P < 0.001\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        144,
+        85,
+        852,
+        393
+      ]
+    ],
+    "page_idx": 19
+  }
+]

preprint/preprint__0120cbbdf5abcce247bf35686d0d3fbc3c94f93c709d874b56ecf9271a6516aa/preprint__0120cbbdf5abcce247bf35686d0d3fbc3c94f93c709d874b56ecf9271a6516aa.mmd

@@ -0,0 +1,426 @@
+
+# Pt nanoshell with ultra-high NIR-β photothermal conversion efficiency mediates multifunctional neuromodulation for cardiac protection  
+
+Lei Fu lei fu@whu.edu.cn  
+
+Wuhan University https://orcid.org/0000- 0003- 1356- 4422Chenlu WangWuhan UniversityLiping ZhouWuhan UniversityChengzhe LiuWuhan UniversityJiaming QiaoWuhan UniversityXinrui HanWuhan UniversityLuyang WangWuhan UniversityYaxi LiuWuhan UniversityBi XuWuhan UniversityQinfang QiuWuhan UniversityZizhuo ZhangWuhan UniversityJiale WangWuhan UniversityXiaoya ZhouWuhan UniversityMengqi ZengWuhan University https://orcid.org/0000- 0002- 1442- 052X  
+
+Lilei Yu
+
+<--- Page Split --->
+
+## Article  
+
+## Keywords:  
+
+Posted Date: March 15th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3985327/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on July 28th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 50557- w.
+
+<--- Page Split --->
+
+# Pt nanoshell with ultra-high NIR-II photothermal conversion efficiency mediates multifunctional neuromodulation for cardiac protection  
+
+Chenlu Wang \(^{1,\dagger}\) , Liping Zhou \(^{2,3,4,\dagger}\) , Chengzhe Liu \(^{2,3,4,\dagger}\) , Jiaming Qiao \(^{2,3,4}\) , Xinrui Han \(^{2,3,4}\) , Luyang Wang \(^{1}\) , Yaxi Liu \(^{1}\) , Bi Xu \(^{1}\) , Qinfang Qiu \(^{2,3,4}\) , Zizhuo Zhang \(^{2,3,4}\) , Jiale Wang \(^{2,3,4}\) , Xiaoya Zhou \(^{2,3,4*}\) , Mengqi Zeng \(^{1}\) , Lilei Yu \(^{2,3,4*}\) , Lei Fu \(^{1,3,4*}\)  
+
+\(^{1}\) College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, China. \(^{2}\) Cardiovascular Hospital, Renmin Hospital of Wuhan University, Wuhan 430060, China; Hubei Key Laboratory of Autonomic Nervous System Modulation, Wuhan 430060, China; Cardiac Autonomic Nervous System Research Center of Wuhan University, Wuhan 430060, China; Hubei Key Laboratory of Cardiology, Wuhan 430060, China; Cardiovascular Research Institute, Wuhan University, Wuhan, 430060, China. \(^{3}\) Taikang Center for Life and Medical Sciences, Wuhan University, Wuhan 430060, China. \(^{4}\) Institute of Molecular Medicine, Renmin Hospital of Wuhan University, Wuhan 430060, China.  
+
+\(^{*}\) E- mail: leifu@whu.edu.cn; lileiyu@whu.edu.cn; whuzhouxiaoya@whu.edu.cn  
+
+\(^{†}\) These authors contributed equally: Chenlu Wang, Liping Zhou, Chengzhe Liu.
+
+<--- Page Split --->
+
+The autonomic nervous system plays a pivotal role in the pathophysiology of cardiovascular diseases. Regulating it is essential for preventing and treating acute ventricular arrhythmias (VAs). Photothermal neuromodulation is a nonimplanted technique, but the response temperature ranges of transient receptor potential vanilloid 1 (TRPV1) and TWIK- elated \(\mathbf{K}^{+}\) Channel 1 (TREK1) exhibit differences while being closely aligned, and the acute nature of VAs require that it must be rapid and precise. However, the low photothermal conversion efficiency (PCE) still poses limitations on achieving rapid and precise treatment. Here, we achieved nearly perfect blackbody absorption and one of the highest PCE in the second near infrared (NIR- II) window (73.7% at 1064 nm) via a Pt nanoparticle shell (PtNP- shell). By precisely manipulating the photothermal effect, we successfully achieved rapid and precise multifunctional neuromodulation encompassing neural activation (41.0–42.9 °C) and inhibition (45.0–46.9 °C). The NIR-II photothermal modulation additionally achieved bi- directional reversible autonomic modulation and conferred protection against acute VAs associated with myocardial ischemia and reperfusion injury in interventional therapy.  
+
+Cardiovascular disease has emerged as a leading cause of mortality, with acute myocardial infarction being one of the most pernicious ailments<sup>1,2</sup>. Myocardial ischemia (MI) frequently precipitates acute ventricular arrhythmias (VAs), impeding prompt and efficacious treatment for acute myocardial infarction. Furthermore, conventional interventional procedures for MI are unable to circumvent concomitant myocardial reperfusion injury and associated VAs. The autonomic nervous system, encompassing sympathetic and parasympathetic nerves, plays a role in cardiovascular modulation; both are naturally antagonistic. Sympathetic inhibition or parasympathetic activation has been shown to stabilize cardiac electrophysiology, safeguard against MI
+
+<--- Page Split --->
+
+and reduce the incidence of VAs \(^{3}\) .  
+
+In recent years, several studies have demonstrated that light- activated nanotransducers can induce local heating effects, leading to the activation or inhibition of nerves \(^{4 - 6}\) . This discovery is attributed to the identification of temperature- sensitive ion channels in neurons, such as transient receptor potential vanilloid 1 (TRPV1) \(^{7}\) and TWIK- elated K \(^{+}\) Channel 1 (TREK1) \(^{8}\) . The activation of specific temperature- sensitive ion channels necessitates precise temperature ranges \(^{7 - 9}\) . Considering the acute nature of neural responses, a therapeutic strategy with rapid and accurate modulation is required. The second near infrared (NIR- II) photothermal is expected to realize noninvasive and nonimplanted neuromodulation. However, its neural response rate and accuracy are currently limited by low photothermal conversion efficiency (PCE).  
+
+Here we report a near blackbody NIR- II Pt nanoparticle shell (PtNP- shell) for protection against MI and myocardial reperfusion injury accompanying intervention. The PtNP- shell, synthesized through a simple electrocoupling substitution reaction using liquid metal nanoparticles as templates (Fig. 1a), possesses surface pores and a hollow structure. It demonstrates nearly perfect blackbody absorption, enhanced absorption of light, and then one of the highest PCE in the NIR- II window (73.7% at 1064 nm). By leveraging the local heating effect mediated by PtNP- shell, we achieved rapid, efficient, and precise multifunctional autonomic neuromodulation. Specifically, parasympathetic activation and sympathetic inhibition were accomplished by activating TRPV1 (41.0–42.9 °C) and TREK1 (45.0–46.9 °C) channels, respectively. Photothermal autonomic neuromodulation mediated by PtNP- shell effectively stabilized cardiac electrophysiology and reduced VAs incidence in both myocardial ischemia- reperfusion (I/R) injury model and MI model, respectively (Fig. 1b).
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 | The synthesis steps of the PtNP-shell and the concept of mediating precise photothermal effects for cardioprotection. a, The synthesis steps of PtNP-shell and schematic diagram of photothermal effect. b, Schematic diagram of multifunctional autonomic modulation mediated by photothermal effect of PtNP-shell for precise cardioprotection against myocardial I/R injury and MI-induced VAs. </center>  
+
+## Result and discussion  
+
+## Synthesis and Characterization of PtNP-shell  
+
+The PtNP- shell was synthesized through an electrocoupling substitution reaction between chloroplatinate and Ga nanoparticles (GaNPs). Ga nanoparticles were obtained by sonication of pure metal Ga. To achieve a balanced particle size and oxidation degree of GaNPs, pure gallium was sequentially sonicated in ethanol and water for 30 minutes to obtain gallium nanoparticles with reduced oxidation (Supplementary Fig. 1a). In accordance with the electrochemical redox potential of the redox couple \((\mathrm{Ga}^{3 + } / \mathrm{Ga} - 0.529 \mathrm{V}; \mathrm{PtCl}_6^{2 - } / \mathrm{PtCl}_4^{2 - }: 0.726 \mathrm{V}; \mathrm{PtCl}_4^{2 - } / \mathrm{Pt}: 0.758 \mathrm{V})^{10,11}, \mathrm{Pt} (\mathrm{IV}) \mathrm{can be in situ}\) reduced by Ga and encapsulated on the surface of GaNPs to form a core- shell structure
+
+<--- Page Split --->
+
+(Supplementary Fig. 1b, c). The hollow PtNP-shell is synthesized after completion of the reaction (Fig. 2a). Simultaneously with the reduction of Pt (IV), Ga oxide is formed, creating the skeleton of the PtNP-shell (right in Fig. 2a). The surface of the PtNP-shell exhibits a rough texture (Supplementary Fig. 2). The scanning transmission electron microscopy (STEM) images reveal numerous irregular and uneven pores on its surface (Supplementary Fig. 3a) and PtNP-shell is composed of Pt nanoparticles (PtNPs) with \(2 - 5 \mathrm{nm}\) (Fig. 2b). High-resolution TEM (HR-TEM) image is acquired to character the structure of PtNPs. As shown in Supplementary Fig. 3b, PtNPs exhibits single crystal structure with a lattice stripe spacing of \(0.23 \mathrm{nm}\) corresponding to the (111) crystal plane. Meanwhile, the corresponding Fast Fourier Transform (FFT) pattern (inset in Supplementary Fig. 3b) shows the typical diffraction patterns of face-centered cubic structure along [111] zone axis.  
+
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 | Characterization of PtNP-shell. a, TEM image of PtNP-shell (Right: element mapping). b, STEM images of PtNP-shell surface. c, XRD spectrum of PtNP-shell (Inset: SAED pattern). d, UV-vis-NIR absorption spectrum of PtNP-shell ( \(75 \mu \mathrm{g} \cdot \mathrm{mL}^{-1}\) ). e, Temperature elevation curves of PtNP-shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{-1}\) ) under NIR-II laser irradiation ( \(1 \mathrm{W} \cdot \mathrm{cm}^{2}\) ). f, Calculation of the PCE at \(1064 \mathrm{nm}\) (PtNP-shell: \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{-1}\) ). </center>
+
+<--- Page Split --->
+
+In the X- ray power diffraction (XRD) spectrogram result (Fig. 2c), all peaks can be attributed to the crystal phase of Pt (JCPDS: 87- 0640), consistent with the selected area electron diffraction (SAED) pattern findings (inset in Fig. 2c). However, no peaks corresponding to gallium oxide were observed in the XRD spectrogram, possibly due to its low content. The XRD spectrogram (Supplementary Fig. 4) of PtNP- shell prior to reacting with KOH showed that the gallium oxide contained in PtNP- shell was GaOOH (JCPDS: 06- 0180). Additional evidence from X- ray photoelectron spectroscopy (XPS) also suggests that PtNP- shell contains Ga (Supplementary Fig. 5), consistent with energy dispersive X- ray spectroscopy (EDX) analysis (right in Fig. 2a). The peak centred at 1117.59 eV is ascribed to Ga \(2\mathrm{p}_{3 / 2}\) , indicating the presence of \(\mathrm{Ga}^{3 + }\) in PtNP- shell. Meanwhile, the Pt 4f spectrum shows two peaks at 71.56 and 75.02 eV, which result from metallic Pt \(4\mathrm{f}_{7 / 2}\) and Pt \(4\mathrm{f}_{5 / 2}\) . PtNP- shell was treated with KOH (0.67 M) to reduce the gallium oxide content and the surface potential was reduced from 45.8 mV to - 25.7 mV, and then encapsulated with Methoxypoly(Ethylene Glycol) Thiol (mPEG- \(\mathrm{SH}_{5000}\) ) to enhance its biocompatibility and the surface potential was changed to - 19.9 mV. (Supplementary Fig. 6). The statistically averaged hydrated nanoparticle size of PtNP- shell based on the dynamic light scattering diagram was 200.1 nm with uniform size distribution, indicating the nanoparticle was well dispersed in water (Supplementary Fig. 7).  
+
+## Blackbody Absorption and Photothermal Property of PtNP-shell  
+
+Due to the presence of pores and a hollow structure in the PtNP- shell, light propagating in the space bounces at the rough surface of PtNP- shell until it encounters one of the pores, where it continues to bounce within the PtNP- shell. The random distribution of these pores results in completely random light reflection, akin to Brownian motion<sup>12</sup>. Consequently, the probability of light escaping from other pores is extremely low,
+
+<--- Page Split --->
+
+rendering PtNP- shell behave like a blackbody and produce an efficient infrared heater \(^{13 - 15}\) . This enhanced absorption of light by PtNP- shell exhibits nearly perfect blackbody absorption characteristics (Supplementary Fig. 8a). The absorption of PtNP- shell is close to 1 in the range of 250–1300 nm at \(75 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) (Fig. 2d). According to the Lambert- Beer law (A/L = εC, where ε is the extinction coefficient), a linear relationship between absorption intensity (at 1064 nm) and concentration was established, with an extinction coefficient measured as \(13.3 \mathrm{Lg}^{- 1} \mathrm{cm}^{- 1}\) at 1064 nm (Supplementary Fig. 8b). Varying concentrations of PtNP- shell resulted in different shades of grey being generated, with significantly darker greyness observed under identical conditions compared to GaNPs and Pt- coated Ga- In alloy (EGaIn) nanoparticles (GaIn@Pt NPs) (Supplementary Fig. 9a). These distinctive features were characterized by their respective positions within an RGB cube representation, wherein on the diagonal connecting darkest and brightest points, PtNP- shell was found closer to the darkest point than both other materials (Supplementary Fig.9b).  
+
+The photothermal properties of PtNP- shell were verified by irradiating the dispersion of PtNP- shell in water with NIR- II light at \(1064 \mathrm{nm}\) (1 \(\mathrm{W} \cdot \mathrm{cm}^{- 2}\) ). Even in vitro, PtNP- shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) exhibited rapid temperature elevation, achieving a rise from room temperature to \(41.0^{\circ} \mathrm{C}\) and \(45.0^{\circ} \mathrm{C}\) within only 96 s and 133 s, respectively (Fig. 2e). However, for GaNPs (347 s and over 600 s) and GaIn@Pt NPs (278 s and 450 s), it took significantly longer time to reach the same temperatures (Supplementary Fig. 10). The corresponding thermal images of the PtNP- shell with different concentrations under different irradiation times are shown in Supplementary Fig. 11. The heating effect of the PtNP- shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) gradually increased the \(\Delta \mathrm{T}\) from 7.72 \(^{\circ} \mathrm{C}\) to 52.17 \(^{\circ} \mathrm{C}\) When exposed to NIR- II laser for a duration of 600 s while varying the optical power density at 1064 nm between \(0.25 - 1.5 \mathrm{W} \cdot \mathrm{cm}^{- 2}\) (Supplementary Fig. 12).
+
+<--- Page Split --->
+
+The PCE of PtNP- shell was quantified as \(73.7\%\) when balancing the energy input from photons with heat dissipation within the system (Fig. 2f), representing one of the highest PCE at 1064 nm (Supplementary Fig. 13). These results indicate that PtNP- shell exhibits excellent photothermal performance in the NIR- II window. Additionally, no significant changes in temperature or morphology were observed even after five cycles of irradiation (Supplementary Fig. 14), suggesting exceptional photothermal stability.  
+
+## Photothermal of PtNP-shell enables precise modulations of neurons in vitro  
+
+To investigate the photothermal effects of PtNP- shell on neuronal activity at multiple levels, we conducted calcium imaging experiments in hippocampal neuron (HT- 22) cells (Fig. 3a, b). The immunoblotting results revealed abundant expression of both TRPV1 and TREK1 ion channels in HT- 22 cells (Fig. 3c). The direct effect of PtNP- shell on the excitability of these two different ion channels was assessed under NIR- II irradiation using a calcium ion indicator (Fluo- 4 AM). Upon NIR- II laser irradiation, the temperature of the PtNP- shell (+) group increased compared to that of the PtNP- shell (- ) group, resulting in a significantly higher percentage of responding cells (Fig. 3d) (p< 0.001). The micrographs fluorescence intensity curve of HT- 22 neurons cultured with PtNP- shell showed significant \(\mathrm{Ca^{2 + }}\) influx upon NIR- II laser irradiation for \(35 \pm 5\) s and after the temperature reached \(42.0^{\circ}\mathrm{C}\) (Fig. 3e). In contrast, application of NIR- II laser irradiation with PBS did not induce significant \(\mathrm{Ca^{2 + }}\) influx.  
+
+Subsequently, neuronal excitation was induced and calcium signals were increased by perfusion of \(15\mathrm{mM}\) KCl in the PtNP- shell (- ) group and PtNP- shell (+) group (50 \(\mu \mathrm{g}\mathrm{mL}^{- 1}\) ), respectively. This phenomenon can be attributed to the elevation of extracellular potassium ion concentration, which triggers neuronal depolarization and subsequently leads to a substantial increase in intracellular calcium ion concentration<sup>16</sup>. Under NIR- II laser irradiation, the proportion of HT- 22 cells responding to high
+
+<--- Page Split --->
+
+concentration KCl stimulation was significantly lower in the PtNP- shell (+) group compared to that in the PtNP- shell (- ) group at approximately \(46.0^{\circ}\mathrm{C}\) (Fig. 3f). The difference may be due to the activation of the TERK1 ion channel in the PtNP- shell (+) group, which can induce neuronal hyperpolarization and make intracellular and extracellular calcium ion concentrations tend to recover<sup>17</sup>. Interestingly, the PtNP- shell influenced the fluorescence intensity of HT- 22 cells not with a sustained decrease but with an initial rise followed by a subsequent decrease (Fig. 3g). This observation may be associated with the activation of TRPV1 channel at around \(42.0^{\circ}\mathrm{C}^9\) . With increasing temperature, TRPV1 and TREK1 channels were sequentially activated. These findings suggest that PtNP- shell can achieve precise temperature control within a short duration through its own ultra- high PCE for both neuronal excitation and inhibition.  
+
+Cytotoxicity assays were then conducted to investigate the potential neurotoxicity of PtNP- shell application. As shown in Fig. 3h, concentrations of PtNP- shell below 100 \(\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) exhibited no significant toxic effects on HT- 22 cells. Even when the concentration of PtNP- shell was increased to \(200\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) , the survival rate of neuronal cells remained approximately at \(52.11\%\) . Furthermore, the impact of PtNP- shell photothermal stimulation parameters on cell viability were assessed through analysis of HT- 22 cell survival under NIR- II laser irradiation. Notably, when a concentration of 50 \(\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) PtNP- shell and an NIR- II laser with a power density of \(0.5\mathrm{W}\cdot \mathrm{cm}^{- 2}\) were applied for a brief duration, the survival rate exceeded \(92.36\%\) for HT- 22 cells. Even with an increase in power density to \(0.75\mathrm{W}\cdot \mathrm{cm}^{- 2}\) , the survival rate for HT- 22 cells still remained around \(72.68\%\) after 60 s of irradiation (Fig. 3i). These results indicate that PtNP- shell does not induce significant damage to neurons under controlled NIR- II laser irradiation.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 | PtNP-shell photothermal activation of different neuronal ion channels in vitro. a, Flowchart of calcium imaging assay performed on HT-22 cells. b, calcium imaging of HT-22 cells under different experimental conditions. c, Western blotting for TRPV1 and TREK1 from HT-22 and H9c2 cells. Percentage of d, TRPV1 and f, TREK1 groups of HT-22 cells within the field of view of the fluorescence microscope that responded to laser stimulation. Temporal dynamics of \(\mathrm{Ca}^{2 + }\) signals in e, TRPV1 and g, TREK1 groups of cells. The solid lines indicate the mean, and shade represents the standard error of the mean (SEM). h, Cell viability of HT-22 treated with different concentrations of PtNP-shell for \(24\mathrm{h}\) . i, Cell viability of HT-22 treated with NIR-II laser irradiation of different power densities and laser duration. The error bar indicates S.E.M. \(***\mathrm{P}< 0.001\) . </center>  
+
+## PtNP-shell photothermal activation of the parasympathetic nervous system  
+
+Western blotting analysis of peripheral ganglia from the canine autonomic nervous system revealed the expression of TRPV1 and TREK1 heat- sensitive ion channels in both the nodose ganglion (NG) and left stellate ganglion (LSG). Notably, TRPV1 was abundantly expressed in the NG of the parasympathetic nervous system, while TREK1 exhibited higher levels in the LSG of the sympathetic nervous system (Supplementary
+
+<--- Page Split --->
+
+Fig. 15). To investigate whether the photothermal effect induced by PtNP-shell under NIR-II irradiation can precisely regulate the parasympathetic nerve, \(100\mu \mathrm{L}\) PtNP-shell \((50\mu \mathrm{g}\cdot \mathrm{mL}^{- 1})\) and PBS were injected into NG of PtNP-shell group and control group (6 beagle dogs in each group), respectively (Fig. 4a,b). It can be observed that upon irradiation with NIR-II laser \((0.8\mathrm{W}\cdot \mathrm{cm}^{- 2})\) , the temperature of NG injected with PtNP-shell increased to \(41.0^{\circ}\mathrm{C}\) within a very short period of time \((12\pm 3\mathrm{s})\) . Subsequently, the temperature of NG could be kept in the range of \(41.0–42.9^{\circ}\mathrm{C}\) for 5 min by adjusting the power density to \(0.45\mathrm{W}\cdot \mathrm{cm}^{- 2}\) (Fig. 4c-d). As a crucial node within the parasympathetic neural network, activation of NG significantly reduces heart rate (HR) (Fig. 4e) \(^{18}\) . Therefore, NG function was assessed by the maximum decrease in heart rate under direct electrical stimulation. As shown in Fig. 4f-h, NG function and activity was significantly elevated in the PtNP-shell group than in the control group after stimulation. The function and activity of NG recovered close to baseline within three hours after turning off NIR-II laser, indicating that the photothermal modulation induced by PtNP-shell was reversible within NGs (Fig. 4h, Supplementary Fig. 16 and 17).  
+
+In addition, the effective refractive period (ERP) was measured in various regions, including left ventricular apex (LVA), left ventricular base (LVB) and median left ventricular area (LVM). In the PtNP-shell group, the ERP was significantly elevated compared to the control group and remained elevated for \(2\mathrm{~h}\) after photothermal intervention in NG (Supplementary Fig. 18). Furthermore, immunofluorescence staining for Vacht, c- fos, and TRPV1 was performed on NG histopathological sections following photothermal modulation (Fig. 4i). Quantitative analysis (Supplementary Fig. 19) revealed a substantial increase in the proportion of \(\mathrm{TRPV1^{+}}\) \((86.63\pm 2.65\mathrm{vs}45.45\pm 2.98)\) and c- Fos \(^+\) \((77.81\pm 3.91\mathrm{vs}17.27\pm 3.08)\) neurons among VAcH \(^+\) parasympathetic neurons in the PtNP-shell group compared to the control group (all P
+
+<--- Page Split --->
+
+\(< 0.001\) ). These findings suggest that PtNP-shell can precisely regulate temperature and subsequently activate TRPV1 ion channels on NG to enhance parasympathetic activity.  
+
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 | Photothermal activation of the parasympathetic nervous system by PtNP-shell. a, Location of the canine NG. b, Schematic illustration of the process of photothermal modulation of NG. c, Temperature curves of NG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of NG. e, Representative images of HR reduction induced after stimulation of NG with different voltages. Maximal HR changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, \(n = 6\) . h, Quantification of the NG neural activity recordings, \(n = 6\) . i, Representative immunofluorescent images of Vacht (red), c-fos (green) and TRPV1 (pink) in the NG of beagles following different treatments. Data are shown as the mean \(\pm\) S.E.M. \(*P < 0.05\) , \(**P < 0.01\) , \(***P < 0.001\) , ns means that the difference is not statistically significant. </center>
+
+<--- Page Split --->
+
+1 PtNP-shell photothermal activation of NG reduces I/R injury and associated VAs2 Following I/R injury, electrocardiography (ECG) was recorded to monitor the3 occurrence of VAs events within 1 h, including ventricular premature beats (VPBs),4 ventricular tachycardia (VT) and ventricular fibrillation (VF) (Fig. 5c)19. Under NIR-II5 laser irradiation, the PtNP-shell group exhibited a lower incidence of sustained VTs6 (duration \(>30\) s) or VF compared to the control group (50% vs. 83%) (Fig. 5d).7 Moreover, the number of recorded VPBs (70.83 ± 5.38 vs. 116.00 ± 6.36, \(\mathrm{P}< 0.05\) ),8 VTs (3.17 ± 0.87 vs. 8.83 ± 2.15, \(\mathrm{P}< 0.05\) ) and duration of the VTs (7.00 ± 3.173s vs.9 26.83 ± 7.89s, \(\mathrm{P}< 0.05\) ) in the PtNP-shell group were significantly reduced compared10 to that in the control group (Fig. 5e- g).  
+
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 | PtNP-shell photothermal activation of the parasympathetic nervous system improves myocardial I/R injury. Modulation of NG to protect against myocardial I/R injury and associated VAs a, schematic diagram and b, flowchart. c, Representative visual depictions of VAs, including VPB, VT and VF. d, Quantitative analysis the ratio of sVT and VF incidence between different groups, \(\mathrm{n} = 6\) . Quantitative analysis the number of e, VPBs, f, VTs and g, the duration of sVT of beagles. Effects on ventricular ERP at different sites in beagles treatment with PtNP-shell or control h, before and i, after myocardial I/R injury modelling. Levels of markers of myocardial injury, including j, MYO and k, c-TnI, after different treatments in beagles. Data are shown as the mean \(\pm\) S.E.M. \(^{*}\mathrm{P}< 0.05\) , \(^{**}P< 0.01\) , \(^{***}\mathrm{P}< 0.001\) . </center>
+
+<--- Page Split --->
+
+Animal modeling and intervention manipulations were conducted to further elucidate the protective effects of precise modulation of NG by PtNP- shell against myocardial I/R injury and associated VAs, following the experimental protocols depicted in Figure 5a,b. PtNP- shell and PBS were microinjected into the NG of the PtNP- shell group and control group, respectively, each consisting of six beagle dogs. The NG was subsequently exposed to NIR- II laser irradiation for a duration of 5 minutes prior to occlusion of the left anterior descending (LAD) coronary artery for reperfusion therapy.  
+
+There were no statistically significant differences between the two groups in terms of preoperative ERP for LVB, LVM, and LVA. In the postoperative period, all three positions showed shortened ERPs in the control group. The PtNP- shell group exhibited significantly higher ERPs compared to the control group, indicating that photothermal modulation of nerves by PtNP- shell has a protective effect on cardiac electrophysiology (Fig. 5h- i). Serum Elisa assay revealed reduced levels of myocardial injury markers (MYO and c- TnI) after I/R injury in the PtNP- shell group compared to the control group (all \(\mathrm{p}< 0.05\) , Fig. 5j,k). Postoperatively, heart rate variability analysis demonstrated lower low frequency (LF) and higher high frequency (HF) and the lower ratio of LF to HF (LF/HF) values in the PtNP- shell group compared to the control group (all \(\mathrm{p}< 0.05\) , Supplementary Fig. 20). These results suggest that PtNP- shell exerts cardioprotective effects and reduces VAs by activating parasympathetic nerve.  
+
+## PtNP-shell photothermal inhibition of the sympathetic nervous system  
+
+The sympathetic nervous system was modulated by performing microinjections of PtNP- shell or PBS into the LSG, followed by irradiation with an NIR- II laser (Fig. 6a,b). The temperature curve demonstrates that upon exposure to a NIR- II laser \((0.8\mathrm{W}\cdot \mathrm{cm}^{- 1})\) for \(25\pm 5\mathrm{s}\) , the temperature rapidly escalated to \(45.0^{\circ}\mathrm{C}\) , crossing the range of \(41.0-\)
+
+<--- Page Split --->
+
+42.9 °C within a mere duration of \(6 \pm 1\) s. Subsequently, the power density was immediately decreased to \(0.6 \mathrm{W} \mathrm{cm}^{-2}\) , effectively maintaining LSG at a steady temperature between \(45.0 - 46.9\) °C (Fig. 6c, d). Due to the substantial increase in systolic blood pressure (SBP) induced by LSG activation (Fig. 6e), the function of LSG was evaluated by quantifying the maximum SBP change corresponding to five consecutive incremental voltages of high- frequency electrical stimulation. After 5 min of NIR- II laser irradiation, the activity and function of LSG in the PtNP- shell group were significantly suppressed compared to the control group ( \(p < 0.05\) ) and they returned close to baseline after 3 h (Fig. 6f- h and Supplementary Fig. 21- 22). Prolonged ERP effects were observed in all left ventricles, while the protective effect exhibited a duration of only 1 h (Supplementary Fig. 23). Furthermore, immunofluorescence staining was conducted on LSG tissues to examine the expression of c- fos, tyrosine hydroxylase (TH), and TREK1 (Fig. 6i). The quantitative analysis (Supplementary Fig. 24) revealed a significant decrease in the proportion of c- Fos\(^+\) expression in TH\(^+\) neurons within the PtNP- shell group ( \(8.80 \pm 1.80\) vs. \(44.78 \pm 5.55\) , \(P < 0.001\) ) indicating that PtNP- shell exerted a photothermal inhibitory effect on LSG neurons under NIR- II irradiation. However, the proportion of TREK\(^+\) expression was significantly increased within TH\(^+\) neurons in the PtNP- shell group ( \(83.51 \pm 3.72\) vs. \(57.20 \pm 5.89\) , \(P < 0.01\) ). This increase could lead to hyperpolarization of the cell membrane potential, reduction in neuronal excitability and inhibition of sympathetic nerve activity.
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Fig. 6 | Photothermal inhibition of the sympathetic nervous system by PtNP-shell. a, Location of the canine LSG. b, Schematic illustration of the process of photothermal modulation of LSG. c, Temperature curves of LSG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of LSG. e, Representative images of BP elevation induced after stimulation of LSG with different voltages. Maximal SBP changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, \(n = 6\) . h, Quantification of the LSG neural activity recordings, \(n = 6\) . i, Representative immunofluorescent images of TH (red), c-fos (green) and TREK1 (pink) in the LSG of beagles following different treatments. Data are shown as the mean \(\pm\) S.E.M. \(*P< 0.05\) , \(**P< 0.01\) , \(***P< 0.001\) , ns means that the difference is not statistically significant. </center>
+
+<--- Page Split --->
+
+# PtNP-shell photothermal inhibition of LSG improves MI and reduces associated  
+
+## Vas  
+
+To investigate the cardioprotective effect of PtNP- shell photothermal effect in achieving a targeted LSG temperature of approximately \(46.0^{\circ}\mathrm{C}\) , NIR- II light was administered prior to ligation of the LAD coronary artery (Fig. 7a,b). Under NIR- II laser irradiation, the PtNP- shell group exhibited a significantly reduced incidence of sustained VTs (duration \(>30\) s) or VF compared to the control group ( \(16\%\) vs. \(50\%\) ) (Fig. 7c). In the PtNP- shell group, ECG recordings within infarction 1 exhibited a reduced incidence of VAs events compared to the control group, with fewer VPBs recorded in the PtNP- shell group than in the control group ( \(51.50 \pm 5.53\) vs. \(70.83 \pm 5.375\) , \(\mathrm{P} < 0.05\) , Fig. 7d). However, there were no significant differences between the two groups in terms of VT numbers and duration (Supplementary Fig. 25). Additionally, VA inducibility measurements demonstrated that after photothermal neuromodulation with PtNP- shell, there was a decrease in VA score ( \(1.50 \pm 0.76\) vs. \(4.83 \pm 1.14\) , \(\mathrm{P} < 0.05\) ) effective heart protection (Fig. 7e,f). Furthermore, PtNP- shell photothermal inhibition of LSG produced similar protective effects on ventricular electrophysiological index ERP as activation of NG (Fig. 7g,h), and had higher VF threshold than control group ( \(24.33 \pm 4.24\) vs. \(12.33 \pm 3.16\) , \(\mathrm{P} < 0.05\) , Fig. 7i). In addition, the light inhibition of LSG followed the same trend as heart rate variability after activation of NG (Supplementary Fig. 26). These results suggest that PtNP- shell protects against cardiac damage and reduces VAs by modulating the autonomic nervous system, specifically by decreasing sympathetic activity and enhancing parasympathetic tone.
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Fig. 7 | PtNP-shell photothermal inhibition of the sympathetic nervous system improves MI associated VAs. Modulation of LSG to protect against MI and associated VAs a, schematic diagram and b, flowchart. c, Quantitative analysis the ratio of sVT and VF incidence between different groups, \(n = 6\) . d, Quantitative analysis the number of VPBs of beagles. e, Typical images of VA induced by programmed electrical stimulation. f, Quantitative analysis of VAs score in different groups. Effects on ventricular ERP at different sites in Beagles treatment with PtNP-shell or control g, before and h, after MI modelling. i, Quantitative analysis of VF threshold in different groups. Data are shown as the mean \(\pm\) S.E.M. \(*P < 0.05\) , \(**P < 0.01\) , \(***P < 0.001\) . </center>  
+
+## Biosafety of PtNP-shell for translational applications  
+
+To validate the biocompatibility of PtNP- shell photothermal modulation on the autonomic nervous system, we conducted rapid excision of LSG and NG tissues followed by hematoxylin and eosin (H&E) staining. As shown in Supplementary Fig. 27a, H&E staining did not reveal any indications of neuronal damage in both the PtNP- shell and control groups for both NG and LSG, indicating that the neuromodulation of PtNP- shell is repeatable. Meanwhile, to further investigate the long- term biosafety of PtNP- shell, a microinjection of \(200 \mu \mathrm{l}\) PtNP- shell (50 \(\mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) or PBS was administered into the ganglion of dogs and the tail vein of rats, respectively. After a follow- up period of 30 days, did not reveal any obvious damage in major organs,
+
+<--- Page Split --->
+
+including the heart, liver, spleen, lungs, and kidneys (Supplementary Fig. 27b,c). Furthermore, blood biochemical analyses indicated the absence of hepatotoxicity or nephrotoxicity (Supplementary Fig. 27d-m). These results unequivocally demonstrate that PtNP-shell exhibits exceptional biocompatibility and long-term biological safety.  
+
+## Conclusion  
+
+The PtNP-shell reported in this study exhibits nearly perfect blackbody absorption property, making it an efficient absorber with one of the highest PCE in the NIR-II window (73.7% at 1064 nm). Furthermore, local heating induced by PtNP-shell activation effectively triggers temperature- sensitive ion channels TRPV1 and TREK1, enabling precise and efficient regulation of autonomic nerves. This innovative approach holds great potential for non- invasive treatment of MI and associated VAs, as well as protection against reperfusion injury during interventional therapy.  
+
+The minimal tissue damage caused by light can be disregarded within the maximum permissible exposure (MPE) range, rendering it one of the safest interventions for organisms. The interaction between light and tissue is intricate, and further research could aid in selecting more suitable wavelengths to achieve deeper penetration within the MPE range. Leveraging the nearly impeccable blackbody absorption of PtNP-shell and ultrasound- guided microinjection technology, remote and precise neuromodulation strategies can be developed, holding promise for non- invasive protection against MI and reperfusion injury- associated VAs. The significance of this approach extends beyond VAs as it exhibits broad therapeutic prospects for chronic diseases like refractory hypertension<sup>20</sup> and stable atherosclerosis<sup>21</sup> due to the wide distribution of autonomic nerves and the universality of nerve regulation.
+
+<--- Page Split --->
+
+## 1 Online content  
+
+2 Any methods, additional references, Nature Portfolio reporting summaries, source data, 3 extended data, supplementary information, acknowledgements, peer review 4 information; details of author contributions and competing interests; and statements of 5 data availability are available at https://doi.org/10.1038/xxx.
+
+<--- Page Split --->
+
+2 1 Virani, S. S. et al. Heart disease and stroke statistics—2020 update: a report from the american 3 heart association. Circulation 141, E139-E596 (2020). 4 2 Trayanova, N. A. Learning for prevention of sudden cardiac death. Circul. Res. 128, 185-187 5 (2021). 6 3 Herring, N., Kalla, M. & Paterson, D. J. The autonomic nervous system and cardiac 7 arrhythmias: current concepts and emerging therapies. Nat. Rev. Cardiol. 16, 707-726 (2019). 8 4 Liu, J. S. et al. Antibody-conjugated gold nanoparticles as nanotransducers for second near- 9 infrared photo-stimulation of neurons in rats. Nano Converg. 9, 13 (2022). 10 5 Ye, T. et al. Precise modulation of gold nanorods for protecting against malignant ventricular 11 arrhythmias via near-infrared neuromodulation. Adv. Funct. Mater. 29, 1902128 (2019). 12 6 Zhang, L. et al. AIEgen-based covalent organic frameworks for preventing malignant 13 ventricular arrhythmias via local hyperthermia therapy. Adv. Mater. 35, 2304620 (2023). 14 7 Prescott, E. D. & Julius, D. A modular PIP2 binding site as a determinant of capsaicin receptor 15 sensitivity. Science 300, 1284-1288 (2003). 16 8 Maingret, F. et al. TREK-1 is a heat-activated background \(\mathrm{K^{+}}\) channel. EMBO J. 19, 2483- 17 2491 (2000). 18 9 Grandl, J. et al. Temperature-induced opening of TRPV1 ion channel is stabilized by the pore 19 domain. Nat. Neurosci. 13, 708-714 (2010). 20 10 Zhao, B. et al. Liquid-metal-assisted programmed galvanic engineering of core-shell 21 nanohybrids for microwave absorption. Adv. Funct. Mater. 33, 2302172 (2023). 22 11 Yang, N. L. et al. A general in-situ reduction method to prepare core-shell liquid-metal / metal 23 nanoparticles for photothermally enhanced catalytic cancer therapy. Biomaterials 277, 121125 24 (2021). 25 12 Liu, C. et al. Enhanced energy storage in chaotic optical resonators. Nat. Photonics 7, 474-479 26 (2013). 27 13 Greffet, J. J. et al. Coherent emission of light by thermal sources. Nature 416, 61-64 (2002). 28 14 Mann, D. et al. Electrically driven thermal light emission from individual single-walled carbon 29 nanotubes. Nat. Nanotechnol. 2, 33-38 (2007). 30 15 Granqvist, C. G. Radiative heating and cooling with spectrally selective surfaces. Appl. Opt. 31 20, 2606-2615 (1981). 32 16 Ma, J. X. et al. In vitro model to investigate communication between dorsal root ganglion and 33 spinal cord glia. Int. J. Mol. Sci. 22, 9725 (2021). 34 17 Zyrianova, T. et al. K2P2.1 (TREK-1) potassium channel activation protects against hyperoxia- 35 induced lung injury. Sci. Rep. 10, 22011 (2020). 36 18 Jayaprakash, N. et al. Organ- and function-specific anatomical organization of vagal fibers 37 supports fascicular vagus nerve stimulation. Brain Stimul. 16, 484-506 (2023). 38 19 Zhou, Z. et al. Metabolism regulator adjoncent prevents cardiac remodeling and ventricular 39 arrhythmias via sympathetic modulation in a myocardial infarction model. Basic Res. Cardiol. 40 117, 34 (2022).
+
+<--- Page Split --->
+
+1 20 Mancia, G. & Grassi, G. The autonomic nervous system and hypertension. \*Circul. Res.\* 114, 2 1804–1814 (2014). 3 21 Jiang, Y. Q. \*et al.\* The role of age-associated autonomic dysfunction in inflammation and 4 endothelial dysfunction. \*GeroScience\* 44, 2655–2670 (2022).
+
+<--- Page Split --->
+
+## Methods  
+
+## Chemicals  
+
+The gallium and indium were purchased from Shanghai Minor Metals Co., Ltd. Anhydrous ethanol \((\geq 99.7\%)\) and KOH (AR) were purchased from Sinopharm Chemical Reagent Co., Ltd. \(\mathrm{Na_2PtCl_6}\) ( \(98\%\) ) was purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. mPEG- \(\mathrm{SH}_{5000}\) was purchased from Shanghai Macklin Biochemical Co., Ltd. STR- identified correct HT- 22 cells or human embryonic kidney 293T (HEK- 293T) cells were purchased with the corresponding specialized cell culture media (Procell, Wuhan, China). Anti- NF1, anti- c- fos, anti- TRPV1 antibodies used in western blot and immunofluorescence staining and anti- TREK1 antibody used in immunofluorescence staining were purchased from ABclonal (Wuhan, China). Anti- TREK1 antibody used in western blot was purchased from Santa Cruz Biotechnology (Texas, U.S.). Glyceraldehyde 3- phosphate dehydrogenase (GAPDH) was purchased from Abcam (Cambridge, England). Serum troponin I (c- TnI) and myoglobin (MYO) were purchased from Mibio (Shanghai, China). 4,6- diamidino- 2- phenylindole (DAPI) was purchased from Servicebio (Wuhan, China).  
+
+## Instruments  
+
+The morphology of PtNP- shell was characterized by a F200 transmission electron microscope (TEM) (JEOL, Japan) operated at \(200\mathrm{kV}\) . STEM and HRTEM images were obtained by a JEM- ARM200CF (JEOL, Japan) at \(200\mathrm{kV}\) . The EDX elemental mapping was carried using the JEOL SDD- detector with two \(100\mathrm{mm}^2\) X- ray sensor. X- ray diffraction (XRD) patterns were performed on an SmartLab 9kW X- ray powder diffractometer (Rigaku, Japan). XPS measurements were carried out with a ESCALAB 250Xi spectrometer (Thermo Fisher Scientific, U.S.) under vacuum. Ultraviolet- visible- near- infrared light (UV- Vis- NIR) absorption spectra was collected using a UV
+
+<--- Page Split --->
+
+3600 spectrophotometer (Shimadzu, Japan). Zeta potential (Z) and dynamic light scattering (DLS) were recorded using a Zetasizer Nano ZSP (Malvern Panalytical, U.K.). The fluorescence microscopy images of HT- 22 cells were acquired by FV3000 Microscope (Olympus, Japan), excited with 488 nm laser. Beagle's respiration is maintained by a WATO EX- 20VET ventilator (Mindray, Shenzhen, China). ECG and blood pressure data were recorded by a Lead 7000 Computerized Laboratory System (Jinjiang, Chengdu, China). NIR- II light at 1064 nm is generated by LWIRPD- 1064- 5F laser (Laserwave, Beijing, China). Thermal imaging was obtained by FLIR C2 thermal imager (FLIR, U.S.). High- frequency electrical stimulation was performed by Grass stimulator (Astro- Med; West Warwick, RI, U.S.) The electrical signals of autonomic nerves are recorded by Power Lab data acquisition system (AD Instruments, New South Wales, Australia). Serum biochemical indices were determined by a fully automatic biochemical analyzer BK- 1200 (BIOBASE, Jinan, China).  
+
+## Synthesis of GaNPs  
+
+The GaNPs were obtained by sonication of liquid Ga. The liquid Ga (300 mg) was transferred to anhydrous ethanol (8 mL), and the solution was sonicated by nanoprobe sonication for 1 h (3 seconds on and 3 seconds off) at the power of 290 W. Then the ethanol was replaced with Milli- Q water to continue sonication for 1 h. The solution at the end of sonication was collected and centrifuged at 1000 rpm for 5 min, and the upper liquid layer was aspirated for later use.  
+
+## Synthesis of PtNP-shell  
+
+First, the GaNPs and 3 mL \(\mathrm{Na_2PtCl_6}\) (0.1 M) were evacuated for 30 min and Ar was introduced for 15 min. Then, 3 mL \(\mathrm{Na_2PtCl_6}\) (0.1 M) was added dropwise to GaNPs and the solution was stirred for 4 h. After reaction, the solution was collected and centrifuged at 9000 rpm for 10 min. The solids at the bottom were washed with Milli
+
+<--- Page Split --->
+
+1 Q water for 3 times and finally dispersed in \(6\mathrm{mL}\) Milli- Q for later use.  
+
+## Functionalization of PtNP-shell with mPEG-SH5000  
+
+3 The PtNP- shell was first covered with a small amount of mPEG- SH to protect the structure from KOH. \(30\mathrm{mg}\) mPEG- SH5000 was added to \(6\mathrm{ml}\) PtNP- shell and the solution was stirred for \(12\mathrm{h}\) . After the reaction, the solution was collected and centrifuged at \(9000\mathrm{rpm}\) for \(10\mathrm{min}\) . The solids at the bottom were washed with Milli- Q water for 3 times and dispersed in \(6\mathrm{mL}\) Milli- Q water. The above solution was stirred with \(12\mathrm{mL}\) of KOH (1 M) for \(4\mathrm{h}\) . The reaction- completed solution was collected and centrifuged at \(9000\mathrm{rpm}\) for \(10\mathrm{min}\) , and the solids at the bottom were washed three times with Milli- Q water and finally dispersed in \(6\mathrm{mL}\) Milli- Q water. The above solution was stirred with \(60\mathrm{mg}\) mPEG- SH5000 for \(12\mathrm{h}\) . After the reaction, the solution was collected and centrifuged. The solids at the bottom were washed with Milli- Q water for 3 times and finally dispersed in \(6\mathrm{mL}\) PBS.  
+
+## Synthesis of Ga-In alloy nanoparticles (GaIn NPs)  
+
+The liquid EGaIn was prepared by physically mixing \(75\mathrm{wt}\%\) gallium and \(25\mathrm{wt}\%\) indium at \(200^{\circ}\mathrm{C}\) for \(2\mathrm{h}\) . The liquid EGaIn (300 mg) was transferred to anhydrous ethanol ( \(8\mathrm{mL}\) ), and the solution was sonicated by nanoprobe sonication for \(1\mathrm{h}\) (3 seconds on and 3 seconds off) at the power of \(290\mathrm{W}\) . Then the ethanol was replaced with Milli- Q water to continue sonication for \(1\mathrm{h}\) . The solution at the end of sonication was collected and centrifuged at \(1000\mathrm{rpm}\) for \(5\mathrm{min}\) , and the upper liquid layer was aspirated and set aside.  
+
+## Synthesis of GaIn@Pt NPs  
+
+1 mL \(\mathrm{Na_2PtCl_6}\) ( \(0.1\mathrm{M}\) ) was added dropwise to GaIn NPs and the solution was stirred for \(4\mathrm{h}\) . After reaction, the solution was collected and centrifuged at \(9000\mathrm{rpm}\) for 10
+
+<--- Page Split --->
+
+1 min, washed 3 times with Milli- Q water and dispersed in \(6\mathrm{mL}\) Milli- Q water. The above solution was stirred with \(60\mathrm{mg}\) mPEG- SH \(_{5000}\) for \(12\mathrm{h}\) . After the reaction, the solution was collected and centrifuged. The solids at the bottom were washed with Milli- Q water for 3 times and finally dispersed in \(6\mathrm{mL}\) PBS.  
+
+## Calculation of the photothermal conversion efficiency  
+
+The photothermal conversion of the PtNP- shell has been calculated on the basis of previous work \(^{22,23}\) . The relationship between temperature rise and energy transfer in the system can be described by the Equation S1,  
+
+\[\Sigma_{i}m_{i}c_{i}\frac{dT}{dt} = Q_{abs} - Q_{ext} = Q_{NPS} + Q_{solvent} - Q_{ext} \quad (S1)\]  
+
+where \(Q_{abs}\) is the total energy absorbed by the system, \(Q_{NPS}\) is the energy absorbed by the nanoparticles, \(Q_{solvent}\) is the energy absorbed by the solvent, \(Q_{ext}\) is the energy loss from the system to the environment. \(m_{i}\) and \(c_{i}\) are the mass and specific heat capacity of the solution, respectively. \(T\) is the solution temperature and \(t\) is the irradiation time. The conversion of the light energy into heat energy can be expressed in terms of Equation S2,  
+
+\[Q_{NPS} = I(1 - 10^{-A})\eta \quad (S2)\]  
+
+where \(I\) is the laser power, \(A\) is the absorbance value of PtNP- shell at \(1064\mathrm{nm}\) , \(\eta\) is the photothermal conversion efficiency. \(Q_{solvent}\) can be calculated by the following Equation S3,  
+
+\[Q_{solvent} = hs(T_{solvent} - T_{surr}) \quad (S3)\]  
+
+where \(h\) is the convective heat transfer coefficient and \(s\) is the surface area of the sample cell. \(T_{solvent}\) is the maximum temperature that the solvent can reach under laser irradiation. \(T_{surr}\) is the ambient temperature. \(Q_{ext}\) can also be written as,  
+
+\[Q_{ext} = hs(T - T_{surr}) \quad S4\]  
+
+The heat output will increase with the increase in temperature when the NIR- II
+
+<--- Page Split --->
+
+laser power is determined according to formula S4. The temperature of the system will reach the maximum when the heat input is equal to the heat output, so the following equation can be obtained,  
+
+\[Q_{NPs} + Q_{solvent} = Q_{ext - max} = hs(T_{max} - T_{surr}) \quad \mathrm{S5}\]  
+
+where \(Q_{ext - max}\) is the heat transferred from the system surface through the air when the sample cell reaches equilibrium temperature, and \(T_{max}\) is the equilibrium temperature. Combining equations S2, S3 and S5, \(\eta\) can be expressed as,  
+
+\[\eta = \frac{hs(T_{max} - T_{surr}) - hs(T_{solvent} - T_{surr})}{l(1 - 10^{-A})} = \frac{hs(T_{max} - T_{solvent})}{l(1 - 10^{-A})} \quad \mathrm{S6}\]  
+
+where \(A\) is the PtNP- shell absorption at \(1064\mathrm{nm}\) . To obtain \(hs\) , the dimensionless temperature \(\theta\) is introduced,  
+
+\[\theta = \frac{T - T_{surr}}{T_{max} - T_{surr}} \quad \mathrm{S7}\]  
+
+and a time constant of sample system, \(\tau_{s}\)  
+
+\[\tau_{s} = \frac{\sum_{i}m_{i}c_{i}}{hs} \quad \mathrm{S8}\]  
+
+Combining Equations S1, S4, S7 and S8, the following equation can be obtained,  
+
+\[\frac{d\theta}{dt} = \frac{1}{\tau_{s}}\left[\frac{Q_{NPs} + Q_{solvent}}{hs(T_{max} - T_{surr})} -\theta \right] \quad \mathrm{S9}\]  
+
+After the laser is turned off, in the cooling stage, there is no external input energy, \(Q_{NPs} + Q_{solvent} = 0\) , and equation S9 can be written as,  
+
+\[dt = -\tau_{s}\frac{d\theta}{\theta} \quad \mathrm{S10}\]  
+
+By integrating Equation S10, the following equation can be obtained,  
+
+\[t = -\tau_{s}ln\theta \quad \mathrm{S11}\]  
+
+Therefore, the system heat transfer time constant \((\tau_{s})\) at \(1064\mathrm{nm}\) is \(242.25\mathrm{s}\) (Figure 3f). In addition, m is \(0.3\mathrm{g}\) and c is \(4.2\mathrm{J}\cdot \mathrm{g}^{- 1}\) . Therefore, \(hs\) can be determined from Equation S8. The laser power \((I)\) used here can be determined as 1 W. Then the photothermal conversion efficiency \((\eta)\) of the PtNP- shell at \(1064\mathrm{nm}\) can be calculated
+
+<--- Page Split --->
+
+to be \(73.7\%\) by substituting \(hs\) into Equation S6.  
+
+## Animal preparation and cell culture  
+
+All animal experiments were approved by the Animal Care and Use Committee of Renmin Hospital of Wuhan University (WDRM20230805A). All experimental procedures were in accordance with the Declaration of Helsinki and were conducted according to the guidelines established by the National Institutes of Health. All Beagles \((8 - 12\mathrm{kg})\) were anesthetized intravenously with \(3\%\) sodium pentobarbital \((30\mathrm{mg}\cdot \mathrm{kg}^{- 1}\) induction dose, \(2\mathrm{mg}\cdot \mathrm{kg}^{- 1}\) maintenance dose per hour) and respiration was maintained by endotracheal intubation using a ventilator. Arterial blood pressure was continuously monitored through femoral artery catheterization with a pressure transducer attached. ECG and blood pressure data were recorded throughout the procedure. A heating pad was used to maintain core body temperature at \(36.5\pm 0.5^{\circ}\mathrm{C}\)  
+
+The cells were cultured in a humid incubator containing \(5\% \mathrm{CO}_2\) at a temperature of \(37.0^{\circ}\mathrm{C}\)  
+
+## Detection of TRPV1 and TREK1 expression in vitro and in vivo  
+
+Western blotting was used to assess the expression of TRPV1 and TREK1 in neuronal cells and ganglion tissues. HT- 22 cells or HEK- 293T cells were cultured in six- well plates for \(24 - 48\mathrm{h}\) , then lysed and centrifuged to collect cells. Ganglion tissues were obtained from deceased animals and frozen in liquid nitrogen or stored at \(- 80.0^{\circ}\mathrm{C}\) . Total protein was determined using BCA protein assay reagent after tissue grinded and cells lysed. Afterwards, the procedure was followed according to the manufacturer's instructions. Primary antibodies were anti- TRPV1 and anti- TREK1. Expression levels of specific proteins were normalized to GAPDH.  
+
+## Calcium imaging of neuronal cells
+
+<--- Page Split --->
+
+The effect of PtNP- shell photothermal modulation on ion channels in HT- 22 cells was explored through calcium imaging experiments. HT- 22 cells were incubated in \(35\mathrm{mm}\) confocal dishes for \(24\mathrm{h}\) . Cells were washed 3 times with PBS and then stained with 5 \(\mu \mathrm{M}\) Fluo- 4 AM (dilution ratio 1:500) for \(30\mathrm{min}\) in a cell incubator at \(37.0^{\circ}\mathrm{C}\) , protected from light. To induce activation of TRPV1 and TREK1 ion channels, which had been previously studied \(^{7,8}\) , the culture dish was exposed to NIR- II light ( \(1064\mathrm{nm}\) ), resulting in an elevation of temperature. TRPV1, being a calcium channel, exhibited observable changes in the flow of calcium ions upon activation, while TREK1 as a potassium channel did not display such behavior. Therefore, the effect of PtNP- shell photothermal modulation on neuronal cells via TREK1 was observed by introducing a \(15\mathrm{mM}\) KCl solution prior to NIR- II irradiation. Fluorescence signals at \(525\mathrm{nm}\) were recorded using a confocal microscope with \(488\mathrm{nm}\) as the excitation wavelength. XYT images were acquired and collected under a \(20\mathrm{x}\) objective lens. The average fluorescence intensity of the cells was analyzed using ImageJ software (Fiji). The normalized fluorescence change was calculated as follows: \(\Delta \mathrm{F} / \mathrm{F} = (\mathrm{F - F_0}) / \mathrm{F_0}\) , where F is the original fluorescence signal; \(\mathrm{F_0}\) is the average baseline intensity before irradiation with NIR- II laser.  
+
+## In vitro cytotoxicity assay  
+
+The cytotoxicity of PtNP- shell on neuronal cells was evaluated by CCK- 8 assay. HT- 22 cells were seeded in 96- well plates at a density of \(1 \times 10^{4}\) well \(^{- 1}\) and cultured for 24 h. HT- 22 cells were then treated with different concentrations (10, 25, 50, 100, 150, 200 \(\mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) of PtNP- shell for another 24 h. Cell viability was determined by CCK- 8 assay after incubating with the CCK- 8 reagent for 1 h. To investigate the impact of PtNP- shell's photothermal effect on neuron cell viability, HT- 22 cells were co- cultured with PtNP- shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) for 12 h followed by irradiation with a \(1064\mathrm{nm}\) laser (0.5 and \(0.75\mathrm{W} \cdot \mathrm{cm}^{- 2}\) ) for various durations (10 s, 30 s and 60 s). After incubation again for 12
+
+<--- Page Split --->
+
+h, the absorbance at \(450 \mathrm{nm}\) was recorded using a microplate reader. Cell survival (\%) \(= (OD_{\text{samples}} - OD_{\text{blank}}) / (OD_{\text{control}} - OD_{\text{blank}}) \times 100\%\) .  
+
+## Experimental protocol 1: Activation of the parasympathetic nervous system through PtNP-shell photothermal reduces I/R injury  
+
+Part 1: Exploring the in vivo effects of precise photothermal stimulation of the parasympathetic nervous system by PtNP- shell under NIR- II irradiation. Twelve beagles were randomly assigned to the control group ( \(100 \mu \mathrm{L}\) phosphate- buffered saline (PBS) was microinjected into the NG, \(\mathrm{n} = 6\) ) and the PtNP- shell group ( \(100 \mu \mathrm{L}\) PtNP- shell ( \(50 \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) was microinjected into the NG, \(\mathrm{n} = 6\) ). NG nerve activity, heart rate (HR) and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR- II irradiation (Fig 4b).  
+
+Part 2: The protective effect of PtNP- shell activation of the parasympathetic nervous system against myocardial I/R injury was investigated. The same grouping pattern as in part1 was used, with 5- min NIR- II irradiation of the NG before opening the occluded LAD coronary vessel. Afterwards, ventricular electrophysiological parameters, heart rate variability (HRV) and ECG data were recorded and analyzed (Fig 5b).  
+
+## Experimental protocol 2: PtNP-shell photothermal inhibition of sympathetic nervous system improves MI  
+
+Part 1: The in vivo effects of precise photothermal stimulation of the sympathetic nervous system by PtNP- shell under NIR- II irradiation were explored. Twelve beagles were randomly assigned to the control group ( \(100 \mu \mathrm{L}\) PBS microinjected into the LSG, \(\mathrm{n} = 6\) ) and the PtNP- shell group ( \(100 \mu \mathrm{L}\) PtNP- shell ( \(50 \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) microinjected into the LSG, \(\mathrm{n} = 6\) ). LSG nerve activity, SBP and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR- II
+
+<--- Page Split --->
+
+irradiation (Fig 6b).  
+
+Part 2: To investigate the protective effect of PtNP- shell inhibition of the sympathetic nervous system a improves MI. The same grouping pattern as in part1 was used, with 5- min NIR- II irradiation of the LSG before ligation of LAD vessels. Finally, ventricular electrophysiological parameters, HRV and ECG data were also recorded and analyzed (Fig 7b).  
+
+## PtNP-shell photothermal stimulation of the autonomic nervous system in vivo  
+
+We selected NG and LSG as targets for modulation in the autonomic nervous system to explore the multifunctionality of the PtNP- shell photothermal strategy. A "C" incision is made behind the left ear, and the angle between the occlusal and trapezius muscles served as the access approach<sup>24</sup>. The tissue is bluntly separated to expose the carotid sheath and identify the parasympathetic nerve. Moving upstream along the nerve, a distal expansion is observed as NG (Fig 4a). LSG can be visualized and localized by left- sided thoracotomy according to the method of a previous study (Fig 6a)<sup>25</sup>. PtNP- shell (50 \(\mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) or PBS was slowly injected into 2 sites within the NG and LSG tissues to achieve homogeneous photothermal conversion. Initial vertical irradiation of NIR- II laser (1064 nm) at 0.80 W·cm<sup>- 2</sup> was performed on NG and LSG surfaces. The power density of the NIR- II laser was reduced to 0.45 W·cm<sup>- 2</sup> for continuous irradiation when the temperature of the NG reached 42.0 °C, and was reduced to 0.6 W·cm<sup>- 2</sup> for continuous irradiation when the temperature of the LSG reached 46.0 °C. The NIR- II laser irradiation remains stable with a spot size maintained at 1.0 cm<sup>- 2</sup>. Dual temperature monitoring using thermal imager and T- type thermocouple was performed to plot the temperature- time curve.  
+
+## Functional assessment of autonomic nerves  
+
+The NG is a ganglion located upstream of the cervical parasympathetic nerve and can
+
+<--- Page Split --->
+
+significantly inhibit HR after receiving direct electrical stimulation<sup>18</sup>. The LSG, as an important peripheral sympathetic ganglion, can rapidly elevate blood pressure when activated by electrical stimulation. Based on the functional properties of different autonomic ganglia, we assessed the function of NG and LSG with reference to previous studies<sup>19</sup>. A pair of special electrodes made with silver wires were directly connected to the surfaces of NG and LSG for stimulation. High- frequency electrical stimulation (HFS: 20 Hz, 0.1 ms) was applied to the ganglion. The voltage was set to 5 levels in continuous increments (level 1: 0–2 V; level 2: 2–4 V; level 3: 4–6 V; level 4: 6–8 V; level 5: 8–10 V), while keeping the stimulation voltage values consistent with the baseline at different time points during the experiment. The percentage of sinus rate or AV conduction (measured by the A-H interval) slowing down constructed voltage level/degree of HR decrease curves reflecting NG function. On the other hand, the percentage increase in SBP built the voltage level/degree of SBP increase to reflect LSG function.  
+
+## Activity testing of autonomic nerves  
+
+The activity of different autonomic nerves was assessed based on previous studies<sup>19</sup>. Two specially designed microelectrodes were inserted into the NG and LSG, respectively, while a grounding wire was connected to obtain signals from the autonomic nerves. These electrical signals were recorded by a Power Lab data acquisition system, filtered through a band- pass filter (300–1000 Hz) and amplified 30- 50 times by an amplifier. Finally, the signals were digitized and analyzed in LabChart software (version 8.0, AD Instruments).  
+
+## Construction of myocardial I/R injury model and MI model  
+
+The left anterior descending coronary occlusion (LADO) method was used to establish the MI model<sup>19</sup>. The ligation site was located beneath the first diagonal of the LAD, and
+
+<--- Page Split --->
+
+successful MI model was confirmed by observing ST- segment elevation on the ECG. After ensuring cardiac electrophysiological stabilization, the junction was released to reperfuse the occluded coronary arteries, completing the construction of the myocardial I/R injury model<sup>26</sup>.  
+
+## Ventricular electrophysiological study in vivo  
+
+The cardiac electrophysiological measurements were performed in Beagles using a previously studied protocol<sup>27,28</sup>. The ERP was measured at three locations: LVA, LVB, LVM (located between the LVA and LVB). Malignant arrhythmic events caused by MI and I/R injury were assessed by electrocardiographic recordings in a canine model using Lead 7000 Computerized Laboratory System. VAs was classified according to Lambeth Conventions as VPBs, VT (three and more consecutive VPBs) and \(\mathrm{VF}^{29}\) . In addition, arrhythmia inducibility was further assessed by programmed ventricular stimulation at the right ventricular apex (RVA). Eight consecutive stimuli (S1S1) were performed at intervals of 330 ms, followed by additional stimuli until VT/VF occurred. Arrhythmia inducibility was assessed based on a modified arrhythmia scoring system<sup>28</sup>. If VF occurs during the evaluation, a defibrillator is required to restore sinus rhythm, followed by a waiting period of 30 min to restore cardiac electrophysiological stability. The VF threshold was assessed in the perimyocardial infarction region. Pacing was initiated using a Grass stimulator with a voltage of 2 V (20 Hz, 0.1 ms duration, 10 s). The stimulation voltage was increased in 2 V increments until VF was induced. The lowest voltage that induced VF was regarded as the VF threshold<sup>30</sup>.  
+
+## HRV analysis  
+
+The ECG data was recorded using the PowerLab data acquisition system. And the ECG segments recorded more than 5 min before modulation and after MI or I/R injury were analyzed by LabChart software with the Lomb- Scargle periodogram algorithm<sup>31</sup>.
+
+<--- Page Split --->
+
+Frequency domain metrics of HRV were calculated, including LF (0.04–0.15 Hz, reflecting sympathetic tone), HF (0.15–0.4 Hz, reflecting parasympathetic tone) and LF/HF (reflecting autonomic balance). The results were expressed in standardized units.  
+
+## Immunofluorescence staining of histopathological sections  
+
+The ganglions were rapidly dissected for histopathological staining after the experimental animals died. Tissues were fixed with \(4\%\) paraformaldehyde, embedded in paraffin, and cut into \(5\mu \mathrm{m}\) - thick sections. NG was stained with multiple immunofluorescence staining using anti- NF1, anti- c- fos and anti- TRPV1 antibodies. And LSG was stained by multiple immunofluorescences using anti- TH, anti- c- fos and anti- TREK1 antibody. Cell nuclei were stained with DAPI. Images were taken at \(100\times\) magnification and analyzed using ImageJ software (Fiji).  
+
+## Enzyme-linked immunosorbent assay (ELISA)  
+
+\(5\mathrm{ml}\) of venous blood was obtained from the jugular vein of each beagle after MI and myocardial I/R injury. After standing for 1 hour, the blood was centrifuged at \(3000\mathrm{rpm}\) for \(15\mathrm{min}\) . The upper serum layer was collected and stored at \(- 80.0^{\circ}\mathrm{C}\) . Myocardial injury levels were detected by c- TnI and myoglobin (MYO). Standard process analyses were performed according to the instructions of each ELISA kit. To evaluate the long- term biosafety and biocompatibility of PtNP- shell in vivo, Beagle dogs and rats were randomly divided into PtNP- shell and PBS groups.  
+
+## Long-term biosafety assay in vivo  
+
+To evaluate the long- term biosafety and biocompatibility of PtNP- shell in vivo, Beagle dogs and rats were randomly divided into two groups: a PtNP- shell group and a PBS group. In the PtNP- shell group, \(200\mu \mathrm{L}\) PtNP- shell ( \(50\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) ) was microinjected into canine ganglion tissue and tail vein of rats to explore long- term biosafety. Blood
+
+<--- Page Split --->
+
+1 and tissue samples were collected from each dog and rat one month after injection. One 2 month after injection, blood samples were collected from the jugular vein of dogs as 3 well as from the inferior vena cava of rats for analysis of serum biochemical indices. 4 Tissue H&E staining was also performed on major organs, including heart, liver, spleen, 5 lung and kidney.  
+
+## Statistical analysis  
+
+7 All graphical data are presented as mean \(\pm\) standard error of the mean (SEM), and the 8 distribution of data was assessed by the Shapiro- Wilk test. Differences between groups 9 were determined using Student's t- test or Mann- Whitney U- test. Data were analyzed 10 and plotted using GraphPad Prism 9.0 software (GraphPad software, Inc., La Jolla, CA, 11 USA). \(\mathrm{P}< 0.05\) was considered statistically different. The p- values are indicated with 12 an asterisk \((*\mathrm{p}< 0.05,^{**} \mathrm{p}< 0.01,^{***} \mathrm{p}< 0.001)\) .  
+
+## Reporting Summary  
+
+14 Further information on research design is available in the Nature Portfolio Reporting 15 Summary linked to this article.  
+
+## Data availability  
+
+17 The main data supporting the results in this study are available within the paper and its 18 Supplementary Information. The raw and analyzed datasets generated during the study 19 are too large to be publicly shared, yet they are available for research purposes from the 20 corresponding authors on reasonable request. Source data are provided with this paper.
+
+<--- Page Split --->
+
+## 1 References  
+
+2 Chechetka, S. A. et al. Light- driven liquid metal nanotransformers for biomedical theranostics. Nat. Commun. 8, 15432 (2017).  3 Zhu, P. et al. Inorganic nanoshell- stabilized liquid metal for targeted photonanomedicine in NIR- II biowindow. Nano Lett. 19, 2128- 2137 (2019).  4 Bruneau, M. & George, B. The juxtacondylar approach to the jugular foramen. Oper. Neurosurg. 63, 75- 80 (2008).  5 Zhang, S. et al. Ultrasound- guided injection of botulinum toxin type A blocks cardiac sympathetic ganglion to improve cardiac remodeling in a large animal model of chronic myocardial infarction. Heart Rhythm 19, 2095- 2104 (2022).  6 Chen, M. X. et al. Low- level vagus nerve stimulation attenuates myocardial ischemic reperfusion injury by antioxidative stress and antiapoptosis reactions in canines. J. Cardiovasc. Electrophysiol. 27, 224- 231 (2016).  7 Yu, L. L. et al. Optogenetic modulation of cardiac sympathetic nerve activity to prevent ventricular arrhythmias. J. Am. Coll. Cardiol. 70, 2778- 2790 (2017).  8 Yu, L. et al. Chronic intermittent low- level stimulation of tragus reduces cardiac autonomic remodeling and ventricular arrhythmia inducibility in a post- infarction canine model. JACC Clin. Electrophysiol. 2, 330- 339 (2016).  9 Walker, M. J. A. et al. The lambeth conventions: guidelines for the study of arrhythmias in ischaemia, infarction, and reperfusion. Cardiovasc. Res. 22, 447- 455 (1988).  10 Dalonzo, A. J. et al. Effects of cromakalim or pinacidil on pacing- and ischemia- induced ventricular fibrillation in the anesthetized pig. Basic Res. Cardiol. 89, 163- 176 (1994).  11 Lai, Y. et al. Non- invasive transcutaneous vagal nerve stimulation improves myocardial performance in doxorubicin- induced cardiotoxicity. Cardiovasc. Res. 118, 1821- 1834 (2022).  
+
+## Acknowledgements  
+
+The research was supported by the National Natural Science Foundation of China (grants 22025303, 82241057, 82270532 and 82200556); and the National Key Research and Development Program of China (grant 2023YFC2705705); and Foundation for Innovative Research Groups of Natural Science Foundation of Hubei Province, China (grant 2021CFA010). We thank the Core Facility of Wuhan University for their substantial supports in sample characterization, including SEM, XPS, DLS and XRD. We thank the Center for Electron Microscopy at Wuhan University for their support of STEM, HRTEM and EDX characterization. We also thank Meimei Zhang in the institute for advanced studies of Wuhan University for their assistance in TEM characterization.  
+
+## Author contributions  
+
+L.F., L.L.Y. and X.Y.Z. conceived the research concept. L.F., L.L.Y. and X.Y.Z.
+
+<--- Page Split --->
+
+1 supervised the research; C.L.W., L.P.Z., C.Z.L., J.M.Q., X.R.H., B.X., Q.F.Q., Z.Z.Z.2 and J.L.W. performed the experiments; C.L.W., L.P.Z., C.Z.L., L.Y.W. and Y.X.L.3 discussed the results; C.L.W., L.P.Z. and C.Z.L. analysed the data and cowrote the4 manuscript. All authors commented on the manuscript.  
+
+5 Competing interests6 The authors declare no competing interests.  
+
+7 Additional information8 Supplementary information The online version contains supplementary material9 available at10 Correspondence and requests for materials should be addressed to Xiaoya Zhou,11 Lilei Yu or Lei Fu12 Peer review information13 Reprints and permissions information is available at
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- supplementaryinformation.docx
+
+<--- Page Split --->

