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preprint/preprint__058b96ab087d835fa63b04a30fdaedd9181f846e45e28f9d3a407df85e5d2a78/images_list.json

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+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1: Ring attractor network model [10,31,36,37]. (A) Schematic representation of the model. The central ring forms the main body of the model based on its recurrent connections (labeled with ①). Its reciprocal offset connections with the rotation CW and CCW rings (labeled with ② and ③) creates a push-pull mechanism that modulates the intrinsically controlled neural activity of the central ring based on external inputs from the CW and CCW velocity neurons (labeled with ④). An additional external input is provided to the central ring from the visual ring (labeled with ⑤), corresponding to a set of sensory neurons that are tuned to visual landmarks. (B) Synaptic weight function \\(W_{c c}:S^{1}\\to \\mathbb{R}\\) that describes the recurrent connections within the central ring according to the well-known local excitation and global inhibition pattern. (C) Numerical demonstration of how recurrent connectivity within the central ring can autonomously maintain a persistent activity bump. Simulation of the central ring neurons was started with initial conditions that are assigned pseudo-randomly (light green line labeled with ①). Within \"100 milliseconds, a bump of activity emerges (medium green line labeled with ①). Eventually, the firing rates converge to an equilibrium, forming a persistent bump of activity (dark green line labeled with ①). (D) Tuning curves of CCW and CW velocity neurons shown with blue-dashed and red-dashed lines, respectively.",
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+  {
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+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2: Models of the ring attractor's position representation. (A) The position representation \\(\\theta\\) , decoded from the peak location of an example ansatz solution \\(r_{\\mathrm{c}}^{*}\\) to the central ring's firing rates. (B) Model of path integration. Top left: Circular track with uniformly spaced points. Top right: internal representation of this track with a spatially inhomogenous path-integration (PI) gain that ranges from 0.6 at \\(\\theta = \\pi\\) to 1.4 at \\(\\theta = 0\\) . The position representation \\(\\theta\\) is visualized here by the pale brown rat. As the rat moves through physical space at velocity \\(v\\) , the representation moves through neural space at \\(k(\\theta)v\\) . Bottom: Firing rate of uniformly distributed cells in the neural space as a function of the animal's position in physical space. Left shows a 'traditional' network model, including a single, global PI gain of 1. Right shows our unconstrained network model with the spatially inhomogenous PI gain in the top row. (C) Stabilizing visual feedback. Top: The central ring's activity bump \\(r_{\\mathrm{c}}^{*}\\) (green) and the bump-shaped synaptic input \\(I_{\\mathrm{vis}}\\) to the central ring from the visual ring (pink). The activities of both rings are aligned with respect to the same neural space, so in this example, the visual ring bump is \"ahead of\" the central ring bump. Bottom: The function \\(\\beta\\) captures the stabilizing feedback from visual landmarks. Note that \\(\\beta\\) operates on the difference, \\(\\theta^{*} - \\theta\\) , so here, the \\(x\\) axis is a dummy variable. (D) Model of path integration with visual feedback. The pale brown rat symbolizes the internal representation of the animal's position as in (B), while the medium brown rat symbolizes the animal's actual location as represented by the visual drive. Left: the temporal change in the position representation is visualized by two arrows acting on the pale brown rat, one corresponding to updating by the path integration term \\(k(\\theta)v\\) and the other corresponding to updating by the visual feedback term \\(\\beta (\\theta^{*} - \\theta)\\) . Note that in this position, the PI gain is \"low\" and thus PI underestimates position relative to the landmarks. Right: Same as Left but PI overestimates position relative to the landmarks due to \"high\" PI gain in this position.",
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+  },
+  {
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+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3: Numerical simulation of the two example gain update rules. For both simulations, we chose the initial condition \\(k_{0}(0) = 1\\) and the parameters \\(\\beta (\\tilde{\\theta}) = 0.66\\times \\sin (\\tilde{\\theta})\\) , \\(k^{*} = 1.5\\) , \\(\\mu = 0.02\\) . The gain choices imply that the initial value of gain error is \\(\\tilde{k} (0) = 0.5\\) . Additionally, we chose \\(\\eta = 0.12\\) for the second example. (A) Temporal progression of the smoothed animal's velocity from an experiment in [35]. (B) Simulated error trajectories under example gain update rule 1. As soon as the animal begins its movement at \\(t = 0\\) , the positional error \\(\\tilde{\\theta}\\) (black line relative to the left y axis) quickly increases because of the nonzero gain error \\(\\tilde{k}\\) (purple line relative to the right y axis). As the animal recalibrates its gain, the gain error gradually converges to zero (i.e., \\(\\tilde{k}\\to 0\\) ), accompanied by positional error gradually converging to zero also (i.e., \\(\\tilde{\\theta}\\to 0\\) ). In addition to these gradual convergent trends, the error trajectories include many fast, transitory changes. As can be seen from the black line, the instantaneous value of positional error \\(\\tilde{\\theta}\\) is correlated with the animal's velocity \\(v\\) also. For example, when animal slows down, the positional error decreases, becoming zero when the velocity is zero. This is a reflection of the relatively increased landmark stabilization \\(\\beta (\\tilde{\\theta})\\) when path integration inputs \\(kv\\) are decreased. On the other hand, the temporal changes in the gain are correlated with the multiplication of the positional error \\(\\tilde{\\theta}\\) and the animal's velocity \\(v\\) as determined by the gain update rule \\(g_{0}\\) . When the animal pauses temporarily around minutes 5 and 20 (i.e., \\(v = 0\\) ), the positional error \\(\\tilde{\\theta}\\) is completely corrected by landmarks (i.e., \\(\\tilde{\\theta} = 0\\) ), causing the gain updates to pause also (i.e., \\(\\frac{d\\tilde{k}}{dt} = 0\\) ). As the animal continues moving, the positional error and the velocity fine-tune the gain until the gain error converges to zero, demonstrating that the system can achieve complete gain recalibration. (C) Simulated error trajectories under example gain update rule 2. The convention is the same as panel B. The error trajectories exhibit similar trends to the panel B except that their final values do not converge to zero, demonstrating that the system can only achieve partial gain recalibration.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4: Visualization of mechanistic constraints for a numerical simulation based on a hypothetical gain update rule \\(g_{0}(k_{0},\\hat{\\theta},v) = \\mu \\hat{\\theta} v\\) Except for the animal's velocity profile, we chose the parameters and initial conditions the same as Fig. 3B. For color coding, we use Fig. 1A as the reference, where red and blue denote the CW and CCW rotation rings, and green denotes the central ring. (A) Top graph shows the simulated velocity of the animal (purple line) on the right y axis and the temporal progression of the positional error (black line) on the left y axis. Notice the synchronous fluctuations in the positional error and the animal's velocity. As explained in Fig. 3B, these synchronous fluctuations occur because the positional error is correlated with the animal's velocity. Bottom graph shows the PI and visual gains with solid and dashed purple lines, respectively, on the right y axis and the time-integral of the positional error with the black line on the left y axis. Notice that as the PI gain gradually converges to the visual gain, the temporal progression of the time-integral of the positional error follows a very similar trajectory. This similarity indicates that the integration gain reflects the past accumulation of positional representation errors, thus opening up the possibility for the network to track the time-integral of the error as a proxy signal to encode the integration gain. (B) The mechanistic constraint for recalibration through plasticity of the velocity-to-rotation ring connections. Top graph shows the mean firing rates of the CCW and CW rotation rings over time with blue and red lines. Notice that they are similar to the trajectory of the positional error in panel A, except that the changes in the CW rotation ring's mean firing rate (red line) is the negative of those in the CCW rotation ring's mean firing rate. Bottom graph shows the direct relationship between mean firing rates and positional error in the attractor's representation. (C) The mechanistic constraint for recalibration through plasticity of the rotation-to-central ring connections. Top graph shows the mean firing rates of either the rotation rings or the central ring over time with the orange line. Notice that the changes in these firing rates follow a similar trend as the temporal progression of the positional error. Bottom graph shows this relationship directly (the positive correlation is chosen arbitrarily as our analysis does not provide a conclusive insight into the required direction). (D) The mechanistic constraint for recalibration through changes in the velocity neurons' slopes. Top graph shows the mean firing rate of the CCW and CW rotation rings, the same quantities as panel B. However, unlike panel B where the mean firing rates were similar to the instantaneous positional error, the mean firing rates in this panel are similar to the time-integral of the error. Bottom graph shows this relationship between the mean firing rates and the time-integral of the error directly. (E) The mechanistic constraint for recalibration through changes in the rotation rings' activity bumps. Top graph shows the bump width of both rotation rings over time. Similar to how the mean firing rates of the rotation rings encode the time-integral of the positional error in panel D, the bump widths encode the time-integral of the error in this panel. Bottom graph shows this relationship directly. (F) The mechanistic constraint for recalibration through changes in the central ring's activity bump. Top graph shows the temporal progression of the mean firing rate of the central ring, which is tightly but negatively correlated with the temporal progression of the time-integral of the positional error. Bottom graph shows this relationship directly.",
+    "footnote": [],
+    "bbox": [
+      [
+        155,
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+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5: A modified ring attractor network model. (A) A proposed connectivity pattern that varies firing rate of population X3 as a monotonic function of the difference in the activity-bump locations of populations X1 and X2. Arrow and circle terminals denote excitatory and inhibitory connections, respectively. (B) Schematic diagrams depicting the computation within the proposed connectivity in panel (A). The first row shows the activity of the X2 population (yellow) relative to the activity of the X1 population (green) for different conditions: CW difference (left column), no difference (middle column), and CCW difference (right column). The second row shows the synaptic inputs to the X3 population from the excitatory X1 (green line) and inhibitory X2 (yellow line) populations. The fourth row shows the resulting firing rates of the X3 population. (C) Schematic representation of the model. Solid and dashed lines denote hardwired and plastic connections, respectively. The labels M1, M2, M3, correspond to the three modifications made to the classical ring attractor: M1 is the association ring, M2 refers to the plasticity of the velocity-to-rotation-ring connections, and M3 refers to the hardwired, offset association-to-rotation connections. (D) Numerical simulation demonstrating the association of the visual ring's activity with