preprint/preprint__0120cbbdf5abcce247bf35686d0d3fbc3c94f93c709d874b56ecf9271a6516aa/preprint__0120cbbdf5abcce247bf35686d0d3fbc3c94f93c709d874b56ecf9271a6516aa_det.mmd

@@ -0,0 +1,551 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 863, 207]]<|/det|>
+# Pt nanoshell with ultra-high NIR-β photothermal conversion efficiency mediates multifunctional neuromodulation for cardiac protection  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 235, 275]]<|/det|>
+Lei Fu lei fu@whu.edu.cn  
+
+<|ref|>text<|/ref|><|det|>[[44, 300, 568, 920]]<|/det|>
+Wuhan University https://orcid.org/0000- 0003- 1356- 4422Chenlu WangWuhan UniversityLiping ZhouWuhan UniversityChengzhe LiuWuhan UniversityJiaming QiaoWuhan UniversityXinrui HanWuhan UniversityLuyang WangWuhan UniversityYaxi LiuWuhan UniversityBi XuWuhan UniversityQinfang QiuWuhan UniversityZizhuo ZhangWuhan UniversityJiale WangWuhan UniversityXiaoya ZhouWuhan UniversityMengqi ZengWuhan University https://orcid.org/0000- 0002- 1442- 052X  
+
+<|ref|>text<|/ref|><|det|>[[44, 928, 108, 945]]<|/det|>
+Lilei Yu
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 106, 104, 124]]<|/det|>
+## Article  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 144, 136, 162]]<|/det|>
+## Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 181, 315, 200]]<|/det|>
+Posted Date: March 15th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 220, 474, 239]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3985327/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 257, 914, 300]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 317, 535, 337]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 372, 910, 416]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on July 28th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 50557- w.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[120, 85, 822, 184]]<|/det|>
+# Pt nanoshell with ultra-high NIR-II photothermal conversion efficiency mediates multifunctional neuromodulation for cardiac protection  
+
+<|ref|>text<|/ref|><|det|>[[144, 210, 855, 298]]<|/det|>
+Chenlu Wang \(^{1,\dagger}\) , Liping Zhou \(^{2,3,4,\dagger}\) , Chengzhe Liu \(^{2,3,4,\dagger}\) , Jiaming Qiao \(^{2,3,4}\) , Xinrui Han \(^{2,3,4}\) , Luyang Wang \(^{1}\) , Yaxi Liu \(^{1}\) , Bi Xu \(^{1}\) , Qinfang Qiu \(^{2,3,4}\) , Zizhuo Zhang \(^{2,3,4}\) , Jiale Wang \(^{2,3,4}\) , Xiaoya Zhou \(^{2,3,4*}\) , Mengqi Zeng \(^{1}\) , Lilei Yu \(^{2,3,4*}\) , Lei Fu \(^{1,3,4*}\)  
+
+<|ref|>text<|/ref|><|det|>[[144, 328, 852, 610]]<|/det|>
+\(^{1}\) College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, China. \(^{2}\) Cardiovascular Hospital, Renmin Hospital of Wuhan University, Wuhan 430060, China; Hubei Key Laboratory of Autonomic Nervous System Modulation, Wuhan 430060, China; Cardiac Autonomic Nervous System Research Center of Wuhan University, Wuhan 430060, China; Hubei Key Laboratory of Cardiology, Wuhan 430060, China; Cardiovascular Research Institute, Wuhan University, Wuhan, 430060, China. \(^{3}\) Taikang Center for Life and Medical Sciences, Wuhan University, Wuhan 430060, China. \(^{4}\) Institute of Molecular Medicine, Renmin Hospital of Wuhan University, Wuhan 430060, China.  
+
+<|ref|>text<|/ref|><|det|>[[144, 636, 797, 656]]<|/det|>
+\(^{*}\) E- mail: leifu@whu.edu.cn; lileiyu@whu.edu.cn; whuzhouxiaoya@whu.edu.cn  
+
+<|ref|>text<|/ref|><|det|>[[144, 682, 792, 701]]<|/det|>
+\(^{†}\) These authors contributed equally: Chenlu Wang, Liping Zhou, Chengzhe Liu.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 84, 852, 595]]<|/det|>
+The autonomic nervous system plays a pivotal role in the pathophysiology of cardiovascular diseases. Regulating it is essential for preventing and treating acute ventricular arrhythmias (VAs). Photothermal neuromodulation is a nonimplanted technique, but the response temperature ranges of transient receptor potential vanilloid 1 (TRPV1) and TWIK- elated \(\mathbf{K}^{+}\) Channel 1 (TREK1) exhibit differences while being closely aligned, and the acute nature of VAs require that it must be rapid and precise. However, the low photothermal conversion efficiency (PCE) still poses limitations on achieving rapid and precise treatment. Here, we achieved nearly perfect blackbody absorption and one of the highest PCE in the second near infrared (NIR- II) window (73.7% at 1064 nm) via a Pt nanoparticle shell (PtNP- shell). By precisely manipulating the photothermal effect, we successfully achieved rapid and precise multifunctional neuromodulation encompassing neural activation (41.0–42.9 °C) and inhibition (45.0–46.9 °C). The NIR-II photothermal modulation additionally achieved bi- directional reversible autonomic modulation and conferred protection against acute VAs associated with myocardial ischemia and reperfusion injury in interventional therapy.  
+
+<|ref|>text<|/ref|><|det|>[[144, 627, 852, 907]]<|/det|>
+Cardiovascular disease has emerged as a leading cause of mortality, with acute myocardial infarction being one of the most pernicious ailments<sup>1,2</sup>. Myocardial ischemia (MI) frequently precipitates acute ventricular arrhythmias (VAs), impeding prompt and efficacious treatment for acute myocardial infarction. Furthermore, conventional interventional procedures for MI are unable to circumvent concomitant myocardial reperfusion injury and associated VAs. The autonomic nervous system, encompassing sympathetic and parasympathetic nerves, plays a role in cardiovascular modulation; both are naturally antagonistic. Sympathetic inhibition or parasympathetic activation has been shown to stabilize cardiac electrophysiology, safeguard against MI
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[150, 84, 422, 101]]<|/det|>
+and reduce the incidence of VAs \(^{3}\) .  
+
+<|ref|>text<|/ref|><|det|>[[144, 116, 853, 430]]<|/det|>
+In recent years, several studies have demonstrated that light- activated nanotransducers can induce local heating effects, leading to the activation or inhibition of nerves \(^{4 - 6}\) . This discovery is attributed to the identification of temperature- sensitive ion channels in neurons, such as transient receptor potential vanilloid 1 (TRPV1) \(^{7}\) and TWIK- elated K \(^{+}\) Channel 1 (TREK1) \(^{8}\) . The activation of specific temperature- sensitive ion channels necessitates precise temperature ranges \(^{7 - 9}\) . Considering the acute nature of neural responses, a therapeutic strategy with rapid and accurate modulation is required. The second near infrared (NIR- II) photothermal is expected to realize noninvasive and nonimplanted neuromodulation. However, its neural response rate and accuracy are currently limited by low photothermal conversion efficiency (PCE).  
+
+<|ref|>text<|/ref|><|det|>[[144, 444, 852, 857]]<|/det|>
+Here we report a near blackbody NIR- II Pt nanoparticle shell (PtNP- shell) for protection against MI and myocardial reperfusion injury accompanying intervention. The PtNP- shell, synthesized through a simple electrocoupling substitution reaction using liquid metal nanoparticles as templates (Fig. 1a), possesses surface pores and a hollow structure. It demonstrates nearly perfect blackbody absorption, enhanced absorption of light, and then one of the highest PCE in the NIR- II window (73.7% at 1064 nm). By leveraging the local heating effect mediated by PtNP- shell, we achieved rapid, efficient, and precise multifunctional autonomic neuromodulation. Specifically, parasympathetic activation and sympathetic inhibition were accomplished by activating TRPV1 (41.0–42.9 °C) and TREK1 (45.0–46.9 °C) channels, respectively. Photothermal autonomic neuromodulation mediated by PtNP- shell effectively stabilized cardiac electrophysiology and reduced VAs incidence in both myocardial ischemia- reperfusion (I/R) injury model and MI model, respectively (Fig. 1b).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[147, 85, 848, 444]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 459, 852, 555]]<|/det|>
+<center>Fig. 1 | The synthesis steps of the PtNP-shell and the concept of mediating precise photothermal effects for cardioprotection. a, The synthesis steps of PtNP-shell and schematic diagram of photothermal effect. b, Schematic diagram of multifunctional autonomic modulation mediated by photothermal effect of PtNP-shell for precise cardioprotection against myocardial I/R injury and MI-induced VAs. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[150, 588, 366, 607]]<|/det|>
+## Result and discussion  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 625, 540, 644]]<|/det|>
+## Synthesis and Characterization of PtNP-shell  
+
+<|ref|>text<|/ref|><|det|>[[145, 658, 852, 907]]<|/det|>
+The PtNP- shell was synthesized through an electrocoupling substitution reaction between chloroplatinate and Ga nanoparticles (GaNPs). Ga nanoparticles were obtained by sonication of pure metal Ga. To achieve a balanced particle size and oxidation degree of GaNPs, pure gallium was sequentially sonicated in ethanol and water for 30 minutes to obtain gallium nanoparticles with reduced oxidation (Supplementary Fig. 1a). In accordance with the electrochemical redox potential of the redox couple \((\mathrm{Ga}^{3 + } / \mathrm{Ga} - 0.529 \mathrm{V}; \mathrm{PtCl}_6^{2 - } / \mathrm{PtCl}_4^{2 - }: 0.726 \mathrm{V}; \mathrm{PtCl}_4^{2 - } / \mathrm{Pt}: 0.758 \mathrm{V})^{10,11}, \mathrm{Pt} (\mathrm{IV}) \mathrm{can be in situ}\) reduced by Ga and encapsulated on the surface of GaNPs to form a core- shell structure
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[100, 81, 855, 465]]<|/det|>
+(Supplementary Fig. 1b, c). The hollow PtNP-shell is synthesized after completion of the reaction (Fig. 2a). Simultaneously with the reduction of Pt (IV), Ga oxide is formed, creating the skeleton of the PtNP-shell (right in Fig. 2a). The surface of the PtNP-shell exhibits a rough texture (Supplementary Fig. 2). The scanning transmission electron microscopy (STEM) images reveal numerous irregular and uneven pores on its surface (Supplementary Fig. 3a) and PtNP-shell is composed of Pt nanoparticles (PtNPs) with \(2 - 5 \mathrm{nm}\) (Fig. 2b). High-resolution TEM (HR-TEM) image is acquired to character the structure of PtNPs. As shown in Supplementary Fig. 3b, PtNPs exhibits single crystal structure with a lattice stripe spacing of \(0.23 \mathrm{nm}\) corresponding to the (111) crystal plane. Meanwhile, the corresponding Fast Fourier Transform (FFT) pattern (inset in Supplementary Fig. 3b) shows the typical diffraction patterns of face-centered cubic structure along [111] zone axis.  
+
+<|ref|>image<|/ref|><|det|>[[144, 494, 850, 775]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[100, 787, 851, 884]]<|/det|>
+<center>Fig. 2 | Characterization of PtNP-shell. a, TEM image of PtNP-shell (Right: element mapping). b, STEM images of PtNP-shell surface. c, XRD spectrum of PtNP-shell (Inset: SAED pattern). d, UV-vis-NIR absorption spectrum of PtNP-shell ( \(75 \mu \mathrm{g} \cdot \mathrm{mL}^{-1}\) ). e, Temperature elevation curves of PtNP-shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{-1}\) ) under NIR-II laser irradiation ( \(1 \mathrm{W} \cdot \mathrm{cm}^{2}\) ). f, Calculation of the PCE at \(1064 \mathrm{nm}\) (PtNP-shell: \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{-1}\) ). </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 80, 853, 696]]<|/det|>
+In the X- ray power diffraction (XRD) spectrogram result (Fig. 2c), all peaks can be attributed to the crystal phase of Pt (JCPDS: 87- 0640), consistent with the selected area electron diffraction (SAED) pattern findings (inset in Fig. 2c). However, no peaks corresponding to gallium oxide were observed in the XRD spectrogram, possibly due to its low content. The XRD spectrogram (Supplementary Fig. 4) of PtNP- shell prior to reacting with KOH showed that the gallium oxide contained in PtNP- shell was GaOOH (JCPDS: 06- 0180). Additional evidence from X- ray photoelectron spectroscopy (XPS) also suggests that PtNP- shell contains Ga (Supplementary Fig. 5), consistent with energy dispersive X- ray spectroscopy (EDX) analysis (right in Fig. 2a). The peak centred at 1117.59 eV is ascribed to Ga \(2\mathrm{p}_{3 / 2}\) , indicating the presence of \(\mathrm{Ga}^{3 + }\) in PtNP- shell. Meanwhile, the Pt 4f spectrum shows two peaks at 71.56 and 75.02 eV, which result from metallic Pt \(4\mathrm{f}_{7 / 2}\) and Pt \(4\mathrm{f}_{5 / 2}\) . PtNP- shell was treated with KOH (0.67 M) to reduce the gallium oxide content and the surface potential was reduced from 45.8 mV to - 25.7 mV, and then encapsulated with Methoxypoly(Ethylene Glycol) Thiol (mPEG- \(\mathrm{SH}_{5000}\) ) to enhance its biocompatibility and the surface potential was changed to - 19.9 mV. (Supplementary Fig. 6). The statistically averaged hydrated nanoparticle size of PtNP- shell based on the dynamic light scattering diagram was 200.1 nm with uniform size distribution, indicating the nanoparticle was well dispersed in water (Supplementary Fig. 7).  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 716, 707, 735]]<|/det|>
+## Blackbody Absorption and Photothermal Property of PtNP-shell  
+
+<|ref|>text<|/ref|><|det|>[[144, 747, 853, 899]]<|/det|>
+Due to the presence of pores and a hollow structure in the PtNP- shell, light propagating in the space bounces at the rough surface of PtNP- shell until it encounters one of the pores, where it continues to bounce within the PtNP- shell. The random distribution of these pores results in completely random light reflection, akin to Brownian motion<sup>12</sup>. Consequently, the probability of light escaping from other pores is extremely low,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 82, 853, 530]]<|/det|>
+rendering PtNP- shell behave like a blackbody and produce an efficient infrared heater \(^{13 - 15}\) . This enhanced absorption of light by PtNP- shell exhibits nearly perfect blackbody absorption characteristics (Supplementary Fig. 8a). The absorption of PtNP- shell is close to 1 in the range of 250–1300 nm at \(75 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) (Fig. 2d). According to the Lambert- Beer law (A/L = εC, where ε is the extinction coefficient), a linear relationship between absorption intensity (at 1064 nm) and concentration was established, with an extinction coefficient measured as \(13.3 \mathrm{Lg}^{- 1} \mathrm{cm}^{- 1}\) at 1064 nm (Supplementary Fig. 8b). Varying concentrations of PtNP- shell resulted in different shades of grey being generated, with significantly darker greyness observed under identical conditions compared to GaNPs and Pt- coated Ga- In alloy (EGaIn) nanoparticles (GaIn@Pt NPs) (Supplementary Fig. 9a). These distinctive features were characterized by their respective positions within an RGB cube representation, wherein on the diagonal connecting darkest and brightest points, PtNP- shell was found closer to the darkest point than both other materials (Supplementary Fig.9b).  
+
+<|ref|>text<|/ref|><|det|>[[144, 541, 853, 890]]<|/det|>
+The photothermal properties of PtNP- shell were verified by irradiating the dispersion of PtNP- shell in water with NIR- II light at \(1064 \mathrm{nm}\) (1 \(\mathrm{W} \cdot \mathrm{cm}^{- 2}\) ). Even in vitro, PtNP- shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) exhibited rapid temperature elevation, achieving a rise from room temperature to \(41.0^{\circ} \mathrm{C}\) and \(45.0^{\circ} \mathrm{C}\) within only 96 s and 133 s, respectively (Fig. 2e). However, for GaNPs (347 s and over 600 s) and GaIn@Pt NPs (278 s and 450 s), it took significantly longer time to reach the same temperatures (Supplementary Fig. 10). The corresponding thermal images of the PtNP- shell with different concentrations under different irradiation times are shown in Supplementary Fig. 11. The heating effect of the PtNP- shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) gradually increased the \(\Delta \mathrm{T}\) from 7.72 \(^{\circ} \mathrm{C}\) to 52.17 \(^{\circ} \mathrm{C}\) When exposed to NIR- II laser for a duration of 600 s while varying the optical power density at 1064 nm between \(0.25 - 1.5 \mathrm{W} \cdot \mathrm{cm}^{- 2}\) (Supplementary Fig. 12).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 83, 852, 268]]<|/det|>
+The PCE of PtNP- shell was quantified as \(73.7\%\) when balancing the energy input from photons with heat dissipation within the system (Fig. 2f), representing one of the highest PCE at 1064 nm (Supplementary Fig. 13). These results indicate that PtNP- shell exhibits excellent photothermal performance in the NIR- II window. Additionally, no significant changes in temperature or morphology were observed even after five cycles of irradiation (Supplementary Fig. 14), suggesting exceptional photothermal stability.  
+
+<|ref|>sub_title<|/ref|><|det|>[[144, 290, 795, 309]]<|/det|>
+## Photothermal of PtNP-shell enables precise modulations of neurons in vitro  
+
+<|ref|>text<|/ref|><|det|>[[144, 320, 852, 703]]<|/det|>
+To investigate the photothermal effects of PtNP- shell on neuronal activity at multiple levels, we conducted calcium imaging experiments in hippocampal neuron (HT- 22) cells (Fig. 3a, b). The immunoblotting results revealed abundant expression of both TRPV1 and TREK1 ion channels in HT- 22 cells (Fig. 3c). The direct effect of PtNP- shell on the excitability of these two different ion channels was assessed under NIR- II irradiation using a calcium ion indicator (Fluo- 4 AM). Upon NIR- II laser irradiation, the temperature of the PtNP- shell (+) group increased compared to that of the PtNP- shell (- ) group, resulting in a significantly higher percentage of responding cells (Fig. 3d) (p< 0.001). The micrographs fluorescence intensity curve of HT- 22 neurons cultured with PtNP- shell showed significant \(\mathrm{Ca^{2 + }}\) influx upon NIR- II laser irradiation for \(35 \pm 5\) s and after the temperature reached \(42.0^{\circ}\mathrm{C}\) (Fig. 3e). In contrast, application of NIR- II laser irradiation with PBS did not induce significant \(\mathrm{Ca^{2 + }}\) influx.  
+
+<|ref|>text<|/ref|><|det|>[[144, 716, 852, 899]]<|/det|>
+Subsequently, neuronal excitation was induced and calcium signals were increased by perfusion of \(15\mathrm{mM}\) KCl in the PtNP- shell (- ) group and PtNP- shell (+) group (50 \(\mu \mathrm{g}\mathrm{mL}^{- 1}\) ), respectively. This phenomenon can be attributed to the elevation of extracellular potassium ion concentration, which triggers neuronal depolarization and subsequently leads to a substantial increase in intracellular calcium ion concentration<sup>16</sup>. Under NIR- II laser irradiation, the proportion of HT- 22 cells responding to high
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 83, 852, 430]]<|/det|>
+concentration KCl stimulation was significantly lower in the PtNP- shell (+) group compared to that in the PtNP- shell (- ) group at approximately \(46.0^{\circ}\mathrm{C}\) (Fig. 3f). The difference may be due to the activation of the TERK1 ion channel in the PtNP- shell (+) group, which can induce neuronal hyperpolarization and make intracellular and extracellular calcium ion concentrations tend to recover<sup>17</sup>. Interestingly, the PtNP- shell influenced the fluorescence intensity of HT- 22 cells not with a sustained decrease but with an initial rise followed by a subsequent decrease (Fig. 3g). This observation may be associated with the activation of TRPV1 channel at around \(42.0^{\circ}\mathrm{C}^9\) . With increasing temperature, TRPV1 and TREK1 channels were sequentially activated. These findings suggest that PtNP- shell can achieve precise temperature control within a short duration through its own ultra- high PCE for both neuronal excitation and inhibition.  
+
+<|ref|>text<|/ref|><|det|>[[144, 444, 852, 856]]<|/det|>
+Cytotoxicity assays were then conducted to investigate the potential neurotoxicity of PtNP- shell application. As shown in Fig. 3h, concentrations of PtNP- shell below 100 \(\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) exhibited no significant toxic effects on HT- 22 cells. Even when the concentration of PtNP- shell was increased to \(200\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) , the survival rate of neuronal cells remained approximately at \(52.11\%\) . Furthermore, the impact of PtNP- shell photothermal stimulation parameters on cell viability were assessed through analysis of HT- 22 cell survival under NIR- II laser irradiation. Notably, when a concentration of 50 \(\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) PtNP- shell and an NIR- II laser with a power density of \(0.5\mathrm{W}\cdot \mathrm{cm}^{- 2}\) were applied for a brief duration, the survival rate exceeded \(92.36\%\) for HT- 22 cells. Even with an increase in power density to \(0.75\mathrm{W}\cdot \mathrm{cm}^{- 2}\) , the survival rate for HT- 22 cells still remained around \(72.68\%\) after 60 s of irradiation (Fig. 3i). These results indicate that PtNP- shell does not induce significant damage to neurons under controlled NIR- II laser irradiation.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[145, 81, 850, 480]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 492, 852, 670]]<|/det|>
+<center>Fig. 3 | PtNP-shell photothermal activation of different neuronal ion channels in vitro. a, Flowchart of calcium imaging assay performed on HT-22 cells. b, calcium imaging of HT-22 cells under different experimental conditions. c, Western blotting for TRPV1 and TREK1 from HT-22 and H9c2 cells. Percentage of d, TRPV1 and f, TREK1 groups of HT-22 cells within the field of view of the fluorescence microscope that responded to laser stimulation. Temporal dynamics of \(\mathrm{Ca}^{2 + }\) signals in e, TRPV1 and g, TREK1 groups of cells. The solid lines indicate the mean, and shade represents the standard error of the mean (SEM). h, Cell viability of HT-22 treated with different concentrations of PtNP-shell for \(24\mathrm{h}\) . i, Cell viability of HT-22 treated with NIR-II laser irradiation of different power densities and laser duration. The error bar indicates S.E.M. \(***\mathrm{P}< 0.001\) . </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[145, 704, 795, 722]]<|/det|>
+## PtNP-shell photothermal activation of the parasympathetic nervous system  
+
+<|ref|>text<|/ref|><|det|>[[144, 736, 852, 887]]<|/det|>
+Western blotting analysis of peripheral ganglia from the canine autonomic nervous system revealed the expression of TRPV1 and TREK1 heat- sensitive ion channels in both the nodose ganglion (NG) and left stellate ganglion (LSG). Notably, TRPV1 was abundantly expressed in the NG of the parasympathetic nervous system, while TREK1 exhibited higher levels in the LSG of the sympathetic nervous system (Supplementary
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 81, 854, 563]]<|/det|>
+Fig. 15). To investigate whether the photothermal effect induced by PtNP-shell under NIR-II irradiation can precisely regulate the parasympathetic nerve, \(100\mu \mathrm{L}\) PtNP-shell \((50\mu \mathrm{g}\cdot \mathrm{mL}^{- 1})\) and PBS were injected into NG of PtNP-shell group and control group (6 beagle dogs in each group), respectively (Fig. 4a,b). It can be observed that upon irradiation with NIR-II laser \((0.8\mathrm{W}\cdot \mathrm{cm}^{- 2})\) , the temperature of NG injected with PtNP-shell increased to \(41.0^{\circ}\mathrm{C}\) within a very short period of time \((12\pm 3\mathrm{s})\) . Subsequently, the temperature of NG could be kept in the range of \(41.0–42.9^{\circ}\mathrm{C}\) for 5 min by adjusting the power density to \(0.45\mathrm{W}\cdot \mathrm{cm}^{- 2}\) (Fig. 4c-d). As a crucial node within the parasympathetic neural network, activation of NG significantly reduces heart rate (HR) (Fig. 4e) \(^{18}\) . Therefore, NG function was assessed by the maximum decrease in heart rate under direct electrical stimulation. As shown in Fig. 4f-h, NG function and activity was significantly elevated in the PtNP-shell group than in the control group after stimulation. The function and activity of NG recovered close to baseline within three hours after turning off NIR-II laser, indicating that the photothermal modulation induced by PtNP-shell was reversible within NGs (Fig. 4h, Supplementary Fig. 16 and 17).  
+
+<|ref|>text<|/ref|><|det|>[[144, 575, 853, 890]]<|/det|>
+In addition, the effective refractive period (ERP) was measured in various regions, including left ventricular apex (LVA), left ventricular base (LVB) and median left ventricular area (LVM). In the PtNP-shell group, the ERP was significantly elevated compared to the control group and remained elevated for \(2\mathrm{~h}\) after photothermal intervention in NG (Supplementary Fig. 18). Furthermore, immunofluorescence staining for Vacht, c- fos, and TRPV1 was performed on NG histopathological sections following photothermal modulation (Fig. 4i). Quantitative analysis (Supplementary Fig. 19) revealed a substantial increase in the proportion of \(\mathrm{TRPV1^{+}}\) \((86.63\pm 2.65\mathrm{vs}45.45\pm 2.98)\) and c- Fos \(^+\) \((77.81\pm 3.91\mathrm{vs}17.27\pm 3.08)\) neurons among VAcH \(^+\) parasympathetic neurons in the PtNP-shell group compared to the control group (all P
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 83, 851, 135]]<|/det|>
+\(< 0.001\) ). These findings suggest that PtNP-shell can precisely regulate temperature and subsequently activate TRPV1 ion channels on NG to enhance parasympathetic activity.  
+
+<|ref|>image<|/ref|><|det|>[[144, 165, 850, 670]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[144, 684, 852, 863]]<|/det|>
+<center>Fig. 4 | Photothermal activation of the parasympathetic nervous system by PtNP-shell. a, Location of the canine NG. b, Schematic illustration of the process of photothermal modulation of NG. c, Temperature curves of NG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of NG. e, Representative images of HR reduction induced after stimulation of NG with different voltages. Maximal HR changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, \(n = 6\) . h, Quantification of the NG neural activity recordings, \(n = 6\) . i, Representative immunofluorescent images of Vacht (red), c-fos (green) and TRPV1 (pink) in the NG of beagles following different treatments. Data are shown as the mean \(\pm\) S.E.M. \(*P < 0.05\) , \(**P < 0.01\) , \(***P < 0.001\) , ns means that the difference is not statistically significant. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[101, 82, 852, 400]]<|/det|>
+1 PtNP-shell photothermal activation of NG reduces I/R injury and associated VAs2 Following I/R injury, electrocardiography (ECG) was recorded to monitor the3 occurrence of VAs events within 1 h, including ventricular premature beats (VPBs),4 ventricular tachycardia (VT) and ventricular fibrillation (VF) (Fig. 5c)19. Under NIR-II5 laser irradiation, the PtNP-shell group exhibited a lower incidence of sustained VTs6 (duration \(>30\) s) or VF compared to the control group (50% vs. 83%) (Fig. 5d).7 Moreover, the number of recorded VPBs (70.83 ± 5.38 vs. 116.00 ± 6.36, \(\mathrm{P}< 0.05\) ),8 VTs (3.17 ± 0.87 vs. 8.83 ± 2.15, \(\mathrm{P}< 0.05\) ) and duration of the VTs (7.00 ± 3.173s vs.9 26.83 ± 7.89s, \(\mathrm{P}< 0.05\) ) in the PtNP-shell group were significantly reduced compared10 to that in the control group (Fig. 5e- g).  
+
+<|ref|>image<|/ref|><|det|>[[192, 425, 803, 720]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 734, 850, 911]]<|/det|>
+<center>Fig. 5 | PtNP-shell photothermal activation of the parasympathetic nervous system improves myocardial I/R injury. Modulation of NG to protect against myocardial I/R injury and associated VAs a, schematic diagram and b, flowchart. c, Representative visual depictions of VAs, including VPB, VT and VF. d, Quantitative analysis the ratio of sVT and VF incidence between different groups, \(\mathrm{n} = 6\) . Quantitative analysis the number of e, VPBs, f, VTs and g, the duration of sVT of beagles. Effects on ventricular ERP at different sites in beagles treatment with PtNP-shell or control h, before and i, after myocardial I/R injury modelling. Levels of markers of myocardial injury, including j, MYO and k, c-TnI, after different treatments in beagles. Data are shown as the mean \(\pm\) S.E.M. \(^{*}\mathrm{P}< 0.05\) , \(^{**}P< 0.01\) , \(^{***}\mathrm{P}< 0.001\) . </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 83, 852, 333]]<|/det|>
+Animal modeling and intervention manipulations were conducted to further elucidate the protective effects of precise modulation of NG by PtNP- shell against myocardial I/R injury and associated VAs, following the experimental protocols depicted in Figure 5a,b. PtNP- shell and PBS were microinjected into the NG of the PtNP- shell group and control group, respectively, each consisting of six beagle dogs. The NG was subsequently exposed to NIR- II laser irradiation for a duration of 5 minutes prior to occlusion of the left anterior descending (LAD) coronary artery for reperfusion therapy.  
+
+<|ref|>text<|/ref|><|det|>[[144, 345, 852, 725]]<|/det|>
+There were no statistically significant differences between the two groups in terms of preoperative ERP for LVB, LVM, and LVA. In the postoperative period, all three positions showed shortened ERPs in the control group. The PtNP- shell group exhibited significantly higher ERPs compared to the control group, indicating that photothermal modulation of nerves by PtNP- shell has a protective effect on cardiac electrophysiology (Fig. 5h- i). Serum Elisa assay revealed reduced levels of myocardial injury markers (MYO and c- TnI) after I/R injury in the PtNP- shell group compared to the control group (all \(\mathrm{p}< 0.05\) , Fig. 5j,k). Postoperatively, heart rate variability analysis demonstrated lower low frequency (LF) and higher high frequency (HF) and the lower ratio of LF to HF (LF/HF) values in the PtNP- shell group compared to the control group (all \(\mathrm{p}< 0.05\) , Supplementary Fig. 20). These results suggest that PtNP- shell exerts cardioprotective effects and reduces VAs by activating parasympathetic nerve.  
+
+<|ref|>sub_title<|/ref|><|det|>[[144, 757, 754, 776]]<|/det|>
+## PtNP-shell photothermal inhibition of the sympathetic nervous system  
+
+<|ref|>text<|/ref|><|det|>[[144, 790, 853, 907]]<|/det|>
+The sympathetic nervous system was modulated by performing microinjections of PtNP- shell or PBS into the LSG, followed by irradiation with an NIR- II laser (Fig. 6a,b). The temperature curve demonstrates that upon exposure to a NIR- II laser \((0.8\mathrm{W}\cdot \mathrm{cm}^{- 1})\) for \(25\pm 5\mathrm{s}\) , the temperature rapidly escalated to \(45.0^{\circ}\mathrm{C}\) , crossing the range of \(41.0-\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 78, 853, 765]]<|/det|>
+42.9 °C within a mere duration of \(6 \pm 1\) s. Subsequently, the power density was immediately decreased to \(0.6 \mathrm{W} \mathrm{cm}^{-2}\) , effectively maintaining LSG at a steady temperature between \(45.0 - 46.9\) °C (Fig. 6c, d). Due to the substantial increase in systolic blood pressure (SBP) induced by LSG activation (Fig. 6e), the function of LSG was evaluated by quantifying the maximum SBP change corresponding to five consecutive incremental voltages of high- frequency electrical stimulation. After 5 min of NIR- II laser irradiation, the activity and function of LSG in the PtNP- shell group were significantly suppressed compared to the control group ( \(p < 0.05\) ) and they returned close to baseline after 3 h (Fig. 6f- h and Supplementary Fig. 21- 22). Prolonged ERP effects were observed in all left ventricles, while the protective effect exhibited a duration of only 1 h (Supplementary Fig. 23). Furthermore, immunofluorescence staining was conducted on LSG tissues to examine the expression of c- fos, tyrosine hydroxylase (TH), and TREK1 (Fig. 6i). The quantitative analysis (Supplementary Fig. 24) revealed a significant decrease in the proportion of c- Fos\(^+\) expression in TH\(^+\) neurons within the PtNP- shell group ( \(8.80 \pm 1.80\) vs. \(44.78 \pm 5.55\) , \(P < 0.001\) ) indicating that PtNP- shell exerted a photothermal inhibitory effect on LSG neurons under NIR- II irradiation. However, the proportion of TREK\(^+\) expression was significantly increased within TH\(^+\) neurons in the PtNP- shell group ( \(83.51 \pm 3.72\) vs. \(57.20 \pm 5.89\) , \(P < 0.01\) ). This increase could lead to hyperpolarization of the cell membrane potential, reduction in neuronal excitability and inhibition of sympathetic nerve activity.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[150, 80, 850, 592]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[150, 604, 850, 784]]<|/det|>
+<center>Fig. 6 | Photothermal inhibition of the sympathetic nervous system by PtNP-shell. a, Location of the canine LSG. b, Schematic illustration of the process of photothermal modulation of LSG. c, Temperature curves of LSG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of LSG. e, Representative images of BP elevation induced after stimulation of LSG with different voltages. Maximal SBP changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, \(n = 6\) . h, Quantification of the LSG neural activity recordings, \(n = 6\) . i, Representative immunofluorescent images of TH (red), c-fos (green) and TREK1 (pink) in the LSG of beagles following different treatments. Data are shown as the mean \(\pm\) S.E.M. \(*P< 0.05\) , \(**P< 0.01\) , \(***P< 0.001\) , ns means that the difference is not statistically significant. </center>
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[147, 84, 850, 101]]<|/det|>
+# PtNP-shell photothermal inhibition of LSG improves MI and reduces associated  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 118, 183, 133]]<|/det|>
+## Vas  
+
+<|ref|>text<|/ref|><|det|>[[144, 145, 853, 794]]<|/det|>
+To investigate the cardioprotective effect of PtNP- shell photothermal effect in achieving a targeted LSG temperature of approximately \(46.0^{\circ}\mathrm{C}\) , NIR- II light was administered prior to ligation of the LAD coronary artery (Fig. 7a,b). Under NIR- II laser irradiation, the PtNP- shell group exhibited a significantly reduced incidence of sustained VTs (duration \(>30\) s) or VF compared to the control group ( \(16\%\) vs. \(50\%\) ) (Fig. 7c). In the PtNP- shell group, ECG recordings within infarction 1 exhibited a reduced incidence of VAs events compared to the control group, with fewer VPBs recorded in the PtNP- shell group than in the control group ( \(51.50 \pm 5.53\) vs. \(70.83 \pm 5.375\) , \(\mathrm{P} < 0.05\) , Fig. 7d). However, there were no significant differences between the two groups in terms of VT numbers and duration (Supplementary Fig. 25). Additionally, VA inducibility measurements demonstrated that after photothermal neuromodulation with PtNP- shell, there was a decrease in VA score ( \(1.50 \pm 0.76\) vs. \(4.83 \pm 1.14\) , \(\mathrm{P} < 0.05\) ) effective heart protection (Fig. 7e,f). Furthermore, PtNP- shell photothermal inhibition of LSG produced similar protective effects on ventricular electrophysiological index ERP as activation of NG (Fig. 7g,h), and had higher VF threshold than control group ( \(24.33 \pm 4.24\) vs. \(12.33 \pm 3.16\) , \(\mathrm{P} < 0.05\) , Fig. 7i). In addition, the light inhibition of LSG followed the same trend as heart rate variability after activation of NG (Supplementary Fig. 26). These results suggest that PtNP- shell protects against cardiac damage and reduces VAs by modulating the autonomic nervous system, specifically by decreasing sympathetic activity and enhancing parasympathetic tone.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[144, 85, 852, 393]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[148, 405, 852, 567]]<|/det|>
+<center>Fig. 7 | PtNP-shell photothermal inhibition of the sympathetic nervous system improves MI associated VAs. Modulation of LSG to protect against MI and associated VAs a, schematic diagram and b, flowchart. c, Quantitative analysis the ratio of sVT and VF incidence between different groups, \(n = 6\) . d, Quantitative analysis the number of VPBs of beagles. e, Typical images of VA induced by programmed electrical stimulation. f, Quantitative analysis of VAs score in different groups. Effects on ventricular ERP at different sites in Beagles treatment with PtNP-shell or control g, before and h, after MI modelling. i, Quantitative analysis of VF threshold in different groups. Data are shown as the mean \(\pm\) S.E.M. \(*P < 0.05\) , \(**P < 0.01\) , \(***P < 0.001\) . </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 597, 603, 616]]<|/det|>
+## Biosafety of PtNP-shell for translational applications  
+
+<|ref|>text<|/ref|><|det|>[[144, 629, 852, 911]]<|/det|>
+To validate the biocompatibility of PtNP- shell photothermal modulation on the autonomic nervous system, we conducted rapid excision of LSG and NG tissues followed by hematoxylin and eosin (H&E) staining. As shown in Supplementary Fig. 27a, H&E staining did not reveal any indications of neuronal damage in both the PtNP- shell and control groups for both NG and LSG, indicating that the neuromodulation of PtNP- shell is repeatable. Meanwhile, to further investigate the long- term biosafety of PtNP- shell, a microinjection of \(200 \mu \mathrm{l}\) PtNP- shell (50 \(\mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) or PBS was administered into the ganglion of dogs and the tail vein of rats, respectively. After a follow- up period of 30 days, did not reveal any obvious damage in major organs,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 83, 852, 201]]<|/det|>
+including the heart, liver, spleen, lungs, and kidneys (Supplementary Fig. 27b,c). Furthermore, blood biochemical analyses indicated the absence of hepatotoxicity or nephrotoxicity (Supplementary Fig. 27d-m). These results unequivocally demonstrate that PtNP-shell exhibits exceptional biocompatibility and long-term biological safety.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 234, 263, 253]]<|/det|>
+## Conclusion  
+
+<|ref|>text<|/ref|><|det|>[[146, 270, 852, 488]]<|/det|>
+The PtNP-shell reported in this study exhibits nearly perfect blackbody absorption property, making it an efficient absorber with one of the highest PCE in the NIR-II window (73.7% at 1064 nm). Furthermore, local heating induced by PtNP-shell activation effectively triggers temperature- sensitive ion channels TRPV1 and TREK1, enabling precise and efficient regulation of autonomic nerves. This innovative approach holds great potential for non- invasive treatment of MI and associated VAs, as well as protection against reperfusion injury during interventional therapy.  
+
+<|ref|>text<|/ref|><|det|>[[145, 500, 852, 848]]<|/det|>
+The minimal tissue damage caused by light can be disregarded within the maximum permissible exposure (MPE) range, rendering it one of the safest interventions for organisms. The interaction between light and tissue is intricate, and further research could aid in selecting more suitable wavelengths to achieve deeper penetration within the MPE range. Leveraging the nearly impeccable blackbody absorption of PtNP-shell and ultrasound- guided microinjection technology, remote and precise neuromodulation strategies can be developed, holding promise for non- invasive protection against MI and reperfusion injury- associated VAs. The significance of this approach extends beyond VAs as it exhibits broad therapeutic prospects for chronic diseases like refractory hypertension<sup>20</sup> and stable atherosclerosis<sup>21</sup> due to the wide distribution of autonomic nerves and the universality of nerve regulation.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[110, 84, 279, 101]]<|/det|>
+## 1 Online content  
+
+<|ref|>text<|/ref|><|det|>[[108, 115, 853, 234]]<|/det|>
+2 Any methods, additional references, Nature Portfolio reporting summaries, source data, 3 extended data, supplementary information, acknowledgements, peer review 4 information; details of author contributions and competing interests; and statements of 5 data availability are available at https://doi.org/10.1038/xxx.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[100, 100, 853, 899]]<|/det|>
+2 1 Virani, S. S. et al. Heart disease and stroke statistics—2020 update: a report from the american 3 heart association. Circulation 141, E139-E596 (2020). 4 2 Trayanova, N. A. Learning for prevention of sudden cardiac death. Circul. Res. 128, 185-187 5 (2021). 6 3 Herring, N., Kalla, M. & Paterson, D. J. The autonomic nervous system and cardiac 7 arrhythmias: current concepts and emerging therapies. Nat. Rev. Cardiol. 16, 707-726 (2019). 8 4 Liu, J. S. et al. Antibody-conjugated gold nanoparticles as nanotransducers for second near- 9 infrared photo-stimulation of neurons in rats. Nano Converg. 9, 13 (2022). 10 5 Ye, T. et al. Precise modulation of gold nanorods for protecting against malignant ventricular 11 arrhythmias via near-infrared neuromodulation. Adv. Funct. Mater. 29, 1902128 (2019). 12 6 Zhang, L. et al. AIEgen-based covalent organic frameworks for preventing malignant 13 ventricular arrhythmias via local hyperthermia therapy. Adv. Mater. 35, 2304620 (2023). 14 7 Prescott, E. D. & Julius, D. A modular PIP2 binding site as a determinant of capsaicin receptor 15 sensitivity. Science 300, 1284-1288 (2003). 16 8 Maingret, F. et al. TREK-1 is a heat-activated background \(\mathrm{K^{+}}\) channel. EMBO J. 19, 2483- 17 2491 (2000). 18 9 Grandl, J. et al. Temperature-induced opening of TRPV1 ion channel is stabilized by the pore 19 domain. Nat. Neurosci. 13, 708-714 (2010). 20 10 Zhao, B. et al. Liquid-metal-assisted programmed galvanic engineering of core-shell 21 nanohybrids for microwave absorption. Adv. Funct. Mater. 33, 2302172 (2023). 22 11 Yang, N. L. et al. A general in-situ reduction method to prepare core-shell liquid-metal / metal 23 nanoparticles for photothermally enhanced catalytic cancer therapy. Biomaterials 277, 121125 24 (2021). 25 12 Liu, C. et al. Enhanced energy storage in chaotic optical resonators. Nat. Photonics 7, 474-479 26 (2013). 27 13 Greffet, J. J. et al. Coherent emission of light by thermal sources. Nature 416, 61-64 (2002). 28 14 Mann, D. et al. Electrically driven thermal light emission from individual single-walled carbon 29 nanotubes. Nat. Nanotechnol. 2, 33-38 (2007). 30 15 Granqvist, C. G. Radiative heating and cooling with spectrally selective surfaces. Appl. Opt. 31 20, 2606-2615 (1981). 32 16 Ma, J. X. et al. In vitro model to investigate communication between dorsal root ganglion and 33 spinal cord glia. Int. J. Mol. Sci. 22, 9725 (2021). 34 17 Zyrianova, T. et al. K2P2.1 (TREK-1) potassium channel activation protects against hyperoxia- 35 induced lung injury. Sci. Rep. 10, 22011 (2020). 36 18 Jayaprakash, N. et al. Organ- and function-specific anatomical organization of vagal fibers 37 supports fascicular vagus nerve stimulation. Brain Stimul. 16, 484-506 (2023). 38 19 Zhou, Z. et al. Metabolism regulator adjoncent prevents cardiac remodeling and ventricular 39 arrhythmias via sympathetic modulation in a myocardial infarction model. Basic Res. Cardiol. 40 117, 34 (2022).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 83, 850, 159]]<|/det|>
+1 20 Mancia, G. & Grassi, G. The autonomic nervous system and hypertension. \*Circul. Res.\* 114, 2 1804–1814 (2014). 3 21 Jiang, Y. Q. \*et al.\* The role of age-associated autonomic dysfunction in inflammation and 4 endothelial dysfunction. \*GeroScience\* 44, 2655–2670 (2022).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[101, 85, 240, 104]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[101, 123, 241, 140]]<|/det|>
+## Chemicals  
+
+<|ref|>text<|/ref|><|det|>[[144, 152, 853, 600]]<|/det|>
+The gallium and indium were purchased from Shanghai Minor Metals Co., Ltd. Anhydrous ethanol \((\geq 99.7\%)\) and KOH (AR) were purchased from Sinopharm Chemical Reagent Co., Ltd. \(\mathrm{Na_2PtCl_6}\) ( \(98\%\) ) was purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. mPEG- \(\mathrm{SH}_{5000}\) was purchased from Shanghai Macklin Biochemical Co., Ltd. STR- identified correct HT- 22 cells or human embryonic kidney 293T (HEK- 293T) cells were purchased with the corresponding specialized cell culture media (Procell, Wuhan, China). Anti- NF1, anti- c- fos, anti- TRPV1 antibodies used in western blot and immunofluorescence staining and anti- TREK1 antibody used in immunofluorescence staining were purchased from ABclonal (Wuhan, China). Anti- TREK1 antibody used in western blot was purchased from Santa Cruz Biotechnology (Texas, U.S.). Glyceraldehyde 3- phosphate dehydrogenase (GAPDH) was purchased from Abcam (Cambridge, England). Serum troponin I (c- TnI) and myoglobin (MYO) were purchased from Mibio (Shanghai, China). 4,6- diamidino- 2- phenylindole (DAPI) was purchased from Servicebio (Wuhan, China).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 624, 256, 640]]<|/det|>
+## Instruments  
+
+<|ref|>text<|/ref|><|det|>[[144, 654, 853, 904]]<|/det|>
+The morphology of PtNP- shell was characterized by a F200 transmission electron microscope (TEM) (JEOL, Japan) operated at \(200\mathrm{kV}\) . STEM and HRTEM images were obtained by a JEM- ARM200CF (JEOL, Japan) at \(200\mathrm{kV}\) . The EDX elemental mapping was carried using the JEOL SDD- detector with two \(100\mathrm{mm}^2\) X- ray sensor. X- ray diffraction (XRD) patterns were performed on an SmartLab 9kW X- ray powder diffractometer (Rigaku, Japan). XPS measurements were carried out with a ESCALAB 250Xi spectrometer (Thermo Fisher Scientific, U.S.) under vacuum. Ultraviolet- visible- near- infrared light (UV- Vis- NIR) absorption spectra was collected using a UV
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 82, 853, 498]]<|/det|>
+3600 spectrophotometer (Shimadzu, Japan). Zeta potential (Z) and dynamic light scattering (DLS) were recorded using a Zetasizer Nano ZSP (Malvern Panalytical, U.K.). The fluorescence microscopy images of HT- 22 cells were acquired by FV3000 Microscope (Olympus, Japan), excited with 488 nm laser. Beagle's respiration is maintained by a WATO EX- 20VET ventilator (Mindray, Shenzhen, China). ECG and blood pressure data were recorded by a Lead 7000 Computerized Laboratory System (Jinjiang, Chengdu, China). NIR- II light at 1064 nm is generated by LWIRPD- 1064- 5F laser (Laserwave, Beijing, China). Thermal imaging was obtained by FLIR C2 thermal imager (FLIR, U.S.). High- frequency electrical stimulation was performed by Grass stimulator (Astro- Med; West Warwick, RI, U.S.) The electrical signals of autonomic nerves are recorded by Power Lab data acquisition system (AD Instruments, New South Wales, Australia). Serum biochemical indices were determined by a fully automatic biochemical analyzer BK- 1200 (BIOBASE, Jinan, China).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 520, 319, 537]]<|/det|>
+## Synthesis of GaNPs  
+
+<|ref|>text<|/ref|><|det|>[[144, 551, 853, 735]]<|/det|>
+The GaNPs were obtained by sonication of liquid Ga. The liquid Ga (300 mg) was transferred to anhydrous ethanol (8 mL), and the solution was sonicated by nanoprobe sonication for 1 h (3 seconds on and 3 seconds off) at the power of 290 W. Then the ethanol was replaced with Milli- Q water to continue sonication for 1 h. The solution at the end of sonication was collected and centrifuged at 1000 rpm for 5 min, and the upper liquid layer was aspirated for later use.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 758, 350, 776]]<|/det|>
+## Synthesis of PtNP-shell  
+
+<|ref|>text<|/ref|><|det|>[[144, 789, 852, 907]]<|/det|>
+First, the GaNPs and 3 mL \(\mathrm{Na_2PtCl_6}\) (0.1 M) were evacuated for 30 min and Ar was introduced for 15 min. Then, 3 mL \(\mathrm{Na_2PtCl_6}\) (0.1 M) was added dropwise to GaNPs and the solution was stirred for 4 h. After reaction, the solution was collected and centrifuged at 9000 rpm for 10 min. The solids at the bottom were washed with Milli
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 83, 721, 101]]<|/det|>
+1 Q water for 3 times and finally dispersed in \(6\mathrm{mL}\) Milli- Q for later use.  
+
+<|ref|>sub_title<|/ref|><|det|>[[146, 125, 589, 144]]<|/det|>
+## Functionalization of PtNP-shell with mPEG-SH5000  
+
+<|ref|>text<|/ref|><|det|>[[144, 156, 853, 504]]<|/det|>
+3 The PtNP- shell was first covered with a small amount of mPEG- SH to protect the structure from KOH. \(30\mathrm{mg}\) mPEG- SH5000 was added to \(6\mathrm{ml}\) PtNP- shell and the solution was stirred for \(12\mathrm{h}\) . After the reaction, the solution was collected and centrifuged at \(9000\mathrm{rpm}\) for \(10\mathrm{min}\) . The solids at the bottom were washed with Milli- Q water for 3 times and dispersed in \(6\mathrm{mL}\) Milli- Q water. The above solution was stirred with \(12\mathrm{mL}\) of KOH (1 M) for \(4\mathrm{h}\) . The reaction- completed solution was collected and centrifuged at \(9000\mathrm{rpm}\) for \(10\mathrm{min}\) , and the solids at the bottom were washed three times with Milli- Q water and finally dispersed in \(6\mathrm{mL}\) Milli- Q water. The above solution was stirred with \(60\mathrm{mg}\) mPEG- SH5000 for \(12\mathrm{h}\) . After the reaction, the solution was collected and centrifuged. The solids at the bottom were washed with Milli- Q water for 3 times and finally dispersed in \(6\mathrm{mL}\) PBS.  
+
+<|ref|>sub_title<|/ref|><|det|>[[145, 528, 585, 547]]<|/det|>
+## Synthesis of Ga-In alloy nanoparticles (GaIn NPs)  
+
+<|ref|>text<|/ref|><|det|>[[144, 559, 852, 777]]<|/det|>
+The liquid EGaIn was prepared by physically mixing \(75\mathrm{wt}\%\) gallium and \(25\mathrm{wt}\%\) indium at \(200^{\circ}\mathrm{C}\) for \(2\mathrm{h}\) . The liquid EGaIn (300 mg) was transferred to anhydrous ethanol ( \(8\mathrm{mL}\) ), and the solution was sonicated by nanoprobe sonication for \(1\mathrm{h}\) (3 seconds on and 3 seconds off) at the power of \(290\mathrm{W}\) . Then the ethanol was replaced with Milli- Q water to continue sonication for \(1\mathrm{h}\) . The solution at the end of sonication was collected and centrifuged at \(1000\mathrm{rpm}\) for \(5\mathrm{min}\) , and the upper liquid layer was aspirated and set aside.  
+
+<|ref|>sub_title<|/ref|><|det|>[[146, 800, 382, 818]]<|/det|>
+## Synthesis of GaIn@Pt NPs  
+
+<|ref|>text<|/ref|><|det|>[[144, 831, 852, 881]]<|/det|>
+1 mL \(\mathrm{Na_2PtCl_6}\) ( \(0.1\mathrm{M}\) ) was added dropwise to GaIn NPs and the solution was stirred for \(4\mathrm{h}\) . After reaction, the solution was collected and centrifuged at \(9000\mathrm{rpm}\) for 10
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 82, 852, 202]]<|/det|>
+1 min, washed 3 times with Milli- Q water and dispersed in \(6\mathrm{mL}\) Milli- Q water. The above solution was stirred with \(60\mathrm{mg}\) mPEG- SH \(_{5000}\) for \(12\mathrm{h}\) . After the reaction, the solution was collected and centrifuged. The solids at the bottom were washed with Milli- Q water for 3 times and finally dispersed in \(6\mathrm{mL}\) PBS.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 224, 612, 243]]<|/det|>
+## Calculation of the photothermal conversion efficiency  
+
+<|ref|>text<|/ref|><|det|>[[147, 255, 852, 341]]<|/det|>
+The photothermal conversion of the PtNP- shell has been calculated on the basis of previous work \(^{22,23}\) . The relationship between temperature rise and energy transfer in the system can be described by the Equation S1,  
+
+<|ref|>equation<|/ref|><|det|>[[247, 353, 747, 383]]<|/det|>
+\[\Sigma_{i}m_{i}c_{i}\frac{dT}{dt} = Q_{abs} - Q_{ext} = Q_{NPS} + Q_{solvent} - Q_{ext} \quad (S1)\]  
+
+<|ref|>text<|/ref|><|det|>[[145, 394, 852, 580]]<|/det|>
+where \(Q_{abs}\) is the total energy absorbed by the system, \(Q_{NPS}\) is the energy absorbed by the nanoparticles, \(Q_{solvent}\) is the energy absorbed by the solvent, \(Q_{ext}\) is the energy loss from the system to the environment. \(m_{i}\) and \(c_{i}\) are the mass and specific heat capacity of the solution, respectively. \(T\) is the solution temperature and \(t\) is the irradiation time. The conversion of the light energy into heat energy can be expressed in terms of Equation S2,  
+
+<|ref|>equation<|/ref|><|det|>[[372, 594, 625, 615]]<|/det|>
+\[Q_{NPS} = I(1 - 10^{-A})\eta \quad (S2)\]  
+
+<|ref|>text<|/ref|><|det|>[[145, 628, 852, 714]]<|/det|>
+where \(I\) is the laser power, \(A\) is the absorbance value of PtNP- shell at \(1064\mathrm{nm}\) , \(\eta\) is the photothermal conversion efficiency. \(Q_{solvent}\) can be calculated by the following Equation S3,  
+
+<|ref|>equation<|/ref|><|det|>[[333, 728, 663, 749]]<|/det|>
+\[Q_{solvent} = hs(T_{solvent} - T_{surr}) \quad (S3)\]  
+
+<|ref|>text<|/ref|><|det|>[[145, 762, 852, 848]]<|/det|>
+where \(h\) is the convective heat transfer coefficient and \(s\) is the surface area of the sample cell. \(T_{solvent}\) is the maximum temperature that the solvent can reach under laser irradiation. \(T_{surr}\) is the ambient temperature. \(Q_{ext}\) can also be written as,  
+
+<|ref|>equation<|/ref|><|det|>[[380, 862, 617, 882]]<|/det|>
+\[Q_{ext} = hs(T - T_{surr}) \quad S4\]  
+
+<|ref|>text<|/ref|><|det|>[[186, 896, 850, 915]]<|/det|>
+The heat output will increase with the increase in temperature when the NIR- II
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[102, 82, 852, 168]]<|/det|>
+laser power is determined according to formula S4. The temperature of the system will reach the maximum when the heat input is equal to the heat output, so the following equation can be obtained,  
+
+<|ref|>equation<|/ref|><|det|>[[265, 179, 730, 201]]<|/det|>
+\[Q_{NPs} + Q_{solvent} = Q_{ext - max} = hs(T_{max} - T_{surr}) \quad \mathrm{S5}\]  
+
+<|ref|>text<|/ref|><|det|>[[144, 214, 850, 303]]<|/det|>
+where \(Q_{ext - max}\) is the heat transferred from the system surface through the air when the sample cell reaches equilibrium temperature, and \(T_{max}\) is the equilibrium temperature. Combining equations S2, S3 and S5, \(\eta\) can be expressed as,  
+
+<|ref|>equation<|/ref|><|det|>[[249, 312, 745, 346]]<|/det|>
+\[\eta = \frac{hs(T_{max} - T_{surr}) - hs(T_{solvent} - T_{surr})}{l(1 - 10^{-A})} = \frac{hs(T_{max} - T_{solvent})}{l(1 - 10^{-A})} \quad \mathrm{S6}\]  
+
+<|ref|>text<|/ref|><|det|>[[144, 360, 850, 411]]<|/det|>
+where \(A\) is the PtNP- shell absorption at \(1064\mathrm{nm}\) . To obtain \(hs\) , the dimensionless temperature \(\theta\) is introduced,  
+
+<|ref|>equation<|/ref|><|det|>[[410, 424, 586, 456]]<|/det|>
+\[\theta = \frac{T - T_{surr}}{T_{max} - T_{surr}} \quad \mathrm{S7}\]  
+
+<|ref|>text<|/ref|><|det|>[[100, 470, 480, 489]]<|/det|>
+and a time constant of sample system, \(\tau_{s}\)  
+
+<|ref|>equation<|/ref|><|det|>[[424, 500, 573, 530]]<|/det|>
+\[\tau_{s} = \frac{\sum_{i}m_{i}c_{i}}{hs} \quad \mathrm{S8}\]  
+
+<|ref|>text<|/ref|><|det|>[[185, 543, 846, 564]]<|/det|>
+Combining Equations S1, S4, S7 and S8, the following equation can be obtained,  
+
+<|ref|>equation<|/ref|><|det|>[[357, 575, 637, 610]]<|/det|>
+\[\frac{d\theta}{dt} = \frac{1}{\tau_{s}}\left[\frac{Q_{NPs} + Q_{solvent}}{hs(T_{max} - T_{surr})} -\theta \right] \quad \mathrm{S9}\]  
+
+<|ref|>text<|/ref|><|det|>[[100, 620, 848, 672]]<|/det|>
+After the laser is turned off, in the cooling stage, there is no external input energy, \(Q_{NPs} + Q_{solvent} = 0\) , and equation S9 can be written as,  
+
+<|ref|>equation<|/ref|><|det|>[[413, 684, 583, 716]]<|/det|>
+\[dt = -\tau_{s}\frac{d\theta}{\theta} \quad \mathrm{S10}\]  
+
+<|ref|>text<|/ref|><|det|>[[144, 728, 710, 748]]<|/det|>
+By integrating Equation S10, the following equation can be obtained,  
+
+<|ref|>equation<|/ref|><|det|>[[415, 760, 579, 780]]<|/det|>
+\[t = -\tau_{s}ln\theta \quad \mathrm{S11}\]  
+
+<|ref|>text<|/ref|><|det|>[[144, 794, 850, 916]]<|/det|>
+Therefore, the system heat transfer time constant \((\tau_{s})\) at \(1064\mathrm{nm}\) is \(242.25\mathrm{s}\) (Figure 3f). In addition, m is \(0.3\mathrm{g}\) and c is \(4.2\mathrm{J}\cdot \mathrm{g}^{- 1}\) . Therefore, \(hs\) can be determined from Equation S8. The laser power \((I)\) used here can be determined as 1 W. Then the photothermal conversion efficiency \((\eta)\) of the PtNP- shell at \(1064\mathrm{nm}\) can be calculated
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 84, 544, 102]]<|/det|>
+to be \(73.7\%\) by substituting \(hs\) into Equation S6.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 127, 461, 144]]<|/det|>
+## Animal preparation and cell culture  
+
+<|ref|>text<|/ref|><|det|>[[144, 157, 852, 475]]<|/det|>
+All animal experiments were approved by the Animal Care and Use Committee of Renmin Hospital of Wuhan University (WDRM20230805A). All experimental procedures were in accordance with the Declaration of Helsinki and were conducted according to the guidelines established by the National Institutes of Health. All Beagles \((8 - 12\mathrm{kg})\) were anesthetized intravenously with \(3\%\) sodium pentobarbital \((30\mathrm{mg}\cdot \mathrm{kg}^{- 1}\) induction dose, \(2\mathrm{mg}\cdot \mathrm{kg}^{- 1}\) maintenance dose per hour) and respiration was maintained by endotracheal intubation using a ventilator. Arterial blood pressure was continuously monitored through femoral artery catheterization with a pressure transducer attached. ECG and blood pressure data were recorded throughout the procedure. A heating pad was used to maintain core body temperature at \(36.5\pm 0.5^{\circ}\mathrm{C}\)  
+
+<|ref|>text<|/ref|><|det|>[[144, 487, 850, 537]]<|/det|>
+The cells were cultured in a humid incubator containing \(5\% \mathrm{CO}_2\) at a temperature of \(37.0^{\circ}\mathrm{C}\)  
+
+<|ref|>sub_title<|/ref|><|det|>[[144, 561, 693, 579]]<|/det|>
+## Detection of TRPV1 and TREK1 expression in vitro and in vivo  
+
+<|ref|>text<|/ref|><|det|>[[144, 592, 852, 842]]<|/det|>
+Western blotting was used to assess the expression of TRPV1 and TREK1 in neuronal cells and ganglion tissues. HT- 22 cells or HEK- 293T cells were cultured in six- well plates for \(24 - 48\mathrm{h}\) , then lysed and centrifuged to collect cells. Ganglion tissues were obtained from deceased animals and frozen in liquid nitrogen or stored at \(- 80.0^{\circ}\mathrm{C}\) . Total protein was determined using BCA protein assay reagent after tissue grinded and cells lysed. Afterwards, the procedure was followed according to the manufacturer's instructions. Primary antibodies were anti- TRPV1 and anti- TREK1. Expression levels of specific proteins were normalized to GAPDH.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 867, 444, 884]]<|/det|>
+## Calcium imaging of neuronal cells
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 81, 853, 595]]<|/det|>
+The effect of PtNP- shell photothermal modulation on ion channels in HT- 22 cells was explored through calcium imaging experiments. HT- 22 cells were incubated in \(35\mathrm{mm}\) confocal dishes for \(24\mathrm{h}\) . Cells were washed 3 times with PBS and then stained with 5 \(\mu \mathrm{M}\) Fluo- 4 AM (dilution ratio 1:500) for \(30\mathrm{min}\) in a cell incubator at \(37.0^{\circ}\mathrm{C}\) , protected from light. To induce activation of TRPV1 and TREK1 ion channels, which had been previously studied \(^{7,8}\) , the culture dish was exposed to NIR- II light ( \(1064\mathrm{nm}\) ), resulting in an elevation of temperature. TRPV1, being a calcium channel, exhibited observable changes in the flow of calcium ions upon activation, while TREK1 as a potassium channel did not display such behavior. Therefore, the effect of PtNP- shell photothermal modulation on neuronal cells via TREK1 was observed by introducing a \(15\mathrm{mM}\) KCl solution prior to NIR- II irradiation. Fluorescence signals at \(525\mathrm{nm}\) were recorded using a confocal microscope with \(488\mathrm{nm}\) as the excitation wavelength. XYT images were acquired and collected under a \(20\mathrm{x}\) objective lens. The average fluorescence intensity of the cells was analyzed using ImageJ software (Fiji). The normalized fluorescence change was calculated as follows: \(\Delta \mathrm{F} / \mathrm{F} = (\mathrm{F - F_0}) / \mathrm{F_0}\) , where F is the original fluorescence signal; \(\mathrm{F_0}\) is the average baseline intensity before irradiation with NIR- II laser.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 617, 369, 635]]<|/det|>
+## In vitro cytotoxicity assay  
+
+<|ref|>text<|/ref|><|det|>[[144, 648, 853, 900]]<|/det|>
+The cytotoxicity of PtNP- shell on neuronal cells was evaluated by CCK- 8 assay. HT- 22 cells were seeded in 96- well plates at a density of \(1 \times 10^{4}\) well \(^{- 1}\) and cultured for 24 h. HT- 22 cells were then treated with different concentrations (10, 25, 50, 100, 150, 200 \(\mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) of PtNP- shell for another 24 h. Cell viability was determined by CCK- 8 assay after incubating with the CCK- 8 reagent for 1 h. To investigate the impact of PtNP- shell's photothermal effect on neuron cell viability, HT- 22 cells were co- cultured with PtNP- shell ( \(50 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) for 12 h followed by irradiation with a \(1064\mathrm{nm}\) laser (0.5 and \(0.75\mathrm{W} \cdot \mathrm{cm}^{- 2}\) ) for various durations (10 s, 30 s and 60 s). After incubation again for 12
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 83, 850, 135]]<|/det|>
+h, the absorbance at \(450 \mathrm{nm}\) was recorded using a microplate reader. Cell survival (\%) \(= (OD_{\text{samples}} - OD_{\text{blank}}) / (OD_{\text{control}} - OD_{\text{blank}}) \times 100\%\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 158, 849, 210]]<|/det|>
+## Experimental protocol 1: Activation of the parasympathetic nervous system through PtNP-shell photothermal reduces I/R injury  
+
+<|ref|>text<|/ref|><|det|>[[144, 222, 852, 440]]<|/det|>
+Part 1: Exploring the in vivo effects of precise photothermal stimulation of the parasympathetic nervous system by PtNP- shell under NIR- II irradiation. Twelve beagles were randomly assigned to the control group ( \(100 \mu \mathrm{L}\) phosphate- buffered saline (PBS) was microinjected into the NG, \(\mathrm{n} = 6\) ) and the PtNP- shell group ( \(100 \mu \mathrm{L}\) PtNP- shell ( \(50 \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) was microinjected into the NG, \(\mathrm{n} = 6\) ). NG nerve activity, heart rate (HR) and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR- II irradiation (Fig 4b).  
+
+<|ref|>text<|/ref|><|det|>[[144, 453, 852, 635]]<|/det|>
+Part 2: The protective effect of PtNP- shell activation of the parasympathetic nervous system against myocardial I/R injury was investigated. The same grouping pattern as in part1 was used, with 5- min NIR- II irradiation of the NG before opening the occluded LAD coronary vessel. Afterwards, ventricular electrophysiological parameters, heart rate variability (HRV) and ECG data were recorded and analyzed (Fig 5b).  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 659, 849, 709]]<|/det|>
+## Experimental protocol 2: PtNP-shell photothermal inhibition of sympathetic nervous system improves MI  
+
+<|ref|>text<|/ref|><|det|>[[144, 722, 852, 907]]<|/det|>
+Part 1: The in vivo effects of precise photothermal stimulation of the sympathetic nervous system by PtNP- shell under NIR- II irradiation were explored. Twelve beagles were randomly assigned to the control group ( \(100 \mu \mathrm{L}\) PBS microinjected into the LSG, \(\mathrm{n} = 6\) ) and the PtNP- shell group ( \(100 \mu \mathrm{L}\) PtNP- shell ( \(50 \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) microinjected into the LSG, \(\mathrm{n} = 6\) ). LSG nerve activity, SBP and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR- II
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 83, 310, 101]]<|/det|>
+irradiation (Fig 6b).  
+
+<|ref|>text<|/ref|><|det|>[[144, 115, 852, 268]]<|/det|>
+Part 2: To investigate the protective effect of PtNP- shell inhibition of the sympathetic nervous system a improves MI. The same grouping pattern as in part1 was used, with 5- min NIR- II irradiation of the LSG before ligation of LAD vessels. Finally, ventricular electrophysiological parameters, HRV and ECG data were also recorded and analyzed (Fig 7b).  
+
+<|ref|>sub_title<|/ref|><|det|>[[144, 290, 815, 309]]<|/det|>
+## PtNP-shell photothermal stimulation of the autonomic nervous system in vivo  
+
+<|ref|>text<|/ref|><|det|>[[144, 319, 852, 835]]<|/det|>
+We selected NG and LSG as targets for modulation in the autonomic nervous system to explore the multifunctionality of the PtNP- shell photothermal strategy. A "C" incision is made behind the left ear, and the angle between the occlusal and trapezius muscles served as the access approach<sup>24</sup>. The tissue is bluntly separated to expose the carotid sheath and identify the parasympathetic nerve. Moving upstream along the nerve, a distal expansion is observed as NG (Fig 4a). LSG can be visualized and localized by left- sided thoracotomy according to the method of a previous study (Fig 6a)<sup>25</sup>. PtNP- shell (50 \(\mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) ) or PBS was slowly injected into 2 sites within the NG and LSG tissues to achieve homogeneous photothermal conversion. Initial vertical irradiation of NIR- II laser (1064 nm) at 0.80 W·cm<sup>- 2</sup> was performed on NG and LSG surfaces. The power density of the NIR- II laser was reduced to 0.45 W·cm<sup>- 2</sup> for continuous irradiation when the temperature of the NG reached 42.0 °C, and was reduced to 0.6 W·cm<sup>- 2</sup> for continuous irradiation when the temperature of the LSG reached 46.0 °C. The NIR- II laser irradiation remains stable with a spot size maintained at 1.0 cm<sup>- 2</sup>. Dual temperature monitoring using thermal imager and T- type thermocouple was performed to plot the temperature- time curve.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 857, 522, 874]]<|/det|>
+## Functional assessment of autonomic nerves  
+
+<|ref|>text<|/ref|><|det|>[[144, 889, 848, 908]]<|/det|>
+The NG is a ganglion located upstream of the cervical parasympathetic nerve and can
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 81, 853, 530]]<|/det|>
+significantly inhibit HR after receiving direct electrical stimulation<sup>18</sup>. The LSG, as an important peripheral sympathetic ganglion, can rapidly elevate blood pressure when activated by electrical stimulation. Based on the functional properties of different autonomic ganglia, we assessed the function of NG and LSG with reference to previous studies<sup>19</sup>. A pair of special electrodes made with silver wires were directly connected to the surfaces of NG and LSG for stimulation. High- frequency electrical stimulation (HFS: 20 Hz, 0.1 ms) was applied to the ganglion. The voltage was set to 5 levels in continuous increments (level 1: 0–2 V; level 2: 2–4 V; level 3: 4–6 V; level 4: 6–8 V; level 5: 8–10 V), while keeping the stimulation voltage values consistent with the baseline at different time points during the experiment. The percentage of sinus rate or AV conduction (measured by the A-H interval) slowing down constructed voltage level/degree of HR decrease curves reflecting NG function. On the other hand, the percentage increase in SBP built the voltage level/degree of SBP increase to reflect LSG function.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 553, 460, 570]]<|/det|>
+## Activity testing of autonomic nerves  
+
+<|ref|>text<|/ref|><|det|>[[144, 583, 852, 800]]<|/det|>
+The activity of different autonomic nerves was assessed based on previous studies<sup>19</sup>. Two specially designed microelectrodes were inserted into the NG and LSG, respectively, while a grounding wire was connected to obtain signals from the autonomic nerves. These electrical signals were recorded by a Power Lab data acquisition system, filtered through a band- pass filter (300–1000 Hz) and amplified 30- 50 times by an amplifier. Finally, the signals were digitized and analyzed in LabChart software (version 8.0, AD Instruments).  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 823, 666, 842]]<|/det|>
+## Construction of myocardial I/R injury model and MI model  
+
+<|ref|>text<|/ref|><|det|>[[147, 855, 850, 907]]<|/det|>
+The left anterior descending coronary occlusion (LADO) method was used to establish the MI model<sup>19</sup>. The ligation site was located beneath the first diagonal of the LAD, and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 83, 851, 202]]<|/det|>
+successful MI model was confirmed by observing ST- segment elevation on the ECG. After ensuring cardiac electrophysiological stabilization, the junction was released to reperfuse the occluded coronary arteries, completing the construction of the myocardial I/R injury model<sup>26</sup>.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 225, 538, 243]]<|/det|>
+## Ventricular electrophysiological study in vivo  
+
+<|ref|>text<|/ref|><|det|>[[144, 254, 852, 770]]<|/det|>
+The cardiac electrophysiological measurements were performed in Beagles using a previously studied protocol<sup>27,28</sup>. The ERP was measured at three locations: LVA, LVB, LVM (located between the LVA and LVB). Malignant arrhythmic events caused by MI and I/R injury were assessed by electrocardiographic recordings in a canine model using Lead 7000 Computerized Laboratory System. VAs was classified according to Lambeth Conventions as VPBs, VT (three and more consecutive VPBs) and \(\mathrm{VF}^{29}\) . In addition, arrhythmia inducibility was further assessed by programmed ventricular stimulation at the right ventricular apex (RVA). Eight consecutive stimuli (S1S1) were performed at intervals of 330 ms, followed by additional stimuli until VT/VF occurred. Arrhythmia inducibility was assessed based on a modified arrhythmia scoring system<sup>28</sup>. If VF occurs during the evaluation, a defibrillator is required to restore sinus rhythm, followed by a waiting period of 30 min to restore cardiac electrophysiological stability. The VF threshold was assessed in the perimyocardial infarction region. Pacing was initiated using a Grass stimulator with a voltage of 2 V (20 Hz, 0.1 ms duration, 10 s). The stimulation voltage was increased in 2 V increments until VF was induced. The lowest voltage that induced VF was regarded as the VF threshold<sup>30</sup>.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 790, 268, 807]]<|/det|>
+## HRV analysis  
+
+<|ref|>text<|/ref|><|det|>[[147, 821, 850, 909]]<|/det|>
+The ECG data was recorded using the PowerLab data acquisition system. And the ECG segments recorded more than 5 min before modulation and after MI or I/R injury were analyzed by LabChart software with the Lomb- Scargle periodogram algorithm<sup>31</sup>.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[150, 83, 853, 168]]<|/det|>
+Frequency domain metrics of HRV were calculated, including LF (0.04–0.15 Hz, reflecting sympathetic tone), HF (0.15–0.4 Hz, reflecting parasympathetic tone) and LF/HF (reflecting autonomic balance). The results were expressed in standardized units.  
+
+<|ref|>sub_title<|/ref|><|det|>[[150, 192, 650, 210]]<|/det|>
+## Immunofluorescence staining of histopathological sections  
+
+<|ref|>text<|/ref|><|det|>[[144, 223, 852, 440]]<|/det|>
+The ganglions were rapidly dissected for histopathological staining after the experimental animals died. Tissues were fixed with \(4\%\) paraformaldehyde, embedded in paraffin, and cut into \(5\mu \mathrm{m}\) - thick sections. NG was stained with multiple immunofluorescence staining using anti- NF1, anti- c- fos and anti- TRPV1 antibodies. And LSG was stained by multiple immunofluorescences using anti- TH, anti- c- fos and anti- TREK1 antibody. Cell nuclei were stained with DAPI. Images were taken at \(100\times\) magnification and analyzed using ImageJ software (Fiji).  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 463, 552, 481]]<|/det|>
+## Enzyme-linked immunosorbent assay (ELISA)  
+
+<|ref|>text<|/ref|><|det|>[[144, 494, 852, 711]]<|/det|>
+\(5\mathrm{ml}\) of venous blood was obtained from the jugular vein of each beagle after MI and myocardial I/R injury. After standing for 1 hour, the blood was centrifuged at \(3000\mathrm{rpm}\) for \(15\mathrm{min}\) . The upper serum layer was collected and stored at \(- 80.0^{\circ}\mathrm{C}\) . Myocardial injury levels were detected by c- TnI and myoglobin (MYO). Standard process analyses were performed according to the instructions of each ELISA kit. To evaluate the long- term biosafety and biocompatibility of PtNP- shell in vivo, Beagle dogs and rats were randomly divided into PtNP- shell and PBS groups.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 735, 437, 752]]<|/det|>
+## Long-term biosafety assay in vivo  
+
+<|ref|>text<|/ref|><|det|>[[144, 765, 852, 885]]<|/det|>
+To evaluate the long- term biosafety and biocompatibility of PtNP- shell in vivo, Beagle dogs and rats were randomly divided into two groups: a PtNP- shell group and a PBS group. In the PtNP- shell group, \(200\mu \mathrm{L}\) PtNP- shell ( \(50\mu \mathrm{g}\cdot \mathrm{mL}^{- 1}\) ) was microinjected into canine ganglion tissue and tail vein of rats to explore long- term biosafety. Blood
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 83, 852, 234]]<|/det|>
+1 and tissue samples were collected from each dog and rat one month after injection. One 2 month after injection, blood samples were collected from the jugular vein of dogs as 3 well as from the inferior vena cava of rats for analysis of serum biochemical indices. 4 Tissue H&E staining was also performed on major organs, including heart, liver, spleen, 5 lung and kidney.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 258, 310, 275]]<|/det|>
+## Statistical analysis  
+
+<|ref|>text<|/ref|><|det|>[[144, 289, 852, 473]]<|/det|>
+7 All graphical data are presented as mean \(\pm\) standard error of the mean (SEM), and the 8 distribution of data was assessed by the Shapiro- Wilk test. Differences between groups 9 were determined using Student's t- test or Mann- Whitney U- test. Data were analyzed 10 and plotted using GraphPad Prism 9.0 software (GraphPad software, Inc., La Jolla, CA, 11 USA). \(\mathrm{P}< 0.05\) was considered statistically different. The p- values are indicated with 12 an asterisk \((*\mathrm{p}< 0.05,^{**} \mathrm{p}< 0.01,^{***} \mathrm{p}< 0.001)\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 496, 328, 514]]<|/det|>
+## Reporting Summary  
+
+<|ref|>text<|/ref|><|det|>[[144, 528, 850, 579]]<|/det|>
+14 Further information on research design is available in the Nature Portfolio Reporting 15 Summary linked to this article.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 603, 293, 620]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[144, 634, 852, 753]]<|/det|>
+17 The main data supporting the results in this study are available within the paper and its 18 Supplementary Information. The raw and analyzed datasets generated during the study 19 are too large to be publicly shared, yet they are available for research purposes from the 20 corresponding authors on reasonable request. Source data are provided with this paper.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[108, 84, 245, 101]]<|/det|>
+## 1 References  
+
+<|ref|>text<|/ref|><|det|>[[100, 115, 853, 576]]<|/det|>
+2 Chechetka, S. A. et al. Light- driven liquid metal nanotransformers for biomedical theranostics. Nat. Commun. 8, 15432 (2017).  3 Zhu, P. et al. Inorganic nanoshell- stabilized liquid metal for targeted photonanomedicine in NIR- II biowindow. Nano Lett. 19, 2128- 2137 (2019).  4 Bruneau, M. & George, B. The juxtacondylar approach to the jugular foramen. Oper. Neurosurg. 63, 75- 80 (2008).  5 Zhang, S. et al. Ultrasound- guided injection of botulinum toxin type A blocks cardiac sympathetic ganglion to improve cardiac remodeling in a large animal model of chronic myocardial infarction. Heart Rhythm 19, 2095- 2104 (2022).  6 Chen, M. X. et al. Low- level vagus nerve stimulation attenuates myocardial ischemic reperfusion injury by antioxidative stress and antiapoptosis reactions in canines. J. Cardiovasc. Electrophysiol. 27, 224- 231 (2016).  7 Yu, L. L. et al. Optogenetic modulation of cardiac sympathetic nerve activity to prevent ventricular arrhythmias. J. Am. Coll. Cardiol. 70, 2778- 2790 (2017).  8 Yu, L. et al. Chronic intermittent low- level stimulation of tragus reduces cardiac autonomic remodeling and ventricular arrhythmia inducibility in a post- infarction canine model. JACC Clin. Electrophysiol. 2, 330- 339 (2016).  9 Walker, M. J. A. et al. The lambeth conventions: guidelines for the study of arrhythmias in ischaemia, infarction, and reperfusion. Cardiovasc. Res. 22, 447- 455 (1988).  10 Dalonzo, A. J. et al. Effects of cromakalim or pinacidil on pacing- and ischemia- induced ventricular fibrillation in the anesthetized pig. Basic Res. Cardiol. 89, 163- 176 (1994).  11 Lai, Y. et al. Non- invasive transcutaneous vagal nerve stimulation improves myocardial performance in doxorubicin- induced cardiotoxicity. Cardiovasc. Res. 118, 1821- 1834 (2022).  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 590, 317, 606]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[144, 621, 853, 840]]<|/det|>
+The research was supported by the National Natural Science Foundation of China (grants 22025303, 82241057, 82270532 and 82200556); and the National Key Research and Development Program of China (grant 2023YFC2705705); and Foundation for Innovative Research Groups of Natural Science Foundation of Hubei Province, China (grant 2021CFA010). We thank the Core Facility of Wuhan University for their substantial supports in sample characterization, including SEM, XPS, DLS and XRD. We thank the Center for Electron Microscopy at Wuhan University for their support of STEM, HRTEM and EDX characterization. We also thank Meimei Zhang in the institute for advanced studies of Wuhan University for their assistance in TEM characterization.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 852, 333, 869]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[144, 883, 848, 902]]<|/det|>
+L.F., L.L.Y. and X.Y.Z. conceived the research concept. L.F., L.L.Y. and X.Y.Z.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 82, 852, 202]]<|/det|>
+1 supervised the research; C.L.W., L.P.Z., C.Z.L., J.M.Q., X.R.H., B.X., Q.F.Q., Z.Z.Z.2 and J.L.W. performed the experiments; C.L.W., L.P.Z., C.Z.L., L.Y.W. and Y.X.L.3 discussed the results; C.L.W., L.P.Z. and C.Z.L. analysed the data and cowrote the4 manuscript. All authors commented on the manuscript.  
+
+<|ref|>text<|/ref|><|det|>[[108, 234, 503, 283]]<|/det|>
+5 Competing interests6 The authors declare no competing interests.  
+
+<|ref|>text<|/ref|><|det|>[[108, 316, 852, 536]]<|/det|>
+7 Additional information8 Supplementary information The online version contains supplementary material9 available at10 Correspondence and requests for materials should be addressed to Xiaoya Zhou,11 Lilei Yu or Lei Fu12 Peer review information13 Reprints and permissions information is available at
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 92, 768, 112]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 365, 149]]<|/det|>
+- supplementaryinformation.docx
+
+<--- Page Split --->

preprint/preprint__0129baf8281eddc2ad657d6e8fa589609bc12adf1490795c312275d391cb9313/images_list.json

@@ -0,0 +1,92 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Fabrication of surface engineered mPOC/HA implants. a. Illustration shows the combination of UV lithography and contact printing to fabricate free-standing mPOC/HA micropillars. b. SEM image shows the micropillar structures made of mPOC/HA. c. Optical microscope image and d. cross-section analysis of mPOC/HA micropillars. e. Surface scanning of flat and micropillar implants by AFM. f. Surface roughness of flat and micropillar implants. N.S., no significant difference, \\(\\mathrm{n} = 3\\) biological replicates. g. Degradation test and h. calcium release of flat and micropillar mPOC/HA implants. N.S., no significant difference, \\(\\mathrm{n} = 4\\) biological replicates, insert plot shows the initial release of calcium within \\(24\\mathrm{h}\\) . i. Representative images of flat and micropillar implants at different time points after accelerated degradation.",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        95,
+        876,
+        599
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Nuclear deformation promotes osteogenic differentiation of hMSCs. a. Staining of nucleus (green) and F-actin (red) of hMSCs on flat and micropillar mPOC/HA surfaces. Insert: high magnification of cell nucleus. Dashed lines indicate micropillars. b. Analysis of nuclear shape index of hMSCs. \\(\\mathrm{n} = 117\\) (flat) and 132 (pillar) collected from 3 biological replicates, \\(\\mathrm{***p< 0.0001}\\) . c. Orthogonal view of cell nucleus on flat and micropillar surfaces. d. Nuclear volume analysis based on 3D construction of the confocal images of cell nuclei. \\(\\mathrm{n} = 35\\) cells collected from 3 biological replicates, \\(\\mathrm{***p< 0.0001}\\) . e. Initial cell attachment on flat and micropillar surfaces. \\(\\mathrm{n} = 5\\) biological replicates, N.S., no significant difference. f. SEM images show the cell attachment on flat and micropillar mPOC/HA surfaces. g. Live/dead staining of hMSCs on flat and micropillar surfaces at 72 h in osteogenic medium. h. Cell metabolic activity of cells on flat and micropillar surfaces tested by a MTT assay. \\(\\mathrm{n} = 5\\) biological replicates, \\(\\mathrm{***p< 0.0001}\\) . i. Cell proliferation tested via DNA content after 72 h induction. \\(\\mathrm{n} = 5\\) biological replicates, N.S., no significant difference. j. ALP staining of hMSCs on flat and micropillar surfaces after 7 d induction. k. ALP activity test of cells after 7 d osteogenic induction. \\(\\mathrm{n} = 3\\) biological replicates. l. Blot images of osteogenic marker OCN and RUNX2 in cells cultured on flat and micropillar implants. GAPDH is shown as a control. Quantification m. OCN and n. RUNX2 according to western blot tests. \\(\\mathrm{n} = 3\\) biological replicates, \\(\\mathrm{***p< 0.0001}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
+        93,
+        880,
+        456
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Secretome of hMSCs on flat and micropillar mPOC/HA surfaces. a. PCA plot of differentially expressed proteins secreted by hMSCs on flat and micropillars. Cyan: flat; Red: micropillar. b. Volcano plot of proteins secreted by hMSCs seeded on micropillars compared to the flat surface. Blue dots and orange dots indicate significantly downregulated and upregulated proteins secreted by cells on micropillars compared to those on flat surface. Grey dots indicate",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        90,
+        884,
+        799
+      ]
+    ],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. The paracrine effect of cells with/without nuclear deformation tested through transwell assay. a. Schematic illustration of the experiment setup. b. ALP staining and c. quantification of ALP positive cells on transwell membrane incubated with undeformed and deformed MSCs \\((n = 3)\\) . d. ARS staining and e. quantification of cells on transwell membrane incubated with undeformed and deformed MSCs \\((n = 6)\\) . f. Immunofluorescence staining images of collagen in ECM of cells on transwell membrane incubated with undeformed and deformed MSCs. g. The coverage of collagen analyzed according to the staining images \\((n = 4)\\) . h. EDS images showing Ca, P, and SEM images of cells on transwell membrane incubated with undeformed and deformed MSCs.",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        123,
+        870,
+        506
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. mPOC/HA micropillar implant promotes bone regeneration in vivo. a. Image shows implantation of hMSC seeded flat and micropillar mPOC/HA scaffolds. b. Staining images of nuclei (green) and F-actin (red) of cells on the implants. c. Representative \\(\\mu \\mathrm{CT}\\) images of a typical animal implanted with hMSC-seeded flat (left) and micropillar (right) scaffolds at 12-weeks post-surgery. d. Regenerated bone volume in the defect region ( \\(\\mathrm{n} = 5\\) animals). e. Trichrome staining of the defect tissue treated with flat and micropillar implants. f. Average thickness of regenerated tissues with implantation of flat and micropillar scaffolds ( \\(\\mathrm{n} = 5\\) animals). IHC staining of osteogenic marker, g. OPN and h. OCN, in regenerated tissues with flat and micropillar implants.",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        95,
+        875,
+        620
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. Spatial transcriptomic analysis of tissues regenerated with flat and micropillar implants. a. Spatial plot of Colla2 expression profile in tissues regenerated with flat mPOC/HA implant and micropillar mPOC/HA implant. Arrow indicates enhanced expression around dura layer. b. The heatmap showing the top ten up- and down-regulated DEGs (pillar vs flat) in tissues regenerated with flat mPOC/HA implant, micropillar mPOC/HA implant, and native skull tissue. c. Gene Ontology analysis results based on the top 100 up-regulated genes (pillar vs flat). d. Deconvoluted cell types in each spatial capture location in flat and micropillar groups. Each pie chart shows the deconvoluted cell type proportions of the capture location. e. Bar plots of the cell type proportions in tissues regenerated with flat mPOC/HA implant and micropillar mPOC/HA implant. LMPs, MSCs, and fibroblasts are the predominant cell types. f. Violin plot of the proportion of LMPs in flat and micropillar groups. g. Top enriched processes associated with LMP compared with other cell lineages. LMP: late mesenchymal progenitor cells; MSC: mesenchymal stromal cells; OLC: MSC-descendant osteolineage cells",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        90,
+        877,
+        560
+      ]
+    ],
+    "page_idx": 16
+  }
+]

preprint/preprint__0129baf8281eddc2ad657d6e8fa589609bc12adf1490795c312275d391cb9313/preprint__0129baf8281eddc2ad657d6e8fa589609bc12adf1490795c312275d391cb9313_det.mmd