the central ring's activity through Hebbian plasticity. Top and bottom rows show the initial and final values of the simulated variables. The left column shows the firing rates of the central (green) and visual (pink) rings. The middle column visualizes the weight matrix describing the visual-to-association ring connections. The right column shows the firing rates of the association ring (yellow) and the synaptic inputs from the visual ring (pink). (E) Tuning curves depicting the relationships between the rotation rings' mean and peak firing rates vs. the error (left and right graph, respectively). The color coding is the same as panel C. (F) Numerical simulations of the gain recalibration within the proposed model. The top shows the the recalibration of PI gain (green) toward the visual gain (pink) in a selected simulation. The middle shows the progression of the weights of the velocity-to-rotation ring connections (four samples normalized to initial condition of the weights with the opacity changes from the lightest ( \\(t = 0\\) min) and to the darkest green ( \\(t = 30\\) min) corresponding to chronological order of the samples.). The bottom shows the final values of the PI gain for various visual gains (green line) and the hypothetical perfect recalibration (dashed black line). (G) Numerical simulation demonstrating how visual landmarks correct positional error. The top panel shows the progression of the bump locations of the visual (pink) and central rings (green). Bottom panel shows the mean firing rate of CW (red) and CCW (blue) rotation rings over time.",
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preprint/preprint__05a18c267c6d7dedb4a7e980e586fa6f60b4fb0553596df82b5ab1b095ebd821/images_list.json

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preprint/preprint__05a18c267c6d7dedb4a7e980e586fa6f60b4fb0553596df82b5ab1b095ebd821/preprint__05a18c267c6d7dedb4a7e980e586fa6f60b4fb0553596df82b5ab1b095ebd821.mmd

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+
+# Climate action and gender equality matter most for China's sustainable development  
+
+Chaoyang Wu  
+
+wucyeigsnrr.ac.cn  
+
+Institute of Geographic Sciences and Natural Resources Research https://orcid.org/0000- 0001- 6163- 8209  
+
+Qiang Xing Aerospace Information Research Institute, Chinese Academy of Sciences  
+
+Fang Chen International Research Center of Big Data for Sustainable Development Goals  
+
+Jianguo Liu Michigan State University https://orcid.org/0000- 0001- 6344- 0087  
+
+Prajal Pradhan Potsdam Institute for Climate Impact Research https://orcid.org/0000- 0003- 0491- 5489  
+
+Brett Bryan Deakin University https://orcid.org/0000- 0003- 4834- 5641  
+
+Thomas Schaubroeck Luxembourg Institute of Science and Technology  
+
+Luis Roman Carrasco National University of Singapore https://orcid.org/0000- 0002- 2894- 1473  
+
+Alemu Gonsamo McMaster University https://orcid.org/0000- 0002- 2461- 618X  
+
+Yunkai Li College of Water Resource & Civil Engineering, China Agriculture University  
+
+Xiuzhi Chen China Agricultural University https://orcid.org/0000- 0002- 9371- 4648  
+
+Xiangzheng Deng Chinese Academy of Sciences https://orcid.org/0000- 0002- 7993- 5540  
+
+Andrea Albanese Luxembourg Institute of Socio- Economic Research  
+
+Yingjie Li Stanford University  
+
+Zhenci Xu
+
+<--- Page Split --->
+
+## Article  
+
+## Keywords:  
+
+Posted Date: June 29th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3053894/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on March 13th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 46491- 6.
+
+<--- Page Split --->
+
+## Abstract  
+
+Rescuing Sustainable Development Goals (SDGs) from failing requires understanding their interactions networks, i.e., synergies and trade- offs, at national and especially sub- national levels, where SDGs were delivered. This understanding will help identifying the key hurdles and opportunities to prioritize the 17 SDGs in a indivisible manner for a country. However, current research on SDG priorities at sub- national levels remains limited mainly due to difficulty in data collection. Here, we collect a unified annual dataset of 102 indicators covering national and 31 provinces in China over 2000–2020. We analyze the importance of the 17 SDGs at national, provincial and regional levels through synergy and trade- off networks. The key SDGs in trade- off (provincial: 12/31, regional: 1/6) differ more than synergy (provincial: 7/31, regional: 0). Nevertheless, combating climate change (SDG13) and improving gender equality (SDG5) are overall key hurdles for China to achieving 2030 agenda. Focusing on poverty eradication (SDG1) and increasing clean water and sanitation (SDG6) have highly compound positive effect. Our findings provide essential knowledge and insight on adopting common but diffrentiaed SDGs priorities and balance mattering China's sustainable development.  
+
+## Introduction  
+
+The 2030 Agenda for Sustainable Development, consisting of the 17 Sustainable Development Goals (SDGs) and 169 targets, is a global agenda for people, the planet, and prosperity to transform the world onto a sustainable and resilient path<sup>1</sup>. However, SDGs have had a limited transformative impact<sup>2, 3</sup>. A reason for this failure of SDGs is their selective implementation without considering their complex interactions<sup>4</sup>. As a system of interacting components, SDGs have complex interconnections with synergies (a pair of SDGs improve or deteriorate together) and trade- offs (one SDG improves while the other deteriorates), which play essential roles in achieving or inhibiting their effectiveness<sup>4–6</sup>. These complex interactions largely depend on strategies to achieve an SDG. For example, infrastructure like roads are necessary for poverty alleviation (SDG1) and economic development (SDG8) but may be detrimental for coast (SDG14) and land ecosystem (SDG15)<sup>7</sup>. Thus, to rescue SDGs from failing, it is essential to understand their synergies and trade- offs for determining priorities and improving the balance and integrity of policies towards achieving the 2030 Agenda holistically<sup>4,8</sup>.  
+
+Systems thinking and analysis to assess the complex interactions among all 17 SDGs is at the forefront of sustainability research<sup>9</sup>. Existing SDG studies qualitatively evaluate SDG interactions by literature review<sup>10,23</sup>, expert rating<sup>11–13</sup>, text mining<sup>14</sup>. The model- based analysis focuses more on environmental SDGs, less on social and economic dimensions<sup>15</sup>. With public database, some research used network analysis to quantitatively analyze the differences in SDG interaction networks at global and national levels<sup>16–18</sup>. However, due to economic, social and environmental heterogeneity, SDG interactions may vary at a local or sub- national level within a country, where SDGs were actually implemented<sup>3–4,16</sup>. Understanding variations in SDG interaction networks at different spatial levels, especially at the sub
+
+<--- Page Split --->
+
+national level, remain a fundamental research gap, which in fact are essential for identifying context- and location- specific strategies for an integrated SDG implementation, especially for big countries.  
+
+As the largest developing country in geographic area and population, China has experienced rapid economic development over the past few decades. However, it has also faced social problems and environmental challenges while striving a rapid economic development \(^{19 - 20}\) . Still, earlier studies suggested the uneven progress among the 17 SDGs at the sub- national level as a significant challenge for China's sustainable development \(^{21 - 22}\) . We fill the above- highlighted research gaps by addressing the following two questions from synergy and trade- off perspectives. (1) What are the common SDG priorities among provincial, regional and national levels? (2) How much are the differentiated priorities for synergy and trade- off?  
+
+To this end, we collected as much data as possible to cover all 17 SDGs at national and sub- national levels simultaneously on a yearly basis from 2000 to 2020. In total, a unified dataset of 102 indicators were used in our analysis, consisting of 31 provinces in China (see Methods). We proposed synergy and trade- off networks at national and sub- national levels, respectively. The synergy and trade- off intensity was set to be the weighted edge and the hub score of the 17 goals were set to be the nodes in the networks (see Methods). We analyzed the hub score to determine which goal served as the central hub in the synergy and trade- off networks. The larger the hub score represented the more important the node as the central hub in the networks. We analyzed these variations at national, provincial and regional levels among 17 goals. Our findings can provide essential knowledge and insights on the priority of the SDGs to accelerate implementing the SDGs in a holistic manner at different spatial levels in China.  
+
+## Results  
+
+## The SDGs priority at the national level  
+
+At the national level, 1023 out of 5100 indicators pairs showed synergy, and 374 pairs showed trade- off with the average ABS(R) (absolute value of Spearman Correlation coefficient R) of 0.95 and 0.94 for both indicators and goals (Bonferroni corrected \(p < 0.05\) and ABS(R) \(> 0.6\) ) (Fig. 1(a) and 1(b) for indicators, see SI for more details, Fig. 2(a) and 2(d) for goals). The average Ratio (ratio of the number of the selected indicator pairs out of the total number of all possible combinations among goals) was 0.69 and 0.31 for synergy and trade- off (Fig. 2(b) and 2(e)). Overall, we found that China faced challenges on SDG13 (Climate Change Action), SDG5 (Gender Equality), SDG17 (Partnerships for the Goals), and SDG16 (Peace, Justice and Strong Institutions), which showed highest hub scores in the trade- off network (0.96, 1, 0.86 and 0.81) and lowest in synergy (0.16, 0.46, 0.52 and 0.65) (Fig. 2(c) and 2(f)). SDG12 (Responsible Consumption and Production) showed a comparable score between synergy (0.69) and trade- off (0.71). China achieved great co- benefits on the other 12 goals with the score in synergy higher than trade- off (Fig. 2(c) and 2(f), see SI for more details).
+
+<--- Page Split --->
+
+## The similarity and differences of SDGs priority among provinces  
+
+Among the 158,100 indicator pairs from the 31 provinces, 19,046 pairs showed synergy and 6,067 pairs showed trade- off with the averaged ABS(R) of 0.94 and 0.92, respectively (Bonferroni corrected \(\mathsf{p}< 0.05\) and \(\mathsf{ABS(R)} > 0.6\) ) (see SI Tab. S1 and the data file for more details). Among goals, we found that SDG13 (Climate Action) and SDG5 (Gender Equality) had the lower hub scores in synergy on average (0.19 and 0.34) (Fig. 3(a), 3(c) and 3(e)) and higher in trade- off (0.76 for both) for 19 provinces (Fig. 3(b), 3(d) and 3(f), see SI for more details). The highest goal in trade- off differed among the other 12 provinces (Fig. 3(b) and 3(d), see SI for more details). We also found that most of the SDGs had the higher scores in synergy than trade- off. Among them, SDG1 (No Poverty), SDG6 (Clean Water and Sanitation), showed the high scores in synergy (0.98 and 0.97) for 24 provinces (Fig. 3(a), 3(c) and 3(e)) and lower in trade- off (0.35 and 0.42) (Fig. 3(b), 3(d) and 3(f), see SI for more details). The highest goal in synergy differed among the other 7 provinces (Fig. 3(a) and 3(c), see SI for more details).  