@@ -0,0 +1,383 @@
+<|ref|>title<|/ref|><|det|>[[44, 107, 796, 208]]<|/det|>
+# Micropillar-induced changes in cell nucleus morphology enhance bone regeneration by modulating the secretome  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 323, 277]]<|/det|>
+Guillermo Ameer  g- ameer@northwestern.edu  
+
+<|ref|>text<|/ref|><|det|>[[42, 300, 630, 950]]<|/det|>
+Northwestern University https://orcid.org/0000- 0001- 6023- 048X  Xinlong Wang  Northwestern University https://orcid.org/0000- 0001- 8978- 2851  Yiming Li  Northwestern University https://orcid.org/0000- 0003- 2111- 3939  Zitong Lin  Northwestern University  Indira Pla  Northwestern University  Raju Gajjela  Northwestern University  Basil Mattamana  Northwestern University  Maya Joshi  Northwestern University https://orcid.org/0000- 0002- 6028- 475X  Yugang Liu  Northwestern University https://orcid.org/0000- 0001- 5304- 3459  Huifeng Wang  Northwestern University  Amy Zun  Northwestern University  Hao Wang  The University of Chicago  Ching Wai  Northwestern University  Vasundhara Agrawal  Northwestern University https://orcid.org/0000- 0003- 0913- 9298  Cody Dunton
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[50, 45, 269, 64]]<|/det|>
+Northwestern University  
+
+<|ref|>text<|/ref|><|det|>[[44, 70, 269, 110]]<|/det|>
+Chongwen Duan  Northwestern University  
+
+<|ref|>text<|/ref|><|det|>[[44, 116, 269, 156]]<|/det|>
+Bin Jiang  Northwestern University  
+
+<|ref|>text<|/ref|><|det|>[[44, 162, 627, 203]]<|/det|>
+Vadim Backman  Northwestern University  https://orcid.org/0000- 0003- 1981- 1818  
+
+<|ref|>text<|/ref|><|det|>[[44, 209, 417, 250]]<|/det|>
+Tong Chuan He  The University of Chicago Medical Center  
+
+<|ref|>text<|/ref|><|det|>[[44, 255, 648, 297]]<|/det|>
+Russell Reid  Section of Plastic Surgery, The University of Chicago Medical Centre  
+
+<|ref|>text<|/ref|><|det|>[[44, 302, 627, 343]]<|/det|>
+Yuan Luo  Northwestern University  https://orcid.org/0000- 0003- 0195- 7456  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 383, 103, 401]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 421, 137, 440]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 459, 319, 479]]<|/det|>
+Posted Date: January 7th, 2025  
+
+<|ref|>text<|/ref|><|det|>[[44, 498, 475, 517]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 5530535/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 535, 912, 578]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 596, 535, 616]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 652, 910, 695]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on July 11th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 60760-y.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 88, 883, 139]]<|/det|>
+## Microtopography-induced changes in cell nucleus morphology enhance bone regeneration by modulating the cellular secretome  
+
+<|ref|>text<|/ref|><|det|>[[115, 147, 883, 242]]<|/det|>
+Xinlong Wang \(^{1,2}\) , Yiming Li \(^{3}\) , Zitong Lin \(^{3}\) , Indira Pla \(^{4}\) , Raju Gajjela \(^{4}\) , Basil Baby Mattamana \(^{4}\) , Maya Joshi \(^{1}\) , Yugang Liu \(^{1,2}\) , Huifeng Wang \(^{1,2}\) , Amy B. Zun \(^{1}\) , Hao Wang \(^{5}\) , Ching- Man Wai \(^{6}\) , Vasundhara Agrawal \(^{2,7}\) , Cody L. Dunton \(^{2,7}\) , Chongwen Duan \(^{1,2}\) , Bin Jiang \(^{1,2,8}\) , Vadim Backman \(^{1,2,7,9}\) , Tong- Chuan He \(^{1,5}\) , Russell R. Reid \(^{1,10}\) , Yuan Luo \(^{3,11,12}\) , Guillermo A. Ameer \(^{1,2,7,8,11,13,14*}\)  
+
+<|ref|>text<|/ref|><|det|>[[112, 252, 888, 690]]<|/det|>
+\(^{1}\) Center for Advanced Regenerative Engineering, Northwestern University, Evanston, IL 60208, USA \(^{2}\) Department of Biomedical Engineering, Northwestern University, Evanston, IL 60208, USA \(^{3}\) Department of Preventive Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA \(^{4}\) Proteomics Center of Excellence, Northwestern University, Evanston, IL 60208, USA \(^{5}\) Molecular Oncology Laboratory, Department of Orthopedic Surgery and Rehabilitation Medicine, The University of Chicago Medical Center, Chicago, IL 60637, USA \(^{6}\) Center for Genetic Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA \(^{7}\) Center for Physical Genomics and Engineering, Northwestern University, Evanston, IL 60208, USA \(^{8}\) Department of Surgery, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA \(^{9}\) Chemistry of Life Process Institute, Northwestern University, Evanston, IL 60208, USA \(^{10}\) Laboratory of Craniofacial Biology and Development, Section of Plastic and Reconstructive Surgery, Department of Surgery, The University of Chicago Medical Center, Chicago, IL 60637, USA \(^{11}\) Northwestern University Clinical and Translational Sciences Institute, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA \(^{12}\) Center for Collaborative AI in Healthcare, Institute for AI in Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA \(^{13}\) International Institute for Nanotechnology, Northwestern University, Evanston, IL 60208, USA \(^{14}\) Simpson Querrey Institute for Bionanotechnology, Northwestern University, Chicago, IL 60611, USA
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[116, 91, 190, 107]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[115, 124, 882, 386]]<|/det|>
+Nuclear morphology, which modulates chromatin architecture, plays a critical role in regulating gene expression and cell functions. While most research has focused on the direct effects of nuclear morphology on cell fate, its impact on the cell secrete and surrounding cells remains largely unexplored, yet is especially crucial for cell- based therapies. In this study, we fabricated implants with a micropillar topography using methacrylated poly(octamethylene citrate)/hydroxyapatite (mPOC/HA) composites to investigate how micropillar- induced nuclear deformation influences cell paracrine signaling for osteogenesis and cranial bone regeneration. In vitro, cells with deformed nuclei showed enhanced secretion of proteins that support extracellular matrix (ECM) organization, which promoted osteogenic differentiation in neighboring human mesenchymal stromal cells (hMSCs). In a mouse model with critical- size cranial defects, nuclear- deformed hMSCs on micropillar mPOC/HA implants elevated Col1a2 expression, contributing to bone matrix formation, and drove cell differentiation toward osteogenic progenitor cells. These findings indicate that micropillars not only enhance the osteogenic differentiation of human mesenchymal stromal cells (hMSCs) but also modulate the secrete, thereby influencing the fate of surrounding cells through paracrine effects.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 404, 223, 420]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[115, 437, 882, 733]]<|/det|>
+The nucleus is a dynamic organelle that changes its morphology in response to the cell's status. Its morphology has critical influence on nuclear mechanics, chromatin organization, gene expression, cell functionality and disease development.2- 5 Abnormal nuclear morphologies, such as invagination and blebbing, have functional implications in several human disorders, including cancer, accelerated aging, thyroid disorders, and different types of neuro- muscular diseases.6,7 In addition, severe nuclear deformation is also observed during tissue development, cell migration, proliferation, and differentiation.2 Several structural components within the nucleus—including the nuclear envelope, lamins, nuclear actin, and chromatin—work together to determine its shape and structure.8 Although the underlying mechanisms are not yet fully understood, nuclear deformation has been found to affect cell behaviors through mechanotransduction processes.9 In addition, nuclear morphological changes have been reported to affect nuclear membrane tension and unfolding, which regulate the structure of the nuclear pore complex.10 This, in turn, influences the nuclear shuttling of transcription factors (e.g., YAP) and ions (e.g., Ca2+), ultimately impacting cell functions.11,12 In our previous study, we demonstrated that altering nuclear morphology using micropillar topography affects nuclear lamin A/C assembly, which, in turn, influences chromatin tethering, packing, and condensation.13 These changes affect transcriptional accessibility and responsiveness, thereby regulating gene expression and stem cell differentiation.  
+
+<|ref|>text<|/ref|><|det|>[[115, 750, 882, 891]]<|/det|>
+To manipulate nuclear morphology, various biophysical tools have been developed, including atomic force microscopy (AFM) nanoindentation, optical, magnetic, and acoustic tweezers, microfluidic devices, micropipette aspiration, plate compression, substrate deformation, and surface topography modulation.14- 21 Among these methods, regulating the surface topography of materials is more accessible and has broader implications for regenerative engineering. One commonly used approach is the fabrication of pillar structures, which are employed to deform cell nuclei and study nuclear properties such as mechanics and deformability.22 These micropillar designs have been utilized to manipulate various cell functions, including migration, adhesion,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 882, 195]]<|/det|>
+proliferation, and differentiation. \(^{23 - 26}\) A wide range of materials can be used to create these structures, such as poly- L- lactic acid (PLLA), poly(lactide- co- glycolide) (PLGA), OrmoComp (an organic- inorganic hybrid polymer), and methacrylated poly(octamethylene citrate) (mPOC). \(^{13,26 - 28}\) Among these options, mPOC is particularly suitable for bone regeneration due to its major component, citrate, which acts as a metabolic factor to enhance the osteogenesis of mesenchymal stromal cells (MSCs). \(^{29}\)  
+
+<|ref|>text<|/ref|><|det|>[[115, 211, 882, 578]]<|/det|>
+Although the influence of nuclear morphogenesis on the functions of individual cells is being intensively investigated, its role in regulating cellular secretion remains unclear. Bioactive molecules secreted by cells are crucial for intercellular communication, affecting various biological processes such as inflammation, cell survival, differentiation, and tissue regeneration. \(^{30,31}\) The success of many cell and exosome- based therapies relies on the cellular secretome. In this study, we fabricated micropillars to manipulate nuclear morphology and investigated their effects on the secretome of human mesenchymal stromal cells (hMSCs). We incorporated hydroxyapatite (HA), the primary inorganic component of native bone tissue, with micropatterned methacrylated poly(octamethylene citrate) (mPOC) to create the micropillars, promoting bone formation. Our results showed that mPOC/HA micropillars facilitated osteogenic differentiation of hMSCs compared to flat mPOC/HA samples in vitro. Secretome analysis revealed that hMSCs with deformed nuclei exhibited higher expression levels of bioactive factors associated with extracellular matrix (ECM) components and organization, as well as ossification. In vivo, both mPOC/HA flat and micropillar scaffolds seeded with hMSCs resulted in new bone formation; however, the micropillar group demonstrated significantly greater new bone volume and regenerated tissue thickness. Spatial transcriptomic analysis further confirmed elevated expression of genes related to the regulation of ECM structures, consistent with the secretome analysis results. These findings suggest that the influence of nuclear deformation on the osteogenesis of hMSCs operates through similar mechanisms in both in vitro and in vivo environments. Therefore, microtopography engineering of scaffold to control nuclear morphology is a promising approach to enhance bone regeneration.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 594, 179, 611]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 622, 880, 660]]<|/det|>
+## Influence of micropillar structures on physical and chemical properties of mPOC/HA implants  
+
+<|ref|>text<|/ref|><|det|>[[115, 669, 882, 896]]<|/det|>
+mPOC prepolymer was synthesized according to our previous report, \(^{32}\) and its successful synthesis was confirmed via the nuclear magnetic resonance (1H NMR) spectrum (Fig. S1a- c). The size of HA nanoparticles is around \(100 \mathrm{nm}\) , as characterized by dynamic light scattering (DLS) (Fig. S1d). To mimic the nature of bone composition, \(^{33} 60\%\) (w/w) HA was mixed with mPOC, and the slurry was used to fabricate flat and micropillar implants using a combination of UV lithography and the contact printing method (Fig. 1a). The square micropillars, with dimensions of 5 by 5 in side length and spacing, were fabricated (Fig. 1b). The height of the micropillars is around \(8 \mu \mathrm{m}\) , which can cause significant nuclear deformation (Fig. 1c,d). \(^{27}\) Fourier transform infrared (FTIR) spectrum shows a similar typical peak of functional groups in mPOC and mPOC/HA implants (Fig. S1e). The surface roughness of the implants was scanned using an atomic force microscope (AFM) (Fig. 1e). The analysis result indicates that the topography didn’t affect the surface roughness of the implants (Fig. 1f). Additionally, we tested the hydrophilicity of flat and micropillar implants via
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 882, 145]]<|/det|>
+water contact angle measurement (Fig. S2). Although, at the initial state, the flat surface was more hydrophilic, there was no significant difference in the water contact angle after a 5- minute stabilization process.  
+
+<|ref|>text<|/ref|><|det|>[[114, 155, 882, 437]]<|/det|>
+The mechanical properties of the implants were tested using the nano- indentation method. The force- indentation curve of the flat sample has a sharper slope, indicating it is stiffer than the micropillar sample (Fig. S3a). The Young's Modulus of the flat sample \((0.95 \pm 0.12 \mathrm{GPa})\) is significantly higher than that of the micropillars \((0.48 \pm 0.02 \mathrm{GPa})\) and the lateral modulus of the micropillars \((46.88 \pm 1.49 \mathrm{MPa})\) (Fig. S3b,c). However, based on a previous report, the high modulus of the substrates is beyond the threshold that cells can distinguish and does not have an influence on nuclear morphology manipulation. \(^{34,35}\) Accelerated degradation and calcium release tests of the implants were performed in DPBS at \(75^{\circ} \mathrm{C}\) with agitation. \(^{36}\) There is a burst weight loss and calcium release of both flat and micropillar samples at day 1, followed by a gradual change until day 10, and another increase in the degradation and calcium release rate from day 10 to 14 (Fig. 1g,h). The micropillar structure enhanced the degradation and calcium release, but not significantly. According to the images of the samples captured at different time points, the initial burst degradation and calcium release can be attributed to the fast surface erosion of both scaffolds, as many small pores can be observed on their surfaces. From day 10 to 14, scaffolds started break into pieces that may lead to another burst degradation and calcium release (Fig. 1i).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 95, 876, 599]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 606, 883, 775]]<|/det|>
+<center>Figure 1. Fabrication of surface engineered mPOC/HA implants. a. Illustration shows the combination of UV lithography and contact printing to fabricate free-standing mPOC/HA micropillars. b. SEM image shows the micropillar structures made of mPOC/HA. c. Optical microscope image and d. cross-section analysis of mPOC/HA micropillars. e. Surface scanning of flat and micropillar implants by AFM. f. Surface roughness of flat and micropillar implants. N.S., no significant difference, \(\mathrm{n} = 3\) biological replicates. g. Degradation test and h. calcium release of flat and micropillar mPOC/HA implants. N.S., no significant difference, \(\mathrm{n} = 4\) biological replicates, insert plot shows the initial release of calcium within \(24\mathrm{h}\) . i. Representative images of flat and micropillar implants at different time points after accelerated degradation. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 682, 109]]<|/det|>
+## Nuclear deformation facilitates osteogenic differentiation of hMSCs  
+
+<|ref|>text<|/ref|><|det|>[[115, 118, 883, 287]]<|/det|>
+Nuclear deformation facilitates osteogenic differentiation of hMSCshMSCs were cultured on the flat and micropillar mPOC/HA surfaces in osteogenic medium and stained for F- actin and nuclei after 3 days (Fig. 2a). Noticeable deformation in both the nucleus and cytoskeleton was observed, consistent with mPOC micropillars. The Nuclear shape index (NSI) was calculated to assess the degree of nuclear deformation. A significantly lower NSI value, indicating more severe deformation, was found in the micropillar group (Fig. 2b). Confocal images were then employed to evaluate the 3D geometry of cell nuclei (Fig. 2c). 3D reconstruction analysis revealed that several geometric parameters, including nuclear volume, surface area, and project area, were significantly decreased on micropillars, while nuclear height was significantly increased (Fig. 2d and Fig. S4).  
+
+<|ref|>text<|/ref|><|det|>[[115, 297, 883, 466]]<|/det|>
+We then investigated the impact of micropillars on cell adhesion, a crucial aspect for manipulating cell function. Initial cell attachment tests revealed that the micropillar structure did not influence cell attachment on the implants (Fig. 2e). SEM imaging of cell adhesion demonstrated that cells formed lamellipodia on flat surfaces but exhibited more filopodia on micropillars (Fig. 2f). Filopodia were observed on the top, side, and bottom of micropillars, indicating that cells were sensing the 2.5D environment using these antennae- like structures. The majority of cells were found to be viable on both flat and micropillar substrates, as evidenced by live/dead staining (Fig. 2g and Fig. S5). While the micropillars reduced cell metabolic activity (Fig. 2h), there was no significant impact on cell proliferation after 3 days of culture (Fig. 2i).  
+
+<|ref|>text<|/ref|><|det|>[[115, 476, 883, 626]]<|/det|>
+To assess the impact of mPOC/HA micropillars on the osteogenesis of hMSCs, we stained ALP (alkaline phosphate) on a substrate with a combination of half flat and half micropillar structures (Fig. 2j). Quantification results demonstrated a significant increase in ALP activity on the micropillars (Fig. 2k). Furthermore, additional osteogenic differentiation markers of hMSCs, including RUNX2 and osteocalcin (OCN), were quantified through western blot analysis (Fig. 2l). The quantification of these proteins revealed a significant increase in both RUNX2 and OCN in cells on micropillars, confirming that the structures can effectively promote the osteogenic differentiation of hMSCs (Fig. 2m,n).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[123, 93, 880, 456]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 469, 884, 790]]<|/det|>
+<center>Figure 2. Nuclear deformation promotes osteogenic differentiation of hMSCs. a. Staining of nucleus (green) and F-actin (red) of hMSCs on flat and micropillar mPOC/HA surfaces. Insert: high magnification of cell nucleus. Dashed lines indicate micropillars. b. Analysis of nuclear shape index of hMSCs. \(\mathrm{n} = 117\) (flat) and 132 (pillar) collected from 3 biological replicates, \(\mathrm{***p< 0.0001}\) . c. Orthogonal view of cell nucleus on flat and micropillar surfaces. d. Nuclear volume analysis based on 3D construction of the confocal images of cell nuclei. \(\mathrm{n} = 35\) cells collected from 3 biological replicates, \(\mathrm{***p< 0.0001}\) . e. Initial cell attachment on flat and micropillar surfaces. \(\mathrm{n} = 5\) biological replicates, N.S., no significant difference. f. SEM images show the cell attachment on flat and micropillar mPOC/HA surfaces. g. Live/dead staining of hMSCs on flat and micropillar surfaces at 72 h in osteogenic medium. h. Cell metabolic activity of cells on flat and micropillar surfaces tested by a MTT assay. \(\mathrm{n} = 5\) biological replicates, \(\mathrm{***p< 0.0001}\) . i. Cell proliferation tested via DNA content after 72 h induction. \(\mathrm{n} = 5\) biological replicates, N.S., no significant difference. j. ALP staining of hMSCs on flat and micropillar surfaces after 7 d induction. k. ALP activity test of cells after 7 d osteogenic induction. \(\mathrm{n} = 3\) biological replicates. l. Blot images of osteogenic marker OCN and RUNX2 in cells cultured on flat and micropillar implants. GAPDH is shown as a control. Quantification m. OCN and n. RUNX2 according to western blot tests. \(\mathrm{n} = 3\) biological replicates, \(\mathrm{***p< 0.0001}\) . </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[116, 89, 880, 108]]<|/det|>
+## Micropillars modulate the secretome of hMSCs that regulate extracellular matrix formation.  
+
+<|ref|>text<|/ref|><|det|>[[115, 118, 882, 438]]<|/det|>
+Micropillars modulate the secretome of hMSCs that regulate extracellular matrix formation.Previously, we demonstrated the ability of micropillar implants to enhance in vivo bone formation.<sup>13</sup> However, the newly formed bone was not in close contact with the implant. Consequently, we hypothesized that nuclear deformation on micropillars might impact cellular secretion, thereby influencing osteogenesis through paracrine effects. To test this hypothesis, secretome analysis was conducted using medium collected from flat and micropillar samples. Differences in protein secretion levels between the two groups were depicted through principal component analysis (PCA) and a volcano plot, revealing a significant influence of nuclear deformation on the secretome (Fig. 3a,b). Gene ontology (GO) analysis was performed to annotate the significantly altered proteins in relevant processes.<sup>38</sup> Top changes in cellular component, molecular functions, biological processes, and biological pathways indicated that micropillars predominantly affected extracellular matrix (ECM)- related processes (Fig. 3c and Fig. S6- 8). Moreover, ossification and collagen fibril organization were identified as biological processes significantly overrepresented by differentially expressed proteins (Fig. 3d). The heatmap plot of proteins associated with collagen- containing extracellular matrix and ossification showed predominant upregulation on micropillars (Fig. 3e). The linkages of proteins and GO terms in biological process highlighted that ECM organization forms the largest cluster and is closely associated with the ossification process (Fig. 3f).  
+
+<|ref|>text<|/ref|><|det|>[[115, 448, 883, 672]]<|/det|>
+Reactome pathway analysis was further conducted to assess potential downstream effects of secretome changes on micropillars.<sup>39</sup> Results indicated that pathways related to ECM organization, ECM proteoglycans, and collagen fibril crosslinking were among the top 15 pathways significantly overrepresented by differential expressed pathways (DEP), predominantly showing upregulation (Fig. 3g and Fig. S9). We also noticed an upregulation in the degradation of the ECM on micropillars, indicating enhanced ECM remodeling which a crucial factor for tissue regeneration.<sup>40</sup> These findings suggest that micropillars can influence the ECM formation of hMSCs through paracrine effects. Additionally, we performed proteomic analysis using cells cultured on flat and micropillar mPOC/HA scaffolds (Fig. S10). PCA and volcano plots indicated significant influences of nuclear deformation on protein expression. Pathway analysis revealed significant changes in many cell proliferation- related processes, consistent with previous transcriptomic tests on micropillars.<sup>13</sup>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 884, 799]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 798, 884, 893]]<|/det|>
+<center>Figure 3. Secretome of hMSCs on flat and micropillar mPOC/HA surfaces. a. PCA plot of differentially expressed proteins secreted by hMSCs on flat and micropillars. Cyan: flat; Red: micropillar. b. Volcano plot of proteins secreted by hMSCs seeded on micropillars compared to the flat surface. Blue dots and orange dots indicate significantly downregulated and upregulated proteins secreted by cells on micropillars compared to those on flat surface. Grey dots indicate </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 882, 258]]<|/det|>
+non- significantly changed proteins. A threshold of expression greater than 2 times fold- change with \(p< 0.05\) was considered to be significant. Proteins that are related with collagen- ECM pathways are labelled. c. Top 4 significantly enriched GO and Pathways based on their adjusted p- values. d. The most significant enriched GO terms of the biological domain with respect to biological process. e. Heatmap of proteins that are related with collagen- containing extracellular matrix and ossification. F indicates flat samples and P indicates pillar samples, \(n = 3\) biological replicates for each group. f. The linkages of proteins and GO terms in biological process related with collagen fibers, ECM, and ossification as a network. g. Heatmap of top 15 enriched terms plotted based on Reactome pathway analysis.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 297, 881, 334]]<|/det|>
+## Nuclear deformed cells facilitate osteogenic differentiation of undeformed cells by affecting ECM.  
+
+<|ref|>text<|/ref|><|det|>[[114, 344, 884, 682]]<|/det|>
+Since the micropillar surfaces can modulate the secrete of hMSCs, we investigated whether the deformed cells could influence the osteogenic differentiation of undeformed cells using a transwell assay (Fig. 4a). The flat and micropillar mPOC/HA surfaces were fabricated at the bottom of cell culture plates to manipulate the nuclear morphology of hMSCs, while undeformed hMSCs were seeded on a transwell membrane with 400 nm nanopores, allowing the exchange of growth factors. After cell attachment, all samples were cultured in osteogenic induction medium. ALP staining of the cells on the transwell membrane showed a higher number of ALP- positive cells when co- cultured with nuclear- deformed cells, indicating enhanced osteogenic differentiation (Fig. 4b,c). Additionally, Alizarin Red S (ARS) staining confirmed increased calcium deposition—a key step in osteogenesis—when the cells were cultured above the micropillar- treated cells (Fig. 4d,e). Based on the secreteome analysis, hMSCs on micropillars appear to promote osteogenesis in the transwell culture by secreting proteins that enhance ECM structure and organization. Collagen staining revealed higher coverage, stronger staining intensity, and more interconnected collagen network structures in the transwell co- cultured with micropillar- treated cells (Fig. 4f,g). In addition, energy dispersive X- ray spectroscopy (EDS) images showed more Ca and P deposition in the transwell co- cultured with micropillar- treated cells (Fig. 4h). Together with the secreteome analysis, these findings suggest that the proteins secreted by cells with deformed nuclei improve ECM organization in undeformed cells, thereby promoting osteogenesis.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 123, 870, 506]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 517, 883, 685]]<|/det|>
+<center>Figure 4. The paracrine effect of cells with/without nuclear deformation tested through transwell assay. a. Schematic illustration of the experiment setup. b. ALP staining and c. quantification of ALP positive cells on transwell membrane incubated with undeformed and deformed MSCs \((n = 3)\) . d. ARS staining and e. quantification of cells on transwell membrane incubated with undeformed and deformed MSCs \((n = 6)\) . f. Immunofluorescence staining images of collagen in ECM of cells on transwell membrane incubated with undeformed and deformed MSCs. g. The coverage of collagen analyzed according to the staining images \((n = 4)\) . h. EDS images showing Ca, P, and SEM images of cells on transwell membrane incubated with undeformed and deformed MSCs. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 725, 655, 744]]<|/det|>
+## mPOC/HA micropillar implant promotes bone formation in vivo  
+
+<|ref|>text<|/ref|><|det|>[[114, 753, 883, 905]]<|/det|>
+To test the in vivo regeneration efficacy of mPOC/HA scaffolds, we created a critical size cranial defect model in nude mice. Two 4 mm diameter critical defects were made on the left and right sides of the skull tissue for the implantation of flat and micropillar scaffolds, respectively (Fig. 5a). The scaffolds were seeded with hMSCs for 24 hours to allow for cell attachment and nuclear deformation (Fig. 5b). After 12 weeks, micro CT was performed to evaluate the bone formation in the living animals. Based on the images, newly formed bone can be observed in the defect area with both flat and micropillar mPOC/HA implants (Fig. 5c and Fig. S11). Comparing this to our previous study using mPOC alone, \(^{13}\) the integration of HA clearly enhanced bone regeneration
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 89, 882, 145]]<|/det|>
+efficacy in vivo. Furthermore, larger bone segments were observed with the micropillar implant treatment. Quantification results confirmed a significantly increased bone volume with micropillar implant treatment (Fig. 5d).  
+
+<|ref|>text<|/ref|><|det|>[[114, 155, 882, 380]]<|/det|>
+Histology analysis was further performed to evaluate the influences of flat and micropillar mPOC/HA implants on bone regeneration. Trichrome staining images revealed that defects treated with micropillar implants exhibited more osteoid tissue (Fig. 5e and Fig. S12). Moreover, both flat and micropillar mPOC/HA implants showed evidence of newly formed bone tissue, indicating enhanced bone regeneration compared to the mPOC alone scaffold. As no bone segment was observed with flat mPOC implant treatment. \(^{13}\) The thickness of the regenerated tissue was quantified, and the results demonstrated a significant enhancement with micropillar implant treatment (Fig. 5f). Positive staining of osteogenesis markers, including osteopontin (OPN) and osteocalcin (OCN), was observed throughout the regenerated tissues with both flat and micropillar implants, indicating osteoid tissue formation (Fig. 5g,h). The tissue appeared more compact in the micropillar group compared to the flat group. Furthermore, regenerated bone segments were more frequently observed with micropillar implant treatment.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 95, 875, 620]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 630, 884, 782]]<|/det|>
+<center>Figure 5. mPOC/HA micropillar implant promotes bone regeneration in vivo. a. Image shows implantation of hMSC seeded flat and micropillar mPOC/HA scaffolds. b. Staining images of nuclei (green) and F-actin (red) of cells on the implants. c. Representative \(\mu \mathrm{CT}\) images of a typical animal implanted with hMSC-seeded flat (left) and micropillar (right) scaffolds at 12-weeks post-surgery. d. Regenerated bone volume in the defect region ( \(\mathrm{n} = 5\) animals). e. Trichrome staining of the defect tissue treated with flat and micropillar implants. f. Average thickness of regenerated tissues with implantation of flat and micropillar scaffolds ( \(\mathrm{n} = 5\) animals). IHC staining of osteogenic marker, g. OPN and h. OCN, in regenerated tissues with flat and micropillar implants. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 881, 127]]<|/det|>
+## Micropillar implants facilitated bone regeneration in vivo via regulation of ECM organization and stem cell differentiation.  
+
+<|ref|>text<|/ref|><|det|>[[114, 136, 882, 494]]<|/det|>
+Histological analyses showed more new bone formation with micropillar implants, although the new bone tissue did not directly interact with the micropillar surfaces. To further investigate the transcription profile of the regenerated tissue, we performed spatial transcriptomics (ST) analyses with both flat and pillar samples (Fig. S13). ST represents a powerful tool to investigate the cellular environment and tissue organization by providing a detailed map of gene expression within the native tissue context. Differential gene expression (DGE) analysis revealed changes in expression levels between the two groups. Although only a few genes showed significant differences, all of them were related to ECM structure or organization (Fig. S13). Notably, the expression of Colla2, critical for type I collagen formation (comprising \(90\%\) of the bone matrix), was enhanced in the micropillar group (Fig. 6a). This expression showed a gradient, increasing toward the dura layer, possibly due to the osteogenic contribution of dura cells. We then plotted a heatmap showing the top 10 up- regulated and down- regulated differentially expressed genes (pillar vs. flat) in comparison with those in native skull bone (Fig. 6b). The heatmap indicated that the tissue regenerated with micropillar implants had expression patterns more similar to native skull bone than the flat group. Gene Ontology (GO) analysis of DGEs was further performed to annotate their relevant biological processes (Fig. 6c). Protein localization to extracellular matrix and crosslinking of collagen fibrils were among the top 5 up- regulated processes in the micropillar group. These results are consistent with the secreteome test, all indicating that micropillar structures can influence ECM organization via paracrine effects.  
+
+<|ref|>text<|/ref|><|det|>[[114, 503, 882, 824]]<|/det|>
+To further investigate the relationship between cell type composition and the regenerated tissues, we performed cellular deconvolution on the ST data using single- cell RNA sequencing (scRNA- seq) references from previously published studies. Several major cell lineages involved in bone regeneration were considered when deconvoluting the data (Fig. 6d). The most abundant cell type in regenerated tissues was late mesenchymal progenitor cells (LMPs), followed by MSCs and fibroblasts (Fig. 6e). There were also small proportions of MSC- descendant osteolineage cells (OLCs), osteocytes, osteoblasts, and chondrocytes. LMPs are identified as the late stage of MSCs through osteogenic differentiation. Among all cell types, the proportion of LMPs, which have high expression of marker genes associated with osteoblasts, was significantly increased in regenerated tissues with micropillar implants, indicating that these deformed cells facilitate the differentiation of MSCs toward the osteolineage (Fig. 6f). Additionally, GO analysis of DGEs (LMP versus other cell types) was performed to investigate the roles of LMPs in regenerated tissue. The results suggest that LMPs do not directly contribute to osteogenesis, a role performed by osteoblasts and osteocytes. Instead, LMPs can affect ECM formation, as the process of extracellular matrix organization is one of the top involved pathways (Fig. 6g). Thus, the results indicate that micropillar implants can facilitate skull tissue regeneration by promoting the differentiation of MSCs and ECM organization via paracrine effects.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 90, 877, 560]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 572, 883, 817]]<|/det|>
+<center>Figure 6. Spatial transcriptomic analysis of tissues regenerated with flat and micropillar implants. a. Spatial plot of Colla2 expression profile in tissues regenerated with flat mPOC/HA implant and micropillar mPOC/HA implant. Arrow indicates enhanced expression around dura layer. b. The heatmap showing the top ten up- and down-regulated DEGs (pillar vs flat) in tissues regenerated with flat mPOC/HA implant, micropillar mPOC/HA implant, and native skull tissue. c. Gene Ontology analysis results based on the top 100 up-regulated genes (pillar vs flat). d. Deconvoluted cell types in each spatial capture location in flat and micropillar groups. Each pie chart shows the deconvoluted cell type proportions of the capture location. e. Bar plots of the cell type proportions in tissues regenerated with flat mPOC/HA implant and micropillar mPOC/HA implant. LMPs, MSCs, and fibroblasts are the predominant cell types. f. Violin plot of the proportion of LMPs in flat and micropillar groups. g. Top enriched processes associated with LMP compared with other cell lineages. LMP: late mesenchymal progenitor cells; MSC: mesenchymal stromal cells; OLC: MSC-descendant osteolineage cells </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 206, 107]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[115, 118, 882, 380]]<|/det|>
+Micropiliars, as a typical topographical feature, have been extensively studied for their ability to regulate cell functions. Recent researches have shown that rigid micropiliars can deform nuclear morphology, which in turn promotes the osteogenic differentiation of mesenchymal stem cells (MSCs), generating significant interest for bone regeneration applications.26,27 Our previous work demonstrated that mPOC micropiliars enhanced bone regeneration in a mouse cranial defect model.13 The mPOC, a citrate- based biomaterial (CBB), is an excellent candidate for bone regeneration because citrate, an important organic component of bone, plays key roles in skeletal development and bone healing by influencing bone matrix formation and the metabolism of bone- related cells.47 In this study, hydroxyapatite (HA) was incorporated into mPOC to further enhance its regenerative potential, leveraging HA's well- known osteoconductive properties.48 Both in vitro and in vivo experiments confirmed that the addition of HA significantly improved bone regeneration compared to mPOC alone.13 Moreover, several products made from CBB/HA composites have recently received FDA clearance, highlighting the promising clinical potential of mPOC/HA micropiliars for bone regeneration applications.49  
+
+<|ref|>text<|/ref|><|det|>[[115, 391, 882, 654]]<|/det|>
+Despite recent intensive investigations into nuclear morphogenesis, little is known about its influence on cellular secretion, which can regulate neighboring cells and is critical for regenerative engineering. Previous studies have shown that nuclear mechanotransduction, activated by substrate stiffening or cellular compression, can impact cell secretions.50,51 Here, we found that cells with deformed nuclei exhibited higher expression levels of ECM components and binding proteins that support collagen- enriched ECM organization. Additionally, soluble proteins secreted by these deformed cells were able to diffuse and modulate ECM secretion and organization in neighboring cells, as demonstrated by a transwell assay. The ECM is a complex, dynamic environment with tightly regulated mechanical and biochemical properties that affect essential cell functions, including adhesion, proliferation, and differentiation.52 ECM fiber alignment increases local matrix stiffness, which promotes higher force generation and increases cell stiffness, creating a positive feedback loop between cells and the matrix.53 Furthermore, the organized ECM enhances calcium recruitment and accelerates mineralization, contributing to effective bone regeneration.  
+
+<|ref|>text<|/ref|><|det|>[[115, 664, 882, 869]]<|/det|>
+Implantation of the flat and micropillar mPOC/HA scaffolds seeded with MSCs resulted in larger new bone volume formation in vivo compared to previous studies using mPOC alone, a finding likely due to the osteoconductive properties of HA. ST analysis revealed a significant upregulation of genes encoding cartilage oligomeric matrix protein (COMP) and fibromodulin (FMOD) in the micropillar group, consistent with the secreteome analysis. COMP binds to matrix proteins like collagen, enhancing ECM organization and assembly.54 As an ECM protein, COMP also promotes osteogenesis by binding to bone morphogenetic protein 2 (BMP- 2), increasing its local concentration and boosting its biological activity.55 FMOD, with a strong affinity for the HA matrix, helps attenuate osteoclast precursor maturation, thereby influencing osteoblast- osteoclast crosstalk.56 These results suggest that nuclear deformation induced by micropiliars may promote osteogenesis in neighboring cells via matricrine effects.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 89, 882, 239]]<|/det|>
+Despite the enhanced bone regeneration observed, mPOC/HA implants did not achieve complete healing of the cranial defect, likely due to the limited interaction surface of the film scaffold. The influence of the implants, whether through direct chromatin reprogramming guidance or secretome activity, was restricted to cells at the tissue- scaffold interface. Future efforts should focus on the design and fabrication of 3D micropillar implants using additive manufacturing and composite materials to create a more comprehensive 3D cellular microenvironment that promotes bone regeneration. Additionally, the application of micropillars as a platform for delivering bioactive factors could be explored as a strategy to achieve complete cranial bone healing.  
+
+<|ref|>text<|/ref|><|det|>[[115, 249, 882, 437]]<|/det|>
+In summary, we investigated the effects of nuclear deformation on the cellular secretome using micropillar implants fabricated from an mPOC/HA composite. The mPOC/HA micropillars demonstrated similar properties to a flat substrate in terms of roughness and degradation but had a substantial impact on cellular and nuclear morphology, cell adhesion, cytoskeletal development, and osteogenic differentiation in hMSCs. Nuclear- deformed cells showed increased secretion of proteins and RNA transcriptions that regulate ECM components and organization, promoting osteogenesis in neighboring cells both in vitro and in vivo. These findings suggest that incorporating microtopography into implants holds significant promise for bone regeneration. This study offers valuable insights for the future design and fabrication of bioactive implants in regenerative engineering.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 477, 311, 494]]<|/det|>
+## Materials and Methods  
+
+<|ref|>text<|/ref|><|det|>[[115, 505, 542, 523]]<|/det|>
+Synthesis and characterization of mPOC pre- polymer.  
+
+<|ref|>text<|/ref|><|det|>[[115, 533, 882, 701]]<|/det|>
+The mPOC pre- polymer were synthesized according to a previous report. Briefly, the POC pre- polymer was firstly synthesized by reaction of equal molar of citric acid (Sigma- Aldrich, 251275) and 1,8- octandiol (Sigma- Aldrich, O3303) at \(140^{\circ}\mathrm{C}\) oil bath for 60 min. The product was then purified by precipitation in DI water. After lyophilization, 66g POC pre- polymer was dissolved in 540 ml tetrahydrofuran (THF) and reacted with 0.036 mol imidazole (Sigma- Aldrich, I2399) and 0.4 mol glycidyl methacrylate (Sigma- Aldrich, 151238) at \(60^{\circ}\mathrm{C}\) for 6 h. The final product was then purified by precipitation in DI water and lyophilized for storage at - 20 \(^{\circ}\mathrm{C}\) . Successful synthesis of mPOC pre- polymer was characterized using proton nuclear magnetic resonance (1H- NMR, Bruker A600).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 712, 658, 730]]<|/det|>
+## Fabrication and characterization of mPOC/HA micropillar scaffolds  
+
+<|ref|>text<|/ref|><|det|>[[115, 741, 882, 892]]<|/det|>
+SU- 8 micropillar structures (5x5x8 um) were fabricated according to our previous study. PDMS molds were then fabricated to replicate the invert structures. HA nanoparticles (Sigma- Aldrich, 677418) were mixed with mPOC pre- polymer at weight ratio of 6:4. The \(60\%\) HA was selected to mimic composition of native bone. Photo- initiator (5 mg/ml camphorquinone and ethyl 4- dimethylaminobenzoate) was added to the mPOC/HA slurry. The mixture was then added onto PDMS mold and pressed onto cover glass to prepare free- standing scaffold under exposure with laser (1W, 470 nm). Post- curing of the scaffold was performed in \(80^{\circ}\mathrm{C}\) oven over night. The size of HA nanoparticles was characterized using Dynamic Light Scattering (DLS). The topography of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 202]]<|/det|>
+micropillars was observed using scanning electron microscope (SEM, FEI Quanta 650 ESEM) and characterized using 3D optical microscope (Bruker). Surface roughness of flat and micropillar scaffolds was characterized using atomic force microscope (AFM, Bruker ICON system). The water contact angle was tested using VCA Optima XE system. The compressive modulus of the scaffolds was characterized using a Tribioindenter (Bruker). Based on a previous report, \(^{58}\) the lateral modulus of micropillars was calculated according to the following equations:  
+
+<|ref|>equation<|/ref|><|det|>[[114, 210, 217, 240]]<|/det|>
+\[k_{L} = \frac{3EI}{L^{3}} (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 248, 883, 287]]<|/det|>
+The ' \(\mathrm{kL}\) ' is the lateral stiffness, 'E' is the measured modulus, 'I' is the moment area of inertia, and 'L' is the micropillar height. For square micropillars, 'I' can be described as:  
+
+<|ref|>equation<|/ref|><|det|>[[114, 295, 210, 328]]<|/det|>
+\[I = \frac{a^{4}}{12} (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 336, 883, 374]]<|/det|>
+Where 'a' is the side length of the micropillars. Thus, the lateral modulus of the micropillars ' \(\mathrm{E_{L}}\) ' equals to:  
+
+<|ref|>equation<|/ref|><|det|>[[114, 381, 226, 411]]<|/det|>
+\[E_{L} = \frac{K_{L}L}{A} (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 420, 519, 439]]<|/det|>
+Where 'A' is the cross- section area of micropillars.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 450, 381, 468]]<|/det|>
+## Degradation and calcium release  
+
+<|ref|>text<|/ref|><|det|>[[114, 478, 884, 628]]<|/det|>
+To test the degradation of the mPOC/HA scaffold, the dry weight of mPOC/HA scaffolds at day 0 was recorded as the initial weight. Then the scaffolds were merged in \(1\mathrm{ml}\) DPBS solution in \(75^{\circ}\mathrm{C}\) oven. At each designed time point (1, 2, 3, 5, 7, 10 and 14 d), the scaffolds were rinsed with DI water followed by drying at \(60^{\circ}\mathrm{C}\) . The weight was recorded to calculate the weight loss percentage. The calcium release test was also performed with \(75^{\circ}\mathrm{C}\) DPBS (no calcium, no magnesium). At the designed time points, the elution solution was collected and replaced with fresh DPBS (1 ml). The released calcium was detected with inductively coupled plasma mass spectrometry (ICP- MS, ThermoFisher Element 2). Accumulated calcium release was calculated.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 639, 211, 656]]<|/det|>
+## Cell culture  
+
+<|ref|>text<|/ref|><|det|>[[114, 667, 883, 836]]<|/det|>
+Human mesenchymal stromal cells (hMSCs, PCS- 500- 012) were purchased from the American Type Culture Collection (ATCC) and cultured with the growth medium acquired from ATCC. hMSCs with the passage 4- 6 were seeded onto the flat and micropillar mPOC/HA substrates. To test cell attachment, hMSCs were seeded at 5000 cells/cm \(^2\) and cultured for 3 h followed by PBS rinsing to remove unattached cells. The attached cells were then trypsinized and collected for cell counting. For other experiments, the cells were cultured in growth medium for 24 h to allow cell attachment and spreading followed by incubation with osteogenic induction medium. After 3 d culture, live/dead staining (Thermofisher, L3224), MTT assay (Thermofisher, V13154), and Picogreen assay (Thermofisher, P7589) were performed according to the manufactures' protocol.  
+
+<|ref|>text<|/ref|><|det|>[[115, 847, 350, 865]]<|/det|>
+Nuclear morphology analysis
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 882, 239]]<|/det|>
+After one day of culture, the cells were fixed with \(4\%\) paraformaldehyde, and cell nuclei were stained using SYTOX™ Green (ThermoFisher, S7020) according to the manufacture's instruction. The nuclear shape index (NSI) was analyzed to evaluate 2D nuclear deformation. \(^{27}\) The stained cells were then imaged using a confocal microscope (Leica SP8) to acquire their 3D morphology. Cell nuclei were reconstructed using the Fiji ImageJ software (https://imagej.net/Fiji). Cell nuclear volume, surface area, project area, height, and the ratio of surface area to volume were measured using 3D objects counter plugin. More than 30 nuclei from 3 biological replicates were imaged and analyzed to calculate the statistics.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 252, 355, 269]]<|/det|>
+## Scanning electron microscope  
+
+<|ref|>text<|/ref|><|det|>[[115, 280, 882, 431]]<|/det|>
+To visualize cell adhesion on mPOC/HA scaffolds, cells were fixed with \(3\%\) glutaraldehyde (Electron Microscopy Sciences) and rinsed with DI water. Subsequently, the cells underwent dehydration using a series of ethanol concentrations ( \(30\%\) , \(50\%\) , \(70\%\) , \(90\%\) , and \(100\%\) ) for 5 min each, followed by drying using a critical point dryer (Tousimis Samdri) as per the manual. The dehydrated cells were coated with a \(5\mathrm{nm}\) osmium layer and imaged using a scanning electron microscope (SEM, FEI Quanta 650). Captured images were further enhanced for visualization of cellular architecture using Photoshop. Additionally, cells on transwell were imaged using SEM and EDS analysis was performed to evaluate the calcium and phosphate deposition.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 442, 322, 460]]<|/det|>
+## Osteogenic differentiation  
+
+<|ref|>text<|/ref|><|det|>[[114, 470, 882, 902]]<|/det|>
+hMSCs were seeded onto both flat and micropillar mPOC/HA substrates. One- day post- seeding, osteogenic induction medium (Lonza) was applied to prompt the osteogenic differentiation of hMSCs. After 7 days of induction, cells were washed with PBS buffer and fixed with \(4\%\) paraformaldehyde for 10 minutes. Subsequently, the samples were immersed in a solution of 56 mM 2- amino- 2- methyl- 1,3- propanediol (AMP, pH- 9.9), containing \(0.1\%\) naphthol AS- MX phosphate and \(0.1\%\) fast blue RR salt to stain alkaline phosphatase (ALP). Bright- field images were acquired using a Nikon Eclipse TE2000- U inverted microscope. ALP activity was assessed using the ALP assay kit (K422- 500, Biovision) following the provided manual. Briefly, cells cultured in induction medium for 7 days were homogenized using ALP assay buffer. Subsequently, the non- fluorescent substrate 4- Methylumelliferyl phosphate disodium salt (MUP) was mixed with the homogenized samples to generate a fluorescent signal through its cleavage by ALP. Fluorescence intensity was measured using a Cytation 5 imaging reader (BioTek) at \((\mathrm{Ex / Em} = 360 / 440\mathrm{nm})\) . Enzymatic activity was calculated based on the standard curve and normalized to total DNA content, determined by the Quant- iT PicoGreen dsDNA assay (Invitrogen). The expression levels of OCN and RUNX2 were quantified through Western blot analysis. In brief, cell lysis was performed using radioimmunoprecipitation assay (RIPA) buffer. The relative protein quantities were measured using a Cytation 5 imaging reader. Equal amounts of proteins extracted from flat and micropillar samples were loaded onto a NuPAGE 4- 12% Bis- Tris Gel (Invitrogen) and subsequently transferred to nitrocellulose membranes (Bio- rad). Afterward, membranes were blocked with \(5\%\) milk and incubated with primary antibodies (including GAPDH from Abcam, OCN from Cell Signaling, RUNX2 from Santa Cruz) overnight at \(4^{\circ}\mathrm{C}\) with gentle shaking. Following this, secondary antibodies, diluted at a ratio of 1:5000, were applied and incubated with the membranes at room temperature for 1 hour. Protein bands were
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 882, 163]]<|/det|>
+visualized using the Azure 600 gel imaging system. The acquired images underwent analysis through the 'Gel Analyzer' tool in ImageJ. The intensity of all target protein bands was initially compared to the corresponding GAPDH, and then normalized against a flat surface, which was set as 1. Statistical calculations were based on three biological replicates.  
+
+<|ref|>text<|/ref|><|det|>[[114, 175, 883, 533]]<|/det|>
+Secretome sample preparation: Analysis of secreted proteins is complicated by high concentrations of serum proteins. Our approach reduced initial sample volume to a \(20~\mu \mathrm{l}\) concentrate using a molecular weight cut off filter (50 kDa, Amicon Ultra- 15 centrifugal, Ultracel, Merck). The concentrate above 50KDa was depleted of the most abundant proteins using a High Select HAS / Immunoglobulin Depletion Midi spin column (A36367, Thermo Fisher Scientific), resulting in a filtrate solution (below 50KDa) and a depleted solution per sample. An acetone / TCA (Trichloroacetic acid) protein precipitation was performed on each solution to create protein pellets and an in- solution trypsin digestion was performed on each pellet. \(100~\mu \mathrm{l}\) of re- suspension buffer (8 M urea in \(400~\mathrm{mM}\) ammonium bicarbonate) was added to the pellet and incubated with mixing for 15 minutes. Disulfide bonds were reduced by addition of \(100~\mathrm{mM}\) dithiothreitol and incubated for 45 minutes at \(55~^\circ \mathrm{C}\) . Sulfhydryl groups were alkylated by addition of \(300~\mathrm{mM}\) iodoacetamide and incubated for 45 minutes at \(25~^\circ \mathrm{C}\) shielded from light. Samples were diluted 4- fold with ammonium bicarbonate to reduce the urea concentration below 2 M. Protein digestion was performed by addition of trypsin (MS- grade, Promega) at a 1:50 ratio (enzyme:substrate) and incubated overnight at \(37~^\circ \mathrm{C}\) . Digestion was halted with the addition of \(10\%\) formic acid (FA) to a final concentration of \(0.5\%\) . Peptides were desalted with C18 spin columns (The Nest Group), dried by vacuum centrifugation, and stored at \(- 20~^\circ \mathrm{C}\) . Peptides were resuspended in \(5\%\) ACN (Acetonitrile) / \(0.1\%\) FA for LC- MS analysis. Peptide concentration was quantified using micro BCA (Bicinchoninic acid) protein assay kit (Thermo Scientific, Ref: 23235).  
+
+<|ref|>text<|/ref|><|det|>[[114, 542, 882, 803]]<|/det|>
+Proteome sample preparation: Cells were lysed using cell lysis buffer ( \(0.5\%\) SDS, \(50\mathrm{mM}\) Ambi (Ammonium Bicarbonate), \(50\mathrm{mM}\) NaCl (Sodium Chloride), Halt Protease inhibitor). An acetone / TCA protein precipitation was performed on each lysed samples solution to create protein pellets and an in- solution trypsin digestion was performed on each pellet. \(100~\mu \mathrm{l}\) of re- suspension buffer (8 M urea in \(400~\mathrm{mM}\) ammonium bicarbonate) was added to the pellet and incubated with mixing for 15 minutes. Disulfide bonds were reduced by addition of \(100~\mathrm{mM}\) dithiothreitol and incubated for 45 minutes at \(55~^\circ \mathrm{C}\) . Sulfhydryl groups were alkylated by addition of \(300~\mathrm{mM}\) iodoacetamide and incubated for 45 minutes at \(25~^\circ \mathrm{C}\) shielded from light. Samples were diluted 4- fold with ammonium bicarbonate to reduce the urea concentration below 2 M. Protein digestion was performed by addition of trypsin (MS- grade, Promega) at a 1:50 ratio (enzyme:substrate) and incubated overnight at \(37~^\circ \mathrm{C}\) . Digestion was halted with the addition of \(10\%\) formic acid to a final concentration of \(0.5\%\) . Peptides were desalted with C18 spin columns (The Nest Group), dried by vacuum centrifugation, and resuspended in \(5\%\) ACN/ \(0.1\%\) FA for LC- MS analysis. Peptide concentration was quantified using micro BCA Protein Assay Kit (Thermo Scientific, Ref: 23235).  
+
+<|ref|>text<|/ref|><|det|>[[115, 815, 882, 890]]<|/det|>
+Liquid Chromatography High Resolution Tandem Mass Spectrometry (LC- HRMS/MS) Analysis: Peptides were analyzed using a Vanquish Neo nano- LC coupled to a Exploris 480 hybrid quadrupole- orbitrap mass spectrometer (Thermo Fisher Scientific, USA). The samples were loaded onto the trap column of \(75\mu \mathrm{m}\) internal diameter (ID) x 2cm length (Acclaim PepMapTM
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 882, 390]]<|/det|>
+100, P/N 164535) and analytical separation was performed using a UHPLC C18 column (15cm length \(\times 75\mu \mathrm{m}\) internal diameter, \(1.7\mu \mathrm{m}\) particle size, Ion Opticks, AUR3- 15075C18). For each run, \(1\mu \mathrm{g}\) of peptide sample was injected. Electrospray ionization was performed using a Nanospray Flex Ion Source (Thermo Fisher, ES071) at a positive static spray voltage of \(2.3\mathrm{kV}\) . Peptides were eluted from the analytical column at a flow rate of \(200\mathrm{nL / min}\) using an increasing organic gradient to separate peptides based on their hydrophobicity. Buffer A was \(0.1\%\) formic acid in Optima LC- MS grade water, and buffer B was \(80\%\) acetonitrile, \(19.9\%\) Optima LC- MS grade water, and \(0.1\%\) formic acid: The method duration was 120 minutes. The mass spectrometer was controlled using Xcalibur and operated in a positive polarity. The full scan (MS1) settings used were: mass range 350- 2000 m/z, RF lens \(60\%\) , orbitrap resolution 120,000, normalized AGC target \(300\%\) , maximum injection time of 25 milliseconds, and a \(5\mathrm{E}^{3}\) intensity threshold. Datadependent acquisition (DDA) by TopN was performed through higher- energy collisional dissociation (HCD) of isolated precursor ions with charges of \(2+\) to \(5+\) inclusive. The MS2 settings were: dynamic exclusion mode duration 30 seconds, mass tolerance 5 ppm (both low and high), 2 second cycle time, isolation window \(1.5\mathrm{m / z}\) , \(30\%\) normalized collision energy, orbitrap resolution 15,000, normalized AGC target \(100\%\) , and maximum injection time of 50 milliseconds.  
+
+<|ref|>text<|/ref|><|det|>[[115, 399, 882, 550]]<|/det|>
+Data analysis: Mass spectrometry files (.raw) were converted to Mascot generic format (.mgf) using the Scripps RawConverter program and then analyzed using the Mascot search engine (Matrix Science, version 2.5.1). MS/MS spectra were searched against the SwissProt database of the organism of interest. Search parameters included a fixed modification of cysteine carbamidomethylation, and variable modifications of methionine oxidation, deaminated asparagine and aspartic acid, and acetylated protein N- termini. Two missed tryptic cleavages were permitted. A \(1\%\) false discovery rate (FDR) cutoff was applied at the peptide level. Only proteins with at least two peptides were considered for further study.  
+
+<|ref|>text<|/ref|><|det|>[[115, 560, 882, 860]]<|/det|>
+Label- Free Quantification: The samples were acquired on mass spec and the data were searched against a specific database using the MaxQuant application. \(^{59}\) Label- Free Quantification (LFQ) was obtained by LFQ MS1 intensity. The results were filtered with a minimum of 2 unique peptides. Technical replicates were averaged and intensities were Log2 transformed to achieve a normal distribution of the data. Missing values were filtered to keep only proteins quantified in at least 2 samples per group. For statistics, Student t- Test was applied using \(\mathrm{p}< 0.05\) and \(\mathrm{FC} > 2\) to determine which proteins were significantly up- and down- regulated and visualize it by volcano plot. Downstream analyses and visualizations were done using RStudio software (R version 4.3.2, RStudio version 2024.09.0). Principal component analysis (PCA) was done using 'prcomp' R function to visualize a ability of the differential protein expression to distinguish between biological conditions. Heatmap plot was built using 'ComplexHeatmap' R package. GO and Pathways enrichment analysis was done using 'clusterProfiler' R package \(^{60}\) and annotations with adjusted p- values (FDR, Benjamini- Hochberg) \(< 0.05\) were considered significant. Additional packages used include 'org.Hs.eg.db' for human gene annotations and 'enrichplot' for visualization. This analysis considered the entire set of human protein- coding genes as the reference background.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 315]]<|/det|>
+Transwell assay: The flat and micropillar mPOC/HA surfaces were fabricated in a 24 well plate. The hMSCs were seeded onto the surfaces with 40,000 cells per well. Then a transwell was put in each well and additional hMSCs were seeded inside the transwell (Costar, \(0.4 \mu \mathrm{m}\) polyester membrane) at density of 5,000 cells/ \(\mathrm{cm}^2\) . After cell attachment, osteogenic medium was used to induce osteogenic differentiation of the cells. At 7 days post- induction, the cells on transwell were fixed followed by ALP staining and quantification to investigate the paracrine effect of deformed and undeformed cells on osteogenesis. At 3 weeks post- induction, additional transwells were collected for Alizarin Red S (ARS) staining and quantification to show the calcium deposition influenced by the paracrine effect. At 4 weeks post- induction, the collagen, which is one of the major components in ECM and significantly affected according to the secretome analysis, were stained using anti- collagen antibody (Abcam, ab36064) to investigate the influence of nuclear deformation on ECM organization.  
+
+<|ref|>text<|/ref|><|det|>[[114, 325, 883, 570]]<|/det|>
+In vivo implantation: The animal study was approved by the University of Chicago Animal Care and Use Committee following NIH guidance (ACUP#71745). Eight- week- old female athymic nude mice obtained from Harlan Laboratories were used for the study. The animals were housed in a separately air- conditioned cabinet at temperature of \(24 - 26^{\circ}\mathrm{C}\) with 12:12 light:dark cycle. The surgeries were performed according to the previous report61. Briefly, animals were treated with \(2\%\) isoflurane delivered by \(100\% \mathrm{O}_2\) and maintained with \(1 - 1.5\%\) isoflurane for anaesthesia. Two critical- sized defects (4 mm diameter) were created on the left and right side of skull of each animal followed by implantation of hMSCs seeded flat and micropillar scaffolds, respectively. After implantation of scaffolds, a larger mPOC film \((1 \times 1.5 \mathrm{cm}^2)\) was attached to the skull with thrombin/fibrinogen to prevent displacement of implants. Skin tissue was closed with 5- 0 nylon interrupted sutures and removed after 2 weeks. The animals were monitored after anaesthesia hourly until recovery. Buprenorphine \(50 \mu \mathrm{g} \mathrm{kg}^{- 1}\) and meloxicam \(1 \mathrm{mg} \mathrm{kg}^{- 1}\) were used for pain relief.  
+
+<|ref|>text<|/ref|><|det|>[[114, 579, 883, 749]]<|/det|>
+Micro- CT: Micro- CT images of cranial were performed on the XCUBE (Molecules NV) by the Integrated Small Animal Imaging Research Resource (iSAIRR) at The University of Chicago. Spiral high- resolution computed tomography acquisitions were performed with an X- ray source of \(50 \mathrm{kVp}\) and \(440 \mu \mathrm{A}\) . Volumetric computed tomography images were reconstructed by applying the iterative image space reconstruction algorithm (ISRA) in a \(400 \times 400 \times 370\) format with voxel dimensions of \(100 \times 100 \times 100 \mu \mathrm{m}^3\) . An Amira software (Thermo Scientific) was used for 3D reconstruction of the skull tissue and to analyse the bone formation in the defect area. Scale bars were used to standardize the images. Defect recovery is defined as \((\mathrm{Vi} - \mathrm{Vd}) / \mathrm{Vi} \times 100\%\) , where Vi and Vd represent defect volume at initial and designed timepoints, respectively.  
+
+<|ref|>text<|/ref|><|det|>[[114, 758, 883, 871]]<|/det|>
+Histology analysis: Skull samples were fixed and decalcified in Cal- EX II (Fisher Scientific) for 24 hours, rinsed with PBS, and embedded in paraffin. Tissue sections containing defect sites were cut to \(5 \mu \mathrm{m}\) thickness and stained with H&E and trichrome to assess tissue regeneration. Regenerated tissue thickness was measured using ImageJ, and osteogenesis was evaluated via IHC staining for key osteogenic markers, including OCN and OPN. Mouse skin tissue served as a negative control for all IHC staining.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 89, 882, 183]]<|/det|>
+Spatial transcriptomics: To confirm the RNA quality of each FFPE tissue block, 1- 2 curls (10um thickness each) were used for RNA extraction using Qiagen RNeasy FFPE kit (Qiagen 73504) according to manufactures' protocol. Extracted RNA was examined by Agilent Bioanalyzer RNA pico chip to confirm the \(\mathrm{DV}200 > 30\%\) . Simultaneously, the tissue morphology was examined on HE stained slide to identify region of interest.  
+
+<|ref|>text<|/ref|><|det|>[[115, 194, 882, 249]]<|/det|>
+For each FFPE sample, 1 section (5um thickness) was placed on visium slides. Each slide was incubated at \(42^{\circ}\mathrm{C}\) for 3 hours followed by overnight room temperature incubation. Then, the slide was stored at desiccated slide holder until proceeding to deparaffinization.  
+
+<|ref|>text<|/ref|><|det|>[[115, 260, 882, 408]]<|/det|>
+The deparaffinization, HE staining and imaging and decrosslinking of tissue slides were performed according to 10x Genomics protocol (CG000409 and CG000407) specific for Visium spatial gene expression for FFPE kit. Then, the slides were proceeded to human probe (v2) hybridization and ligation using 10x Genomics Visium spatial gene expression, \(6.5\mathrm{mm}\) kit (10x Genomics, PN- 1000188). The probes were released from tissue slide and captured on visium slide followed by probe extension. Sequencing libraries were prepared according to manufacturer's protocol. Multiplexed libraries were pooled and sequenced on Novaseq X Plus 10Bflowcell 100 cycles kit with following parameter: 28nt for Read 1 and 90nt for Read 2.  
+
+<|ref|>text<|/ref|><|det|>[[115, 419, 882, 518]]<|/det|>
+We visually identified the implant region in each sample. To exclude low quality capture locations, we removed the capture locations with fewer than 500 unique molecular identifiers, fewer than 500 genes, or \(\geq 25\%\) mitochondrial reads. \(^{61}\) We also filtered out the genes that are expressed in fewer than five capture locations. \(^{61}\) After quality control, flat group had 101 capture locations and 12,701 genes, whereas micropillar group had 73 capture locations and 13,371 genes.  
+
+<|ref|>text<|/ref|><|det|>[[115, 528, 882, 620]]<|/det|>
+Differential gene expression analysis: To identify the genes differentially expressed in flat and micropillar groups, we performed Wilcoxon rank- sum tests on the merged dataset (174 capture locations) using the FindAllMarkers function in Seurat V3. \(^{62}\) Our testing was limited to the genes present in both implants, detected in a minimum \(1\%\) of cells in either implant, as well as showing at least 0.1 log- fold difference between the two implants.  
+
+<|ref|>text<|/ref|><|det|>[[115, 632, 882, 743]]<|/det|>
+Cell type deconvolution: To perform cell typing on our data, we first identified three publicly available bone single- cell RNA sequencing (scRNA- seq) references with annotated cell types. \(^{43 - 45}\) The scRNA- seq references were processed, quality controlled, and merged using Seurat V3. Since our samples are nude mice, we excluded all the immune cells from the merged reference. The final merged scRNA- seq dataset contained a total of 12,717 cells and represented all major cell types present in bone tissues.  
+
+<|ref|>text<|/ref|><|det|>[[115, 754, 882, 885]]<|/det|>
+In 10x Visium data, each capture location contains a mixture of cells. \(^{63}\) Therefore, we performed cell type deconvolution to predict the cell type proportions in each capture location using BayesPrism, a Bayesian deconvolution method shown to work on spatial transcriptomics data. \(^{64,65}\) We excluded chromosomes X and Y, ribosomal, and mitochondrial genes from the analysis to reduce batch effects. We also removed the outlier genes with expression greater than \(1\%\) of the total reads in over \(10\%\) of capture locations. To improve cell typing accuracy, we only used the cell type signature genes for deconvolution analysis. The cell type markers were identified based
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 882, 126]]<|/det|>
+on the differential expression analysis results on the merged scRNA- seq reference. The predicted cell type proportions with above 0.5 coefficient of variation were clipped to zero to reduce noise.  
+
+<|ref|>text<|/ref|><|det|>[[115, 136, 882, 286]]<|/det|>
+Cell- type- based analyses: We performed Wilcoxon rank- sum tests using the deconvoluted cell type proportions to test if certain cell types are more prevalent in one implant than the other. We further examined the association between cell type proportions and gene expression levels in the two implants through Kendall's correlation analyses. All the p- values were adjusted for multiple testing through the false discovery rate approach. The proportions of three cell types (chondrocyte, OLC, and osteocyte) had over 50 significantly positively correlated genes. For each of these cell types, we performed pathway enrichment analysis of the significantly positively correlated genes using Metascape. \(^{66}\)  
+
+<|ref|>text<|/ref|><|det|>[[115, 297, 882, 390]]<|/det|>
+Statistical analysis: The results are shown as mean \(\pm\) standard deviation using violin super plots or bar graphs. Statistical analysis was performed using Kyplot software (version 2.0 beta 15). Statistical significance was determined by Student's t- test (flat versus micropillar, two- sided). All experiments presented in the manuscript were repeated at least as two independent experiments with replicates to confirm the results are reproducible.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 430, 271, 448]]<|/det|>
+## Acknowledgement  
+
+<|ref|>text<|/ref|><|det|>[[115, 458, 882, 760]]<|/det|>
+This work was supported by the National Science Foundation (NSF) Emerging Frontiers in Research and Innovation (EFRI) (no. 1830968 to G.A.A.), and National Institutes of Health (NIH) grants U54CA268084 and R01CA228272, NSF grant EFMA- 1830961 (to V.B.). This work was performed as a collaboration between the Center for Advanced Regenerative Engineering (CARE) and the Center for Physical Genomics and Engineering (CPGE) at Northwestern University. This work made use of the EPIC facility, the NUFAB facility, and the BioCryo facility of Northwestern University's NUANCE Center, which has received support from the SHyNE Resource (NSF ECCS- 2025633), the International Institute for Nanotechnology (IIN) and Northwestern's MRSEC programme (NSF DMR- 1720139). Proteomics services were performed by the Northwestern Proteomics Core Facility, generously supported by NCI CCSG P30 CA060553 awarded to the Robert H Lurie Comprehensive Cancer Center, instrumentation award (S10OD025194) from NIH Office of the Director, and the National Resource for Translational and Developmental Proteomics supported by P41 GM108569. We also thank the help from Dr. Hsiu- Ming Tsai at the Department of Radiology, The University of Chicago for microCT imaging. This work also made use of the Northwestern University NUSeq Core and the Biological Imaging Facility (BIF).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 800, 208, 817]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[115, 828, 882, 899]]<|/det|>
+1 Rippe, K. Dynamic organization of the cell nucleus. Curr. Opin. in Genet. Dev. 17, 373- 380 (2007).  
+2 Kalukula, Y., Stephens, A. D., Lammerding, J. & Gabriele, S. Mechanics and functional consequences of nuclear deformations. Nat. Rev. Mol. Cell Biol. 23, 583- 602 (2022).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 90, 886, 875]]<|/det|>
+3 Ramdas, N. M. & Shivashankar, G. V. Cytoskeletal Control of Nuclear Morphology and Chromatin Organization. J. Mol. Biol. 427, 695- 706 (2015).4 Heckenbach, I. et al. Nuclear morphology is a deep learning biomarker of cellular senescence. Nat. Aging 2, 742- 755 (2022).5 Seelbinder, B. et al. Nuclear deformation guides chromatin reorganization in cardiac development and disease. Nat. Biomed. Eng. 5, 1500- 1516 (2021).6 Uhler, C. & Shivashankar, G. V. Nuclear Mechanopathology and Cancer Diagnosis. Trends in cancer 4, 320- 331 (2018).7 Lele, T. P., Levy, D. L. & Mishra, K. Editorial: Nuclear morphology in development and disease. Front. Cell Dev. Biol. 11 (2023).8 Dahl, K. N., Ribeiro, A. J. & Lammerding, J. Nuclear shape, mechanics, and mechanotransduction. Circ. Res. 102, 1307- 1318 (2008).9 Wang, X. et al. Mechanical stability of the cell nucleus - roles played by the cytoskeleton in nuclear deformation and strain recovery. J. Cell Sci. 131 (2018).10 Elosegui- Artola, A. et al. Force Triggers YAP Nuclear Entry by Regulating Transport across Nuclear Pores. Cell 171, 1397- 1410. e1314 (2017).11 Lomakin, A. J. et al. The nucleus acts as a ruler tailoring cell responses to spatial constraints. Science 370, eaba2894 (2020).12 Venturini, V. et al. The nucleus measures shape changes for cellular proprioception to control dynamic cell behavior. Science 370, eaba2644 (2020).13 Wang, X. et al. Chromatin reprogramming and bone regeneration in vitro and in vivo via the microtopography- induced constriction of cell nuclei. Nat. Biomed. Eng. 7, 1514- 1529 (2023).14 Liu, H. et al. In Situ Mechanical Characterization of the Cell Nucleus by Atomic Force Microscopy. ACS Nano 8, 3821- 3828 (2014).15 Kechagia, Z. et al. The laminin- keratin link shields the nucleus from mechanical deformation and signalling. Nat. Mater. 22, 1409- 1420 (2023).16 Wang, X. et al. Intracellular manipulation and measurement with multipole magnetic tweezers. Sci. Robot. 4, eaav6180 (2019).17 Hwang, J. Y. et al. Cell Deformation by Single- beam Acoustic Trapping: A Promising Tool for Measurements of Cell Mechanics. Sci. Rep. 6, 27238 (2016).18 Stöberl, S. et al. Nuclear deformation and dynamics of migrating cells in 3D confinement reveal adaptation of pulling and pushing forces. Sci. Adv. 10, eadm9195 (2024).19 Song, Y. et al. Transient nuclear deformation primes epigenetic state and promotes cell reprogramming. Nat. Mater. 21, 1191- 1199 (2022).20 Shah, P. et al. Nuclear Deformation Causes DNA Damage by Increasing Replication Stress. Curr. Biol. 31, 753- 765. e756 (2021).21 Hanson, L. et al. Vertical nanopillars for in situ probing of nuclear mechanics in adherent cells. Nat. Nanotechnol. 10, 554- 562 (2015).22 Davidson, P. M., Özçelik, H., Hasirci, V., Reiter, G. & Anselme, K. Microstructured Surfaces Cause Severe but Non- Detrimental Deformation of the Cell Nucleus. Adv. Mater. 21, 3586- 3590 (2009).23 Tusamda Wakhloo, N. et al. Actomyosin, vimentin and LINC complex pull on osteosarcoma nuclei to deform on micropillar topography. Biomaterials 234, 119746 (2020).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 90, 886, 895]]<|/det|>
+24 Cao, X. et al. A Chemomechanical Model for Nuclear Morphology and Stresses during Cell Transendothelial Migration. Biophys. J. 111, 1541- 1552 (2016).25 Liu, R., Yao, X., Liu, X. & Ding, J. Proliferation of Cells with Severe Nuclear Deformation on a Micropillar Array. Langmuir : the ACS journal of surfaces and colloids 35, 284- 299 (2019).26 Carthew, J. et al. Precision Surface Microtopography Regulates Cell Fate via Changes to Actomyosin Contractility and Nuclear Architecture. Adv. Sci. 8, 2003186 (2021).27 Liu, X. et al. Subcellular cell geometry on micropillars regulates stem cell differentiation. Biomaterials 111, 27- 39 (2016).28 Long, Y., Sun, Y., Jin, L., Qin, Y. & Zeng, Y. Micropillars in Biomechanics: Role in Guiding Mesenchymal Stem Cells Differentiation and Bone Regeneration. Adv. Mater. Interfaces 11, 2300703 (2024).29 Xu, H. et al. Citric Acid: A Nexus Between Cellular Mechanisms and Biomaterial Innovations. Adv. Mater. 36, 2402871 (2024).30 Epstein, S. E., Luger, D. & Lipinski, M. J. Paracrine- Mediated Systemic Anti- Inflammatory Activity of Intravenously Administered Mesenchymal Stem Cells. Circ. Res. 121, 1044- 1046 (2017).31 Burdon, T. J., Paul, A., Noiseux, N., Prakash, S. & Shum- Tim, D. Bone Marrow Stem Cell Derived Paracrine Factors for Regenerative Medicine: Current Perspectives and Therapeutic Potential. Bone Marrow Res. 2011, 207326 (2011).32 Wang, Y., Kibbe, M. R. & Ameer, G. A. Photo- crosslinked biodegradable elastomers for controlled nitric oxide delivery. Biomater. Sci. 1, 625- 632 (2013).33 Fernando, S., McEnery, M. & Guelcher, S. A. in Advances in Polyurethane Biomaterials (eds Stuart L. Cooper & Jianjun Guan) 481- 501 (Woodhead Publishing, 2016).34 Ghibaudo, M. et al. Traction forces and rigidity sensing regulate cell functions. Soft Matter 4, 1836- 1843 (2008).35 Badique, F. et al. Directing nuclear deformation on micropillared surfaces by substrate geometry and cytoskeleton organization. Biomaterials 34, 2991- 3001 (2013).36 Ryu, H. et al. Materials and Design Approaches for a Fully Bioresorbable, Electrically Conductive and Mechanically Compliant Cardiac Patch Technology. Adv. Sci. 10, 2303429 (2023).37 Khalili, A. A. & Ahmad, M. R. A Review of Cell Adhesion Studies for Biomedical and Biological Applications. Int. J. Mol. Sci 16, 18149- 18184 (2015).38 Tomczak, A. et al. Interpretation of biological experiments changes with evolution of the Gene Ontology and its annotations. Sci. Rep. 8, 5115 (2018).39 Fabregat, A. et al. Reactome pathway analysis: a high- performance in- memory approach. BMC Bioinformatics 18, 142 (2017).40 Lu, P., Takai, K., Weaver, V. M. & Werb, Z. Extracellular matrix degradation and remodeling in development and disease. Cold Spring Harb Perspect Biol. 3 (2011).41 Zeng, Z., Li, Y., Li, Y. & Luo, Y. Statistical and machine learning methods for spatially resolved transcriptomics data analysis. Genome Biol. 23, 83 (2022).42 Yu, M. et al. Cranial Suture Regeneration Mitigates Skull and Neurocognitive Defects in Craniosynostosis. Cell 184, 243- 256. e218 (2021).43 Dillard, L. J. et al. Single- Cell Transcriptomics of Bone Marrow Stromal Cells in Diversity Outbred Mice: A Model for Population- Level scRNA- Seq Studies. J. Bone Miner. Res. 38, 1350- 1363 (2023).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 90, 886, 875]]<|/det|>
+44 Han, X. et al. Mapping the Mouse Cell Atlas by Microwell-Seq. Cell 172, 1091- 1107. e1017 (2018).45 Baryawno, N. et al. A Cellular Taxonomy of the Bone Marrow Stroma in Homeostasis and Leukemia. Cell 177, 1915- 1932. e1916 (2019).46 Zhong, L. et al. Single cell transcriptomics identifies a unique adipose lineage cell population that regulates bone marrow environment. eLife 9, e54695 (2020).47 Ma, C. et al. Citrate- based materials fuel human stem cells by metabonegenic regulation. Proc. Natl. Acad. Sci. USA 115, E11741- E11750 (2018).48 Woodard, J. R. et al. The mechanical properties and osteoconductivity of hydroxyapatite bone scaffolds with multi- scale porosity. Biomaterials 28, 45- 54 (2007).49 Wang, H., Huddleston, S., Yang, J. & Ameer, G. A. Enabling Proregenerative Medical Devices via Citrate- Based Biomaterials: Transitioning from Inert to Regenerative Biomaterials. Adv. Mater. 36, 2306326 (2024).50 Vilar, A. et al. Substrate mechanical properties bias MSC paracrine activity and therapeutic potential. Acta Biomater. 168, 144- 158 (2023).51 Li, Y. et al. 3D micropattern force triggers YAP nuclear entry by transport across nuclear pores and modulates stem cells paracrine. Natl. Sci. Rev. 10 (2023).52 Karamanos, N. K. et al. A guide to the composition and functions of the extracellular matrix. The FEBS J. 288, 6850- 6912 (2021).53 Saraswathibhatla, A., Indana, D. & Chaudhuri, O. Cell- extracellular matrix mechanotransduction in 3D. Nat. Rev. Mol. Cell Biol. 24, 495- 516 (2023).54 Cui, J. & Zhang, J. Cartilage Oligomeric Matrix Protein, Diseases, and Therapeutic Opportunities. Int. J. Mol. Sci. 23, 9253 (2022).55 Ishida, K. et al. Cartilage oligomeric matrix protein enhances osteogenesis by directly binding and activating bone morphogenetic protein- 2. Bone 55, 23- 35 (2013).56 Zheng, Z., Granado, H. S. & Li, C. Fibromodulin, a Multifunctional Matricellular Modulator. J. Dent. Res. 102, 125- 134 (2023).57 Feng, X. Chemical and Biochemical Basis of Cell- Bone Matrix Interaction in Health and Disease. Curr. Chem. Biol. 3, 189- 196 (2009).58 Alapan, Y., Younesi, M., Akkus, O. & Gurkan, U. A. Anisotropically Stiff 3D Micropillar Niche Induces Extraordinary Cell Alignment and Elongation. Adv. Healthc. Mater. 5, 1884- 1892 (2016).59 Cox, J. & Mann, M. MaxQuant enables high peptide identification rates, individualized p.p.b.- range mass accuracies and proteome- wide protein quantification. Nat. Biotech. 26, 1367- 1372 (2008).60 Yu, G., Wang, L. G., Han, Y. & He, Q. Y. clusterProfiler: an R package for comparing biological themes among gene clusters. Omics : a journal of integrative biology 16, 284- 287 (2012).61 Qian, J. et al. A pan- cancer blueprint of the heterogeneous tumor microenvironment revealed by single- cell profiling. Cell Res. 30, 745- 762 (2020).62 Stuart, T. et al. Comprehensive Integration of Single- Cell Data. Cell 177, 1888- 1902. e1821 (2019).63 Li, B. et al. Benchmarking spatial and single- cell transcriptomics integration methods for transcript distribution prediction and cell type deconvolution. Nat. Methods 19, 662- 670 (2022).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 89, 884, 211]]<|/det|>
+64 Chu, T., Wang, Z., Pe'er, D. & Danko, C. G. Cell type and gene expression deconvolution with BayesPrism enables Bayesian integrative analysis across bulk and single- cell RNA sequencing in oncology. Nat. Cancer 3, 505- 517 (2022).65 Niec, R. E. et al. Lymphatics act as a signaling hub to regulate intestinal stem cell activity. Cell Stem Cell 29, 1067- 1082. e1018 (2022).66 Zhou, Y. et al. Metascape provides a biologist- oriented resource for the analysis of systems- level datasets. Nat. Commun. 10, 1523 (2019).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 43, 245, 63]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 80, 585, 95]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[55, 108, 955, 202]]<|/det|>
+SupplementaryTable1.xlsxSupplementaryTable2.xlsxSupplementaryTable3.xlsxSupplementaryTable4.xlsxSupplementMicrotopographyinducedchangesincellnucleusmorphologyenhanceboneregenerationbymodulatingthecellularsecretome.pdf
+
+<--- Page Split --->

preprint/preprint__030d32ff9b730af3688e796beaceb960542869b68e0c2941b54bdcec394c4d7e/preprint__030d32ff9b730af3688e796beaceb960542869b68e0c2941b54bdcec394c4d7e.mmd

@@ -0,0 +1,354 @@
+
+# A Novel Approach for Classifying Battery and Pseudocapacitor Materials Using Capacitive Tendency and Supervised Machine Learning  
+
+Siraprapha Deebansok  VISTEC  
+
+Jie Deng  Institute for Advanced Study & College of Food and Biological Engineering, Chengdu University  
+
+Etienne Le Calvez  University of Nantes  
+
+Yachao ZHU  ICGM https://orcid.org/0000- 0001- 8057- 3754  
+
+Olivier Crosnier  Université de Nantes  
+
+Thierry Brousse  Institut des Matériaux Jean Rouxel, CNRS UMR 6502 - Université de Nantes https://orcid.org/0000- 0002- 1715- 0377  
+
+Olivier Fontaine (Olivier.fontaine@vistec.ac.th)  
+
+VISTEC (Vidyasirimedhi Institute of Science and Technology) https://orcid.org/0000- 0002- 1804- 5990  
+
+## Article  
+
+Keywords:  
+
+Posted Date: May 29th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 2930525/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on February 7th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 45394-w.
+
+<--- Page Split --->
+
+# A Novel Approach for Classifying Battery and Pseudocapacitor Materials  
+
+# Using Capacitive Tendency and Supervised Machine Learning  
+
+Siraprapha Deebansok,<sup>a</sup> Jie Deng,<sup>b</sup> Etienne Le Calvez,<sup>c,d</sup> Yachao Zhu,<sup>e</sup> Olivier Crosnier,<sup>c,d</sup> Thierry Brousse,<sup>c,d</sup> Olivier Fontaine<sup>a,f</sup>  
+
+<sup>a</sup> Molecular Electrochemistry for Energy laboratory, VISTEC, Institute of Science and Technology, Rayong, 21210, Thailand.  
+
+<sup>b</sup> Institute for Advanced Study & College of Food and Biological Engineering, Chengdu University, Chengdu 610106, China.  
+
+<sup>c</sup> Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, 44000 Nantes, France.  
+
+<sup>d</sup> Réseau sur le Stockage Électrochimique de l'Énergie (RS2E), CNRS FR 3459, 33 rue Saint Leu, 80039 Amiens, France.  
+
+<sup>e</sup> ICGM, Université de Montpellier, CNRS, 34293 Montpellier, France.  
+
+<sup>f</sup> Institut Universitaire de France, 75005 Paris, France.  
+
+\* Corresponding author. Email: Olivier Fontaine: olivier.fontaine@vistec.ac.th
+
+<--- Page Split --->
+
+## Abstract  
+
+In recent decades, there have been more than 100,000 scientific articles dedicated to developing electrode materials for supercapacitors and batteries. A heated debate nonetheless persists surrounding the standards for determining electrochemical behavior involving faradaic reactions, since the electrochemical signals produced by the various electrode materials and their different physicochemical properties often complicate matters. The difficulty lies in determining which group these materials fall into through simple binary classification as there can be an overlap between battery and pseudocapacitor signals and because both materials are faradaic in origin. To solve this conundrum, we applied supervised machine- learning toward a statistical analysis of electrochemical signals, and consequently developed a new standard which we called capacitive tendency. This predictor not only surpasses the limitations of human- based classification but also provides statistical tendencies regarding electrochemical behavior. Notably, and of particular importance to the electrochemical energy storage community publishing over a hundred articles weekly, we have created an online tool for easy classification of their data.
+
+<--- Page Split --->
+
+## Introduction  
+
+In the energy storage research field, batteries are one of the most studied types of devices owing to their use in a wide range of applications including electronic equipment, electric vehicles and for medical and military purposes. \(^{[1]}\) On the other hand, pseudocapacitive electrodes have attracted a considerable amount of attention due to their superior power capability. \(^{[2]}\) Both of these energy storage systems are generally composed of various types of electrode materials exhibiting electrochemical signals that may or may not resemble one another. \(^{[3]}\)  
+
+It is common knowledge that electric double layer capacitors (EDLCs) rely on a non- faradaic process without any electron transfer, whereas batteries and pseudocapacitors are governed by faradaic reactions. \(^{[4]}\) The latter processes are generally depicted by peaks on Cyclic Voltammograms (CVs) and plateaus on Galvanostatic Charge- Discharge (GCD) curves (Figure 1). \(^{[5]}\) Nowadays, some faradaic electrode materials display electrochemical signals similar to those of EDLCs, such as the rectangular/quasi- rectangular CV and the sloping GCD curve. \(^{[6, 7]}\) This characteristic has been found in a wide variety of transition metal oxides (RuO \(_2\) , \(^{[8]}\) MnO \(_2\) \(^{[9, 10]}\) ), conducting polymers (poly(3,4- ethylenedioxythiophene) \(^{[11, 12]}\) , polyaniline \(^{[13, 14]}\) ), and carbides (MXene) \(^{[15]}\) ). Numerous studies are underway focusing on faradaic electrode materials and including the behavior of pseudocapacitors and batteries, where both involve redox reactions, in keeping with the concept proposed by Conway et al. \(^{[4]}\) . Currently, owing to the vast amounts of materials studied, guidelines for distinguishing between the two are still largely inadequate, with some studies even contradicting the conventional definition of Conway et al., as later supported by Brousse et al. and other researchers in the field. \(^{[7]}\)  
+
+Indeed, electrochemical signals are numerous and complex, varying according to the choice of electrode materials, as shown in Figure 1, hence the difficulty in identifying and categorizing
+
+<--- Page Split --->
+
+these materials based on electrochemical signals. Recently, Fleischmann et al. \(^{[16]}\) , in a perspective paper, postulated the importance of a unified understanding when it comes to the electrochemical signals found in capacitors and batteries. The authors proposed the concept of electrolyte confinement that could impact the electrochemical behavior as a transition as a 'spectrum' from battery- to capacitor- type signals. It depicts the continuum of the signal from one state to another by altering the degree of confinement depending on, for example, the pore size of the electrode materials or the spacing size between MXene layers. Their work highlights the significance of successful quantification in order to move away from the postulate and arrive at a quantifiable spectral variable. It is shown that understanding the overlap and transition in electrochemical signals essentially requires a clear- cut classification of electrode material types based on their electrochemical behaviors (in CV and GCD). Unfortunately, the scientific elements presented by the authors are comparable to a mathematical conjecture, meaning that the proposed continuum is not supported by any mathematical variable or formalism. It is merely the subject of a postulate. Nonetheless, stating that the continuum is necessary does not diminish its importance. However, it becomes apparent that a mathematical variable must be added to quantify and measure this variation within the continuum. In order to metric this concept of 'continuum spectrum' and to provide the quantitative value to it, we analyze for the first time to the best of our knowledge the electrochemical signals with the help of supervised machine- learning. Our method is based on data science driven- supervised machine learning for achieving the descriptor, "capacitive tendency" that allows our community to develop metric, as a next step following this postulate.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 | Illustration of CVs and GCD curves of a pseudocapacitor without ambiguity (a and d, respectively), and a battery (c and f, respectively). CV and GCD curve with ambiguity (b and e, respectively). </center>  
+
+To date, computing techniques have been used as somewhat satisfactory tools toward ascertaining the charge storage mechanism behind various electrochemical signatures. \(^{[17 - 20]}\) It has been popular in the energy storage community that extracting the information such as electrochemical, chemical, and physical properties from literatures is essential, when big data has been generated with large number of scientific papers every year. Text mining was used to gather information of Li- ion battery research and development involving in several processes such as electrode synthesis, electrochemical performance, processing condition parameters, where the models are based on machine- learning (ML), natural language processing (NLP), Named Entity Recognition (NER). \(^{[21,22]}\) Recently, text- mining algorithms have been developed to efficiently extract various specific information of the materials from the article such as BatteryDataExtractor using bidirectional- encoder representations from transformers (BERT), \(^{[23]}\) and Li- ion battery annotated corpus (LIBAC) based on NER. \(^{[24]}\) However, using ML for electrochemical signal interpretation has not been done.  
+
+In this work, ML approach is used to interpret the CV and GCD signals by way of a supervised ML descriptor aimed at analyzing and determining the capacitive behavior of electrode materials found in thousands of scientific papers, as illustrated in Figure 2. Since our nuanced
+
+<--- Page Split --->
+
+classification is substantially different from the binary identification by human as only being battery or pseudocapacitor among various electrochemical signals, we propose a new definition called capacitive tendency. This tendency is not only able to classify a large majority of relevant materials, but also to depict possible behaviors of the material in question. Hence, this artificial intelligence (AI) power will be the only important tool to help transforming the information from images to accurate values based on big database available in the electrochemical energy storage community. In addition to this, we provide an online tool kit which uses supervised machine- learning to easily classify materials. Today, the large amount of literature sometimes leads to a misuse of the proposed definitions, to reduce this definitional mishap, our work will reduce these errors. Our work thus serves to put forward a new concept toward understanding and labeling the various electrochemical signatures of energy storage devices. Above all, it also offers a unique opportunity to unify the complex electrochemical signatures of more than 100,000 scientific papers through supervised ML.  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2 | Image extraction from scientific papers followed by CV and GCD classifications based on ResNet50 architecture. </center>
+
+<--- Page Split --->
+
+## Methods  
+
+## Dataset Construction  
+
+In the present paper, all datasets are in the form of images extracted using PyMuPDF library in Python language from more than 3,300 scientific papers. The first dataset, or Output 1, was obtained by figures extracting using OpenCV which provides (2,979) \(GCD\) , (5,598) \(CV\) and other images such as crystal structure image (which will not be used in the further classification steps). The \(GCD\) s and \(CV\) s were then labeled as belonging to one of two classes, namely batteries or pseudocapacitors without ambiguity, to be used for model training (80% of total data), as well as for validation (20% of total data) in Process 2 and Process 3 for \(GCD\) and \(CV\) classification, respectively. From Process 3, Output 3 was obtained and categorized into three types of training sets: 100% battery, 50% battery/pseudocapacitor, and 100% pseudocapacitor. This output was then further refined in Processes 4 and 5, as illustrated in Figure 3b. Moreover, cross- validation was performed with the experts in the field with the number of meetings.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3 | (a) CV and GCD datasets obtained after classification by Process 1, splitting them into training and validation datasets for further GCD and CV classification in Process 2 and Process 3, respectively. (b) The outputs from Process 3 are used in this final classification step to obtain the capacitive tendency based on percentage confidence rating of the prediction. (c) Table of processes, inputs and outputs performed/used to obtain these results. </center>  
+
+## Validation of classification architectures  
+
+In this work, Convolutional Neural Networks (CNNs) were selected for use as the image classification architectures.[25] Benchmarking was conducted on five different CNN models, including ResNet50,[26] MobileNetV2,[27] VGG16,[28] Xception[29] and 8- Layer CNN[25] (see Supplementary Figures ESI 1- 2), to compare model performance. It was carried out based on five metrics, including: Accuracy, Sensitivity, Specificity, Precision, and F- Score[30] (see
+
+<--- Page Split --->
+
+Supplementary Figures ESI 3 and Eq. ESI 1- 5). During the model training cycles, the number of training and validation iterations can impact the accuracy of the prediction since this is related to the experience gained over time by the ML model. Moreover, binary cross entropy \((BCE)\) loss, \(^{[31]}\) calculated from the prediction error as shown in Eq. 1, was minimized along the number of training iterations to optimize predictor performance.  
+
+\[L_{BCE} = -\frac{1}{n} (\sum_{i = 1}^{n}y_{i}\cdot \log (\hat{y}_{i})y_{i}\cdot \log (\hat{y}_{i}) + (1 - y_{i})\cdot \log (1 - \hat{y}_{i}))\qquad \mathrm{Eq.1}\]  
+
+Where \(y_{i}\) is the ground truth label (0 or 1, in this case battery or pseudocapacitor), \(\hat{y}\) is the predicted value, and n is the output size. \(^{[31]}\)  
+
+## Machine-learning for CV/GCD classification procedures  
+
+The ML architecture displaying the best performance after the validation step (further explained in the Results and Discussion section) was selected for use in this work as will be supervised during classification processes. ResNet50 was exploited in different steps denoted as Processes 1, 2, 3, 4, and 5 (as summarized in Figure 3c) according to the types of inputs and outputs. All of the images extracted from scientific papers were then categorized by Process 1 (ResNet50 model) which yielded Output 1, comprising GCDs, CVs and other images (such as optical image). GCDs from Output 1 were then classified using Process 2, and CVs were separately classified by Process 3, thereby providing the resulting prediction (Output 2: classified GCDs, and Output 3: classified CVs) of either battery or pseudocapacitor with a percentage confidence rating of \(0 - 100\%\) , while the errors were monitored and minimized to improve the prediction. Here, the capacitive tendency \((0 - 100\%)\) was firstly defined by the percentage confidence value, indicating the probability of CV shape as peak (0% capacitive tendency) and box shape (100% capacitive tendency). In the final step (Figure 3b), the classified CVs (in Output 3) were labeled according to four percentage confidence classes —
+
+<--- Page Split --->
+
+\(100\%\) battery, \(50\%\) battery, \(50\%\) pseudocapacitor and \(100\%\) pseudocapacitor — before being further modeled in Processes 4 and 5 to provide the capacitive tendency based on a percentage confidence of \(0 - 100\%\) .  
+
+An alternative way to understand the definition of capacitive tendency is to analyse it as the deviation from the ideal of the purely capacitive signal (is easy to recognize). When the trained model is confident that the curve is close to a rectangle (for CV) or a triangle (for GCD), then this implies that the curve is close to an ideal capacitive signal. On the contrary, a curve whose confidence value is close to zero means that the curve has a different contribution. Basically, the capacitive tendency reflects the analysis of the signal shape. It is information based on a geometric shape. Of course, alternatives could be used. However, the use of the classical formalism, as indicated in the "ideal CVs" area in Figure 4a, is impossible when the shape of the electrochemical signal deviates from this ideal. In the purely mathematical domain, the possibility of adding a rectangle to a closed geometric shape (a CV is a closed geometric shape) is a complex mathematical situation. It is the concept of Inscribed rectangular problem in mathematics. Thus, our data science- driven by supervised deep learning approach is a suitable alternative.  
+
+## Results and Discussion  
+
+This section explains how the models for CV and GCD classification were established for this specific dataset through the validation of different CNN architectures. The selection was based on well- known parameters including Accuracy, Sensitivity, Specificity, Accuracy, and F- Score. Moreover, the most accurate model was developed for use as the descriptor in order to determine the capacitive tendency of the various electrochemical behaviors, by applying the experimental data of various electrode materials. Ultimately, the selected model is destined for use by electrochemists as a tool for determining the nature of their materials.
+
+<--- Page Split --->
+
+## The issues surrounding electrochemical signal identification  
+
+The rapidly increasing number of scientific publications involving the study of capacitive materials over the last decade points to the importance of this field of study (as shown in Figure 4). It was found that the 3,300 papers contain around 5,600 CVs and 3,000 GCDs, which generates a massive amount of data and thereby renders human- based interpretation extremely challenging. Furthermore, the CV signals measured by these experiments are mostly performed in complex situations, and thus to not produce the perfect curves obtained in theoretical demonstrations using various common types of electrode materials (Figures 4). This also holds true for GCD signals acquired from experimental measurements. The whole limitation of the analyses in the field is summarised in figure 4a, most of the electrochemical signals are too far from the ideal signal to be analysed with the tools proposed in the state- of- the- art.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4 | Illustration of a) experimental CVs and GCDs of different electrode materials including \(MnO_2\) , \(V_2C\) , \(RuO_x\) , \(LaMnO_3\) , \(Ti_3C_2T_x\) , \(H_2TiNb_6O_{18}\) , \(Ag_1\) , \(3xLa_{1-x}NbO_3\) , \(Nb_2O_5\) , \(nano-MnS_2\) , \(bulk-MoS_2\) , \(TiO_2\) , and \(NaFePO_4\) , theoretical b) CVs and c) GCDs undergoing different electrochemical processes, and d) Number of publications involving capacitive and battery electrode materials from 2012 to 2022. (Google Scholar, August 28th, 2022). </center>  
+
+In this study, these CVs and GCDs were analyzed via supervised ML trained with datasets extracted from over 4,000 scientific papers (see DOI in Supplementary Information). In the following section, various Convolutional Neural Network architectures are validated and
+
+<--- Page Split --->
+
+selected based on the evaluations explained in the experimental section, by applying the theoretical CV and GCD curves.  
+
+## Validation of architectures  
+
+To select the Convolutional Neural Network architecture best suited to our datasets, the validation of a total of five models (ResNet50, MobileNetV2, VGG16, Xception, and 8- Layer CNN) was first performed using Processes 2 and 3 with different types of input and output (Table ESI 1). These architectures were chosen based on the reported accuracy ranking ascribed to the models' performance from ImageNet validation. [42, 43] In this step, the prediction was governed by binary classification to obtain only two different outputs, namely (i) battery or (ii) pseudocapacitor, since the model had been trained and supervised with CV and GCD datasets without ambiguity. ResNet50 was found to be the most accurate and precise one out of all the models (Table ESI 2) and was thus selected to further prediction in the next step. Moreover, ResNet50 is more adapted to the variety of data that will be input by the users, for example, plot with different frame and font styles and different color curves.  
+
+To demonstrate the efficiency of the model, 5598 CVs and 2979 GCDs were randomly selected and entered into the classifier according to Processes 2 and 3. Figure ESI 9 clearly demonstrates that the majority of predicted datasets showed a 100 % confidence rating, which would suggest that our ML model displays a high level of precision and reliability with a negligible risk of error.
+
+<--- Page Split --->
+
+## Validation of theoretical CVs and GCDs  
+
+In this part, the simulations of CV and GCD images were done using basic equations from theoretical electrochemistry including Faradaic process with peak- shaped CV, \(^{[44]}\) and EDLC with box- shaped CV which relies on Eq. 2 and Eq. 3. The simulated images were then classified by the trained model (process 4- 5). The equation for CVs showing redox peaks is given as follows:  
+
+\[\frac{i}{i_{max}} = \frac{e^{\frac{F}{R\cdot T}}(E - E_{peak}^{0})}{1 + \left(e^{\frac{F}{R\cdot T}}(E - E_{peak}^{0})\right)^{2}} \quad \text{Eq. 2,}\]  
+
+where \(\frac{i}{i_{max}}\) is the normalized current of the peak current function, \(F\) is the Faraday constant, \(R\) is the gas constant, \(T\) is the temperature, \(E\) is the applied potential and \(E_{peak}^{0}\) is the peak potential. The box- shaped EDLC current function is given by:  
+
+\[\frac{i}{i_{max}} = 1 - e^{-\frac{t}{R\cdot C}} \quad \text{Eq. 3,}\]  
+
+where \(C\) is the capacitance, \(R\) is the resistance and \(t\) is the charging period. \(^{[45]}\) It was shown that capacitive behavior is more pronounced the further the CV shape deviates from peaked to rectangular (Figure 5a).  
+
+Furthermore, simulating number of theoretical \(GCD\) images with the transition in curvature from straight to plateau feature could be applied with the classification model (process 2) in order to see the region of ambiguity. Using Eq. 4 by varying M parameter:  
+
+\[E = M\cdot \left(\frac{R\cdot T}{n\cdot F}\right)\log \left(\frac{\sqrt{t} - \sqrt{t}}{\sqrt{t}}\right) + E_{\tau /4} \quad \text{Eq. 4,}\]  
+
+where \(E\) is the potential, \(n\) is the number of electron transfers, \(t\) is the charging/discharging time, \(\tau\) is the time constant, \(E_{\tau /4}\) is the quarter- wave potential and \(M\) is the mathematical factor permitting the manipulation of the galvanostatic curve to show either a plateau feature (as
+
+<--- Page Split --->
+
+found in battery material measurements) or straight line (as in supercapacitor material measurements), the continuum GCD curves were obtained, as shown in Figure 5b (blue, grey, and purple lines).  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5 | The illustration of (a) classified theoretical CVs with Gaussian and box shapes as the components, and (b) classified theoretical galvanostatic charge (I) and discharge (II) curves obtained by using Eq 4. with a varying M parameter. The color of each curve is related to the probability of being battery (purple gradient bar) or capacitive material (blue gradient bar). </center>  
+
+Figure 5b(I) shows that a battery- type signature was found to apply for an \(M\) value range of between 1.6 and 7 (purple zone, with a 90- 100% confidence rating), whereas the prediction point to a pseudocapacitor- type for \(M\) values of between 7.1 and 19.6 (blue zone, with a 70- 100% confidence rating). Similarly, this result was also observed for theoretical discharging profiles, as shown in Figure 5b(II). However, in the grey zone when M is around
+
+<--- Page Split --->
+
+7.0 during charge and 9.4 during discharge, respectively, the predictor was hesitant to define the signal type, suggesting that a certain ambiguity occurs when the curvature of the \(GCD\) signal is somewhere between a straight line and a plateau, as has already been observed and which is consistent with experimental measurements related to pseudocapacitive materials (Figure 6c). The most pertinent conclusion that can be drawn from this calculation is that our model demonstrated the transition region of \(GCD\) signals in accordance with the continuum transition concept as proposed by Fleischmann et al. \(^{[16]}\) . Our model clearly demonstrates the source of the confusion for both humans and computers, which stems from the fact that these behaviors all originate from faradaic processes where electron transfer is the elementary step. This explains why the results of theoretical studies only hold true for basic scenarios. More complex behaviors, however, are frequently observed in experimental measurements and account for vast amounts of data, as depicted in Figure 4.  
+
+## Revealing the nature of electrode materials through supervised machine-learning  
+
+In accordance with the main purpose of this study, namely overcoming human limitations when it comes to understanding electrochemical signals, the objective in this section concerned clarifying the behavior of faradaic electrode materials. To this end, experimental \(CVs\) from Figure 4 were applied to the model to predict the capacitive tendency behavior of various electrode materials that conventionally can be calculated from \(\mathrm{dQ / dV} =\) constant in only simple cases such as supercapacitor materials but could be too complex to apply for pseudocapacitors. Well- known pseudocapacitive and battery materials from the literature, such as \(MnO_2\) and \(NMC\) , were compared not only to separate the signals produced by Processes 2 and 3 according to the conventional binary classification, but also to establish a new standard that we called capacitive tendency. Processes 4 and 5 broadened the classification range to create a statistical tendency representing an interpretable value: in the range of \(0\%\) denoting a
+
+<--- Page Split --->
+
+battery, to \(100\%\) being a pseudocapacitor. Finally, we were able to predict the capacitive behavior of various electrode materials from experimental data, as demonstrated in Figure 6.  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6 | Capacitive tendency prediction of experimental voltammograms of (a) the well-known pseudocapacitor and battery electrode materials \(MnO_2\) [46] and \(NMC\) [47] respectively, compared with the ambiguous CVs of \(Ag_{1 - 3x}La_{x}N_{2}NbO_{3}\) [37] and \(H_2TiNbO_{18}\) [36], respectively. Predicted (b) CVs and (c) GCDs of other electrode materials from the literature, as per Figure 4. </center>  
+
+As previously mentioned, the exemplary rectangular and peak shapes are unfortunately not often present when it comes to systems exhibiting fast charge/discharge behavior or when pseudocapacitive materials are investigated. Electrochemists thus find it difficult to analyze the voltammograms correctly in the face of such a variety of shapes, with even the \(CVs\) of \(V_2C\) , \(Nb_2O_5\) and nano- \(MoS_2\) electrode materials (Figure 6b) displaying a similar capacitive tendency of around \(52 - 53\%\) . This finding served to emphasize the necessity of using machine- learning
+
+<--- Page Split --->
+
+as a decisive tool for interpreting CV signals displaying a complexity that is beyond human discernment.  
+
+## The limitation of the binary classification battery vs. pseudocapacitor  
+
+During this phase of our research, numerous scientific articles containing the keyword "battery" (2011 articles) or "pseudocapacitor" (1346 articles) (see Supplementary Information for DOI) were analyzed using our supervised ML model to provide a statistical analysis of the number of papers containing a keyword that was in contradiction to their signals. Briefly, the articles were randomly selected and their relevant CV and GCD signals were extracted and then simply classified into either battery or pseudocapacitive type using only Processes 2 and 3. The outputs in Figure 7 depict that around \(67\%\) of the papers with a "pseudocapacitor" keyword are consistent with their experimental observations. Unexpectedly, however, nearly \(50\%\) of the articles with a "battery" keyword displayed contradicting signals. These results serve to reinforce the fact that human- based interpretation could greatly benefit from being replaced with computing techniques such as ML. Apparently, our machine- learning classification technique showed the significant portion of the articles using binary keywords (battery or pseudocapacitor) that contradict (mismatched) with their electrochemical signal (Supporting Information Section 8.1- 8.6).
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Figure 7 | (a) The methodology behind the title classification of papers as either a battery or pseudocapacitor, followed by (b) CV and GCD extraction and then (c) the matched/mismatched outputs using our classifiers (Processes 1, 2 and 3). The percentage correlation between titles for pseudocapacitor and battery materials vs. correctly classified CVs and GCDs. </center>  
+
+This result perfectly shows the limit of the binary approach in the field. Because analysing a binary classification leads to this misclassification by the authors. Our approach, using capacitive tendency, allows a unification of the measurements, by including them in a "spectrum" as proposed by Frieshman et al[16], in a mathematical conjecture.
+
+<--- Page Split --->
+
+## Online tool kit for CV/GCD classification  
+
+Online tool kit for CV/GCD classificationIn order to facilitate the task of users worldwide when it comes to classifying the electrochemical behaviors (battery or pseudocapacitor) of their experimental data (CVs and GCDs), we have launched an online tool for analyzing these signals and providing an output in the form of a capacitive trend (or percentage confidence rating). It is publicly available at http://supercapacitor- battery- artificialintelligence.vistec.ac.th, and details are also provided in the Supporting Information.  
+
+![](images/Figure_8.jpg)
+
+<center>Figure 8 | The online tool kit for CV and GCD classification based on our model. </center>  
+
+## Conclusion  
+
+ConclusionThe research presented herein has successfully managed to resolve the decades- old conundrum concerning the interpretation of electrochemical signals from CVs and GCDs by making full use of advanced computing technology in order to classify the behavior of
+
+<--- Page Split --->
+
+materials as battery- like or pseudocapacitor- like. Specifically, we demonstrated that supervised ML is a powerful and accurate way to distinguish between these often complex signals. Our study also highlights the recurrent issue of the titles of scientific papers often contradicting the results of their own data, especially when it comes to those articles with “battery” in the title. This emphasizes the importance of using computer- based modelling for prediction as opposed to human- based analysis, which is far slower and more subjective and that leads to much unnecessary disagreement and debate. As a major contribution to our peers in the electrochemical energy storage community, we are delighted to announce a unique online tool based on our model toward simple online classification via our distinguishing marker, called capacitance tendency, affording them the possibility of a quick and easy standard to refer to when attempting to determine the nature of their new materials. Last but not least, featuring text- mining of material information with our classification tool could be an ultimate strategy for future perspectives on artificial intelligence for energy storage technology.  
+
+## Data and code availability  
+
+Machine- learning models and datasets are made publicly available at GitHub repository: https://github.com/ice555mee/TB- robot_code- data or contact the author (olivier.fontaine@vistec.ac.th) for more information. The instruction is provided in both supporting information and on Github repository. The website is available via the link: http://supercapacitor- battery- artificialintelligence.vistec.ac.th/  
+
+## References  
+
+1. Mahmud, S., et al., Recent advances in lithium-ion battery materials for improved electrochemical performance: A review. Results in Engineering, 2022. 15: p. 100472.
+
+<--- Page Split --->
+
+2. Choi, C., et al., Achieving high energy density and high power density with pseudocapacitive materials. Nature Reviews Materials, 2020. 5(1): p. 5-19. 
+
+3. Brousse, T., D. Bélanger, and J.W. Long, To Be or Not To Be Pseudocapacitive? Journal of The Electrochemical Society, 2015. 162(5): p. A5185-A5189. 
+
+4. Ardizzone, S., G. Fregonara, and S. Trasatti, "Inner" and "outer" active surface of RuO2 electrodes. Electrochimica Acta, 1990. 35(1): p. 263-267. 
+
+5. Mathis, T.S., et al., Energy Storage Data Reporting in Perspective—Guidelines for Interpreting the Performance of Electrochemical Energy Storage Systems. Advanced Energy Materials, 2019. 9(39): p. 1902007. 
+
+6. Chodankar, N.R., et al., True Meaning of Pseudocapacitors and Their Performance Metrics: Asymmetric versus Hybrid Supercapacitors. Small, 2020. 16(37): p. 2002806. 
+
+7. Brousse, T., D. Bélanger, and J.W. Long, To Be or Not To Be Pseudocapacitive. Journal of The Electrochemical Society, 2015. 162. 
+
+8. Zheng, J.P., P.J. Cygan, and T.R. Jow, Hydrous Ruthenium Oxide as an Electrode Material for Electrochemical Capacitors. Journal of The Electrochemical Society, 1995. 142(8): p. 2699-2703. 
+
+9. Lee, H.Y. and J.B. Goodenough, Supercapacitor Behavior with KCl Electrolyte. Journal of Solid State Chemistry, 1999. 144(1): p. 220-223. 
+
+10. Jabeen, N., et al., Enhanced Pseudocapacitive Performance of α-MnO2 by Cation Preinsertion. ACS Applied Materials & Interfaces, 2016. 8(49): p. 33732-33740. 
+
+11. Yoon, S.-B. and K.-B. Kim, Effect of poly(3,4-ethylenedioxythiophene) (PEDOT) on the pseudocapacitive properties of manganese oxide (MnO2) in the PEDOT/MnO2/multiwall carbon nanotube (MWNT) composite. Electrochimica Acta, 2013. 106: p. 135-142. 
+
+12. Lei, C., P. Wilson, and C. Lekakou, Effect of poly(3,4-ethylenedioxythiophene) (PEDOT) in carbon-based composite electrodes for electrochemical supercapacitors. Journal of Power Sources, 2011. 196(18): p. 7823-7827. 
+
+13. Liu, T., et al., Polyaniline and Polypyrrole Pseudocapacitor Electrodes with Excellent Cycling Stability. Nano Letters, 2014. 14(5): p. 2522-2527. 
+
+14. Yu, G., et al., Hybrid nanostructured materials for high-performance electrochemical capacitors. Nano Energy, 2013. 2(2): p. 213-234. 
+
+15. Li, Y., et al., A general Lewis acidic etching route for preparing MXenes with enhanced electrochemical performance in non-aqueous electrolyte. Nature Materials, 2020. 19(8): p. 894-899. 
+
+16. Fleischmann, S., et al., Continuous transition from double-layer to Faradaic charge storage in confined electrolytes. Nature Energy, 2022. 7(3): p. 222-228. 
+
+17. Zhang, X., et al., Interpretable learning of voltage for electrode design of multivalent metal-ion batteries. npj Computational Materials, 2022. 8(1): p. 175. 
+
+18. Zhang, Y., et al., Identifying degradation patterns of lithium ion batteries from impedance spectroscopy using machine learning. Nature Communications, 2020. 11(1): p. 1706. 
+
+19. Swift, M.W., J.W. Swift, and Y. Qi, Modeling the electrical double layer at solid-state electrochemical interfaces. Nature Computational Science, 2021. 1(3): p. 212-220.
+
+<--- Page Split --->
+
+20. Zhang, K., et al., Self-supervised image quality assessment for X-ray tomographic images of Li-ion battery. npj Computational Materials, 2022. 8(1): p. 194.  
+
+21. El - Bousiydy, H., et al., What Can Text Mining Tell Us About Lithium - Ion Battery Researchers' Habits? Batteries & Supercaps, 2021. 4(5): p. 758-766.  
+
+22. Mahbub, R., et al., Text mining for processing conditions of solid-state battery electrolytes. Electrochemistry Communications, 2020. 121.  
+
+23. Huang, S. and J.M. Cole, BatteryDataExtractor: battery-aware text-mining software embedded with BERT models. Chem Sci, 2022. 13(39): p. 11487-11495.  
+
+24. El-Bousiydy, H., et al., LIBAC: An Annotated Corpus for Automated "Reading" of the Lithium-Ion Battery Research Literature. Chemistry of Materials, 2023. 35(5): p. 1849-1857.  
+
+25. Yamashita, R., et al., Convolutional neural networks: an overview and application in radiology. Insights into Imaging, 2018. 9(4): p. 611-629.  
+
+26. He, K., et al., Deep Residual Learning for Image Recognition. 2016. 770-778.  
+
+27. Sandler, M., et al., MobileNetV2: Inverted Residuals and Linear Bottlenecks. 2018. 4510-4520.  
+
+28. Simonyan, K. and A. Zisserman Very Deep Convolutional Networks for Large-Scale Image Recognition. 2014. arXiv:1409.1556.  
+
+29. Chollet, F. Xception: Deep Learning with Depthwise Separable Convolutions. in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 2017.  
+
+30. Lever, J., M. Krzywinski, and N. Altman, Classification evaluation. Nature Methods, 2016. 13(8): p. 603-604.  
+
+31. Zhang, Z. and M.R. Sabuncu. Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels. in NeurIPS. 2018.  
+
+32. Zhao, X., et al., Prepared MnO2 with different crystal forms as electrode materials for supercapacitors: experimental research from hydrothermal crystallization process to electrochemical performances. RSC Advances, 2017. 7(64): p. 40286-40294.  
+
+33. Shan, Q., et al., Two-dimensional vanadium carbide (V2C) MXene as electrode for supercapacitors with aqueous electrolytes. Electrochemistry Communications, 2018. 96: p. 103-107.  
+
+34. Zhang, J., et al., Template Synthesis of Tubular Ruthenium Oxides for Supercapacitor Applications. The Journal of Physical Chemistry C, 2010. 114(32): p. 13608-13613.  
+
+35. Mefford, J.T., et al., Anion charge storage through oxygen intercalation in LaMnO3 perovskite pseudocapacitor electrodes. Nature Materials, 2014. 13(7): p. 726-732.  
+
+36. Miranda, J., et al., Revisiting Rb2TiNb6O18 as electrode materials for energy storage devices. Electrochemistry Communications, 2022. 137: p. 107249.  
+
+37. Le Calvez, E., et al., Investigating the Perovskite Ag1-3xLaxNbO3 as a High-Rate Negative Electrode for Li-Ion Batteries. Frontiers in Chemistry, 2022. 10.  
+
+38. Lian, Y., et al., Optimization Design and Application of Niobium-Based Materials in Electrochemical Energy Storage. Advanced Energy and Sustainability Research, 2020. 1(1): p. 2000038.
+
+<--- Page Split --->
+
+39. Cook, J.B., et al., Suppression of Electrochemically Driven Phase Transitions in Nanostructured MoS2 Pseudocapacitors Probed Using Operando X-ray Diffraction. ACS Nano, 2019. 13(2): p. 1223-1231.  
+40. Li, X., et al., Orderly integration of porous TiO2(B) nanosheets into bunchy hierarchical structure for high-rate and ultralong-lifespan lithium-ion batteries. Nano Energy, 2017. 31: p. 1-8.  
+41. Karthik, M., et al., Design and fabrication of NaFePO4/MWCNTs hybrid electrode material for sodium-ion battery. Journal of Materials Science: Materials in Electronics, 2020. 31(23): p. 21792-21801.  
+42. Zhang, D., et al., Knowledge Graph-Based Image Classification Refinement. IEEE Access, 2019. 7: p. 57678-57690.  
+43. Zhang, D. and T. Zhou, Deep Convolutional Neural Network Using Transfer Learning for Fault Diagnosis. IEEE Access, 2021. 9: p. 43889-43897.  
+44. Waelder, J., et al., A Description of the Faradaic Current in Cyclic Voltammetry of Adsorbed Redox Species on Semiconductor Electrodes. Journal of the American Chemical Society, 2022. 144(14): p. 6410-6419.  
+45. Costentin, C. and J.-M. Saveant, Ohmic drop correction in electrochemical techniques. Multiple potential step chronoamperometry at the test bench. Energy Storage Materials, 2020. 24: p. 1-3.  
+46. Goikolea, E., et al., Synthesis of nanosized MnO2 prepared by the polyol method and its application in high power supercapacitors. Materials for Renewable and Sustainable Energy, 2013. 2(3): p. 16.  
+47. Zukalová, M., et al., LiNi1/3Mn1/3Co1/3O2 with morphology optimized for novel concept of 3D Li accumulator. International Journal of Energy Research, 2020. 44(11): p. 9082-9092.  
+
+## Acknowledgements  
+
+Website hosting is supported by Vidyasirimedhi Institute of Science and Technology server.  
+
+This work is supported by funding from Thailand Science Research and Innovation (TSRI)  
+
+(Grant No. FRB660004/0457).  
+
+## Competing interests  
+
+The authors declare no competing interests.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- ESISUB1.docx
+
+<--- Page Split --->

preprint/preprint__032a07311eb9bb5f9f4a079bca8cd4decf50b0f2c1fa36d909d6d9fbdf969e73/preprint__032a07311eb9bb5f9f4a079bca8cd4decf50b0f2c1fa36d909d6d9fbdf969e73.mmd