+
+## The comparison of SDGs priority among regionals  
+
+For the 6 geographical regions in China, we found that SDG13 (Climate Action) and SDG5 (Gender Equality) had the highest average hub scores in trade- off (0.73 and 0.72) of all regions and the lowest in synergy (0.19 and 0.37). SDG14 (Life below Water) had a comparable score between synergy (0.30) and trade- off (0.35). The other 14 goals had higher synergy than trade- off. Among them, SDG1 (No Poverty) and SDG6 (Clean Water and Sanitation) had the highest synergy (Fig. 4(a) and 4(d)). At the regional level, we found that SDG1 and SDG6 dominated all the 6 regions in synergy (Fig. 4(b) and 4(c)). SDG13 and SDG5 dominated all the regions except for Northeast China, where SDG4 (Quality Education) had the highest trade- off (Fig. 4(e) and 4(f)). The trade- off in SDG5 in southern regions were also higher than the northern regions (Fig. 4(e)). The trade- off in SDG13 presented an opposite pattern between north and south, i.e. it increased from east to west in the north, while it decreased in the south (Fig. 4 (f)).  
+
+## Discussion and policy implication  
+
+We used social network analysis to quantitatively and systematically identify the priorities of the 17 SDGs through SDGs interaction networks using a unified dataset of 102 indicators at the sub- national and national levels in China. This understanding helps prioritize goals to implement the SDGs in an integrated and holistic way, so synergies can be reinforced and trade- offs can be mitigated.  
+
+Combatting climate change (SDG13) can reinforce all 17 SDGs \(^{23}\) . Gender equality (SDG5) is an enabler and accelerator for all the SDGs \(^{24}\) . Nevertheless, China became the world's largest emitter of carbon dioxide (CO2) in 2006 \(^{25}\) . China slipped from 63rd position in 2006 to 106th in the global gender gap rankings among 153 countries in 2019 \(^{26 - 27}\) . The gender gap in labor force participation between men and women rised from 9% to almost 15% between 1990s and 2020 \(^{26 - 27}\) . These brought serious trade- offs along with the rapid economic development. The most important is that China overall needs to take
+
+<--- Page Split --->
+
+decisive actions to mitigate the negative impact from SDG13 (Climate Action) and SDG5 (Gender Equality) (see SI for more discussions).  
+
+Poverty alleviation (SDG1) can have compound positive effects on all SDGs<sup>17</sup>. Water (SDG6) is a vital and irreplaceable resource for life and therefore underpins all SDGs<sup>28</sup>. By the end of 2020, Chinese government declared to the world that the poverty alleviation targets have been fulfilled as scheduled, lifting all 98.99 million rural people out of absolute poverty under the current standard<sup>29</sup>. The popularity rate of water supply reached 99.0% in urban area<sup>30</sup>. The centralized water supply and tap water reached 88% and 83% in rural areas<sup>30</sup>. The popularity rate of sanitary toilets in rural areas increased from 35.3% to more than 68% between 2017 and 2020<sup>30</sup>. China needs continuing their great efforts to maintain the highly compound positive impact from SDG1 (No Poverty) and SDG6 (Clean Water and Sanitation) on the whole.  
+
+Besides the common priorities, the key SDGs also differ at provincial and regional levels, especially in the trade- off network. Differentiated policies should be considered based on their own key SDGs. At the provincial level, Beijing and Chongqing needs to reduce the dominated trade- off in their rapid economic development (SDG8)<sup>31- 32</sup>. Xinjiang faces great trade- off from social dimension and the key priority is to improve the inequalities (SDG10)<sup>33</sup>. Tibet has poor health condition and needs to mitigate the highly negative impact from good health and well- being (SDG3)<sup>34</sup>. Heilongjiang and Jilin face high trade- off from their traditional industry<sup>35</sup>, the most important is to reduce the negative impact from industry (SDG9), and the consumption and production sectors (SDG12), respectively. At the regional level, Northeast China ought to mitigate the great trade- off from quality education (SDG4) through cooperation with other provinces outside the region<sup>36</sup>. East and Northwest China need to reduce the negative impact from high carbon emission per capita (SDG13)<sup>37- 38</sup> and the southern part of China should focus on mitigating the great trade- off from gender equality (SDG5) along with their rapid economic development, including East, Central South and Southwest China<sup>20,26</sup>.  
+
+To make the results meaningful in statistics, we used Bonferroni correction to avoid many possible spurious positives when several statistical tests being performed simultaneously<sup>39</sup>. We knew that the 17 goals, as the basic needs for humanity's survival and development on the planet, were related with each other and each indicator reflected one aspect of the goal it belonged to<sup>1- 3</sup>. We further used expert knowledge to explain the association between indicators for all the selected indicator pairs (see the thematic excel file in SI for more details). SDG synergies and trade- offs may be also affected by cross- boundary interactions through flows of energy, people, technology, financial capital, etc. Future research and policy on SDGs interaction can further account for cross- boundary issues and their complex mechanisms behind them<sup>40</sup>.  
+
+With over two decades of data over China, we provide new insights into the common but differentiated SDGs priorities at provincial, regional, and national levels through interaction networks. Although the key SDGs in trade- off differed more than synergy at both provincial and regional levels, SDG13 (Climate
+
+<--- Page Split --->
+
+Action) and SDG5 (Gender Equality) are the key hurdles for China to achieving 2030 agenda. SDG1 (No Poverty) and SDG6 (Clean Water and Sanitation) can have compound positive impact. Our study also provides China's example for determining priorities and improving the balance and integrity of measures towards achieving the SDGs to the other countries in the world.  
+
+## Declarations  
+
+## Data availability  
+
+All data are available in the supplementary information.  
+
+## Code availability  
+
+All R scripts used to process the data are available from the corresponding authors upon request.  
+
+Acknowledgments: We thank Prof. Mark Stafford Smith from Commonwealth Scientific and Industrial Research Organization (CSIRO), Australia for providing comments on improving the quality of the paper. This study was supported by Strategic Priority Research Program of the Chinese Academy of Sciences grant (XDA19040103), National Natural Science Foundation of China grant (42125101) and CAS Interdisciplinary Innovation Team grant (JCTD- 2020- 05).  
+
+## Author contributions:  
+
+Conceptualization: CYW, FC  Methodology: QX, PPYKL, XZC, AA  Investigation: QX, CYW  Visualization: QX, CYW  Funding acquisition: CYW, FC  Project administration: CYW, FC  Supervision: CYW, JGL, PP  Writing – original draft: QX, CYW, JGL  Writing – review & editing: PP, BB, TS, LRC, YKL, XZC, AG, XZD, YJL, ZCX  
+
+Competing interests: Authors declare that they have no competing interests.  
+
+## References
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+<--- Page Split --->
+
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+(In Chinese).  
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+42. Sachs, J., Lafortune, G., Kroll, C., Fuller, G., Woelm, F.. From Crisis to Sustainable Development: the SDGs as Roadmap to 2030 and Beyond. Sustainable Development Report 2022, Cambridge: Cambridge University Press, doi.org/10.1017/9781009210058 (2022).  
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+<--- Page Split --->
+
+49. Hauke, J., & Kossowski, T. Comparison of values of Pearson's and Spearman's correlation coefficients on the same sets of data. Quaestiones Geographicae, 30(2), 87 (2011).  
+50. Warchold, A., Pradhan, P. & Kropp, J. P. Variations in sustainable development goal interactions: population, regional, and income disaggregation. Sustain. Dev. 29, 285-299 (2020).  
+51. Borgatti, Stephen P., et al. "Network analysis in the social sciences", Science 323.5916, 892-895 (2009).  
+52. Luke, Douglas A., and Jenine K. Harris. Network analysis in public health: history, methods, and applications, Annu. Rev. Public Health 28, 69 (2007).  
+53. Felipe-Lucia M R, Soliveres S, Penone C, et al. Land-use intensity alters networks between biodiversity, ecosystem functions, and services. Proc. Natl. Acad. Sci. U.S.A. 117(45): 28140-28149 (2020).  
+54. Horvath, Steve. Weighted network analysis: applications in genomics and systems biology. Springer Science & Business Media (2011).  
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+
+## Methods  
+
+## Data collection and pre-processing  
+
+We selected indicators based on the definitions of goals, targets, and indicators in the UN official SDGs documents<sup>41</sup>, the 2022 SDG Index and Dashboards Report from the Sustainable Development Solutions Network<sup>42</sup>, and some recent studies<sup>20, 22</sup>. For each SDG, we chose as many SDG indicators as feasible from the list of recommended indicators based on available data at the sub- national and national levels simultaneously and the availability of the indicators across the temporal scale.  
+
+Data for the selected indicators in this study were obtained from the following official sources: the National Bureau of Statistics of the People's Republic of China, the China Statistical Yearbook<sup>43</sup>, the Finance Yearbook of China<sup>44</sup>, the China Statistical Yearbook on the Environment<sup>45</sup>, the Educational Statistics Yearbook of China<sup>46</sup>, the China Health Statistics Yearbook<sup>47</sup>, the China Energy Statistical Yearbook<sup>48</sup>, and other 9 Yearbooks from various ministries, such as insurance, urban construction, tourism, transportation & communications, industry, civil affairs, marine, forestry and population. See SI Tab. S2 for a list of SDGs and their corresponding indicators, data sources, and the period used in this paper.  
+
+If the indicator had different elements, the average value of all the elements was calculated for the analysis. For example, the proportion of the population covered by insurance (endowment,
+
+<--- Page Split --->
+
+unemployment, and medicare) (SDG 1, Indicator 1.3.1) was calculated from the average of that covered by endowment, unemployment, and medicare insurance. The averaged SDGs' indicators included the following: 1.3.1, 1.4.1, 2.3.1, 4. a.L, 4. c.1, 8.4.2, 9.1.2 and 12.2.2 (SI Tab. S2). We originally collected data for 118 indicators at national and sub- national levels annually. Then, the data were narrowed down to 102 indicators after the averaged calculation of various elements within one indicator. These data for 102 indicators are related to 81 targets and 17 goals.  