@@ -0,0 +1,188 @@
+
+# Responsive nucleus accumbens deep brain stimulation restores eating control in severe obesity  
+
+Casey Halpern ( \(\boxed{ \begin{array}{r l} \end{array} }\) casey.halpern@pennmedicine.upenn.edu )  
+
+University of Pennsylvania  
+
+Rajat Shivacharan Stanford  
+
+Cammie Rolle University of Pennsylvania  
+
+Daniel Barbosa University of Pennsylvania  
+
+Tricia Cunningham Stanford  
+
+Austin Feng Stanford  
+
+Noriah Johnson Stanford  
+
+Debra Safer Stanford  
+
+Cara Bohen Stanford  
+
+Corey Keller Stanford  
+
+Vivek Buch Stanford  
+
+Jonathan Parker Stanford  
+
+Dan Azagury Stanford  
+
+Peter Tass Stanford  
+
+Mahendra Bhati Stanford  
+
+Robert Malenka Stanford University  
+
+James Lock
+
+<--- Page Split --->
+
+## Brief Communication  
+
+# Keywords:  
+
+Posted Date: March 15th, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1432380/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 Medicine on August 29th, 2022. See the published version at https://doi.org/10.1038/s41591- 022- 01941- w.
+
+<--- Page Split --->
+
+## Abstract  
+
+Craving that precede loss of control (LOC) over food consumption present an opportunity for intervention in patients suffering from binge eating disorder (BED). Here, we used responsive deep brain stimulation (DBS) to record NAc electrophysiology during food cravings preceding LOC eating in two patients with BED and severe obesity (NCT03868670). Increased NAc low- frequency oscillations prominent during food cravings were used to guide DBS delivery. Over 6 months, we observed improved self- control of food intake and weight loss. These findings provide early support for restoring inhibitory control with electrophysiologically- guided NAc DBS. Further work is required to determine scalability of this approach. Trial Registration # NCT03868670.  
+
+## Introduction  
+
+Loss of control (LOC) eating, or the subjective sense that one cannot stop eating, is associated with binge eating - defined by the consumption of an objectively large amount of food in a short period of time accompanied by a sense of LOC.1 LOC eating is often characterized by the loss of inhibitory control in response to appetitive cues and cravings leading to binge eating2. Recurrent and distressing episodes of binge eating are the key features of binge eating disorder (BED). BED is the most common eating disorder, affecting up to 3 percent of U.S. adults, and is the most severe form of LOC eating based on volume of food consumed'. It is associated with obesity, decreased quality of life and premature mortality.3  
+
+Most treatments for obesity fail to address LOC eating directly, limiting the efficacy of even the most aggressive interventions such as bariatric surgery.4,5 Clinical evidence supports a role of cravings for preferred food, or intense desires to consume specific palatable foods, prior to the onset of LOC and binge eating.6,7 Particularly in individuals who are overweight or obese, food cravings have been linked with LOC among those diagnosed with BED.8 Given this, recent studies have examined neural signals associated with food craving in the pursuit of identifying a biomarker used to trigger deep brain stimulation (i.e., responsive DBS or rDBS) and inhibit onset of LOC eating when patients may be most atrisk.  
+
+In the effort to identify such a craving biomarker, previous work in mice found that anticipation of a high- fat food reward was associated with increased low- frequency oscillatory power in the NAc.9 This work supported a growing body of evidence across species reporting electrophysiological, neurochemical, and functional neuroimaging activities within circuits involving the NAc that correlate to reward anticipation,10- 13 and that predict consequential behavioral outcomes.14 Using low- frequency delta- band power as a biomarker to trigger delivery of a brief train of high- frequency electrical stimulation to the NAc (here after referred to as rDBS) resulted in significant and lasting attenuation of binge- like eating in mice sensitized to high fat food,9 while conventional, continuous DBS appeared to lose efficacy over time.15,16
+
+<--- Page Split --->
+
+Here, we report the proof of concept in this first- in- human study designed to characterize human NAC electrophysiology of craving as it relates to LOC eating. We sought to identify changes in NAC electrophysiology associated with moments of food craving and LOC eating during controlled in- clinic behavioral tasks and to assess the generalization of this effect to LOC eating events in a naturalistic setting and outside the behavioral laboratory. Finally, we implemented rDBS triggered by NAC electrophysiology identified in behavioral and naturalistic assessments, and report here initial results on the potential efficacy of this novel intervention. This study was performed under a U.S. Food and Drug Administration Investigational Device Exemption (G180079) using the NeuroPace Responsive Neurostimulation (RNS) System<sup>17</sup>.  
+
+## Methods  
+
+## PRESTUDY PROCEDURES  
+
+Two adult women with BED and treatment- refractory severe (grade III) obesity, despite bariatric surgery were recruited for this study, approved by Stanford's Institutional Review Board (IRB- 46563) (see appendix for participant characteristics). Designed with a staggered enrollment, each subject progressed through the study stages shown in Fig. 1A. Both subjects underwent stereotactic implantation of bilateral depth electrodes, each with four contacts.<sup>18</sup> The two distal contacts were positioned in the NAC and the two proximal contacts traversed the anterior limb of the internal capsule (Fig. 1B).<sup>19</sup>  
+
+## RECORDING PHASE  
+
+Immediately following implantation, subjects entered a 6- month recording phase, during which naturalistic in- lab assessments and ambulatory real- world assessments were performed to identify an electrophysiological biomarker for rDBS in the consecutive stimulation phase. From each hemisphere, activity was recorded from the ventral and dorsal NAC (see appendix for details). Subjects underwent two assessments to evaluate NAC electrophysiology during: 1) anticipation (pre- consumption) of food during standard meals and LOC eating (i.e., Multi- Item Buffet assessment; in- lab naturalistic testing); and 2) states of hunger and craving (pre- consumption) (i.e., ambulatory assessment; real- world testing).  
+
+## STIMULATION PHASE  
+
+Following the recording phase, both subjects underwent single- blinded stimulation survey testing in which they received brief bursts of electrical stimulation across all electrode contacts to screen for acute effects. This was followed by a single- blinded, staged, on- off stimulation safety testing period to assess for possible side effects of rDBS. Subjects then entered the 10–12 month open- label stimulation phase of the study. In this phase, rDBS was delivered using a bipolar montage of the two NAC electrode contacts. Both subjects received bilateral NAC rDBS via depth electrodes connected to a NeuroPace RNS system to detect and inhibit LOC eating events. Stimulation was delivered at 125 Hz in two 5 second bursts with a charge density of 0.5–1.5 μC/cm.<sup>17</sup> Detections and stimulations occurred approximately 400 times/day with a stimulation limit set to 700 bouts (or approximately 117 min) per day in order to limit unnecessary
+
+<--- Page Split --->
+
+stimulation at night. Based on the recording phase, each subject's device was programmed to detect brief increases in low- frequency activity in both the left and right ventral NAc (see appendix). These detections of low- frequency activity triggered bilateral NAc rDBS ( \(\sim 1\mu \mathrm{C} / \mathrm{cm}^2\) charge density, 10s duration). Low- frequency triggered bilateral stimulation has been well tolerated by both subjects. Neither subject 1 nor 2 experienced a serious adverse event, and all reported events were self- limited (Table S4). Examination of sensitivity and specificity can be found in the appendix (Figures S1, S2).  
+
+## Results  
+
+RECORDING PHASE  
+
+MULTI- ITEM BUFFET: NAC ELECTROPHYSIOLOGY DURING IN- LAB LOC EATING. In this assessment, we investigated each subject's LOC by modeling the at- risk environment in a controlled setting \(^{20}\) . Using mood provocation (see appendix), we assessed LOC (1–5 Likert severity scale) during presentation of a high calorie buffet of the subject's preferred foods while recording synchronized video- NAc LFP (Local Field Potential) activity. Analogous to our pre- clinical work, we analyzed and compared bite onset during the buffet to standard meals. Results showed low- frequency power increases immediately prior to LOC eating. Specifically, increases in left ventral NAc low- frequency (2–8 Hz) power were observed for both subjects during LOC immediately preceding (within 2 seconds) the videoed bite onset (see appendix) (mean ± s.e. dB power \([V^2 /\mathrm{Hz}]\) : Subject 1, \(2.4 \pm 1.5, \mathrm{n} = 16\) bites; Subject 2, \(5.6 \pm 3.1, \mathrm{n} = 12\) bites). In contrast, increases in low- frequency power were not observed immediately prior to bites during standard meals (Subject 1, \(0.6 \pm 1.0, \mathrm{n} = 15\) bites; Subject 2, \(0.3 \pm 0.9, \mathrm{n} = 11\) bites) (Fig. 1C, Student's t- test, \(p < 0.05\) ). There were no statistical changes in any of the other recorded frequency bands in either subject (Student's t- test, \(p > 0.05\) ).  
+
+AMBULATORY ASSESSMENT: NAC ELECTROPHYSIOLOGY DURING REAL- WORLD LOC EATING EVENTS. We analyzed electrophysiology acquired during real- world behavioral states (see appendix) to validate the lab findings. Low- frequency power increases during LOC eating were corroborated with real- world assessments. Specifically, significantly higher low- frequency oscillatory power (Fig. 2A) in bilateral ventral NAc was found during subject- reported LOC eating events (craving- red trace, mean ± s.e. power \([V^2 /\mathrm{Hz}]\) : Subject 1, left NAc: \(0.21 \pm 0.11\) , right NAc: \(0.16 \pm 0.06, \mathrm{n} = 10\) events; Subject 2, left NAc: \(0.58 \pm 0.14\) , right NAc: \(0.21 \pm 0.07, \mathrm{n} = 71\) events) when compared to control periods (control- black trace, Subject 1, left NAc: \(0.1 \pm 0.04\) , right NAc: \(0.04 \pm 0.01, \mathrm{n} = 9\) events; Subject 2, left NAc: \(0.19 \pm 0.04\) , right NAc: \(0.09 \pm 0.04, \mathrm{n} = 80\) events) and periods of hunger (hunger- blue trace, Subject 1, left NAc: \(0.06 \pm 0.01\) , right NAc: \(0.03 \pm 0.01, \mathrm{n} = 13\) events; Subject 2, left NAc: \(0.27 \pm 0.11\) , right NAc: \(0.11 \pm 0.03, \mathrm{n} = 37\) events) (Fig. 2A, one- way ANOVA, Subject 1, left NAc: \(f = 3.50, \mathrm{P} = 0.04\) , right NAc: \(f = 4.95, \mathrm{P} = 0.03\) ; Subject 2, left NAc: \(f = 5.14, \mathrm{P} = 0.02\) , right NAc: \(f = 0.07, \mathrm{P} = 0.93\) ). Consistent with the in- clinic tasks, there were no differences in any other frequency band during at- risk moments in the ambulatory setting.  
+
+SIGNAL DETECTION: BILATERAL NAC DETECTION. For each subject, we programmed the device to detect brief increases in low- frequency activity in both the left and right ventral NAc. To confirm that the signal
+
+<--- Page Split --->
+
+being detected was in the low- frequency range, we analyzed the power spectra of the NAc LFP activity in the 5 seconds prior to a detection and found that the Area detectors (see appendix) were detecting low- frequency activity in the left and right ventral NAc (Fig. 2B). For this analysis, we compared detection made in stored LFPs during reported LOC eating events and awake events. For Subject 1, increased low- frequency power compared to baseline NAc LFP signal (average 2- minute window) was identified in \(74.4\%\) (67/90) of reported LOC eating event detections and \(63.2\%\) (84/133) of the awake detections \((X2(1,N = 223) = 24.54,p< 0.05)\) . For Subject 2, increased low- frequency power was identified in \(76.9\%\) (30/39) reported LOC eating event detections and \(45.8\%\) (22/48) awake detections \((X2(1,N = 87) = 14.82,p< 0.05)\) .  
+
+## STIMULATION PHASE  
+
+CHANGE in LOC EATING and Weight. Both subjects reported an increased sense of self- regulation and control over food intake specific to cravings and related eating behavior. Further, both subjects showed a decrease in the reported frequency of LOC eating events from baseline to 6- months post- stimulation (i.e. the primary endpoint), as assessed by the Eating Disorder Examination (EDE), and LOC severity, as assessed by the Eating Loss of Control Scale, across the 28- day period during the baseline month compared to 6- months post- stimulation month (LOC Frequency: Subject 1 = 80% decrease; Subject 2 = 87% decrease; LOC episode severity: Subject 1: 9- point improvement \((p = 0.09)\) ; Subject 2: 15- point improvement \((p = 0.05)\) ) (Fig. 3A,B). Notably, by the end of the 6- month follow- up period, Subject 1 exhibited substantial improvement in BED severity, while Subject 2 no longer met criteria for BED (i.e., fewer than average of 4 binge eating events per- month over the prior consecutive 3 months for no more BE diagnosis), which met our primary endpoint (Fig. 3C). Corroborating their subjective reports (Fig. 3), 6- month outcomes showed a decrease in body weight (kg and % reduction) and BMI for both subjects: Subject 1 = - 5.9 kg, - 4.5%, and - 2.2 kg/m², respectively; Subject 2 = - 8.2 kg, - 5.8%, and - 2.9 kg/m², respectively) (Fig. 3D,E).  
+
+## Discussion  
+
+In summary, this study identified NAc low- frequency oscillatory power as a signal associated with LOC craving, and then implemented this biomarker to guide rDBS delivery in two subjects with BED and severe obesity. In the recording phase, in- lab assessments implicated NAc low- frequency signalling during naturalistic LOC eating. The generalizability of this signal to real- world settings was then corroborated by our finding that low- frequency oscillatory power was increased during real- world LOC eating events compared to non- LOC events. In the stimulation phase, 6 months of bilateral NAc rDBS triggered by low- frequency power was found to improve LOC eating, as well as reduce body weight and BMI. Optimization of stimulation parameters is still ongoing in both subjects, and four additional subjects are expected to be implanted following a supplement approval to our investigational device exemption. We encountered early challenges when capturing LOC eating events in the real world. A training period was necessary prior to surgery for both subjects to learn to identify and document their LOC eating behaviors. This involved having a psychiatrist (DS) with expertise in obesity and eating disorders discuss with each patient her
+
+<--- Page Split --->
+
+personal understanding of LOC eating. As we report (see appendix), while sensitivity of low- frequency detections to LOC eating was high, low- frequency oscillations in the NAC were not always specific to food craving and LOC eating compared to non- LOC eating events. Ongoing work seeks to optimize detection algorithms and improve the sensitivity and specificity of rDBS for LOC eating. Further, real- world LOC electrophysiology detected from ambulatory recordings was specific to bilateral, ventral NAC delta (2- 4Hz), whereas in- lab experiments found effects in both delta and theta (2- 8Hz) and were limited to the left ventral NAC. In addition, because real- world data capture was not time- locked to specific bite events during LOC and standard meals, the ambulatory and multi- item buffet data reflect different time windows respective to the LOC events. We also note that while the frequencies within which we found our effects here contained the delta signal identified in mice<sup>9</sup>, the effects from in- lab testing were broader and inclusive of theta frequencies. Importantly, one difficulty with the low- frequency biomarker signal is its presence during normal physiological processes such as sleep<sup>21,22</sup>. To account for detection and stimulation during sleep, we limited rDBS delivery to awake hours (7am- 10pm). Finally, the upfront cost of implantable devices is high; thus long- term follow- up of LOC eating as well as BMI beyond the study period will be necessary to assess societal cost- effectiveness of this intervention based on our decision analyses<sup>23</sup>.  
+
+In conclusion, NAC rDBS improved LOC eating frequency and severity in two patients with BED and severe obesity. These findings were associated with weight loss even during this early follow- up period, suggesting patients can lose weight without instruction to change their diet or physical activity (efforts which are often unsuccessful). This is a testament to the potential clinical significance of this novel intervention and supports continued study in this FDA- guided first- in- human, early feasibility trial.  
+
+## Declarations  
+
+## Acknowledgments  
+
+This work was supported by the National Institute of Health (5UH3NS103446- 02). The authors thank the study subjects' for their dedication and commitment to this novel, first- in- human exploratory trial; the members of the Stanford Clinical and Translational Research Unit and the Departments of Neurosurgery and Psychiatry at Stanford Medicine for space to conduct in clinic assessments; the Suthana laboratory for in- clinic tool support; Ian Kratter, Tom Prieto, Vyvian Ngo, Bharati Sanjanwala for support during surgery and intraoperative testing; Emily Mirro, Tara L. Skarpaas, Nick Hasulak, Tom Tcheng for providing technical support for the NeuroPace RNS System.  
+
+## Competing Interests  
+
+No funding from NeuroPace was received for this study nor were data analyses reported here conducted by NeuroPace employees. CHH, RSS, and CER have patents related to sensing and brain stimulation for the treatment of neuropsychiatric disorders.
+
+<--- Page Split --->
+
+## References  
+
+1. Association., A.P. Diagnostic and statistical manual of mental disorders (5th ed.). (2013).  
+2. Reents, J. & Pedersen, A. Differences in Food Craving in Individuals With Obesity With and Without Binge Eating Disorder. Front Psychol 12, 660880 (2021).  
+3. Hudson, J.I., et al. Longitudinal study of the diagnosis of components of the metabolic syndrome in individuals with binge-eating disorder. Am J Clin Nutr 91, 1568–1573 (2010).  
+4. White, M.A., Kalarchian, M.A., Masheb, R.M., Marcus, M.D. & Grilo, C.M. Loss of control over eating predicts outcomes in bariatric surgery patients: a prospective, 24-month follow-up study. J Clin Psychiatry 71, 175–184 (2010).  
+5. Chao, A.M., et al. Binge-eating disorder and the outcome of bariatric surgery in a prospective, observational study: Two-year results. Obesity (Silver Spring) 24, 2327–2333 (2016).  
+6. Grucza, R.A., Przybeck, T.R. & Cloninger, C.R. Prevalence and correlates of binge eating disorder in a community sample. Compr Psychiatry 48, 124–131 (2007).  
+7. McCuen-Wurst, C., Ruggieri, M. & Allison, K.C. Disordered eating and obesity: associations between binge-eating disorder, night-eating syndrome, and weight-related comorbidities. Ann N Y Acad Sci 1411, 96–105 (2018).  
+8. Bohon, C., Stice, E. & Spoor, S. Female emotional eaters show abnormalities in consummatory and anticipatory food reward: a functional magnetic resonance imaging study. Int J Eat Disord 42, 210–221 (2009).  
+9. Wu, H., et al. Closing the loop on impulsivity via nucleus accumbens delta-band activity in mice and man. Proc Natl Acad Sci U S A 115, 192–197 (2018).  
+10. Roitman, M.F., Stuber, G.D., Phillips, P.E., Wightman, R.M. & Carelli, R.M. Dopamine operates as a subsecond modulator of food seeking. J Neurosci 24, 1265–1271 (2004).  
+11. Smith, C.T., et al. Modulation of impulsivity and reward sensitivity in intertemporal choice by striatal and midbrain dopamine synthesis in healthy adults. J Neurophysiol 115, 1146–1156 (2016).  
+12. Taha, S.A. & Fields, H.L. Inhibitions of nucleus accumbens neurons encode a gating signal for reward-directed behavior. J Neurosci 26, 217–222 (2006).  
+13. Christoffel, D.J., et al. Input-specific modulation of murine nucleus accumbens differentially regulates hedonic feeding. Nat Commun 12, 2135 (2021).  
+14. Demos, K.E., Heatherton, T.F. & Kelley, W.M. Individual differences in nucleus accumbens activity to food and sexual images predict weight gain and sexual behavior. J Neurosci 32, 5549–5552 (2012).  
+15. Wu, H., et al. Local accumbens in vivo imaging during deep brain stimulation reveals a strategy-dependent amelioration of hedonic feeding. Proc Natl Acad Sci U S A 118(2021).  
+16. Halpern, C.H., et al. Amelioration of binge eating by nucleus accumbens shell deep brain stimulation in mice involves D2 receptor modulation. J Neurosci 33, 7122–7129 (2013).
+
+<--- Page Split --->
+
+17. Wu, H., et al. Brain-Responsive Neurostimulation for Loss of Control Eating: Early Feasibility Study. Neurosurgery 87, 1277-1288 (2020).  
+18. Parker, J.J., et al. First-in-human implantation protocol and ambulatory nucleus accumbens region electrophysiologic surveillance paradigm for patient-tailored responsive closed-loop deep brain stimulation for loss of control eating disorder. Neuron (2021).  
+19. Barbosa, D., et al. The obese state is associated with a perturbed impulsivity circuit in binge-prone females. Under Review (2021).  
+20. Telch, C.F. & Agras, W.S. Do emotional states influence binge eating in the obese? Int J Eat Disord 20, 271-279 (1996).  
+21. Adamantidis, A.R., Gutierrez Herrera, C. & Gent, T.C. Oscillating circuitries in the sleeping brain. Nat Rev Neurosci 20, 746-762 (2019).  
+22. Oishi, Y., et al. Slow-wave sleep is controlled by a subset of nucleus accumbens core neurons in mice. Nat Commun 8, 734 (2017).  
+23. Mahajan, U.V., et al. Can responsive deep brain stimulation be a cost-effective treatment for severe obesity? Clinical Trials and Investigations 0, 1-9 (2021).  
+
+## Figures
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+Legend not included with this version
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+Legend not included with this version
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>  
+
+Legend not included with this version  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- BITESAppendix.docx
+
+<--- Page Split --->

preprint/preprint__032a07311eb9bb5f9f4a079bca8cd4decf50b0f2c1fa36d909d6d9fbdf969e73/preprint__032a07311eb9bb5f9f4a079bca8cd4decf50b0f2c1fa36d909d6d9fbdf969e73_det.mmd

@@ -0,0 +1,246 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 952, 177]]<|/det|>
+# Responsive nucleus accumbens deep brain stimulation restores eating control in severe obesity  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 583, 216]]<|/det|>
+Casey Halpern ( \(\boxed{ \begin{array}{r l} \end{array} }\) casey.halpern@pennmedicine.upenn.edu )  
+
+<|ref|>text<|/ref|><|det|>[[45, 219, 290, 237]]<|/det|>
+University of Pennsylvania  
+
+<|ref|>text<|/ref|><|det|>[[44, 244, 207, 281]]<|/det|>
+Rajat Shivacharan Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 289, 290, 328]]<|/det|>
+Cammie Rolle University of Pennsylvania  
+
+<|ref|>text<|/ref|><|det|>[[44, 335, 290, 374]]<|/det|>
+Daniel Barbosa University of Pennsylvania  
+
+<|ref|>text<|/ref|><|det|>[[44, 381, 210, 419]]<|/det|>
+Tricia Cunningham Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 427, 150, 465]]<|/det|>
+Austin Feng Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 473, 185, 510]]<|/det|>
+Noriah Johnson Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 518, 150, 556]]<|/det|>
+Debra Safer Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 564, 148, 601]]<|/det|>
+Cara Bohen Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 610, 148, 647]]<|/det|>
+Corey Keller Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 655, 144, 692]]<|/det|>
+Vivek Buch Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 700, 190, 737]]<|/det|>
+Jonathan Parker Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 745, 157, 783]]<|/det|>
+Dan Azagury Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 791, 138, 828]]<|/det|>
+Peter Tass Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 836, 186, 873]]<|/det|>
+Mahendra Bhati Stanford  
+
+<|ref|>text<|/ref|><|det|>[[44, 881, 184, 918]]<|/det|>
+Robert Malenka Stanford University  
+
+<|ref|>text<|/ref|><|det|>[[44, 925, 152, 943]]<|/det|>
+James Lock
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 106, 230, 125]]<|/det|>
+## Brief Communication  
+
+<|ref|>title<|/ref|><|det|>[[44, 144, 135, 163]]<|/det|>
+# Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 181, 315, 201]]<|/det|>
+Posted Date: March 15th, 2022  
+
+<|ref|>text<|/ref|><|det|>[[42, 220, 475, 240]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 1432380/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 257, 910, 300]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 335, 950, 378]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Medicine on August 29th, 2022. See the published version at https://doi.org/10.1038/s41591- 022- 01941- w.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 159, 68]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[41, 82, 940, 264]]<|/det|>
+Craving that precede loss of control (LOC) over food consumption present an opportunity for intervention in patients suffering from binge eating disorder (BED). Here, we used responsive deep brain stimulation (DBS) to record NAc electrophysiology during food cravings preceding LOC eating in two patients with BED and severe obesity (NCT03868670). Increased NAc low- frequency oscillations prominent during food cravings were used to guide DBS delivery. Over 6 months, we observed improved self- control of food intake and weight loss. These findings provide early support for restoring inhibitory control with electrophysiologically- guided NAc DBS. Further work is required to determine scalability of this approach. Trial Registration # NCT03868670.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 287, 207, 313]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[41, 325, 953, 515]]<|/det|>
+Loss of control (LOC) eating, or the subjective sense that one cannot stop eating, is associated with binge eating - defined by the consumption of an objectively large amount of food in a short period of time accompanied by a sense of LOC.1 LOC eating is often characterized by the loss of inhibitory control in response to appetitive cues and cravings leading to binge eating2. Recurrent and distressing episodes of binge eating are the key features of binge eating disorder (BED). BED is the most common eating disorder, affecting up to 3 percent of U.S. adults, and is the most severe form of LOC eating based on volume of food consumed'. It is associated with obesity, decreased quality of life and premature mortality.3  
+
+<|ref|>text<|/ref|><|det|>[[41, 530, 956, 715]]<|/det|>
+Most treatments for obesity fail to address LOC eating directly, limiting the efficacy of even the most aggressive interventions such as bariatric surgery.4,5 Clinical evidence supports a role of cravings for preferred food, or intense desires to consume specific palatable foods, prior to the onset of LOC and binge eating.6,7 Particularly in individuals who are overweight or obese, food cravings have been linked with LOC among those diagnosed with BED.8 Given this, recent studies have examined neural signals associated with food craving in the pursuit of identifying a biomarker used to trigger deep brain stimulation (i.e., responsive DBS or rDBS) and inhibit onset of LOC eating when patients may be most atrisk.  
+
+<|ref|>text<|/ref|><|det|>[[41, 732, 953, 918]]<|/det|>
+In the effort to identify such a craving biomarker, previous work in mice found that anticipation of a high- fat food reward was associated with increased low- frequency oscillatory power in the NAc.9 This work supported a growing body of evidence across species reporting electrophysiological, neurochemical, and functional neuroimaging activities within circuits involving the NAc that correlate to reward anticipation,10- 13 and that predict consequential behavioral outcomes.14 Using low- frequency delta- band power as a biomarker to trigger delivery of a brief train of high- frequency electrical stimulation to the NAc (here after referred to as rDBS) resulted in significant and lasting attenuation of binge- like eating in mice sensitized to high fat food,9 while conventional, continuous DBS appeared to lose efficacy over time.15,16
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 940, 250]]<|/det|>
+Here, we report the proof of concept in this first- in- human study designed to characterize human NAC electrophysiology of craving as it relates to LOC eating. We sought to identify changes in NAC electrophysiology associated with moments of food craving and LOC eating during controlled in- clinic behavioral tasks and to assess the generalization of this effect to LOC eating events in a naturalistic setting and outside the behavioral laboratory. Finally, we implemented rDBS triggered by NAC electrophysiology identified in behavioral and naturalistic assessments, and report here initial results on the potential efficacy of this novel intervention. This study was performed under a U.S. Food and Drug Administration Investigational Device Exemption (G180079) using the NeuroPace Responsive Neurostimulation (RNS) System<sup>17</sup>.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 272, 163, 298]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 313, 271, 332]]<|/det|>
+## PRESTUDY PROCEDURES  
+
+<|ref|>text<|/ref|><|det|>[[42, 350, 956, 490]]<|/det|>
+Two adult women with BED and treatment- refractory severe (grade III) obesity, despite bariatric surgery were recruited for this study, approved by Stanford's Institutional Review Board (IRB- 46563) (see appendix for participant characteristics). Designed with a staggered enrollment, each subject progressed through the study stages shown in Fig. 1A. Both subjects underwent stereotactic implantation of bilateral depth electrodes, each with four contacts.<sup>18</sup> The two distal contacts were positioned in the NAC and the two proximal contacts traversed the anterior limb of the internal capsule (Fig. 1B).<sup>19</sup>  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 508, 218, 526]]<|/det|>
+## RECORDING PHASE  
+
+<|ref|>text<|/ref|><|det|>[[42, 544, 955, 701]]<|/det|>
+Immediately following implantation, subjects entered a 6- month recording phase, during which naturalistic in- lab assessments and ambulatory real- world assessments were performed to identify an electrophysiological biomarker for rDBS in the consecutive stimulation phase. From each hemisphere, activity was recorded from the ventral and dorsal NAC (see appendix for details). Subjects underwent two assessments to evaluate NAC electrophysiology during: 1) anticipation (pre- consumption) of food during standard meals and LOC eating (i.e., Multi- Item Buffet assessment; in- lab naturalistic testing); and 2) states of hunger and craving (pre- consumption) (i.e., ambulatory assessment; real- world testing).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 719, 238, 737]]<|/det|>
+## STIMULATION PHASE  
+
+<|ref|>text<|/ref|><|det|>[[41, 755, 958, 960]]<|/det|>
+Following the recording phase, both subjects underwent single- blinded stimulation survey testing in which they received brief bursts of electrical stimulation across all electrode contacts to screen for acute effects. This was followed by a single- blinded, staged, on- off stimulation safety testing period to assess for possible side effects of rDBS. Subjects then entered the 10–12 month open- label stimulation phase of the study. In this phase, rDBS was delivered using a bipolar montage of the two NAC electrode contacts. Both subjects received bilateral NAC rDBS via depth electrodes connected to a NeuroPace RNS system to detect and inhibit LOC eating events. Stimulation was delivered at 125 Hz in two 5 second bursts with a charge density of 0.5–1.5 μC/cm.<sup>17</sup> Detections and stimulations occurred approximately 400 times/day with a stimulation limit set to 700 bouts (or approximately 117 min) per day in order to limit unnecessary
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 44, 952, 182]]<|/det|>
+stimulation at night. Based on the recording phase, each subject's device was programmed to detect brief increases in low- frequency activity in both the left and right ventral NAc (see appendix). These detections of low- frequency activity triggered bilateral NAc rDBS ( \(\sim 1\mu \mathrm{C} / \mathrm{cm}^2\) charge density, 10s duration). Low- frequency triggered bilateral stimulation has been well tolerated by both subjects. Neither subject 1 nor 2 experienced a serious adverse event, and all reported events were self- limited (Table S4). Examination of sensitivity and specificity can be found in the appendix (Figures S1, S2).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 204, 144, 229]]<|/det|>
+## Results  
+
+<|ref|>text<|/ref|><|det|>[[44, 245, 219, 264]]<|/det|>
+RECORDING PHASE  
+
+<|ref|>text<|/ref|><|det|>[[40, 281, 951, 580]]<|/det|>
+MULTI- ITEM BUFFET: NAC ELECTROPHYSIOLOGY DURING IN- LAB LOC EATING. In this assessment, we investigated each subject's LOC by modeling the at- risk environment in a controlled setting \(^{20}\) . Using mood provocation (see appendix), we assessed LOC (1–5 Likert severity scale) during presentation of a high calorie buffet of the subject's preferred foods while recording synchronized video- NAc LFP (Local Field Potential) activity. Analogous to our pre- clinical work, we analyzed and compared bite onset during the buffet to standard meals. Results showed low- frequency power increases immediately prior to LOC eating. Specifically, increases in left ventral NAc low- frequency (2–8 Hz) power were observed for both subjects during LOC immediately preceding (within 2 seconds) the videoed bite onset (see appendix) (mean ± s.e. dB power \([V^2 /\mathrm{Hz}]\) : Subject 1, \(2.4 \pm 1.5, \mathrm{n} = 16\) bites; Subject 2, \(5.6 \pm 3.1, \mathrm{n} = 12\) bites). In contrast, increases in low- frequency power were not observed immediately prior to bites during standard meals (Subject 1, \(0.6 \pm 1.0, \mathrm{n} = 15\) bites; Subject 2, \(0.3 \pm 0.9, \mathrm{n} = 11\) bites) (Fig. 1C, Student's t- test, \(p < 0.05\) ). There were no statistical changes in any of the other recorded frequency bands in either subject (Student's t- test, \(p > 0.05\) ).  
+
+<|ref|>text<|/ref|><|det|>[[39, 595, 958, 895]]<|/det|>
+AMBULATORY ASSESSMENT: NAC ELECTROPHYSIOLOGY DURING REAL- WORLD LOC EATING EVENTS. We analyzed electrophysiology acquired during real- world behavioral states (see appendix) to validate the lab findings. Low- frequency power increases during LOC eating were corroborated with real- world assessments. Specifically, significantly higher low- frequency oscillatory power (Fig. 2A) in bilateral ventral NAc was found during subject- reported LOC eating events (craving- red trace, mean ± s.e. power \([V^2 /\mathrm{Hz}]\) : Subject 1, left NAc: \(0.21 \pm 0.11\) , right NAc: \(0.16 \pm 0.06, \mathrm{n} = 10\) events; Subject 2, left NAc: \(0.58 \pm 0.14\) , right NAc: \(0.21 \pm 0.07, \mathrm{n} = 71\) events) when compared to control periods (control- black trace, Subject 1, left NAc: \(0.1 \pm 0.04\) , right NAc: \(0.04 \pm 0.01, \mathrm{n} = 9\) events; Subject 2, left NAc: \(0.19 \pm 0.04\) , right NAc: \(0.09 \pm 0.04, \mathrm{n} = 80\) events) and periods of hunger (hunger- blue trace, Subject 1, left NAc: \(0.06 \pm 0.01\) , right NAc: \(0.03 \pm 0.01, \mathrm{n} = 13\) events; Subject 2, left NAc: \(0.27 \pm 0.11\) , right NAc: \(0.11 \pm 0.03, \mathrm{n} = 37\) events) (Fig. 2A, one- way ANOVA, Subject 1, left NAc: \(f = 3.50, \mathrm{P} = 0.04\) , right NAc: \(f = 4.95, \mathrm{P} = 0.03\) ; Subject 2, left NAc: \(f = 5.14, \mathrm{P} = 0.02\) , right NAc: \(f = 0.07, \mathrm{P} = 0.93\) ). Consistent with the in- clinic tasks, there were no differences in any other frequency band during at- risk moments in the ambulatory setting.  
+
+<|ref|>text<|/ref|><|det|>[[42, 909, 956, 954]]<|/det|>
+SIGNAL DETECTION: BILATERAL NAC DETECTION. For each subject, we programmed the device to detect brief increases in low- frequency activity in both the left and right ventral NAc. To confirm that the signal
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 941, 248]]<|/det|>
+being detected was in the low- frequency range, we analyzed the power spectra of the NAc LFP activity in the 5 seconds prior to a detection and found that the Area detectors (see appendix) were detecting low- frequency activity in the left and right ventral NAc (Fig. 2B). For this analysis, we compared detection made in stored LFPs during reported LOC eating events and awake events. For Subject 1, increased low- frequency power compared to baseline NAc LFP signal (average 2- minute window) was identified in \(74.4\%\) (67/90) of reported LOC eating event detections and \(63.2\%\) (84/133) of the awake detections \((X2(1,N = 223) = 24.54,p< 0.05)\) . For Subject 2, increased low- frequency power was identified in \(76.9\%\) (30/39) reported LOC eating event detections and \(45.8\%\) (22/48) awake detections \((X2(1,N = 87) = 14.82,p< 0.05)\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 266, 238, 285]]<|/det|>
+## STIMULATION PHASE  
+
+<|ref|>text<|/ref|><|det|>[[40, 302, 949, 621]]<|/det|>
+CHANGE in LOC EATING and Weight. Both subjects reported an increased sense of self- regulation and control over food intake specific to cravings and related eating behavior. Further, both subjects showed a decrease in the reported frequency of LOC eating events from baseline to 6- months post- stimulation (i.e. the primary endpoint), as assessed by the Eating Disorder Examination (EDE), and LOC severity, as assessed by the Eating Loss of Control Scale, across the 28- day period during the baseline month compared to 6- months post- stimulation month (LOC Frequency: Subject 1 = 80% decrease; Subject 2 = 87% decrease; LOC episode severity: Subject 1: 9- point improvement \((p = 0.09)\) ; Subject 2: 15- point improvement \((p = 0.05)\) ) (Fig. 3A,B). Notably, by the end of the 6- month follow- up period, Subject 1 exhibited substantial improvement in BED severity, while Subject 2 no longer met criteria for BED (i.e., fewer than average of 4 binge eating events per- month over the prior consecutive 3 months for no more BE diagnosis), which met our primary endpoint (Fig. 3C). Corroborating their subjective reports (Fig. 3), 6- month outcomes showed a decrease in body weight (kg and % reduction) and BMI for both subjects: Subject 1 = - 5.9 kg, - 4.5%, and - 2.2 kg/m², respectively; Subject 2 = - 8.2 kg, - 5.8%, and - 2.9 kg/m², respectively) (Fig. 3D,E).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 644, 191, 669]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[40, 683, 956, 955]]<|/det|>
+In summary, this study identified NAc low- frequency oscillatory power as a signal associated with LOC craving, and then implemented this biomarker to guide rDBS delivery in two subjects with BED and severe obesity. In the recording phase, in- lab assessments implicated NAc low- frequency signalling during naturalistic LOC eating. The generalizability of this signal to real- world settings was then corroborated by our finding that low- frequency oscillatory power was increased during real- world LOC eating events compared to non- LOC events. In the stimulation phase, 6 months of bilateral NAc rDBS triggered by low- frequency power was found to improve LOC eating, as well as reduce body weight and BMI. Optimization of stimulation parameters is still ongoing in both subjects, and four additional subjects are expected to be implanted following a supplement approval to our investigational device exemption. We encountered early challenges when capturing LOC eating events in the real world. A training period was necessary prior to surgery for both subjects to learn to identify and document their LOC eating behaviors. This involved having a psychiatrist (DS) with expertise in obesity and eating disorders discuss with each patient her
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 45, 960, 412]]<|/det|>
+personal understanding of LOC eating. As we report (see appendix), while sensitivity of low- frequency detections to LOC eating was high, low- frequency oscillations in the NAC were not always specific to food craving and LOC eating compared to non- LOC eating events. Ongoing work seeks to optimize detection algorithms and improve the sensitivity and specificity of rDBS for LOC eating. Further, real- world LOC electrophysiology detected from ambulatory recordings was specific to bilateral, ventral NAC delta (2- 4Hz), whereas in- lab experiments found effects in both delta and theta (2- 8Hz) and were limited to the left ventral NAC. In addition, because real- world data capture was not time- locked to specific bite events during LOC and standard meals, the ambulatory and multi- item buffet data reflect different time windows respective to the LOC events. We also note that while the frequencies within which we found our effects here contained the delta signal identified in mice<sup>9</sup>, the effects from in- lab testing were broader and inclusive of theta frequencies. Importantly, one difficulty with the low- frequency biomarker signal is its presence during normal physiological processes such as sleep<sup>21,22</sup>. To account for detection and stimulation during sleep, we limited rDBS delivery to awake hours (7am- 10pm). Finally, the upfront cost of implantable devices is high; thus long- term follow- up of LOC eating as well as BMI beyond the study period will be necessary to assess societal cost- effectiveness of this intervention based on our decision analyses<sup>23</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[42, 428, 953, 541]]<|/det|>
+In conclusion, NAC rDBS improved LOC eating frequency and severity in two patients with BED and severe obesity. These findings were associated with weight loss even during this early follow- up period, suggesting patients can lose weight without instruction to change their diet or physical activity (efforts which are often unsuccessful). This is a testament to the potential clinical significance of this novel intervention and supports continued study in this FDA- guided first- in- human, early feasibility trial.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 563, 212, 588]]<|/det|>
+## Declarations  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 605, 207, 624]]<|/det|>
+## Acknowledgments  
+
+<|ref|>text<|/ref|><|det|>[[42, 642, 953, 799]]<|/det|>
+This work was supported by the National Institute of Health (5UH3NS103446- 02). The authors thank the study subjects' for their dedication and commitment to this novel, first- in- human exploratory trial; the members of the Stanford Clinical and Translational Research Unit and the Departments of Neurosurgery and Psychiatry at Stanford Medicine for space to conduct in clinic assessments; the Suthana laboratory for in- clinic tool support; Ian Kratter, Tom Prieto, Vyvian Ngo, Bharati Sanjanwala for support during surgery and intraoperative testing; Emily Mirro, Tara L. Skarpaas, Nick Hasulak, Tom Tcheng for providing technical support for the NeuroPace RNS System.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 817, 220, 836]]<|/det|>
+## Competing Interests  
+
+<|ref|>text<|/ref|><|det|>[[42, 854, 944, 920]]<|/det|>
+No funding from NeuroPace was received for this study nor were data analyses reported here conducted by NeuroPace employees. CHH, RSS, and CER have patents related to sensing and brain stimulation for the treatment of neuropsychiatric disorders.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 196, 68]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[53, 80, 945, 920]]<|/det|>
+1. Association., A.P. Diagnostic and statistical manual of mental disorders (5th ed.). (2013).  
+2. Reents, J. & Pedersen, A. Differences in Food Craving in Individuals With Obesity With and Without Binge Eating Disorder. Front Psychol 12, 660880 (2021).  
+3. Hudson, J.I., et al. Longitudinal study of the diagnosis of components of the metabolic syndrome in individuals with binge-eating disorder. Am J Clin Nutr 91, 1568–1573 (2010).  
+4. White, M.A., Kalarchian, M.A., Masheb, R.M., Marcus, M.D. & Grilo, C.M. Loss of control over eating predicts outcomes in bariatric surgery patients: a prospective, 24-month follow-up study. J Clin Psychiatry 71, 175–184 (2010).  
+5. Chao, A.M., et al. Binge-eating disorder and the outcome of bariatric surgery in a prospective, observational study: Two-year results. Obesity (Silver Spring) 24, 2327–2333 (2016).  
+6. Grucza, R.A., Przybeck, T.R. & Cloninger, C.R. Prevalence and correlates of binge eating disorder in a community sample. Compr Psychiatry 48, 124–131 (2007).  
+7. McCuen-Wurst, C., Ruggieri, M. & Allison, K.C. Disordered eating and obesity: associations between binge-eating disorder, night-eating syndrome, and weight-related comorbidities. Ann N Y Acad Sci 1411, 96–105 (2018).  
+8. Bohon, C., Stice, E. & Spoor, S. Female emotional eaters show abnormalities in consummatory and anticipatory food reward: a functional magnetic resonance imaging study. Int J Eat Disord 42, 210–221 (2009).  
+9. Wu, H., et al. Closing the loop on impulsivity via nucleus accumbens delta-band activity in mice and man. Proc Natl Acad Sci U S A 115, 192–197 (2018).  
+10. Roitman, M.F., Stuber, G.D., Phillips, P.E., Wightman, R.M. & Carelli, R.M. Dopamine operates as a subsecond modulator of food seeking. J Neurosci 24, 1265–1271 (2004).  
+11. Smith, C.T., et al. Modulation of impulsivity and reward sensitivity in intertemporal choice by striatal and midbrain dopamine synthesis in healthy adults. J Neurophysiol 115, 1146–1156 (2016).  
+12. Taha, S.A. & Fields, H.L. Inhibitions of nucleus accumbens neurons encode a gating signal for reward-directed behavior. J Neurosci 26, 217–222 (2006).  
+13. Christoffel, D.J., et al. Input-specific modulation of murine nucleus accumbens differentially regulates hedonic feeding. Nat Commun 12, 2135 (2021).  
+14. Demos, K.E., Heatherton, T.F. & Kelley, W.M. Individual differences in nucleus accumbens activity to food and sexual images predict weight gain and sexual behavior. J Neurosci 32, 5549–5552 (2012).  
+15. Wu, H., et al. Local accumbens in vivo imaging during deep brain stimulation reveals a strategy-dependent amelioration of hedonic feeding. Proc Natl Acad Sci U S A 118(2021).  
+16. Halpern, C.H., et al. Amelioration of binge eating by nucleus accumbens shell deep brain stimulation in mice involves D2 receptor modulation. J Neurosci 33, 7122–7129 (2013).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[47, 44, 936, 405]]<|/det|>
+17. Wu, H., et al. Brain-Responsive Neurostimulation for Loss of Control Eating: Early Feasibility Study. Neurosurgery 87, 1277-1288 (2020).  
+18. Parker, J.J., et al. First-in-human implantation protocol and ambulatory nucleus accumbens region electrophysiologic surveillance paradigm for patient-tailored responsive closed-loop deep brain stimulation for loss of control eating disorder. Neuron (2021).  
+19. Barbosa, D., et al. The obese state is associated with a perturbed impulsivity circuit in binge-prone females. Under Review (2021).  
+20. Telch, C.F. & Agras, W.S. Do emotional states influence binge eating in the obese? Int J Eat Disord 20, 271-279 (1996).  
+21. Adamantidis, A.R., Gutierrez Herrera, C. & Gent, T.C. Oscillating circuitries in the sleeping brain. Nat Rev Neurosci 20, 746-762 (2019).  
+22. Oishi, Y., et al. Slow-wave sleep is controlled by a subset of nucleus accumbens core neurons in mice. Nat Commun 8, 734 (2017).  
+23. Mahajan, U.V., et al. Can responsive deep brain stimulation be a cost-effective treatment for severe obesity? Clinical Trials and Investigations 0, 1-9 (2021).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 430, 143, 456]]<|/det|>
+## Figures
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[55, 70, 825, 710]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 737, 115, 756]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[44, 781, 368, 800]]<|/det|>
+Legend not included with this version
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[95, 66, 765, 777]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 800, 118, 820]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[44, 843, 367, 862]]<|/det|>
+Legend not included with this version
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[57, 49, 880, 216]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 245, 116, 264]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[44, 288, 368, 307]]<|/det|>
+Legend not included with this version  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 330, 311, 357]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 380, 765, 400]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[61, 419, 266, 437]]<|/det|>
+- BITESAppendix.docx
+
+<--- Page Split --->

preprint/preprint__0358cbd719cad92a5106a1d23b164c7a9ee9af38881e700bf32a1c27078c4f3f/preprint__0358cbd719cad92a5106a1d23b164c7a9ee9af38881e700bf32a1c27078c4f3f.mmd