+
+## Synergy and trade-off calculation at the indicator level  
+
+The longitudinal Spearman correlation analyses covering non- linear relations were conducted between all 102 indicators at the 31 sub- national units one by one. The missing indicators data at certain years were dropped individually for each pairwise correlation by using the 'pairwise.complete.observation' mode. A Bonferroni correction was conducted to correct the P value when undertaking this many correlation tests<sup>39</sup>. The absolute value of the correlation coefficient \(|\mathbb{R}|\) more than 0.6 were applied further to select the indicator pairs<sup>5,22,49- 50</sup>. Since a higher value of an indicator did not necessarily mean a positive impact on sustainable development, we made a specific judgment based on the meaning of each indicator. For example, for the malnutrition rate of children under the age of 5 (SDG 2, Indicator 2.2.2), the lower value indicated a positive outcome. In contrast, for the proportion of GDP used to protect the biodiversity and ecosystem (SDG 15, Indicator 15. a.1), a lower value indicated a negative contribution to sustainable development. The detailed judgment table was listed in Supplementary Information, with "+1" indicating the better for sustainable development and "- 1" indicating worse (see SI Table S1). We used expert knowledge to explain the association between indicators for all the selected indicator pairs (see the excel files for more details).  
+
+## Synergy and trade-off calculation at the goal level  
+
+Based on the affiliation between indicator, target and goal<sup>41</sup>, the synergy intensity was calculated as follows:  
+
+\[I n t e n s i t y_{s y n e r g y} = \frac{E N_{s y n e r g y}}{T N_{s y n e r g y}}\times \frac{\sum_{i = 1}^{E N_{s y n e r g y}}|R_{s y n e r g y}|}{E N_{s y n e r g y}} \quad (1)\]  
+
+Where \(I n t e n s i t y_{s y n e r g y}\) was the synergy intensity, \(E N_{s y n e r g y}\) was the number of effective indicator pairs belonging to synergy, \(T N_{s y n e r g y}\) was the total number of indicator pairs between goals, \(R_{s y n e r g y}\) was the Spearman correlation cofficient of the effective indicator pair.  
+
+The trade- off intensity was calculated as follows:
+
+<--- Page Split --->
+
+\[Intensity_{trade - off} = \frac{EN_{trade - off}}{TN_{trade - off}} \times \frac{\sum_{i = 1}^{EN_{trade - off}}|R_{trade - off}|}{EN_{trade - off}} \quad (2)\]  
+
+Where \(Intensity_{trade - off}\) was the trade- off intensity, \(EN_{trade - off}\) was the number of effective indicator pairs belonging to trade- off, \(TN_{trade - off}\) was the total number of indicator pairs between goals, \(R_{trade - off}\) was the Spearman correlation coefficient of the effective indicator pair. If we calculated the synergy and trade- off intensity directly at the goal level, we will ignore the fact that there were both synergies and trade- offs between different SDGs.  
+
+## Network analysis  
+
+Network analysis, which has been applied in social science \(^{51}\) , public heath \(^{52}\) , ecology \(^{53}\) and biology \(^{54}\) to study complex systems, is a holistic approach to studying the complexity of SDG interactions to identify the importance of goals or targets. The synergy and trade- off networks were built separately for the national and 31 provinces using iGraph package in R Studio, respectively \(^{55}\) . Kleinberg's hub centrality score is defined as the principal eigenvector of A\*(A), where A is the adjacency matrix of the graph. Similarly, Kleinberg's authority centrality score is defined as the principal eigenvector of t(A)\*A, where A is the adjacency matrix of the graph. For undirected matrices the adjacency matrix is symmetric and the hub scores are the same as authority scores \(^{56}\) . The hub scores of the 17 SDGs were set as nodes, and the synergy or trade- off intensity among SDGs was set as the weighted edge in the network. These hub scores were used to calculate and assess the importance of the SDGs in the synergy and trade- off networks accounting for the direct and the indirect interactions. The larger the hub score was, the more important the node as a central hub was in the synergy or trade- off networks. The priority of the SDGs was identified based on the hub score in the networks from synergy and trade- off perspectives.  
+
+## The importance of the SDGs at different spatial levels  
+
+At the national level, we combined the 102 indicators in pairs, resulting in 5100 pairs in total. At the provincial level, we combined the 102 indicators in pairs for all the 31 provinces. The number of indicator pairs reached 158, 100 (5100 pairs 31 provinces) pairs in total. From indicator to goal, the importance of the SDGs was analyzed following the procedures above at national and all the provincial levels. For the detailed statistics of the number of the selected indicator pairs and Spearman correlation coefficients of the 31 provinces, please refer to SI Tab. S2. The results at the regional level were aggregated from those at provincial levels following the geographic regions divisions in China (See SI Tab. S3 for more details).  