@@ -0,0 +1,246 @@
+
+# Red Light-Mediated Photoredex Catalysis Promotes Regioselective Switch in the Difunctionalization of Alkenes  
+
+Shoubhik Das  
+
+shoubhik.das@uni- bayreuth.de  
+
+University of Bayreuth https://orcid.org/0000- 0002- 4577- 438X  Tong Zhang  University of Antwerp  
+
+## Article  
+
+Keywords:  
+
+Posted Date: February 12th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3. rs- 3910735/v1  
+
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on June 18th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 49514- 4.
+
+<--- Page Split --->
+
+# Red Light-Mediated Photoredox Catalysis Promotes Regioselective Switch in the Difunctionalization of Alkenes  
+
+Tong Zhanga, and Shoubhik Das\\*a,b  
+
+## AFFILIATIONS:  
+
+a. Department of Chemistry, University of Antwerp, 2020 Antwerp, Belgium  
+b. Department of Chemistry, University of Bayreuth, 95447 Bayreuth, Germany  Corresponding author: shoubhik.das@uni-bayreuth.de  
+
+## Abstract:  
+
+Controlling regioselectivity during difunctionalization of alkenes represents significant challenges, particularly when the installation of both functional groups is involved in radical processes. In this aspect, several functionalized trifluoromethylated \((- CF_3)\) compounds have been accomplished via difunctionalization reactions due to their wide importance in the pharmaceutical sectors, however, all these existing reports are limited to afford the corresponding \(\beta\) - trifluoromethylated products. The main reason for this limitation arises from the fact that \(- CF_3\) group served as an initiator in those reactions and predominantly preferred to be installed at the terminal \((\beta)\) position of an alkene. In contrary, functionalization of the \(- CF_3\) group at the internal \((\alpha)\) position of alkenes provides valuable products but a meticulous approach is necessary to win this regioselectivity switch. Intrigued by this challenge, we have developed an efficient and highly regioselective strategy where \(- CF_3\) group is installed at the \(\alpha\) - position of an alkene and at the end, molecular complexity is achieved via the simultaneous insertion of a sulfonyl fragment \((- SO_2R)\) at the \(\beta\) - position. This strategy provides the simultaneous installation of two important functional groups such as \(- CF_3\) and \(- SO_2R\) groups and both of these functional groups are the key units to attain or to enhance the bioactivity in organic molecules. A precisely regulated sequence of radical generation using red light-mediated photocatalysis facilitates this regioselective switch from the terminal \((\beta)\) position to the internal \((\alpha)\) position. Furthermore, this approach demonstrates distinctive regioselectivity, broad substrate scope and industrial potential for the synthesis of pharmaceuticals under mild reaction conditions.  
+
+## Introduction  
+
+Recently, photoredox catalysis has gained tremendous attention in achieving unique synthetic targets under mild reaction conditions. In most of these cases, short- wavelength light regions \((\lambda_{\max}< 460 \text{nm})\) were utilized to achieve these reactions successfully, however, short- wavelength light regions have severe limitations of potential health risk such as photooxidative damage to the retina and furthermore, they can lead to generate undesired side products and thereby, lower the atom economy of that reaction. Additionally, lower penetration power of short- wavelength light regions causes concern for the scale up of that particular reaction. All these limitations have encouraged scientists to move forward to the longer- wavelength regions such as red light or near- infrared (NIR) regions since these are associated with low health risk factor, generate less side products due to their lower energy and have high penetration power in the solution which in turn assist to scale up the reaction. In longer- wavelength regions as the photocatalysts will be activated by the low- energy, their corresponding redox windows are consequently narrower and that in turn assists to exercise finer control in chemical processes, permitting only specific reactions to take place under defined conditions. Inspired by this, the groups of MacMillan and Rovis have independently developed inspiring photocatalytic strategies for the activation of aryl azide via red light- mediated photoredox catalysis which have been utilized for proximity labeling. Additionally, the utilization of red light- mediated photocatalysis has been increasingly applied across multiple domains to enhance the control of chemical reactions. Thus, it is very clear that the red light- mediated photoredox catalysis can uniquely attain many unsolved
+
+<--- Page Split --->
+
+processes which were impossible by the irradiation of ultraviolet (UV) or blue light and that leads to the growing surge of interest in this field, however, it is imperative to acknowledge that still the applications of red light-mediated strategies in organic synthesis are in the early stage of development.  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Design of the sulfonyltrifluoromethylation of olefins via red light-mediated photocatalysis. </center>  
+
+Difenoxidation of alkenes is a powerful synthetic strategy to attain molecular complexity from readily available starting materials. \(^{15 - 21}\) In this approach, simultaneously two different functional groups are installed across an olefin by the introduction of two new C - C or C - X bonds. Along this direction, tremendous catalytic efforts have been paid to attain molecular complexity to design pharmaceutically relevant compounds. \(^{22 - 48}\) However, the simultaneous introduction of the trifluoromethyl (- CF₃) and the sulfonyl fragment (- SO₂R) via difunctionalization is highly challenging due to the intricate difficulty in circumventing undesired side reactions, therefore, rarely this challenge has been solved in organic synthesis. On the other hand, these two functional groups (- CF₃ and - SO₂R) are highly demanding due to their intrinsic capability to enhance the stability, membrane permeability, and metabolism in bioactive molecules and that is reflected in their wide presence as common pharmaceuticals such as CJ- 17493 and eletriptan which are served as an NK- 1 receptor antagonist, and as a medication for migraine headaches respectively (Figure 1a). \(^{49 - 54}\) To the best of our knowledge, only a single report has been published for the simultaneous introduction of these two functional groups across the alkene moiety, however, the position of the - CF₃ group was always in the
+
+<--- Page Split --->
+
+terminal position \((\beta\) - position).49 Along the same direction, it should be clearly noted that the difunctionalization of alkenes via the introduction of a \(\mathsf{- CF}_3\) group has frequently been employed, however, \(\mathsf{- CF}_3\) group mainly acted as an initiator via the formation of a radical and was always installed to the terminal \((\beta)\) position of an alkene (as depicted by the solid frame in Figure 1b). Followed by this terminal addition, subsequent coupling with other functional groups such as - chloro, - chlorosulfonyl, - amino, - carboxylic acid groups were performed to achieve the difunctionalized products.55- 60 In contrary, reverse regioselectivity of the \(\mathsf{- CF}_3\) group at the internal position \((\alpha)\) in the difunctionalized olefins (indicated by the dashed frame in Figure 1b) is very rare, although this will allow to achieve important pharmaceuticals such as CJ- 17493, apinocaltamide and many more. To the best of our knowledge, only the group of Li presented an elegant thermocatalytic strategy by involving copper/N- fluorobenzenesulfonimide (NFSI) for the introduction of \(\mathsf{- CF}_3\) group at the internal position of an alkene (Figure 1b).30 In this approach, the \(N\) - centered radical, derived from an electrophilic NFSI, served as an initiator to facilitate the addition to the \(\beta\) position of the olefin and the (bpy)Zn(CF3)2 complex was employed as a nucleophilic \(\mathsf{- CF}_3\) reagent.  
+
+Inspired by all these information, we became interested to design a photoredox system for the first time that should install both the \(\mathsf{- CF}_3\) and \(\mathsf{- SO}_2\mathsf{R}\) groups simultaneously in alkenes where the \(\mathsf{- CF}_3\) group should be positioned at the internal position \((\alpha)\) in the difunctionalized product. To achieve a success in this site selectivity, meticulous designing of the photoredox strategy during the coupling of two different functional groups is inevitable. This was absolutely orthogonal in the case of Li's protocol where they worked with only one radical ( \(N\) - centered radical) in attaining the difunctionalized products.30 Specifically, when both the \(\mathsf{- CF}_3\) and \(\mathsf{- SO}_2\mathsf{R}\) radicals coexist, the \(\mathsf{- CF}_3\) radical demonstrates higher propensity to attach to the olefin first.37,57 To overcome this obstacle, we argued to ensure: (1) the formation of the \(\mathsf{- CF}_3\) radical should occur to the subsequent formation of \(\mathsf{- SO}_2\mathsf{R}\) radical which will readily initiate the addition to olefins; (2) we also argued to utilize a copper salt as a catalyst to capture the free \(\mathsf{- CF}_3\) radical since copper- based salts are well known for simultaneous cross- coupling reactions by involving \(\mathsf{- CF}_3\) radical.25- 26 To fulfill these requirements, we attempted to employ a photocatalyst which should be activated by the red light to attain the sulfonyltrifluoromethylated product (Figure 1c).61- 62 The reason behind our rationale to use the red light in our reaction was due to the lower energy of the red light compared to the blue light, photocatalysts activated by the red light are expected to exhibit a narrower redox window, enabling a precisely control of radical generation, thereby should facilitate regioselectivity during the addition of two distinct radicals on alkenes. Owing to the narrower redox window of the red light- activated photocatalyst, it was essential to ensure that the excited state of the photocatalyst \((\mathsf{PC}^*)\) should undergo reduction solely through the sulfinate salts via reductive quenching pathway.44,62 The resulting sulfonyl radical should then be added to the alkene, leading to the formation of the desired carbon- centered radical. At last, the desired product will be achieved by the carbon- centered radical and \(\mathsf{Cu} - \mathsf{CF}_3\) complex via Cu- catalyzed cross- coupling reaction.25- 26 In contrast, we rationalized to avoid the oxidative quenching pathway of the \(\mathsf{PC}^*\) since this would have generated free \(\mathsf{- CF}_3\) radical which would result to the undesired trifluoromethylated side products ( \(\mathsf{- CF}_3\) group at the terminal \((\beta)\) position).37,57 To accomplish this, the photocatalyst was carefully selected based on the redox potentials of sulfinate salts and \(\mathsf{- CF}_3\) reagents and the redox potentials should have fulfilled: \(E_{\mathrm{ox}}(\mathrm{RSO}_2^- )< E(\mathrm{PC}^* /\mathrm{PC}^- ),E_{\mathrm{red}}(\mathrm{CF}_3^+ )< E(\mathrm{PC}^* /\mathrm{PC}^+)\) and \(E(\mathrm{PC}^0 /\mathrm{PC}^- )< E_{\mathrm{red}}(\mathrm{CF}_3^+ )\) (Figure 1c).  
+
+## Results  
+
+## Reaction optimization  
+
+At the outset of the reaction, 4- vinyl- 1,1'- biphenyl (1 equiv.), \(\mathrm{Os(bptpy)_2(PF_6)_2}\) (0.8 mol%), \(\mathrm{NaSO_2Ph}\) (3 equiv.) and \(\mathrm{TTCF_3^+OTF^- }\) (2 equiv.) were employed as the model substrate, photocatalyst, sulfinate salt and \(\mathsf{- CF}_3\) reagent in the presence of copper chloride ( \(\mathrm{CuCl}_2\) , 20 mol%) in dichloromethane (DCM, 0.1 M) to afford the sulfonyltrifluoromethylated product (Figure 1d).5,61- 62 We carefully chosen these reagents ( \(\mathrm{Os(bptpy)_2(PF_6)_2}\) , sodium benzenesulfinate \(\mathrm{(NaSO_2Ph)}\) and trifluoromethyl thianthrenium triflate \(\mathrm{(TTCF_3^+OTF^- )}\) ) based on their redox potential values to match with our scientific rationale: \(E([\mathrm{Os}]^{1\dagger \dagger \dagger}) = +0.93\mathrm{V}\) vs. \(\mathrm{AgCl}\) (3 M KCl), \(E([\mathrm{Os}]^{1\dagger \dagger \dagger}) = -0.67\mathrm{V}\) vs. \(\mathrm{AgCl}\) (3 M KCl)5, \(E_{\mathrm{ox}}(\mathrm{NaSO_2Ph}) = +0.6\mathrm{V}\) vs. \(\mathrm{Ag/AgCl}\) (3 M KCl)57- 58, \(E_{\mathrm{red}}(\mathrm{TTCF_3^+OTF^- }) = -0.69\mathrm{V}\) vs. \(\mathrm{Ag/AgCl}\) (3 M KCl))63. As expected, the performance of the reaction under these conditions did not generate any trifluoromethylated side products (at the terminal position) and only provided the desired product with \(73\%\) of yield. It was also observed that reducing the quantities of \(\mathrm{NaSO_2Ph}\) and \(\mathrm{TTCF_3^+OTF^- }\) , led to a decrease in the yield of the final product (Figure 1d, entries 2- 3). It was necessary to use the excess quantity of sulfinate salts to ensure the faster oxidation of
+
+<--- Page Split --->
+
+sulfinate salt to the \(\cdot \mathrm{SO}_2\mathrm{R}\) radical. In addition, due to the lower solubility in DCM, the use of the excess quantity of sulfinate salts was highly necessary as well as the presence of excess quantity of \(\cdot \mathrm{CF}_3\) reagent accelerated the reaction rate.23,61- 62 Furthermore, the addition of ligands such as \(2,2^{\prime}\) - bipyridine (bpy) and 1,10- phenanthroline (1,10- phen) exerted deleterious effects in the reaction, giving no product under this conditions (Figure 1d, entries 4- 5). We assumed that the presence of ligands occupied the coordination sites for \(\cdot \mathrm{CF}_3\) radical or hindered the binding of \(\cdot \mathrm{CF}_3\) radical to the Cu- center.25 To verify the importance of the appropriate \(\cdot \mathrm{CF}_3\) reagent, alternative electrophilic \(\cdot \mathrm{CF}_3\) sources such as Togni's reagent, Umemoto's reagent, and \(\mathrm{Cu(CF_3)_3bpy}\) were also applied, albeit substantially lower or negligible yield of the desired product was obtained (Figure 1d, entries 6- 10). The rationale behind this could be ascribed to their unsuitable redox potentials, which did not align with \(\mathrm{Os(bptpy)_2(PF_6)_2}\) and consequently, failed to meet the requirements. Furthermore, alternative Cu- salts and solvents were also investigated, but lower or negligible yields of the products were obtained (Figure 1d, entries 11- 13). Finally, control experiments revealed that the presence of the photocatalyst, Cu- salts and red light were essential for this reaction (Figure 1d, entries 14- 16).  
+
+In order to exhibit the red light- mediated regioselective gain for this reaction, reaction conditions under the irradiation of blue light were also compared. Similar to the 'red light system', the crucial combination of the photocatalyst, sulfinate salt and \(\cdot \mathrm{CF}_3\) reagent was determined, namely \([\mathrm{Ru(bpz)_3(PF_6)_2}\) , \(\mathrm{NaSO_2Ph}\) and 5- (trifluoromethyl) dibenzothiophenium triflate (Figure 2b). However, after extensive optimizations via the investigation of each crucial component of this reaction, the highest yield of the desired product reached to \(42\%\) and this could be due to the fact that free \(\cdot \mathrm{CF}_3\) radical was generated faster under these conditions. (See SI 1.3.2). Subsequently, this \(\cdot \mathrm{CF}_3\) radical underwent an addition reaction with styrene, resulted the formation of the undesired \(\beta\) - substituted trifluoromethylated byproduct and the contrast was notably evident in the \(^{19}\mathrm{F}\) NMR spectra (Figure 2c). The 'blue light system' exhibited numerous peaks of side products while the spectrum of the 'red light system' appeared significantly cleaner and mainly contained the \(\cdot \mathrm{CF}_3\) reagent and the desired product. This significant difference highlighted the pronounced regioselectivity gain in the sulfonyltrifluoromethylation of alkenes via the red light- mediated photocatalysis.  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Initial investigation of the reaction under blue and red light with respective photocatalysts. </center>  
+
+## Substrate scope  
+
+With this optimized reaction conditions in hand, we started to evaluate the scope of the sulfonyltrifluoromethylation of alkenes. As shown in the Figure 3, an array of para- substituted styrenes containing diverse electron- donating groups (EDGs) like - methyl, - acetoxy, and - tert- butyl, as well as electron- withdrawing groups (EWGs) such as - halogens provided the corresponding sulfonyltrifluoromethylated products in moderate to excellent yield (Figure 3, 1- 8). Specifically, 4- bromostyrene and 4- chlorostyrene were tolerant under our optimized conditions to provide the desired products (6 and 7), thereby, demonstrated the potential for subsequent functionalization via cross coupling
+
+<--- Page Split --->
+
+reactions. \(^{30}\) Furthermore, the reaction demonstrated compatibility with 2- and 3- substituted styrenes (10- 13), leading to the formation of products in satisfactory yield, regardless of the presence of - EDGs or - EWGs. In comparison, electron- deficient alkenes (9 and 14) exhibited decreased efficiency, however, the use of \(p\) - chlorophenyl sulfinate led to an improvement in the reaction. In general, the difunctionalization of \(\beta\) - substituted styrenes represents increased difficulty due to the hindrance caused by these \(\beta\) - substituents and this hindrance can impede the addition of initiators, such as sulfonyl radicals in this work. \(^{30}\) However, under our optimized reaction conditions, \((E)\) - \(\beta\) - methylstyrene (15) and indene (16) underwent the difunctionalization reaction smoothly and provided the yield of \(46\%\) and \(78\%\) , respectively.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3. Scope of the sulfonyltrifluoromethylation of olefins \(^{a}\) . \(^{a}\) Yields are reported as isolated yield. \(^{b}\) dr value was determined by \(^{1}\) H NMR. </center>  
+
+Encouraged by these results, an extensive exploration of sulfinate salts was conducted within the optimized reaction conditions. To our delight, a diverse array of \(p\) - substituted phenyl sulfinates, encompassing - methyl, - chloro, - bromo, - nitro, and - cyano groups, demonstrated excellent tolerance, yielding the desired products in yields from
+
+<--- Page Split --->
+
+good to excellent (17- 21). Furthermore, aliphatic sulfinates (22 and 23) also proved to be compatible which exhibited strong application potentials in pharmaceutical area such as the modification of azidothymidine which is known as an anti- HIV drug.64 The adaptability of our methodology extended further to sulfinates bearing biphenyl-, cyclopropane-, and thiophene- groups. These substrates smoothly underwent difunctionalization reactions under the irradiation of red light, yielding products in the range of \(35 - 93\%\) (24- 26). This exhibited wide generality of our system to afford various sulfones- containing chemicals, thereby making significant contributions to the field of pharmaceuticals, agrochemicals, and it should be also noted that the synthesis of sulfones- containing chemicals is of paramount importance in organic chemistry.44- 46  
+
+Recently, the focus on late- stage modification has garnered significant interest due to its direct and efficient approach in synthesizing functionalized complex molecules.65- 69 The expedite synthesis of highly- functionalized molecules holds strong promise for its potential utility in various scientific disciplines including drug discovery, materials science, and molecular imaging.69 To evaluate the application of our method on complex molecules, a series of drug molecules and natural products derivatives such as estrone, (S)- (+)- naproxen, dexibuprofen, (1S)- (- )- camphanic acid, indomethacin and adapalene were applied (27- 32). Under our experimental conditions, these diverse drug derivatives, encompassing a variety of functional groups, exhibited excellent tolerance and compatibility. The resulting products were obtained in yields from \(66\%\) to \(88\%\) , indicating high reaction efficiency. This demonstrated the potential of our methodology in facilitating the synthesis of more complex sulfonyltrifluoromethylated molecules. We strongly believe that the - trifluoromethyl and - sulfonyl groups in functionalized drug molecules and natural products should not only improve their inherent properties but should also provide the opportunity for further transformation.  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Post-functionalization of the sulfonyltrifluoromethylated product. </center>  
+
+## Application potentials  
+
+To further examine the application potential, a 4 mmol- scale reaction was carried out which proceeded smoothly in 4 hours and yielded 0.85 grams of the desired product (Figure 4a). Due to the superior light penetration of red light, it became feasible to directly conduct the upscaling of the reaction within a batch reaction system.5 To further demonstrate the synthetic utility of our strategy, the elimination of the - sulfonyl group was achieved through a straightforward strategy by using a mixture of \(\mathrm{Cs_2CO_3}\) and 7- methyl- 1,5,7- triazabicyclo(4.4.0)dec- 5- ene (MTBD), resulting in the production of \(\alpha\) - trifluoromethyl styrene (33) with a yield of \(90\%\) (Figure 4b).62 The mixture of base facilitated the deprotonation and desulfonylation of the sulfonyltrifluoromethylated styrenes to form the \(\alpha\) - trifluoromethyl styrenes. In general, \(\alpha\) - trifluoromethyl styrene derivatives are highly important as versatile synthetic intermediates for the construction of complex fluorinated compounds which are synthesized through methylation of trifluoromethylketones (Wittig reaction) or via transition metal- catalyzed cross- coupling reactions.70- 71 However, compared to these approaches, our strategy enabled the direct synthesis of \(\alpha\) - trifluoromethyl styrene derivatives from styrene, eliminating the requirement of Wittig reagents as well as - borylated or - halide reagents in the processes to improve the atom economy. Additionally, the obtained \(\alpha\) - trifluoromethyl styrene was further transformed into gem- difluorolalkenes (34) in \(86\%\) yield and these fluorinated compounds have strong potential to act as a
+
+<--- Page Split --->
+
+ketone mimic in pharmaceuticals. \(^{72 - 74}\) In fact, substitution of the carbonyl group by the gem- difluoroalkene moiety has shown to enhance the oral bioavailability of therapeutic agents. \(^{72}\) Furthermore, our strategy generated a key intermediate (35) for the synthesis of apinocaltamide (37), T- type calcium channel blocker from 4- bromostyrene (Figure 4c). \(^{75 - 76}\) All these approaches clearly demonstrate the strong potential of our strategy for further applications in designing or modifying pharmaceuticals.  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5. Mechanistic studies. </center>  
+
+## Mechanistic investigations  
+
+Inspired by all these outcomes, we became interested to validate the reaction mechanism of this unique reaction strategy and a series of mechanistic experiments were conducted to validate our mechanistic proposal (Figure 5). At first, (2,2,6,6- Tetramethylpiperidin- 1- yl)oxyl (TEMPO) was added as a radical quenching reagent under the optimized reaction conditions. As expected, trace quantity of the product was obtained and a carbon- centered radical (III) was captured by TEMPO which was detected by the high- resolution mass spectrometry (HRMS) (Figure 5a), indicating that the radical process was involved. To further support the involvement of radicals during the addition of the sulfonyl radical, a radical probe experiment was conducted where the model styrene (39) yielded the ring- opening product 40 (Figure 5b). Upon the addition of sulfonyl radical to 39, a cyclopropylmethyl radical moiety was formed, followed by the rapid ring opening rearrangement relieved the ring strain and finally, resulted the final ring- opening product (40). Additionally, Stern- Volmer fluorescence quenching experiments were conducted, revealing that the sodium sulfinate salt exhibited the highest potential as a quencher for the excited state of the Os- photocatalyst, which was also corroborated by the electrochemical measurements for redox potentials (Figure 5c, see SI 1.4.1). \(^{5}\) In Figure 5c, it demonstrated that as the concentration of sulfinate salt was increased, there was a notable reduction in fluorescence intensity. However, minimal alterations were detected in the case of the - CF₃ reagent, styrene, and CuCl₂. This observation was aligned with the anticipated reductive quenching pathway and supported our design that the generation of - sulfonyl radical was prior than the generation of - CF₃ radical in the reaction, indicating that no free - CF₃ radical was generated and ensured the high regioselectivity switch in this reaction. Furthermore, the form of Cu- CF₃ active species was also investigated and to analyze the possible Cu- CF₃
+
+<--- Page Split --->
+
+active species, various control experiments were carried out (Figure 5d). Initially, we attempted to detect the active species in the absence of styrene under model reaction conditions, while no new peak corresponding to \(\mathrm{Cu^{II} - CF_3}\) was observed in \(1 - 4h\) , however, we observed the presence of the \(\mathrm{Cu^{III}(CF_3)_4}\) anion peak (Experiment A in Figure 6). Due to the potential instability of the \(\mathrm{Cu^{II} - CF_3}\) complex, we further attempted the addition of the bpy ligand to detect the potential existence of the \(\mathrm{Cu^{II} - CF_3}\) in Experiment A. However, only peak of \(\mathrm{TTCF_3^+OTF^-}\) was observed in \(^{19}\mathrm{F}\) NMR (Experiment B in Figure 6). The presence of ligands either occupied the available coordination sites of \(\mathrm{- CF_3}\) radical or impeded the binding of \(\mathrm{- CF_3}\) radical to the \(\mathrm{Cu}\) - center. \(^{25}\) To further verify the \(\mathrm{Cu^{III}(CF_3)_4}\) anionic complex, we synthesized stable \(\mathrm{Me_4NCu^{III}(CF_3)_4}\) complex by following the reference article. \(^{77}\) However, no product was obtained by using \(\mathrm{Me_4NCu^{III}(CF_3)_4}\) complex instead of \(\mathrm{CuCl_2}\) under our optimized reaction conditions (Experiment C in Figure 6). Similarly, to verify the possibility of \(\mathrm{Cu^{I} - CF_3}\) complex as active species, the model reaction was carried out by replacing \(\mathrm{CuCl_2}\) with fresh copper powder \((\mathrm{Cu^0})\) and as expected, no product was obtained under this condition (Experiment D in Figure 6). By analyzing all these experiments, we could assume that the active species \(\mathrm{Cu - CF_3}\) were not in the form of \(\mathrm{Cu^{II} - CF_3}\) or \(\mathrm{Cu^{I} - CF_3}\) complexes but possibly were in the form of \(\mathrm{Cu^{II} - CF_3}\) complex.  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6. NMR spectra of the analysis for \(\mathrm{Cu - CF_3}\) complex. Experiment A: Model reaction in the absence of styrene after \(1h\) and \(4h\) . Experiment B: Experiment A with the addition of bpy (0.5 or 1.5 equiv.) as ligand. Experiment C: Model reaction by replacing \(\mathrm{CuCl_2}\) with \(\mathrm{Me_4NCu^{III}(CF_3)_4}\) complex. Experiment D: Model reaction by replacing \(\mathrm{CuCl_2}\) with fresh \(\mathrm{Cu}\) powder. </center>  
+
+Based on all these mechanistic studies, we proposed a possible mechanism for the overall reaction system (Figure 5e). The excited state of the photocatalyst \([\mathrm{Os^{II}}]^*\) \((E^{1*/1} = +0.93\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl), \(E^{1*/1} = - 0.67\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl)) \(^{5}\) was activated by the red light and exclusively underwent reduction by the sulfinate salts, \(\mathrm{I}\) \((E_{\mathrm{ox}} = +0.4 - 0.6\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl)) \(^{61 - 62}\) to form the sulfonyl radical \(\mathrm{II}\) (Path A) rather than oxidation by \(\mathrm{TTCF_3^+OTF^-}\) IV \((E_{\mathrm{red}} = - 0.69\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl)) \(^{63}\) to generate the free \(\mathrm{- CF_3}\) radical \(\mathbf{V}\) (Path B), which was consistent with
+
+<--- Page Split --->
+
+the result of fluorescence quenching experiments. The formed sulfonyl radical II was added to the alkene to generate a carbon- centered radical III which was verified by the TEMPO quenching experiment and the radical probe experiment. Later, the \(\mathsf{Cu}^{1}\) - species captured the free - \(\mathsf{CF}_3\) radical V, generated through the reduction of IV by [Os] \((E^{III} = - 0.82 \text{V}\) vs. Ag/AgCl (3 M KCl)) \(^5\) , resulted the formation of the \(\mathsf{Cu}^{II} - \mathsf{CF}_3\) complex VI. At last, the final product VII was delivered via the cross- coupling reaction between III and VI.  
+
+## Conclusions  
+
+In summary, we have developed a unique protocol where red light- mediated photocatalysis triggered a regioselective switch during the sulfonyltrifluoromethylation of olefins. This strategy has effectively addressed the challenges associated with regioselective addition of radicals onto alkenes. The broad substrate scope and late- stage transformation demonstrated the high efficiency of these reactions and also proved the excellent tolerance of functional groups. Furthermore, post- functionalization studies highlighted the significant industrial potential of the sulfonyltrifluoromethylated product. Additionally, detailed mechanistic investigations revealed a sequential generation of radicals, followed by Cu- catalyzed cross- coupling reactions. We believe that this strategy will strongly contribute to the regioselective functionalizations and will further inspire the development of additional methods in this field.  
+
+## Methods  
+
+General procedure for sulfonyltrifluoromethylation of olefins. A dried reaction vial with a magnetic stirring bar was charged with \(\mathsf{Os(bptpy)_2(PF_6)_2}\) (0.0008 mmol, 0.8 mol%), \(\mathsf{CuCl_2}\) (0.02 mmol, 20 mol%), \(\mathsf{TT - CF_3^+OTF^- }\) (0.2 mmol, 2 equiv.) and sodium sulfinate (0.3 mmol, 3 equiv.). After charging all these reagents, the vessel was evacuated by using Schlenk techniques and flushed with \(\mathsf{N}_2\) for three times. Under nitrogen gas flow, olefin (0.1 mmol, 1 equiv.) (if liquid, otherwise added before flushing cycle) and dry DCM (0.1 M) were added by using a syringe which was flushed with inert gas. The resulting mixture was stirred for 3 - 4 h under the irradiation of red LED light (EvoluChem™ LED 650PF HCK1012- XX- 014 650 nm 20 mW/cm²) in the EvoluChem PhotoRedOx Box. After the completion of the reaction, the reaction mixture was quenched by adding distilled water (2 mL). The organic phase was extracted and concentrated in vacuo. 1,1,1- Trifluorotoluene was added as internal standard to determine the NMR yield of the functionalized product through \(^{19}\mathrm{F}\) NMR. Purification proceeded via flash column chromatography.  
+
+## Data availability  
+
+All of the data supporting the findings of this study are available within the paper and its Supplementary Information file.  
+
+## Additional information  
+
+Optimization of reactions, Mechanism investigation, General procedure of reactions, characterization of substrates and products and spectra of products could be found in Supporting Information.  
+
+## Author Contributions  
+
+T.Z. and S.D. designed the project. T.Z. developed the reaction, investigated the substrate scope, examined the applications, and studied the reaction mechanism. Finally, T.Z. and S.D. wrote the manuscript.  
+
+## Competing interests  
+
+The authors declare no competing financial interest.  
+
+## Acknowledgement  
+
+S.D. thanks the Francqui start up grant from the University of Antwerp, Belgium, for the financial support. T.Z. thanks FWO SB PhD fellowship for their financial assistance to finish this work. We thank Dr. Rakesh Maiti from University of Bayreuth for helpful discussions. We also thank Mr. Glenn Van Haesendonck from UAntwerpen, Belgium for HRMS measurements.
+
+<--- Page Split --->
+
+## References  
+
+1. Twilton, J., Le, C., Zhang, P., Shaw, M. H., Evans, R. W. & MacMillan, D. W. C. The merger of transition metal and photocatalysis. Nat. Rev. Chem. 1, 0052 (2017).  
+2. Prier, C. K., Rankic, D. A. & MacMillan, D. W. C. Visible Light Photoredox Catalysis with Transition Metal Complexes: Applications in Organic Synthesis. Chem. Rev. 113, 5322–5363 (2013).  
+3. Romero, N. A. & Nicewicz, D. A. Organic Photoredox Catalysis. Chem. Rev. 116, 10075–10166 (2016).  
+4. Cougnard-Gregoire, A., Merle, B. M. J., Aslam, T., Seddon, J. M., Aknin, I., Klaver, C. C. W., Garhofer, G., Layana, A. G., Minnella, A. M., Silva, R. & Delcourt, C. Blue Light Exposure: Ocular Hazards and Prevention—A Narrative Review. Ophthalmol. Ther. 12, 755–788 (2023).  
+5. Ravetz, B. D., Tay, N. E. S., Joe, C. L., Sezen-Edmonds, M., Schmidt, M. A., Tan, Y., Janey, J. M., Eastgate, M. D. & Rovis, T. Development of a Platform for Near-Infrared Photoredox Catalysis. ACS Cent. Sci. 6, 2053–2059 (2020).  
+6. Wang, C., Zhang, H., Zhang, T., Zou, X., Wang, H., Rosenberger, J. E., Vannam, R., Trout, W. S., Grimm, J. B., Lavis, L. D., Thorpe, C., Jia, X., Li, Z. & Fox, J. M. Enabling In Vivo Photocatalytic Activation of Rapid Bioorthogonal Chemistry by Repurposing Silicon-Rhodamine Fluorophores as Cytocompatible Far-Red Photocatalysts. J. Am. Chem. Soc. 143, 10793–10803 (2021).  
+7. Goldschmid, S. L., Bednářová, E., Beck, L. R., Xie, K., Tay, N. E. S., Ravetz, B. D., Li, J., Joe, C. L. & Rovis, T. Tuning the Electrochemical and Photophysical Properties of Osmium-Based Photoredox Catalysts. Synlett 33, 247–258 (2022).  
+8. Goldschmid, S. L., Tay, N. E. S., Joe, C. L., Lainhart, B. C., Sherwood, T. C., Simmons, E. M., Sezen-Edmonds, M. & Rovis, T. Overcoming Photochemical Limitations in Metallaphotoredox Catalysis: Red-Light-Driven C–N Cross-Coupling. J. Am. Chem. Soc. 144, 22409–22415 (2022).  
+9. Cabanero, D. C., Nguyen, J. A., Cazin, C. S. J., Nolan, S. P. & Rovis, T. Deep Red to Near-Infrared Light-Controlled Ruthenium-Catalyzed Olefin Metathesis. ACS Catal. 13, 4384–4390 (2023).  
+10. Buksh, B. F., Knutson, S. D., Oakley, J. V., Bissonnette, N. B., Oblinsky, D. G., Schwoerer, M. P., Seath, C. P., Geri, J. B., Rodriguez-Rivera, F. P., Parker, D. L., Scholes, G. D., Ploss, A. & MacMillan, D. W. C. \(\mu\) Map-Red: Proximity Labeling by Red Light Photocatalysis. J. Am. Chem. Soc. 144, 6154–6162 (2022).  
+11. Tay, N. E. S., Ryu, K. A., Weber, J. L., Olow, A. K., Cabanero, D. C., Reichman, D. R., Oslund, R. C., Fadeyi, O. O. & Rovis, T. Targeted activation in localized protein environments via deep red photoredox catalysis. Nat. Chem. 15, 101–109 (2023).  
+12. Naya, S. I., Kume, T., Akashi, R., Fujishima, M. & Tada, H. Red-Light-Driven Water Splitting by Au(Core)-CdS(Shell) Half-Cut Nanoegg with Heteroepitaxial Junction. J. Am. Chem. Soc. 140, 1251–1254 (2018).  
+13. Dadashi-Silab, S., Lorandi, F., DiTucci, M. J., Sun, M., Szczepaniak, G., Liu, T. & Matyjaszewski, K. Conjugated Cross-linked Phenothiazines as Green or Red Light Heterogeneous Photocatalysts for Copper-Catalyzed Atom Transfer Radical Polymerization. J. Am. Chem. Soc. 143, 9630–9638 (2021).  
+14. Mato, M., Bruzzese, P. C., Takahashi, F., Leutzsch, M., Reijerse, E. J., Schnegg, A., Cornella, J. Oxidative Addition of Aryl Electrophiles into a Red-Light-Active Bismuthinidene. J. Am. Chem. Soc. 145, 18742–18747 (2023).  
+15. Koike, T. & Akita, M. A versatile strategy for difunctionalization of carbon–carbon multiple bonds by photoredox catalysis. Org. Chem. Front. 3, 1345–1349 (2016).  
+16. Yan, M., Lo, J. C., Edwards, J. T. & Baran, P. S. Radicals: Reactive Intermediates with Translational Potential. J. Am. Chem. Soc. 138, 12692–12714 (2016).  
+17. Bian, K.-J., Nemoto Jr., D., Kao, S.-C., He, Y., Li, Y., Wang, X.-S. & West, J. G. Modular Dunctionalization of Unactivated Alkenes through Bio-Inspired Radical Ligand Transfer Catalysis. J. Am. Chem. Soc. 144, 11810–11821 (2022).  
+18. Ju, T., Zhou, Y.-Q., Cao, K.-G., Fu, Q., Ye, J.-H., Sun, G.-Q., Liu, X.-F., Chen, L., Liao, L.-L. & Yu, D.-G. Dicarboxylation of alkenes, allenes and (hetero)arenes with CO2 via visible-light photoredox catalysis. Nat. Catal. 4, 304–311 (2021).  
+19. Song, L., Wang, W., Yue, J.-P., Jiang, Y.-X., Wei, M.-K., Zhang, H.-P., Yan, S.-S., Liao, L.-L. & Yu, D.-G. Visible-light photocatalytic di- and hydro-carboxylation of unactivated alkenes with CO2. Nat. Catal. 5, 832–838 (2022).  
+20. Zhang, W., Chen, Z., Jiang, Y.-X., Liao, L.-L., Wang, W., Ye, J.-H. & Yu, D.-G. Arylcarboxylation of unactivated alkenes with CO2 via visible-light photoredox catalysis. Nat. Commun. 14, 3529 (2023).  
+21. Yue, J.-P., Xu, J.-C., Luo, H.-T., Chen, X.-W., Song, H.-X., Deng, Y., Yuan, L., Ye, J.-H. & Yu, D.-G. Metallaphotoredox-enabled aminocarboxylation of alkenes with CO2. Nat. Catal. 6, 959–968 (2023).  
+22. Allen, A. E. & MacMillan, D. W. C. The Productive Merger of Iodonium Salts and Organocatalysis: A Non-photolytic Approach to the Enantioselective \(\alpha\) -Trifluoromethylation of Aldehydes. J. Am. Chem. Soc. 132, 4986–4987 (2010).  
+23. Nagib, D. A. & MacMillan, D. W. C. Trifluoromethylation of arenes and heteroarenes by means of photoredox catalysis. Nature 480, 224–228 (2011).  
+24. Kautzky, J. A., Wang, T., Evans, R. W. & MacMillan, D. W. C. Decarboxylative Trifluoromethylation of Aliphatic Carboxylic Acids. J. Am. Chem. Soc. 140, 6522–6526 (2018).  
+25. Kornfilt, D. J. P. & MacMillan, D. W. C. Copper-Catalyzed Trifluoromethylation of Alkyl Bromides. J. Am. Chem. Soc. 141, 6853–6858 (2019).  
+26. Sarver, P. J., Bacauanu, V., Schultz, D. M., DiRocco, D. A., Lam, Y.-h., Sherer, E. C. & MacMillan, D. W. C. The merger of decatungstate and copper catalysis to enable aliphatic C(sp3)–H trifluoromethylation. Nat. Chem. 12, 459–467 (2020).  
+27. Shen, H., Liu, Z., Zhang, P., Tan, X., Zhang, Z. & Li, C. Trifluoromethylation of Alkyl Radicals in Aqueous Solution. J. Am. Chem. Soc. 139, 9843–9846 (2017).  
+28. Tan, X., Liu, Z., Shen, H., Zhang, P., Zhang, Z. & Li, C. Silver-Catalyzed Decarboxylative Trifluoromethylation of Aliphatic Carboxylic Acids. J. Am. Chem. Soc. 139, 12430–12433 (2017).  
+29. Xiao, H., Liu, Z., Shen, H., Zhang, B., Zhu, L. & Li, C. Copper-Catalyzed Late-Stage Benzyl C(sp3)–H Trifluoromethylation. Chem 5, 940–949 (2019).  
+30. Xiao, H., Shen, H., Zhu, L. & Li, C. Copper-Catalyzed Radical Aminotrifluoromethylation of Alkenes. J. Am. Chem. Soc. 141, 11440–11445 (2019).  
+31. Zhang, Z., Zhu, L. & Li, C. Copper-Catalyzed Carbotrifluoromethylation of Unactivated Alkenes Driven by Trifluoromethylation of Alkyl Radicals. Chin. J. Chem. 37, 452–456 (2019).  
+32. Zhu, L., Fang, Y. & Li, C. Trifluoromethylation of Alkyl Radicals: Breakthrough and Challenges. Chin. J. Chem. 38, 787–789 (2020).  
+33. Jiang, C., Wang, L., Zhang, H., Chen, P., Guo, Y.-L. & Liu, G. Enantioselective Copper-Catalyzed Trifluoromethylation of Benzylic Radicals via Ring Opening of Cyclopropanols. Chem 6, 2407–2419 (2020).
+
+<--- Page Split --->
+
+34. Xu, P., Fan, W., Chen, P. & Liu, G. Enantioselective Radical Trifluoromethylation of Benzyl C-H Bonds via Cooperative Photoredox and Copper Catalysis. J. Am. Chem. Soc. 144, 13468-13474 (2022).  
+35. Fu, L., Chen, X., Fan, W., Chen, P. & Liu, G. Copper-Catalyzed Asymmetric Functionalization of Vinyl Radicals for the Access to Vinylarene Atropisomers. J. Am. Chem. Soc. 145, 13476-13483 (2023).  
+36. Guo, S., AbuSalim, D. I. & Cook, S. P. Aqueous Benzyl C-H Trifluoromethylation for Late-Stage Functionalization. J. Am. Chem. Soc. 140, 12378-12382 (2018).  
+37. Guo, S., AbuSalim, D. I. & Cook, S. P. 1,2-(Bis)trifluoromethylation of Alkynes:A One-Step Reaction to Install an Underutilized Functional Group. Angew. Chem. Int. Ed. 58, 11704-11708 (2019).  
+38. Choi, G., Lee, G. S., Park, B., Kim, D. & Hong, S. H. Direct C(sp³)-H Trifluoromethylation of Unactivated Alkanes Enabled by Multifunctional Trifluoromethyl Copper Complexes. Angew. Chem. Int. Ed. 60, 5467-5474 (2021).  
+39. Li, X., Shui, Y., Shen, P., Wang, Y.-P., Zhang, C. & Feng, C. A novel type of radical-addition-induced b-fragmentation and ensuing remote functionalization. Chem 8, 2245-2259 (2022).  
+40. Wang, Q., Ni, C., Hu, M., Xie, Q., Liu, Q., Pan, S. & Hu, J. From C1 to C3: Copper-Catalyzed gem-Bis(trifluoromethyl)olefination of α-Diazo Esters with TMSCF₃. Angew. Chem. Int. Ed. 59, 8507-8511 (2020).  
+41. Wang, Q., Tao, Q., Dong, H., Ni, C., Xie, X. & Hu, J. Fluorination Triggers Fluoroalkylation: Nucleophilic Perfluoro-tertbutylation with 1,1-Dibromo-2,2-bis(trifluoromethyl)ethylene (DBBF) and CsF. Angew. Chem. Int. Ed. 60, 27318-27323 (2021).  
+42. Wei, Z., Wen, L., Zhu, K., Wang, Q., Zhao, Y. & Hu, J. Regioselective Aromatic Perfluoro-tert-butylation Using Perfluoro-tert-butyl Phenyl Sulfone and Arynes. J. Am. Chem. Soc. 144, 22281-22288 (2022).  
+43. Meyer, A. U., Straková, K., Slanina, T. & König, B. Eosin Y (EY) Photoredox-Catalyzed Sulfonylation of Alkenes: Scope and Mechanism. Chem. Eur. J. 22, 8694-8699 (2016).  
+44. He, J., Chen, G., Zhang, B., Li, Y., Chen, J.-R., Xiao, W.-J., Liu, F. & Li, C. Catalytic Decarboxylative Radical Sulfonylation. Chem 6, 1149-1159 (2020).  
+45. Ueda, M., Kamikawa, K., Fukuyama, T., Wang, Y.-T., Wu, Y.-K. & Ryu, I. Site-Selective Alkenylation of Unactivated C(sp³)-H Bonds Mediated by Compact Sulfate Radical. Angew. Chem. 133, 3587-3592 (2021).  
+46. Du, X., Cheng-Sánchez, I. & Nevado, C. Dual Nickel/Photoredox-Catalyzed Asymmetric Carbosulfonylation of Alkenes. J. Am. Chem. Soc. 145, 12532-12540 (2023).  
+47. Lasso, J. D., Castillo-Pazos, D. J., Sim, M., Flores, J. B. & Li, C.-J. EDA mediated S-N bond coupling of nitroarenes and sodium sulfinate salts. Chem. Sci. 14, 525-532 (2023).  
+48. Liu, X., Chen, H., Yang, D., Hu, B., Hu, Y., Wang, S., Lan, Y., Lei, A. & Li, J. Anion-Tuning of Organocines Steering Cobalt-Catalyzed Radical Relay Couplings. ACS Catal. 13, 9254-9263 (2023).  
+49. Tanaka, S., Nakayama, Y., Konishi, Y., Koike, T. & Akita, M. Fluoroalkanesulfinate Salts as Dual Fluoroalkyl and SO2 Sources: Atom-Economic Fluoroalkyl-Sulfonylation of Alkenes and Alkynes by Photoredox Catalysis. Org. Lett. 22, 2801-2805 (2020).  
+50. Caron, S., Do, N. M., Sieser, J. E., Arpin, P. & Vazquez, E. Process Research and Development of an NK-1 Receptor Antagonist. Enantioselective Trifluoromethyl Addition to a Ketone in the Preparation of a Chiral Isochroman. Org. Process Res. Dev. 11, 1015-1024 (2007).  
+51. Goadsby, P. J., Ferrari, M. D., Olesen, J., Stovner, L. J., Senard, J. M., Jackson, N. C. & Poole, P. H. Eletriptan in acute migraine: A double-blind, placebo-controlled comparison to sumatriptan. Neurology 54, 156-163 (2000).  
+52. Müller, K., Faeh, C. & Diederich, F. Fluorine in Pharmaceuticals: Looking Beyond Intuition. Science 317, 1881-1886 (2007).  
+53. Purser, S., Moore, P. R., Swallow, S. & Gouverneur, V. Fluorine in medicinal chemistry. Chem. Soc. Rev. 37, 320-330 (2008).  
+54. Zhou, Y., Wang, J., Gu, Z., Wang, S., Zhu, W., AceCa, J. L., Soloshonok, V. A., Izawa, K. & Liu, H. Next Generation of Fluorine-Containing Pharmaceuticals, Compounds Currently in Phase II-III Clinical Trials of Major Pharmaceutical Companies: New Structural Trends and Therapeutic Areas. Chem. Rev. 116, 422-518 (2016).  
+55. Bagal, D. B., Kachkovskiy, G., Knorn, M., Rawner, T., Bhangane, B. M. & Reiser, O. Trifluoromethylchlorosulfonylation of Alkenes: Evidence for an InnerSphere Mechanism by a Copper Phenanthroline Photoredox Catalyst. Angew. Chem. Int. Ed. 54, 6999-7002 (2015).  
+56. Yang, B., Xu, X.-H. & Qing, F.-L. Copper-Mediated Radical 1,2-Bis(trifluoromethylation) of Alkenes with Sodium Trifluoromethanesulfinate. Org. Lett. 17, 1906-1909 (2015).  
+57. Wang, F., Wang, D., Wan, X., Wu, L., Chen, P. & Liu, G. Enantioselective Copper-Catalyzed Intermolecular Cyanotrifluoromethylation of Alkenes via Radical Process. J. Am. Chem. Soc. 138, 15547-15550 (2016).  
+58. Yatham, V. R., Shen, Y. & Martin, R. Catalytic Intermolecular Dicarbofunctionalization of Styrenes with CO₂ and Radical Precursors. Angew. Chem. Int. Ed. 56, 10915-10919 (2017).  
+59. Fu, L., Zhou, S., Wan, X., Chen, P. & Liu, G. Enantioselective Trifluoromethylalkylation of Alkenes via Copper-Catalyzed Radical Relay. J. Am. Chem. Soc. 140, 10965-10969 (2018).  
+60. Zhou, S., Zhang, G., Fu, L., Chen, P., Li, Y. & Liu, G. Copper-Catalyzed Asymmetric Cynation of Alkenes via Carbonyl-Assisted Coupling of Alkyl-Substituted Carbon-Centered Radicals. Org. Lett. 22, 6299-6303 (2020).  
+61. Zhu, S., Qin, J., Wang, F., Li, H. & Chu, L. Photoredox-catalyzed branch-selective pyridylation of alkenes for the expedient synthesis of Tripolidine. Nat. Commun. 10, 749 (2019).  
+62. Liu, K. & Studer, A. Direct α-Acylation of Alkenes via N-Heterocyclic Carbene, Sulfinate, and Photoredox Cooperative Triple Catalysis. J. Am. Chem. Soc. 143, 4903-4909 (2021).  
+63. Jia, H., Häring, A. P., Berger, F., Zhang, L. & Ritter, T. Trifluoromethyl Thianthrenium Triflate: A Readily Available Trifluoromethylating Reagent with Formal CF₃⁺, CF₃⁻, and CF₃⁻ Reactivity. J. Am. Chem. Soc. 143, 7623-7628 (2021).  
+64. Al-Masoudi, N. A., Al-Soud, Y. A., Ali, I. A., Schuppler, T., Pannecouque, C. & De Clercq, E. New AZT analogues having 5'-alkylsulfonyl groups: synthesis and anti-HIV activity. Nucleosides Nucleotides Nucleic Acids 26, 223-230 (2007).  
+65. Börgel, J. & Ritter, T. Late-stage functionalization. Chem 6, 1877-1887 (2020).  
+66. Guillemard, L., Kaplaneris, N., Ackermann, L. & Johansson, M. J. Late-stage C-H functionalization offers new opportunities in drug discovery. Nat. Rev. Chem. 5, 522-545 (2021).  
+67. Zhang, Y., Zhang, T. & Das, S. Selective functionalization of benzyllic C (sp3)-H bonds to synthesize complex molecules. Chem 8, 3175-3201 (2022).  
+68. Zhang, T., Vanderghinste, J., Guidetti, A., Doorslaer, S. V., Barcaro, G., Monti, S. & Das, S. Π-Π Stacking Complex Induces Three-Component Coupling Reactions To Synthesize Functionalized Amines. Angew. Chem. Int. Ed. 61, e202212083 (2022).  
+69. Zhang, L. & Ritter, T. A Perspective on Late-Stage Aromatic C-H Bond Functionalization. J. Am. Chem. Soc. 144, 2399-2414 (2022).
+
+<--- Page Split --->
+
+70. Pine, S. H., Pettit, R. J., Geib, G. D., Cruz, S. G., Gallego, C. H., Tijerina, T. & Pine, R. D. Carbonyl methylation using a titanium-aluminum (Tebbe) complex. J. Org. Chem. 50, 1212–1216 (1985).71. Fuchibe, K., Takahashi, M. & Ichikawa, J. Substitution of Two Fluorine Atoms in a Trifluoromethyl Group: Regioselective Synthesis of 3-Fluoropyrazoles. Angew. Chem. Int. Ed. 51, 12059–12062 (2012).72. Lang, S. B., Wiles, R. J., Kelly, C. B. & Molander, G. A. Photoredox Generation of Carbon-Centered Radicals Enables the Construction of 1,1-Difluoroalkene Carbonyl Mimics. Angew. Chem. Int. Ed. 56, 15073–15077 (2017).73. Zhang, J., Yang, J.-D. & Cheng, J.-P. Chemoselective catalytic hydrodefluorination of trifluoromethylalkenes towards mono-/gem-di-fluoro-alkenes under metal-free conditions. Nat. Commun. 12, 2835 (2021).74. Chen, X.-L., Yang, D.-S., Tang, B.-C., Wu, C.-Y., Wang, H.-Y., Ma, J.-T., Zhuang, S.-Y., Yu, Z.-C., Wu, Y.-D. & Wu, A.-X. Direct Hydrodefluorination of CF3-Alkenes via a Mild SN2' Process Using Rongalite as a Masked Proton Reagent. Org. Lett. 25, 2294–2299 (2023).75. Bezençon, O., Heidmann, B., Siegrist, R., Stamm, S., Richard, S., Pozzi, D., Corminboeuf, O., Roch, C., Kessler, M., Ertel, E. A., Reymond, Is., Pfeifer, T., de Kanter, R., Toeroek-Schafroth, M., Moccia, L. G., Mawet, J., Moon, R., Rey, M., Capeleto, B. & Fournier, E. Discovery of a Potent, Selective T-type Calcium Channel Blocker as a Drug Candidate for the Treatment of Generalized Epilepsies. J. Med. Chem. 60, 9769–9789 (2017).76. Phelan, J. P., Lang, S. B., Compton, J. S., Kelly, C. B., Dykstra, R., Gutierrez, O. & Molander, G. A. Redox-Neutral Photocatalytic Cyclopropanation via Radical/Polar Crossover. J. Am. Chem. Soc. 140, 8037–8047 (2018).77. Romine, A. M., Nebra, N., Konovalov, A. I., Martin, E., Benet-Buchholz, J. & Grushin, V. V. Easy Access to the Copper(III) Anion [Cu(CF3)4]−. Angew. Chem. Int. Ed. 54, 2745–2749 (2015).
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+Supportinginformation5. pdf
+
+<--- Page Split --->

preprint/preprint__0358cbd719cad92a5106a1d23b164c7a9ee9af38881e700bf32a1c27078c4f3f/preprint__0358cbd719cad92a5106a1d23b164c7a9ee9af38881e700bf32a1c27078c4f3f_det.mmd

@@ -0,0 +1,295 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 944, 207]]<|/det|>
+# Red Light-Mediated Photoredex Catalysis Promotes Regioselective Switch in the Difunctionalization of Alkenes  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 165, 247]]<|/det|>
+Shoubhik Das  
+
+<|ref|>text<|/ref|><|det|>[[52, 257, 366, 274]]<|/det|>
+shoubhik.das@uni- bayreuth.de  
+
+<|ref|>text<|/ref|><|det|>[[45, 303, 608, 368]]<|/det|>
+University of Bayreuth https://orcid.org/0000- 0002- 4577- 438X  Tong Zhang  University of Antwerp  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 409, 103, 426]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 447, 135, 465]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 485, 336, 503]]<|/det|>
+Posted Date: February 12th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 523, 475, 542]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3. rs- 3910735/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 560, 914, 601]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 621, 533, 640]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 677, 916, 720]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on June 18th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 49514- 4.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[88, 118, 912, 170]]<|/det|>
+# Red Light-Mediated Photoredox Catalysis Promotes Regioselective Switch in the Difunctionalization of Alkenes  
+
+<|ref|>text<|/ref|><|det|>[[90, 181, 349, 198]]<|/det|>
+Tong Zhanga, and Shoubhik Das\\*a,b  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 207, 208, 223]]<|/det|>
+## AFFILIATIONS:  
+
+<|ref|>text<|/ref|><|det|>[[88, 234, 673, 292]]<|/det|>
+a. Department of Chemistry, University of Antwerp, 2020 Antwerp, Belgium  
+b. Department of Chemistry, University of Bayreuth, 95447 Bayreuth, Germany  Corresponding author: shoubhik.das@uni-bayreuth.de  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 311, 168, 327]]<|/det|>
+## Abstract:  
+
+<|ref|>text<|/ref|><|det|>[[87, 338, 914, 608]]<|/det|>
+Controlling regioselectivity during difunctionalization of alkenes represents significant challenges, particularly when the installation of both functional groups is involved in radical processes. In this aspect, several functionalized trifluoromethylated \((- CF_3)\) compounds have been accomplished via difunctionalization reactions due to their wide importance in the pharmaceutical sectors, however, all these existing reports are limited to afford the corresponding \(\beta\) - trifluoromethylated products. The main reason for this limitation arises from the fact that \(- CF_3\) group served as an initiator in those reactions and predominantly preferred to be installed at the terminal \((\beta)\) position of an alkene. In contrary, functionalization of the \(- CF_3\) group at the internal \((\alpha)\) position of alkenes provides valuable products but a meticulous approach is necessary to win this regioselectivity switch. Intrigued by this challenge, we have developed an efficient and highly regioselective strategy where \(- CF_3\) group is installed at the \(\alpha\) - position of an alkene and at the end, molecular complexity is achieved via the simultaneous insertion of a sulfonyl fragment \((- SO_2R)\) at the \(\beta\) - position. This strategy provides the simultaneous installation of two important functional groups such as \(- CF_3\) and \(- SO_2R\) groups and both of these functional groups are the key units to attain or to enhance the bioactivity in organic molecules. A precisely regulated sequence of radical generation using red light-mediated photocatalysis facilitates this regioselective switch from the terminal \((\beta)\) position to the internal \((\alpha)\) position. Furthermore, this approach demonstrates distinctive regioselectivity, broad substrate scope and industrial potential for the synthesis of pharmaceuticals under mild reaction conditions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 648, 195, 665]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[86, 677, 912, 946]]<|/det|>
+Recently, photoredox catalysis has gained tremendous attention in achieving unique synthetic targets under mild reaction conditions. In most of these cases, short- wavelength light regions \((\lambda_{\max}< 460 \text{nm})\) were utilized to achieve these reactions successfully, however, short- wavelength light regions have severe limitations of potential health risk such as photooxidative damage to the retina and furthermore, they can lead to generate undesired side products and thereby, lower the atom economy of that reaction. Additionally, lower penetration power of short- wavelength light regions causes concern for the scale up of that particular reaction. All these limitations have encouraged scientists to move forward to the longer- wavelength regions such as red light or near- infrared (NIR) regions since these are associated with low health risk factor, generate less side products due to their lower energy and have high penetration power in the solution which in turn assist to scale up the reaction. In longer- wavelength regions as the photocatalysts will be activated by the low- energy, their corresponding redox windows are consequently narrower and that in turn assists to exercise finer control in chemical processes, permitting only specific reactions to take place under defined conditions. Inspired by this, the groups of MacMillan and Rovis have independently developed inspiring photocatalytic strategies for the activation of aryl azide via red light- mediated photoredox catalysis which have been utilized for proximity labeling. Additionally, the utilization of red light- mediated photocatalysis has been increasingly applied across multiple domains to enhance the control of chemical reactions. Thus, it is very clear that the red light- mediated photoredox catalysis can uniquely attain many unsolved
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 44, 912, 94]]<|/det|>
+processes which were impossible by the irradiation of ultraviolet (UV) or blue light and that leads to the growing surge of interest in this field, however, it is imperative to acknowledge that still the applications of red light-mediated strategies in organic synthesis are in the early stage of development.  
+
+<|ref|>image<|/ref|><|det|>[[95, 110, 904, 675]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 682, 861, 700]]<|/det|>
+<center>Figure 1. Design of the sulfonyltrifluoromethylation of olefins via red light-mediated photocatalysis. </center>  
+
+<|ref|>text<|/ref|><|det|>[[87, 709, 914, 912]]<|/det|>
+Difenoxidation of alkenes is a powerful synthetic strategy to attain molecular complexity from readily available starting materials. \(^{15 - 21}\) In this approach, simultaneously two different functional groups are installed across an olefin by the introduction of two new C - C or C - X bonds. Along this direction, tremendous catalytic efforts have been paid to attain molecular complexity to design pharmaceutically relevant compounds. \(^{22 - 48}\) However, the simultaneous introduction of the trifluoromethyl (- CF₃) and the sulfonyl fragment (- SO₂R) via difunctionalization is highly challenging due to the intricate difficulty in circumventing undesired side reactions, therefore, rarely this challenge has been solved in organic synthesis. On the other hand, these two functional groups (- CF₃ and - SO₂R) are highly demanding due to their intrinsic capability to enhance the stability, membrane permeability, and metabolism in bioactive molecules and that is reflected in their wide presence as common pharmaceuticals such as CJ- 17493 and eletriptan which are served as an NK- 1 receptor antagonist, and as a medication for migraine headaches respectively (Figure 1a). \(^{49 - 54}\) To the best of our knowledge, only a single report has been published for the simultaneous introduction of these two functional groups across the alkene moiety, however, the position of the - CF₃ group was always in the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[87, 44, 914, 246]]<|/det|>
+terminal position \((\beta\) - position).49 Along the same direction, it should be clearly noted that the difunctionalization of alkenes via the introduction of a \(\mathsf{- CF}_3\) group has frequently been employed, however, \(\mathsf{- CF}_3\) group mainly acted as an initiator via the formation of a radical and was always installed to the terminal \((\beta)\) position of an alkene (as depicted by the solid frame in Figure 1b). Followed by this terminal addition, subsequent coupling with other functional groups such as - chloro, - chlorosulfonyl, - amino, - carboxylic acid groups were performed to achieve the difunctionalized products.55- 60 In contrary, reverse regioselectivity of the \(\mathsf{- CF}_3\) group at the internal position \((\alpha)\) in the difunctionalized olefins (indicated by the dashed frame in Figure 1b) is very rare, although this will allow to achieve important pharmaceuticals such as CJ- 17493, apinocaltamide and many more. To the best of our knowledge, only the group of Li presented an elegant thermocatalytic strategy by involving copper/N- fluorobenzenesulfonimide (NFSI) for the introduction of \(\mathsf{- CF}_3\) group at the internal position of an alkene (Figure 1b).30 In this approach, the \(N\) - centered radical, derived from an electrophilic NFSI, served as an initiator to facilitate the addition to the \(\beta\) position of the olefin and the (bpy)Zn(CF3)2 complex was employed as a nucleophilic \(\mathsf{- CF}_3\) reagent.  
+
+<|ref|>text<|/ref|><|det|>[[86, 269, 914, 670]]<|/det|>
+Inspired by all these information, we became interested to design a photoredox system for the first time that should install both the \(\mathsf{- CF}_3\) and \(\mathsf{- SO}_2\mathsf{R}\) groups simultaneously in alkenes where the \(\mathsf{- CF}_3\) group should be positioned at the internal position \((\alpha)\) in the difunctionalized product. To achieve a success in this site selectivity, meticulous designing of the photoredox strategy during the coupling of two different functional groups is inevitable. This was absolutely orthogonal in the case of Li's protocol where they worked with only one radical ( \(N\) - centered radical) in attaining the difunctionalized products.30 Specifically, when both the \(\mathsf{- CF}_3\) and \(\mathsf{- SO}_2\mathsf{R}\) radicals coexist, the \(\mathsf{- CF}_3\) radical demonstrates higher propensity to attach to the olefin first.37,57 To overcome this obstacle, we argued to ensure: (1) the formation of the \(\mathsf{- CF}_3\) radical should occur to the subsequent formation of \(\mathsf{- SO}_2\mathsf{R}\) radical which will readily initiate the addition to olefins; (2) we also argued to utilize a copper salt as a catalyst to capture the free \(\mathsf{- CF}_3\) radical since copper- based salts are well known for simultaneous cross- coupling reactions by involving \(\mathsf{- CF}_3\) radical.25- 26 To fulfill these requirements, we attempted to employ a photocatalyst which should be activated by the red light to attain the sulfonyltrifluoromethylated product (Figure 1c).61- 62 The reason behind our rationale to use the red light in our reaction was due to the lower energy of the red light compared to the blue light, photocatalysts activated by the red light are expected to exhibit a narrower redox window, enabling a precisely control of radical generation, thereby should facilitate regioselectivity during the addition of two distinct radicals on alkenes. Owing to the narrower redox window of the red light- activated photocatalyst, it was essential to ensure that the excited state of the photocatalyst \((\mathsf{PC}^*)\) should undergo reduction solely through the sulfinate salts via reductive quenching pathway.44,62 The resulting sulfonyl radical should then be added to the alkene, leading to the formation of the desired carbon- centered radical. At last, the desired product will be achieved by the carbon- centered radical and \(\mathsf{Cu} - \mathsf{CF}_3\) complex via Cu- catalyzed cross- coupling reaction.25- 26 In contrast, we rationalized to avoid the oxidative quenching pathway of the \(\mathsf{PC}^*\) since this would have generated free \(\mathsf{- CF}_3\) radical which would result to the undesired trifluoromethylated side products ( \(\mathsf{- CF}_3\) group at the terminal \((\beta)\) position).37,57 To accomplish this, the photocatalyst was carefully selected based on the redox potentials of sulfinate salts and \(\mathsf{- CF}_3\) reagents and the redox potentials should have fulfilled: \(E_{\mathrm{ox}}(\mathrm{RSO}_2^- )< E(\mathrm{PC}^* /\mathrm{PC}^- ),E_{\mathrm{red}}(\mathrm{CF}_3^+ )< E(\mathrm{PC}^* /\mathrm{PC}^+)\) and \(E(\mathrm{PC}^0 /\mathrm{PC}^- )< E_{\mathrm{red}}(\mathrm{CF}_3^+ )\) (Figure 1c).  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 696, 155, 712]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 718, 260, 733]]<|/det|>
+## Reaction optimization  
+
+<|ref|>text<|/ref|><|det|>[[86, 738, 914, 923]]<|/det|>
+At the outset of the reaction, 4- vinyl- 1,1'- biphenyl (1 equiv.), \(\mathrm{Os(bptpy)_2(PF_6)_2}\) (0.8 mol%), \(\mathrm{NaSO_2Ph}\) (3 equiv.) and \(\mathrm{TTCF_3^+OTF^- }\) (2 equiv.) were employed as the model substrate, photocatalyst, sulfinate salt and \(\mathsf{- CF}_3\) reagent in the presence of copper chloride ( \(\mathrm{CuCl}_2\) , 20 mol%) in dichloromethane (DCM, 0.1 M) to afford the sulfonyltrifluoromethylated product (Figure 1d).5,61- 62 We carefully chosen these reagents ( \(\mathrm{Os(bptpy)_2(PF_6)_2}\) , sodium benzenesulfinate \(\mathrm{(NaSO_2Ph)}\) and trifluoromethyl thianthrenium triflate \(\mathrm{(TTCF_3^+OTF^- )}\) ) based on their redox potential values to match with our scientific rationale: \(E([\mathrm{Os}]^{1\dagger \dagger \dagger}) = +0.93\mathrm{V}\) vs. \(\mathrm{AgCl}\) (3 M KCl), \(E([\mathrm{Os}]^{1\dagger \dagger \dagger}) = -0.67\mathrm{V}\) vs. \(\mathrm{AgCl}\) (3 M KCl)5, \(E_{\mathrm{ox}}(\mathrm{NaSO_2Ph}) = +0.6\mathrm{V}\) vs. \(\mathrm{Ag/AgCl}\) (3 M KCl)57- 58, \(E_{\mathrm{red}}(\mathrm{TTCF_3^+OTF^- }) = -0.69\mathrm{V}\) vs. \(\mathrm{Ag/AgCl}\) (3 M KCl))63. As expected, the performance of the reaction under these conditions did not generate any trifluoromethylated side products (at the terminal position) and only provided the desired product with \(73\%\) of yield. It was also observed that reducing the quantities of \(\mathrm{NaSO_2Ph}\) and \(\mathrm{TTCF_3^+OTF^- }\) , led to a decrease in the yield of the final product (Figure 1d, entries 2- 3). It was necessary to use the excess quantity of sulfinate salts to ensure the faster oxidation of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[87, 44, 914, 263]]<|/det|>
+sulfinate salt to the \(\cdot \mathrm{SO}_2\mathrm{R}\) radical. In addition, due to the lower solubility in DCM, the use of the excess quantity of sulfinate salts was highly necessary as well as the presence of excess quantity of \(\cdot \mathrm{CF}_3\) reagent accelerated the reaction rate.23,61- 62 Furthermore, the addition of ligands such as \(2,2^{\prime}\) - bipyridine (bpy) and 1,10- phenanthroline (1,10- phen) exerted deleterious effects in the reaction, giving no product under this conditions (Figure 1d, entries 4- 5). We assumed that the presence of ligands occupied the coordination sites for \(\cdot \mathrm{CF}_3\) radical or hindered the binding of \(\cdot \mathrm{CF}_3\) radical to the Cu- center.25 To verify the importance of the appropriate \(\cdot \mathrm{CF}_3\) reagent, alternative electrophilic \(\cdot \mathrm{CF}_3\) sources such as Togni's reagent, Umemoto's reagent, and \(\mathrm{Cu(CF_3)_3bpy}\) were also applied, albeit substantially lower or negligible yield of the desired product was obtained (Figure 1d, entries 6- 10). The rationale behind this could be ascribed to their unsuitable redox potentials, which did not align with \(\mathrm{Os(bptpy)_2(PF_6)_2}\) and consequently, failed to meet the requirements. Furthermore, alternative Cu- salts and solvents were also investigated, but lower or negligible yields of the products were obtained (Figure 1d, entries 11- 13). Finally, control experiments revealed that the presence of the photocatalyst, Cu- salts and red light were essential for this reaction (Figure 1d, entries 14- 16).  
+
+<|ref|>text<|/ref|><|det|>[[87, 286, 914, 490]]<|/det|>
+In order to exhibit the red light- mediated regioselective gain for this reaction, reaction conditions under the irradiation of blue light were also compared. Similar to the 'red light system', the crucial combination of the photocatalyst, sulfinate salt and \(\cdot \mathrm{CF}_3\) reagent was determined, namely \([\mathrm{Ru(bpz)_3(PF_6)_2}\) , \(\mathrm{NaSO_2Ph}\) and 5- (trifluoromethyl) dibenzothiophenium triflate (Figure 2b). However, after extensive optimizations via the investigation of each crucial component of this reaction, the highest yield of the desired product reached to \(42\%\) and this could be due to the fact that free \(\cdot \mathrm{CF}_3\) radical was generated faster under these conditions. (See SI 1.3.2). Subsequently, this \(\cdot \mathrm{CF}_3\) radical underwent an addition reaction with styrene, resulted the formation of the undesired \(\beta\) - substituted trifluoromethylated byproduct and the contrast was notably evident in the \(^{19}\mathrm{F}\) NMR spectra (Figure 2c). The 'blue light system' exhibited numerous peaks of side products while the spectrum of the 'red light system' appeared significantly cleaner and mainly contained the \(\cdot \mathrm{CF}_3\) reagent and the desired product. This significant difference highlighted the pronounced regioselectivity gain in the sulfonyltrifluoromethylation of alkenes via the red light- mediated photocatalysis.  
+
+<|ref|>image<|/ref|><|det|>[[90, 513, 905, 758]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[90, 766, 866, 784]]<|/det|>
+<center>Figure 2. Initial investigation of the reaction under blue and red light with respective photocatalysts. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[89, 794, 218, 810]]<|/det|>
+## Substrate scope  
+
+<|ref|>text<|/ref|><|det|>[[88, 822, 914, 924]]<|/det|>
+With this optimized reaction conditions in hand, we started to evaluate the scope of the sulfonyltrifluoromethylation of alkenes. As shown in the Figure 3, an array of para- substituted styrenes containing diverse electron- donating groups (EDGs) like - methyl, - acetoxy, and - tert- butyl, as well as electron- withdrawing groups (EWGs) such as - halogens provided the corresponding sulfonyltrifluoromethylated products in moderate to excellent yield (Figure 3, 1- 8). Specifically, 4- bromostyrene and 4- chlorostyrene were tolerant under our optimized conditions to provide the desired products (6 and 7), thereby, demonstrated the potential for subsequent functionalization via cross coupling
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[86, 44, 914, 179]]<|/det|>
+reactions. \(^{30}\) Furthermore, the reaction demonstrated compatibility with 2- and 3- substituted styrenes (10- 13), leading to the formation of products in satisfactory yield, regardless of the presence of - EDGs or - EWGs. In comparison, electron- deficient alkenes (9 and 14) exhibited decreased efficiency, however, the use of \(p\) - chlorophenyl sulfinate led to an improvement in the reaction. In general, the difunctionalization of \(\beta\) - substituted styrenes represents increased difficulty due to the hindrance caused by these \(\beta\) - substituents and this hindrance can impede the addition of initiators, such as sulfonyl radicals in this work. \(^{30}\) However, under our optimized reaction conditions, \((E)\) - \(\beta\) - methylstyrene (15) and indene (16) underwent the difunctionalization reaction smoothly and provided the yield of \(46\%\) and \(78\%\) , respectively.  
+
+<|ref|>image<|/ref|><|det|>[[108, 191, 919, 789]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[86, 800, 912, 834]]<|/det|>
+<center>Figure 3. Scope of the sulfonyltrifluoromethylation of olefins \(^{a}\) . \(^{a}\) Yields are reported as isolated yield. \(^{b}\) dr value was determined by \(^{1}\) H NMR. </center>  
+
+<|ref|>text<|/ref|><|det|>[[88, 847, 912, 898]]<|/det|>
+Encouraged by these results, an extensive exploration of sulfinate salts was conducted within the optimized reaction conditions. To our delight, a diverse array of \(p\) - substituted phenyl sulfinates, encompassing - methyl, - chloro, - bromo, - nitro, and - cyano groups, demonstrated excellent tolerance, yielding the desired products in yields from
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 44, 912, 179]]<|/det|>
+good to excellent (17- 21). Furthermore, aliphatic sulfinates (22 and 23) also proved to be compatible which exhibited strong application potentials in pharmaceutical area such as the modification of azidothymidine which is known as an anti- HIV drug.64 The adaptability of our methodology extended further to sulfinates bearing biphenyl-, cyclopropane-, and thiophene- groups. These substrates smoothly underwent difunctionalization reactions under the irradiation of red light, yielding products in the range of \(35 - 93\%\) (24- 26). This exhibited wide generality of our system to afford various sulfones- containing chemicals, thereby making significant contributions to the field of pharmaceuticals, agrochemicals, and it should be also noted that the synthesis of sulfones- containing chemicals is of paramount importance in organic chemistry.44- 46  
+
+<|ref|>text<|/ref|><|det|>[[88, 191, 912, 390]]<|/det|>
+Recently, the focus on late- stage modification has garnered significant interest due to its direct and efficient approach in synthesizing functionalized complex molecules.65- 69 The expedite synthesis of highly- functionalized molecules holds strong promise for its potential utility in various scientific disciplines including drug discovery, materials science, and molecular imaging.69 To evaluate the application of our method on complex molecules, a series of drug molecules and natural products derivatives such as estrone, (S)- (+)- naproxen, dexibuprofen, (1S)- (- )- camphanic acid, indomethacin and adapalene were applied (27- 32). Under our experimental conditions, these diverse drug derivatives, encompassing a variety of functional groups, exhibited excellent tolerance and compatibility. The resulting products were obtained in yields from \(66\%\) to \(88\%\) , indicating high reaction efficiency. This demonstrated the potential of our methodology in facilitating the synthesis of more complex sulfonyltrifluoromethylated molecules. We strongly believe that the - trifluoromethyl and - sulfonyl groups in functionalized drug molecules and natural products should not only improve their inherent properties but should also provide the opportunity for further transformation.  
+
+<|ref|>image<|/ref|><|det|>[[90, 409, 911, 616]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 633, 667, 650]]<|/det|>
+<center>Figure 4. Post-functionalization of the sulfonyltrifluoromethylated product. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 660, 261, 676]]<|/det|>
+## Application potentials  
+
+<|ref|>text<|/ref|><|det|>[[88, 688, 912, 921]]<|/det|>
+To further examine the application potential, a 4 mmol- scale reaction was carried out which proceeded smoothly in 4 hours and yielded 0.85 grams of the desired product (Figure 4a). Due to the superior light penetration of red light, it became feasible to directly conduct the upscaling of the reaction within a batch reaction system.5 To further demonstrate the synthetic utility of our strategy, the elimination of the - sulfonyl group was achieved through a straightforward strategy by using a mixture of \(\mathrm{Cs_2CO_3}\) and 7- methyl- 1,5,7- triazabicyclo(4.4.0)dec- 5- ene (MTBD), resulting in the production of \(\alpha\) - trifluoromethyl styrene (33) with a yield of \(90\%\) (Figure 4b).62 The mixture of base facilitated the deprotonation and desulfonylation of the sulfonyltrifluoromethylated styrenes to form the \(\alpha\) - trifluoromethyl styrenes. In general, \(\alpha\) - trifluoromethyl styrene derivatives are highly important as versatile synthetic intermediates for the construction of complex fluorinated compounds which are synthesized through methylation of trifluoromethylketones (Wittig reaction) or via transition metal- catalyzed cross- coupling reactions.70- 71 However, compared to these approaches, our strategy enabled the direct synthesis of \(\alpha\) - trifluoromethyl styrene derivatives from styrene, eliminating the requirement of Wittig reagents as well as - borylated or - halide reagents in the processes to improve the atom economy. Additionally, the obtained \(\alpha\) - trifluoromethyl styrene was further transformed into gem- difluorolalkenes (34) in \(86\%\) yield and these fluorinated compounds have strong potential to act as a
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 44, 912, 128]]<|/det|>
+ketone mimic in pharmaceuticals. \(^{72 - 74}\) In fact, substitution of the carbonyl group by the gem- difluoroalkene moiety has shown to enhance the oral bioavailability of therapeutic agents. \(^{72}\) Furthermore, our strategy generated a key intermediate (35) for the synthesis of apinocaltamide (37), T- type calcium channel blocker from 4- bromostyrene (Figure 4c). \(^{75 - 76}\) All these approaches clearly demonstrate the strong potential of our strategy for further applications in designing or modifying pharmaceuticals.  
+
+<|ref|>image<|/ref|><|det|>[[108, 140, 900, 545]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[88, 562, 322, 578]]<|/det|>
+<center>Figure 5. Mechanistic studies. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 589, 299, 605]]<|/det|>
+## Mechanistic investigations  
+
+<|ref|>text<|/ref|><|det|>[[86, 616, 912, 919]]<|/det|>
+Inspired by all these outcomes, we became interested to validate the reaction mechanism of this unique reaction strategy and a series of mechanistic experiments were conducted to validate our mechanistic proposal (Figure 5). At first, (2,2,6,6- Tetramethylpiperidin- 1- yl)oxyl (TEMPO) was added as a radical quenching reagent under the optimized reaction conditions. As expected, trace quantity of the product was obtained and a carbon- centered radical (III) was captured by TEMPO which was detected by the high- resolution mass spectrometry (HRMS) (Figure 5a), indicating that the radical process was involved. To further support the involvement of radicals during the addition of the sulfonyl radical, a radical probe experiment was conducted where the model styrene (39) yielded the ring- opening product 40 (Figure 5b). Upon the addition of sulfonyl radical to 39, a cyclopropylmethyl radical moiety was formed, followed by the rapid ring opening rearrangement relieved the ring strain and finally, resulted the final ring- opening product (40). Additionally, Stern- Volmer fluorescence quenching experiments were conducted, revealing that the sodium sulfinate salt exhibited the highest potential as a quencher for the excited state of the Os- photocatalyst, which was also corroborated by the electrochemical measurements for redox potentials (Figure 5c, see SI 1.4.1). \(^{5}\) In Figure 5c, it demonstrated that as the concentration of sulfinate salt was increased, there was a notable reduction in fluorescence intensity. However, minimal alterations were detected in the case of the - CF₃ reagent, styrene, and CuCl₂. This observation was aligned with the anticipated reductive quenching pathway and supported our design that the generation of - sulfonyl radical was prior than the generation of - CF₃ radical in the reaction, indicating that no free - CF₃ radical was generated and ensured the high regioselectivity switch in this reaction. Furthermore, the form of Cu- CF₃ active species was also investigated and to analyze the possible Cu- CF₃
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 44, 914, 279]]<|/det|>
+active species, various control experiments were carried out (Figure 5d). Initially, we attempted to detect the active species in the absence of styrene under model reaction conditions, while no new peak corresponding to \(\mathrm{Cu^{II} - CF_3}\) was observed in \(1 - 4h\) , however, we observed the presence of the \(\mathrm{Cu^{III}(CF_3)_4}\) anion peak (Experiment A in Figure 6). Due to the potential instability of the \(\mathrm{Cu^{II} - CF_3}\) complex, we further attempted the addition of the bpy ligand to detect the potential existence of the \(\mathrm{Cu^{II} - CF_3}\) in Experiment A. However, only peak of \(\mathrm{TTCF_3^+OTF^-}\) was observed in \(^{19}\mathrm{F}\) NMR (Experiment B in Figure 6). The presence of ligands either occupied the available coordination sites of \(\mathrm{- CF_3}\) radical or impeded the binding of \(\mathrm{- CF_3}\) radical to the \(\mathrm{Cu}\) - center. \(^{25}\) To further verify the \(\mathrm{Cu^{III}(CF_3)_4}\) anionic complex, we synthesized stable \(\mathrm{Me_4NCu^{III}(CF_3)_4}\) complex by following the reference article. \(^{77}\) However, no product was obtained by using \(\mathrm{Me_4NCu^{III}(CF_3)_4}\) complex instead of \(\mathrm{CuCl_2}\) under our optimized reaction conditions (Experiment C in Figure 6). Similarly, to verify the possibility of \(\mathrm{Cu^{I} - CF_3}\) complex as active species, the model reaction was carried out by replacing \(\mathrm{CuCl_2}\) with fresh copper powder \((\mathrm{Cu^0})\) and as expected, no product was obtained under this condition (Experiment D in Figure 6). By analyzing all these experiments, we could assume that the active species \(\mathrm{Cu - CF_3}\) were not in the form of \(\mathrm{Cu^{II} - CF_3}\) or \(\mathrm{Cu^{I} - CF_3}\) complexes but possibly were in the form of \(\mathrm{Cu^{II} - CF_3}\) complex.  
+
+<|ref|>image<|/ref|><|det|>[[95, 290, 905, 740]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[86, 753, 912, 815]]<|/det|>
+<center>Figure 6. NMR spectra of the analysis for \(\mathrm{Cu - CF_3}\) complex. Experiment A: Model reaction in the absence of styrene after \(1h\) and \(4h\) . Experiment B: Experiment A with the addition of bpy (0.5 or 1.5 equiv.) as ligand. Experiment C: Model reaction by replacing \(\mathrm{CuCl_2}\) with \(\mathrm{Me_4NCu^{III}(CF_3)_4}\) complex. Experiment D: Model reaction by replacing \(\mathrm{CuCl_2}\) with fresh \(\mathrm{Cu}\) powder. </center>  
+
+<|ref|>text<|/ref|><|det|>[[86, 825, 912, 910]]<|/det|>
+Based on all these mechanistic studies, we proposed a possible mechanism for the overall reaction system (Figure 5e). The excited state of the photocatalyst \([\mathrm{Os^{II}}]^*\) \((E^{1*/1} = +0.93\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl), \(E^{1*/1} = - 0.67\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl)) \(^{5}\) was activated by the red light and exclusively underwent reduction by the sulfinate salts, \(\mathrm{I}\) \((E_{\mathrm{ox}} = +0.4 - 0.6\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl)) \(^{61 - 62}\) to form the sulfonyl radical \(\mathrm{II}\) (Path A) rather than oxidation by \(\mathrm{TTCF_3^+OTF^-}\) IV \((E_{\mathrm{red}} = - 0.69\mathrm{V}\) vs. \(\mathrm{Ag / AgCl}\) (3 M KCl)) \(^{63}\) to generate the free \(\mathrm{- CF_3}\) radical \(\mathbf{V}\) (Path B), which was consistent with
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[88, 44, 912, 128]]<|/det|>
+the result of fluorescence quenching experiments. The formed sulfonyl radical II was added to the alkene to generate a carbon- centered radical III which was verified by the TEMPO quenching experiment and the radical probe experiment. Later, the \(\mathsf{Cu}^{1}\) - species captured the free - \(\mathsf{CF}_3\) radical V, generated through the reduction of IV by [Os] \((E^{III} = - 0.82 \text{V}\) vs. Ag/AgCl (3 M KCl)) \(^5\) , resulted the formation of the \(\mathsf{Cu}^{II} - \mathsf{CF}_3\) complex VI. At last, the final product VII was delivered via the cross- coupling reaction between III and VI.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 142, 198, 159]]<|/det|>
+## Conclusions  
+
+<|ref|>text<|/ref|><|det|>[[88, 171, 912, 306]]<|/det|>
+In summary, we have developed a unique protocol where red light- mediated photocatalysis triggered a regioselective switch during the sulfonyltrifluoromethylation of olefins. This strategy has effectively addressed the challenges associated with regioselective addition of radicals onto alkenes. The broad substrate scope and late- stage transformation demonstrated the high efficiency of these reactions and also proved the excellent tolerance of functional groups. Furthermore, post- functionalization studies highlighted the significant industrial potential of the sulfonyltrifluoromethylated product. Additionally, detailed mechanistic investigations revealed a sequential generation of radicals, followed by Cu- catalyzed cross- coupling reactions. We believe that this strategy will strongly contribute to the regioselective functionalizations and will further inspire the development of additional methods in this field.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 320, 164, 336]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[87, 348, 912, 516]]<|/det|>
+General procedure for sulfonyltrifluoromethylation of olefins. A dried reaction vial with a magnetic stirring bar was charged with \(\mathsf{Os(bptpy)_2(PF_6)_2}\) (0.0008 mmol, 0.8 mol%), \(\mathsf{CuCl_2}\) (0.02 mmol, 20 mol%), \(\mathsf{TT - CF_3^+OTF^- }\) (0.2 mmol, 2 equiv.) and sodium sulfinate (0.3 mmol, 3 equiv.). After charging all these reagents, the vessel was evacuated by using Schlenk techniques and flushed with \(\mathsf{N}_2\) for three times. Under nitrogen gas flow, olefin (0.1 mmol, 1 equiv.) (if liquid, otherwise added before flushing cycle) and dry DCM (0.1 M) were added by using a syringe which was flushed with inert gas. The resulting mixture was stirred for 3 - 4 h under the irradiation of red LED light (EvoluChem™ LED 650PF HCK1012- XX- 014 650 nm 20 mW/cm²) in the EvoluChem PhotoRedOx Box. After the completion of the reaction, the reaction mixture was quenched by adding distilled water (2 mL). The organic phase was extracted and concentrated in vacuo. 1,1,1- Trifluorotoluene was added as internal standard to determine the NMR yield of the functionalized product through \(^{19}\mathrm{F}\) NMR. Purification proceeded via flash column chromatography.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 528, 226, 545]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[88, 558, 911, 592]]<|/det|>
+All of the data supporting the findings of this study are available within the paper and its Supplementary Information file.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 605, 281, 622]]<|/det|>
+## Additional information  
+
+<|ref|>text<|/ref|><|det|>[[88, 635, 911, 670]]<|/det|>
+Optimization of reactions, Mechanism investigation, General procedure of reactions, characterization of substrates and products and spectra of products could be found in Supporting Information.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 682, 271, 700]]<|/det|>
+## Author Contributions  
+
+<|ref|>text<|/ref|><|det|>[[88, 712, 911, 747]]<|/det|>
+T.Z. and S.D. designed the project. T.Z. developed the reaction, investigated the substrate scope, examined the applications, and studied the reaction mechanism. Finally, T.Z. and S.D. wrote the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 759, 264, 777]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[88, 790, 465, 806]]<|/det|>
+The authors declare no competing financial interest.  
+
+<|ref|>sub_title<|/ref|><|det|>[[88, 819, 250, 836]]<|/det|>
+## Acknowledgement  
+
+<|ref|>text<|/ref|><|det|>[[88, 850, 911, 917]]<|/det|>
+S.D. thanks the Francqui start up grant from the University of Antwerp, Belgium, for the financial support. T.Z. thanks FWO SB PhD fellowship for their financial assistance to finish this work. We thank Dr. Rakesh Maiti from University of Bayreuth for helpful discussions. We also thank Mr. Glenn Van Haesendonck from UAntwerpen, Belgium for HRMS measurements.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[88, 46, 187, 62]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[84, 60, 914, 920]]<|/det|>
+1. Twilton, J., Le, C., Zhang, P., Shaw, M. H., Evans, R. W. & MacMillan, D. W. C. The merger of transition metal and photocatalysis. Nat. Rev. Chem. 1, 0052 (2017).  
+2. Prier, C. K., Rankic, D. A. & MacMillan, D. W. C. Visible Light Photoredox Catalysis with Transition Metal Complexes: Applications in Organic Synthesis. Chem. Rev. 113, 5322–5363 (2013).  
+3. Romero, N. A. & Nicewicz, D. A. Organic Photoredox Catalysis. Chem. Rev. 116, 10075–10166 (2016).  
+4. Cougnard-Gregoire, A., Merle, B. M. J., Aslam, T., Seddon, J. M., Aknin, I., Klaver, C. C. W., Garhofer, G., Layana, A. G., Minnella, A. M., Silva, R. & Delcourt, C. Blue Light Exposure: Ocular Hazards and Prevention—A Narrative Review. Ophthalmol. Ther. 12, 755–788 (2023).  
+5. Ravetz, B. D., Tay, N. E. S., Joe, C. L., Sezen-Edmonds, M., Schmidt, M. A., Tan, Y., Janey, J. M., Eastgate, M. D. & Rovis, T. Development of a Platform for Near-Infrared Photoredox Catalysis. ACS Cent. Sci. 6, 2053–2059 (2020).  
+6. Wang, C., Zhang, H., Zhang, T., Zou, X., Wang, H., Rosenberger, J. E., Vannam, R., Trout, W. S., Grimm, J. B., Lavis, L. D., Thorpe, C., Jia, X., Li, Z. & Fox, J. M. Enabling In Vivo Photocatalytic Activation of Rapid Bioorthogonal Chemistry by Repurposing Silicon-Rhodamine Fluorophores as Cytocompatible Far-Red Photocatalysts. J. Am. Chem. Soc. 143, 10793–10803 (2021).  
+7. Goldschmid, S. L., Bednářová, E., Beck, L. R., Xie, K., Tay, N. E. S., Ravetz, B. D., Li, J., Joe, C. L. & Rovis, T. Tuning the Electrochemical and Photophysical Properties of Osmium-Based Photoredox Catalysts. Synlett 33, 247–258 (2022).  
+8. Goldschmid, S. L., Tay, N. E. S., Joe, C. L., Lainhart, B. C., Sherwood, T. C., Simmons, E. M., Sezen-Edmonds, M. & Rovis, T. Overcoming Photochemical Limitations in Metallaphotoredox Catalysis: Red-Light-Driven C–N Cross-Coupling. J. Am. Chem. Soc. 144, 22409–22415 (2022).  
+9. Cabanero, D. C., Nguyen, J. A., Cazin, C. S. J., Nolan, S. P. & Rovis, T. Deep Red to Near-Infrared Light-Controlled Ruthenium-Catalyzed Olefin Metathesis. ACS Catal. 13, 4384–4390 (2023).  
+10. Buksh, B. F., Knutson, S. D., Oakley, J. V., Bissonnette, N. B., Oblinsky, D. G., Schwoerer, M. P., Seath, C. P., Geri, J. B., Rodriguez-Rivera, F. P., Parker, D. L., Scholes, G. D., Ploss, A. & MacMillan, D. W. C. \(\mu\) Map-Red: Proximity Labeling by Red Light Photocatalysis. J. Am. Chem. Soc. 144, 6154–6162 (2022).  
+11. Tay, N. E. S., Ryu, K. A., Weber, J. L., Olow, A. K., Cabanero, D. C., Reichman, D. R., Oslund, R. C., Fadeyi, O. O. & Rovis, T. Targeted activation in localized protein environments via deep red photoredox catalysis. Nat. Chem. 15, 101–109 (2023).  
+12. Naya, S. I., Kume, T., Akashi, R., Fujishima, M. & Tada, H. Red-Light-Driven Water Splitting by Au(Core)-CdS(Shell) Half-Cut Nanoegg with Heteroepitaxial Junction. J. Am. Chem. Soc. 140, 1251–1254 (2018).  
+13. Dadashi-Silab, S., Lorandi, F., DiTucci, M. J., Sun, M., Szczepaniak, G., Liu, T. & Matyjaszewski, K. Conjugated Cross-linked Phenothiazines as Green or Red Light Heterogeneous Photocatalysts for Copper-Catalyzed Atom Transfer Radical Polymerization. J. Am. Chem. Soc. 143, 9630–9638 (2021).  
+14. Mato, M., Bruzzese, P. C., Takahashi, F., Leutzsch, M., Reijerse, E. J., Schnegg, A., Cornella, J. Oxidative Addition of Aryl Electrophiles into a Red-Light-Active Bismuthinidene. J. Am. Chem. Soc. 145, 18742–18747 (2023).  
+15. Koike, T. & Akita, M. A versatile strategy for difunctionalization of carbon–carbon multiple bonds by photoredox catalysis. Org. Chem. Front. 3, 1345–1349 (2016).  
+16. Yan, M., Lo, J. C., Edwards, J. T. & Baran, P. S. Radicals: Reactive Intermediates with Translational Potential. J. Am. Chem. Soc. 138, 12692–12714 (2016).  
+17. Bian, K.-J., Nemoto Jr., D., Kao, S.-C., He, Y., Li, Y., Wang, X.-S. & West, J. G. Modular Dunctionalization of Unactivated Alkenes through Bio-Inspired Radical Ligand Transfer Catalysis. J. Am. Chem. Soc. 144, 11810–11821 (2022).  
+18. Ju, T., Zhou, Y.-Q., Cao, K.-G., Fu, Q., Ye, J.-H., Sun, G.-Q., Liu, X.-F., Chen, L., Liao, L.-L. & Yu, D.-G. Dicarboxylation of alkenes, allenes and (hetero)arenes with CO2 via visible-light photoredox catalysis. Nat. Catal. 4, 304–311 (2021).  
+19. Song, L., Wang, W., Yue, J.-P., Jiang, Y.-X., Wei, M.-K., Zhang, H.-P., Yan, S.-S., Liao, L.-L. & Yu, D.-G. Visible-light photocatalytic di- and hydro-carboxylation of unactivated alkenes with CO2. Nat. Catal. 5, 832–838 (2022).  
+20. Zhang, W., Chen, Z., Jiang, Y.-X., Liao, L.-L., Wang, W., Ye, J.-H. & Yu, D.-G. Arylcarboxylation of unactivated alkenes with CO2 via visible-light photoredox catalysis. Nat. Commun. 14, 3529 (2023).  
+21. Yue, J.-P., Xu, J.-C., Luo, H.-T., Chen, X.-W., Song, H.-X., Deng, Y., Yuan, L., Ye, J.-H. & Yu, D.-G. Metallaphotoredox-enabled aminocarboxylation of alkenes with CO2. Nat. Catal. 6, 959–968 (2023).  
+22. Allen, A. E. & MacMillan, D. W. C. The Productive Merger of Iodonium Salts and Organocatalysis: A Non-photolytic Approach to the Enantioselective \(\alpha\) -Trifluoromethylation of Aldehydes. J. Am. Chem. Soc. 132, 4986–4987 (2010).  
+23. Nagib, D. A. & MacMillan, D. W. C. Trifluoromethylation of arenes and heteroarenes by means of photoredox catalysis. Nature 480, 224–228 (2011).  
+24. Kautzky, J. A., Wang, T., Evans, R. W. & MacMillan, D. W. C. Decarboxylative Trifluoromethylation of Aliphatic Carboxylic Acids. J. Am. Chem. Soc. 140, 6522–6526 (2018).  
+25. Kornfilt, D. J. P. & MacMillan, D. W. C. Copper-Catalyzed Trifluoromethylation of Alkyl Bromides. J. Am. Chem. Soc. 141, 6853–6858 (2019).  
+26. Sarver, P. J., Bacauanu, V., Schultz, D. M., DiRocco, D. A., Lam, Y.-h., Sherer, E. C. & MacMillan, D. W. C. The merger of decatungstate and copper catalysis to enable aliphatic C(sp3)–H trifluoromethylation. Nat. Chem. 12, 459–467 (2020).  
+27. Shen, H., Liu, Z., Zhang, P., Tan, X., Zhang, Z. & Li, C. Trifluoromethylation of Alkyl Radicals in Aqueous Solution. J. Am. Chem. Soc. 139, 9843–9846 (2017).  
+28. Tan, X., Liu, Z., Shen, H., Zhang, P., Zhang, Z. & Li, C. Silver-Catalyzed Decarboxylative Trifluoromethylation of Aliphatic Carboxylic Acids. J. Am. Chem. Soc. 139, 12430–12433 (2017).  
+29. Xiao, H., Liu, Z., Shen, H., Zhang, B., Zhu, L. & Li, C. Copper-Catalyzed Late-Stage Benzyl C(sp3)–H Trifluoromethylation. Chem 5, 940–949 (2019).  
+30. Xiao, H., Shen, H., Zhu, L. & Li, C. Copper-Catalyzed Radical Aminotrifluoromethylation of Alkenes. J. Am. Chem. Soc. 141, 11440–11445 (2019).  
+31. Zhang, Z., Zhu, L. & Li, C. Copper-Catalyzed Carbotrifluoromethylation of Unactivated Alkenes Driven by Trifluoromethylation of Alkyl Radicals. Chin. J. Chem. 37, 452–456 (2019).  
+32. Zhu, L., Fang, Y. & Li, C. Trifluoromethylation of Alkyl Radicals: Breakthrough and Challenges. Chin. J. Chem. 38, 787–789 (2020).  
+33. Jiang, C., Wang, L., Zhang, H., Chen, P., Guo, Y.-L. & Liu, G. Enantioselective Copper-Catalyzed Trifluoromethylation of Benzylic Radicals via Ring Opening of Cyclopropanols. Chem 6, 2407–2419 (2020).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 42, 916, 920]]<|/det|>
+34. Xu, P., Fan, W., Chen, P. & Liu, G. Enantioselective Radical Trifluoromethylation of Benzyl C-H Bonds via Cooperative Photoredox and Copper Catalysis. J. Am. Chem. Soc. 144, 13468-13474 (2022).  
+35. Fu, L., Chen, X., Fan, W., Chen, P. & Liu, G. Copper-Catalyzed Asymmetric Functionalization of Vinyl Radicals for the Access to Vinylarene Atropisomers. J. Am. Chem. Soc. 145, 13476-13483 (2023).  
+36. Guo, S., AbuSalim, D. I. & Cook, S. P. Aqueous Benzyl C-H Trifluoromethylation for Late-Stage Functionalization. J. Am. Chem. Soc. 140, 12378-12382 (2018).  
+37. Guo, S., AbuSalim, D. I. & Cook, S. P. 1,2-(Bis)trifluoromethylation of Alkynes:A One-Step Reaction to Install an Underutilized Functional Group. Angew. Chem. Int. Ed. 58, 11704-11708 (2019).  
+38. Choi, G., Lee, G. S., Park, B., Kim, D. & Hong, S. H. Direct C(sp³)-H Trifluoromethylation of Unactivated Alkanes Enabled by Multifunctional Trifluoromethyl Copper Complexes. Angew. Chem. Int. Ed. 60, 5467-5474 (2021).  
+39. Li, X., Shui, Y., Shen, P., Wang, Y.-P., Zhang, C. & Feng, C. A novel type of radical-addition-induced b-fragmentation and ensuing remote functionalization. Chem 8, 2245-2259 (2022).  
+40. Wang, Q., Ni, C., Hu, M., Xie, Q., Liu, Q., Pan, S. & Hu, J. From C1 to C3: Copper-Catalyzed gem-Bis(trifluoromethyl)olefination of α-Diazo Esters with TMSCF₃. Angew. Chem. Int. Ed. 59, 8507-8511 (2020).  
+41. Wang, Q., Tao, Q., Dong, H., Ni, C., Xie, X. & Hu, J. Fluorination Triggers Fluoroalkylation: Nucleophilic Perfluoro-tertbutylation with 1,1-Dibromo-2,2-bis(trifluoromethyl)ethylene (DBBF) and CsF. Angew. Chem. Int. Ed. 60, 27318-27323 (2021).  
+42. Wei, Z., Wen, L., Zhu, K., Wang, Q., Zhao, Y. & Hu, J. Regioselective Aromatic Perfluoro-tert-butylation Using Perfluoro-tert-butyl Phenyl Sulfone and Arynes. J. Am. Chem. Soc. 144, 22281-22288 (2022).  
+43. Meyer, A. U., Straková, K., Slanina, T. & König, B. Eosin Y (EY) Photoredox-Catalyzed Sulfonylation of Alkenes: Scope and Mechanism. Chem. Eur. J. 22, 8694-8699 (2016).  
+44. He, J., Chen, G., Zhang, B., Li, Y., Chen, J.-R., Xiao, W.-J., Liu, F. & Li, C. Catalytic Decarboxylative Radical Sulfonylation. Chem 6, 1149-1159 (2020).  
+45. Ueda, M., Kamikawa, K., Fukuyama, T., Wang, Y.-T., Wu, Y.-K. & Ryu, I. Site-Selective Alkenylation of Unactivated C(sp³)-H Bonds Mediated by Compact Sulfate Radical. Angew. Chem. 133, 3587-3592 (2021).  
+46. Du, X., Cheng-Sánchez, I. & Nevado, C. Dual Nickel/Photoredox-Catalyzed Asymmetric Carbosulfonylation of Alkenes. J. Am. Chem. Soc. 145, 12532-12540 (2023).  
+47. Lasso, J. D., Castillo-Pazos, D. J., Sim, M., Flores, J. B. & Li, C.-J. EDA mediated S-N bond coupling of nitroarenes and sodium sulfinate salts. Chem. Sci. 14, 525-532 (2023).  
+48. Liu, X., Chen, H., Yang, D., Hu, B., Hu, Y., Wang, S., Lan, Y., Lei, A. & Li, J. Anion-Tuning of Organocines Steering Cobalt-Catalyzed Radical Relay Couplings. ACS Catal. 13, 9254-9263 (2023).  
+49. Tanaka, S., Nakayama, Y., Konishi, Y., Koike, T. & Akita, M. Fluoroalkanesulfinate Salts as Dual Fluoroalkyl and SO2 Sources: Atom-Economic Fluoroalkyl-Sulfonylation of Alkenes and Alkynes by Photoredox Catalysis. Org. Lett. 22, 2801-2805 (2020).  
+50. Caron, S., Do, N. M., Sieser, J. E., Arpin, P. & Vazquez, E. Process Research and Development of an NK-1 Receptor Antagonist. Enantioselective Trifluoromethyl Addition to a Ketone in the Preparation of a Chiral Isochroman. Org. Process Res. Dev. 11, 1015-1024 (2007).  
+51. Goadsby, P. J., Ferrari, M. D., Olesen, J., Stovner, L. J., Senard, J. M., Jackson, N. C. & Poole, P. H. Eletriptan in acute migraine: A double-blind, placebo-controlled comparison to sumatriptan. Neurology 54, 156-163 (2000).  
+52. Müller, K., Faeh, C. & Diederich, F. Fluorine in Pharmaceuticals: Looking Beyond Intuition. Science 317, 1881-1886 (2007).  
+53. Purser, S., Moore, P. R., Swallow, S. & Gouverneur, V. Fluorine in medicinal chemistry. Chem. Soc. Rev. 37, 320-330 (2008).  
+54. Zhou, Y., Wang, J., Gu, Z., Wang, S., Zhu, W., AceCa, J. L., Soloshonok, V. A., Izawa, K. & Liu, H. Next Generation of Fluorine-Containing Pharmaceuticals, Compounds Currently in Phase II-III Clinical Trials of Major Pharmaceutical Companies: New Structural Trends and Therapeutic Areas. Chem. Rev. 116, 422-518 (2016).  
+55. Bagal, D. B., Kachkovskiy, G., Knorn, M., Rawner, T., Bhangane, B. M. & Reiser, O. Trifluoromethylchlorosulfonylation of Alkenes: Evidence for an InnerSphere Mechanism by a Copper Phenanthroline Photoredox Catalyst. Angew. Chem. Int. Ed. 54, 6999-7002 (2015).  
+56. Yang, B., Xu, X.-H. & Qing, F.-L. Copper-Mediated Radical 1,2-Bis(trifluoromethylation) of Alkenes with Sodium Trifluoromethanesulfinate. Org. Lett. 17, 1906-1909 (2015).  
+57. Wang, F., Wang, D., Wan, X., Wu, L., Chen, P. & Liu, G. Enantioselective Copper-Catalyzed Intermolecular Cyanotrifluoromethylation of Alkenes via Radical Process. J. Am. Chem. Soc. 138, 15547-15550 (2016).  
+58. Yatham, V. R., Shen, Y. & Martin, R. Catalytic Intermolecular Dicarbofunctionalization of Styrenes with CO₂ and Radical Precursors. Angew. Chem. Int. Ed. 56, 10915-10919 (2017).  
+59. Fu, L., Zhou, S., Wan, X., Chen, P. & Liu, G. Enantioselective Trifluoromethylalkylation of Alkenes via Copper-Catalyzed Radical Relay. J. Am. Chem. Soc. 140, 10965-10969 (2018).  
+60. Zhou, S., Zhang, G., Fu, L., Chen, P., Li, Y. & Liu, G. Copper-Catalyzed Asymmetric Cynation of Alkenes via Carbonyl-Assisted Coupling of Alkyl-Substituted Carbon-Centered Radicals. Org. Lett. 22, 6299-6303 (2020).  
+61. Zhu, S., Qin, J., Wang, F., Li, H. & Chu, L. Photoredox-catalyzed branch-selective pyridylation of alkenes for the expedient synthesis of Tripolidine. Nat. Commun. 10, 749 (2019).  
+62. Liu, K. & Studer, A. Direct α-Acylation of Alkenes via N-Heterocyclic Carbene, Sulfinate, and Photoredox Cooperative Triple Catalysis. J. Am. Chem. Soc. 143, 4903-4909 (2021).  
+63. Jia, H., Häring, A. P., Berger, F., Zhang, L. & Ritter, T. Trifluoromethyl Thianthrenium Triflate: A Readily Available Trifluoromethylating Reagent with Formal CF₃⁺, CF₃⁻, and CF₃⁻ Reactivity. J. Am. Chem. Soc. 143, 7623-7628 (2021).  
+64. Al-Masoudi, N. A., Al-Soud, Y. A., Ali, I. A., Schuppler, T., Pannecouque, C. & De Clercq, E. New AZT analogues having 5'-alkylsulfonyl groups: synthesis and anti-HIV activity. Nucleosides Nucleotides Nucleic Acids 26, 223-230 (2007).  
+65. Börgel, J. & Ritter, T. Late-stage functionalization. Chem 6, 1877-1887 (2020).  
+66. Guillemard, L., Kaplaneris, N., Ackermann, L. & Johansson, M. J. Late-stage C-H functionalization offers new opportunities in drug discovery. Nat. Rev. Chem. 5, 522-545 (2021).  
+67. Zhang, Y., Zhang, T. & Das, S. Selective functionalization of benzyllic C (sp3)-H bonds to synthesize complex molecules. Chem 8, 3175-3201 (2022).  
+68. Zhang, T., Vanderghinste, J., Guidetti, A., Doorslaer, S. V., Barcaro, G., Monti, S. & Das, S. Π-Π Stacking Complex Induces Three-Component Coupling Reactions To Synthesize Functionalized Amines. Angew. Chem. Int. Ed. 61, e202212083 (2022).  
+69. Zhang, L. & Ritter, T. A Perspective on Late-Stage Aromatic C-H Bond Functionalization. J. Am. Chem. Soc. 144, 2399-2414 (2022).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[85, 44, 914, 272]]<|/det|>
+70. Pine, S. H., Pettit, R. J., Geib, G. D., Cruz, S. G., Gallego, C. H., Tijerina, T. & Pine, R. D. Carbonyl methylation using a titanium-aluminum (Tebbe) complex. J. Org. Chem. 50, 1212–1216 (1985).71. Fuchibe, K., Takahashi, M. & Ichikawa, J. Substitution of Two Fluorine Atoms in a Trifluoromethyl Group: Regioselective Synthesis of 3-Fluoropyrazoles. Angew. Chem. Int. Ed. 51, 12059–12062 (2012).72. Lang, S. B., Wiles, R. J., Kelly, C. B. & Molander, G. A. Photoredox Generation of Carbon-Centered Radicals Enables the Construction of 1,1-Difluoroalkene Carbonyl Mimics. Angew. Chem. Int. Ed. 56, 15073–15077 (2017).73. Zhang, J., Yang, J.-D. & Cheng, J.-P. Chemoselective catalytic hydrodefluorination of trifluoromethylalkenes towards mono-/gem-di-fluoro-alkenes under metal-free conditions. Nat. Commun. 12, 2835 (2021).74. Chen, X.-L., Yang, D.-S., Tang, B.-C., Wu, C.-Y., Wang, H.-Y., Ma, J.-T., Zhuang, S.-Y., Yu, Z.-C., Wu, Y.-D. & Wu, A.-X. Direct Hydrodefluorination of CF3-Alkenes via a Mild SN2' Process Using Rongalite as a Masked Proton Reagent. Org. Lett. 25, 2294–2299 (2023).75. Bezençon, O., Heidmann, B., Siegrist, R., Stamm, S., Richard, S., Pozzi, D., Corminboeuf, O., Roch, C., Kessler, M., Ertel, E. A., Reymond, Is., Pfeifer, T., de Kanter, R., Toeroek-Schafroth, M., Moccia, L. G., Mawet, J., Moon, R., Rey, M., Capeleto, B. & Fournier, E. Discovery of a Potent, Selective T-type Calcium Channel Blocker as a Drug Candidate for the Treatment of Generalized Epilepsies. J. Med. Chem. 60, 9769–9789 (2017).76. Phelan, J. P., Lang, S. B., Compton, J. S., Kelly, C. B., Dykstra, R., Gutierrez, O. & Molander, G. A. Redox-Neutral Photocatalytic Cyclopropanation via Radical/Polar Crossover. J. Am. Chem. Soc. 140, 8037–8047 (2018).77. Romine, A. M., Nebra, N., Konovalov, A. I., Martin, E., Benet-Buchholz, J. & Grushin, V. V. Easy Access to the Copper(III) Anion [Cu(CF3)4]−. Angew. Chem. Int. Ed. 54, 2745–2749 (2015).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 92, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 328, 150]]<|/det|>
+Supportinginformation5. pdf
+
+<--- Page Split --->

preprint/preprint__035e55afc9c40b2a32b10bb61cbaf9c417c4c43287f20e12b4733b13052ac290/images_list.json

@@ -0,0 +1,62 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1: Atomic structure of phosphorus chains on Ag(111). a, STM topographic image after sublimation of phosphorus atoms on Ag(111) leading to P chains (1) and cyclo-\\(P_{5}\\) domains (2), \\((I_{\\mathrm{T}} = 1 \\mathrm{pA}, V = 0.15 \\mathrm{mV})\\) . The inset shows a STM image of the single, double and triple chains, respectively. b-d, Series of AFM images with CO-terminated tip revealing the armchair structure of single, double and triple P chains, \\((f_{0} = 26 \\mathrm{kHz}, A = 50 \\mathrm{pm})\\) . Scale bars are \\(1 \\mathrm{nm}\\) . e, Atomic configurations of the triple armchair chains obtained by DFT calculations. Phosphorus and silver atoms are shown in orang and gray, respectively. f, Corresponding AFM simulation using the DFT coordinates.",
+    "footnote": [],
+    "bbox": [
+      [
+        112,
+        195,
+        884,
+        604
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2: Atomic structure of the self-assembled cyclo-\\(P_{5}\\) molecules. a, STM image of the self-assembled pentamers on Ag(111), \\((I_{\\mathrm{T}} = 1 \\mathrm{pA}\\) , \\(V = 0.15 \\mathrm{mV}\\) ). Islands systematically shows a superlattice of bright lines rotated by \\(19^{\\circ}\\) with respect to the \\([110]\\) directions of Ag(111). b, Close-up STM topography showing the \\(P_{5}\\) molecules depicted by dashed pentagons. c, Corresponding AFM image revealing the \\(P_{5}\\) chemical structure, \\((f_{0} = 26 \\mathrm{kHz}\\) , \\(A = 50 \\mathrm{pm}\\) ). d, Atomic configurations of the pentamer assembly on Ag(111) obtained by DFT. Phosphorus and silver atoms are shown in orange and gray, respectively. e, Corresponding AFM simulation using the DFT coordinates. f, Site-dependent \\(\\Delta f(Z)\\) spectroscopic curves acquired at one P atoms of a \\(P_{5}\\) molecule (orange), between two \\(P_{5}\\) molecules (brown) and on Ag(111) (black), respectively. The local minima of the \\(\\Delta f(Z)\\) curves indicate the relative height of the phosphorus atoms.",
+    "footnote": [],
+    "bbox": [
+      [
+        111,
+        216,
+        884,
+        528
+      ]
+    ],
+    "page_idx": 24
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3: Charge redistribution at the cyclo-\\(P_{5}\\) /Ag(111) interface. a, Frequency shift \\(\\Delta f\\) as a function of sample bias voltage \\(V_{\\mathrm{s}}\\) , measured across a pentamer domain shown in the STM image (top), (parameters : \\(f_{0} = 26 \\mathrm{kHz}\\) , \\(A = 80 \\mathrm{pm}\\) ). b, Single \\(\\Delta f(V)\\) curves at the pentamer assembly (orange) as compared to the Ag(111) (black). Dashed lines mark the top of the parabola allowing to extract a LCPD shift \\(\\Delta V^{*} = 0.22 \\mathrm{V}\\) . c, Top and side views of the charge redistribution between pentamers and Ag(111). Blue areas show electron accumulation, red areas electron depletion. The isosurface level of the plot is set to \\(\\pm 13 \\times 10^{-3} \\mathrm{e} / \\mathrm{\\AA}^{3}\\) . d, Schematic illustration of the charge redistribution at the \\(P_{5}\\) /Ag(111) interface leading to an inward surface dipole (D) moment and a local work function change \\((\\phi_{\\mathrm{P}_{5} / \\mathrm{Ag}})\\) . The cyclo-\\(P_{5}\\) layer is colored in orange. \\(\\Delta V^{*}\\) refers to the LCPD change.",
+    "footnote": [],
+    "bbox": [
+      [
+        243,
+        179,
+        750,
+        585
+      ]
+    ],
+    "page_idx": 25
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4: Tunneling spectroscopy of the \\(P_{5} / \\mathrm{Ag}\\) interface. a, \\(\\mathrm{d}I / \\mathrm{d}V\\) point-spectra acquired above the \\(P_{5}\\) assembly (orange) and on Ag(111) (black), where precise locations are shown in the STM inset. (parameters: \\(I_{\\mathrm{t}} = 1 \\mathrm{pA}\\) , \\(V_{\\mathrm{s}} = 500 \\mathrm{mV}\\) , \\(A_{\\mathrm{mod}} = 10 \\mathrm{mV}\\) , \\(f = 511 \\mathrm{Hz}\\) ). b, \\(\\mathrm{d}I / \\mathrm{d}V\\) maps at \\(V_{\\mathrm{s}} = -1.25\\) and \\(2.5 \\mathrm{V}\\) corresponding to the valence band energy and the IS interface state, respectively. c, STM topographic image of three \\(P_{5}\\) domains and the corresponding \\(\\mathrm{d}I / \\mathrm{d}V\\) maps of the IS modulation. d, Scheme of the band alignment and the formation of Stark-shifted IPS (orange lines). e, Field-effect resonance tunneling (FERT cross-section acquired across the \\(P_{5}\\) assembly along the dashed line in a, (Set-points: \\(I_{\\mathrm{t}} = 1 \\mathrm{pA}\\) , \\(V_{\\mathrm{s}} = 500 \\mathrm{mV}\\) , \\(A_{\\mathrm{mod}} = 35 \\mathrm{mV}\\) , \\(f = 511 \\mathrm{Hz}\\) ). f, Single FERT spectra of the \\(P_{5}\\) assembly and the Ag(111) substrate, showing the series of \\(\\mathrm{n}^{th}\\) IPS. g, Extracted IPS peak voltages as a function of \\(n^{2 / 3}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        163,
+        884,
+        580
+      ]
+    ],
+    "page_idx": 26
+  }
+]