+
+## Figures
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+The indicator pairs of synergy and trade- off at the national level (a): the distribution of the indicator pairs with numbering of the indicators showing the affiliation between the 102 indicators and 17 goals. The selected criteria are that Bonferroni corrected p value less than 0.05 and the absolute value of the Spearman correlation coefficient R more than 0.6. Each indicator is judged to have a positive or negative impact on sustainable development based on its own meaning. The indicator pairs are divided by 5 groups, including synergy, trade- off, weak synergy, weak trade- off and invalid indicator pairs. Different colors indicate different SDGs following the official UN color palette. (b): The averaged R and number of indicator pairs for each group.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+The synergy and trade- off networks at the goal level (a) and (d): the absolute value of Spearman correlation coefficient R (short for ABS(R)) among goals at the national level. (a) is for synergy and (d) is for trade- off. Set Fig.2(a) as an example, the width of the colored line indicates the arithmetic mean of ABS(R) among goals calculated from the indicator pairs in Fig 1(a). The width of the arc represents the cumulative value of each line width for that goal. The number outside the circle is the scale of each goal. (b) and (e): the ratio of the number of the selected indicator pairs out of the total number of all possible combinations among goals (short for Ratio). (b) is for synergy and (e) is for trade- off. (c) and (f): the networks built upon ABS(R) and Ratio. The thickness of the edge in the network indicates the synergy or trade- off intensity among goals. The thicker the edge is the stronger the intensity is. The size of the circle suggests its importance as a central hub in the network. The larger the circle is, the more important the node as a central hub is. (c) is for synergy (hub score: 0.16- 1) and (f) is for trade- off (hub score: 0.14- 1). In the synergy network the edge is shown in blue and in red in the trade- off networks. Different colors indicate different SDGs following the official UN color palette.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>  
+
+The hubs scores of the 17 SDGs in synergy and trade- off at the provincial level (a) and (b): the hub scores in the synergy (a) and trade- off (b) networks. (c) and (d): the ranking of the 17 SDGs in the synergy (c) and trade- off (d) networks in order of its hub score. (e) and (f): the statistics of the hub score of the 17 SDGs for synergy (e) and trade- off (f). The black line in each box shows the minimum value, lower quartile, median, upper quartile and maximum value from left to right for each SDG. The solid black circle indicates the arithmetic mean value. Different colors indicate different SDGs following the official UN color palette.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4 </center>  
+
+The hub score of the 17 SDGs at the regional level (a) and (d): the hub score in the synergy (a) and trade- off (d) networks. Different colors indicate different SDGs following the official UN color palette. (b) and (e): the spatial pattern of the hub score of SDG5 (Gender equality) in the synergy (b) and trade- off (e) networks. (c) and (f): the spatial pattern of the hub score of SDG13 (Climate action) in the synergy (c) and trade- off (f) networks.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- Explanationsontheassociationbetweenindicators.xlsx- Dataforthesynergyandtradeoffamongindicatorsatnationalandprovinciallevels.xlsx- SupplementaryInformation.docx
+
+<--- Page Split --->

preprint/preprint__05a18c267c6d7dedb4a7e980e586fa6f60b4fb0553596df82b5ab1b095ebd821/preprint__05a18c267c6d7dedb4a7e980e586fa6f60b4fb0553596df82b5ab1b095ebd821_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 933, 175]]<|/det|>
+# Climate action and gender equality matter most for China's sustainable development  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 196, 215]]<|/det|>
+Chaoyang Wu  
+
+<|ref|>text<|/ref|><|det|>[[52, 224, 245, 240]]<|/det|>
+wucyeigsnrr.ac.cn  
+
+<|ref|>text<|/ref|><|det|>[[44, 268, 936, 310]]<|/det|>
+Institute of Geographic Sciences and Natural Resources Research https://orcid.org/0000- 0001- 6163- 8209  
+
+<|ref|>text<|/ref|><|det|>[[44, 317, 684, 356]]<|/det|>
+Qiang Xing Aerospace Information Research Institute, Chinese Academy of Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 362, 728, 404]]<|/det|>
+Fang Chen International Research Center of Big Data for Sustainable Development Goals  
+
+<|ref|>text<|/ref|><|det|>[[44, 409, 636, 450]]<|/det|>
+Jianguo Liu Michigan State University https://orcid.org/0000- 0001- 6344- 0087  
+
+<|ref|>text<|/ref|><|det|>[[44, 455, 820, 496]]<|/det|>
+Prajal Pradhan Potsdam Institute for Climate Impact Research https://orcid.org/0000- 0003- 0491- 5489  
+
+<|ref|>text<|/ref|><|det|>[[44, 502, 564, 542]]<|/det|>
+Brett Bryan Deakin University https://orcid.org/0000- 0003- 4834- 5641  
+
+<|ref|>text<|/ref|><|det|>[[44, 548, 481, 589]]<|/det|>
+Thomas Schaubroeck Luxembourg Institute of Science and Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 595, 696, 636]]<|/det|>
+Luis Roman Carrasco National University of Singapore https://orcid.org/0000- 0002- 2894- 1473  
+
+<|ref|>text<|/ref|><|det|>[[44, 641, 595, 681]]<|/det|>
+Alemu Gonsamo McMaster University https://orcid.org/0000- 0002- 2461- 618X  
+
+<|ref|>text<|/ref|><|det|>[[44, 687, 697, 728]]<|/det|>
+Yunkai Li College of Water Resource & Civil Engineering, China Agriculture University  
+
+<|ref|>text<|/ref|><|det|>[[44, 733, 661, 774]]<|/det|>
+Xiuzhi Chen China Agricultural University https://orcid.org/0000- 0002- 9371- 4648  
+
+<|ref|>text<|/ref|><|det|>[[44, 780, 675, 820]]<|/det|>
+Xiangzheng Deng Chinese Academy of Sciences https://orcid.org/0000- 0002- 7993- 5540  
+
+<|ref|>text<|/ref|><|det|>[[44, 826, 496, 866]]<|/det|>
+Andrea Albanese Luxembourg Institute of Socio- Economic Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 872, 223, 912]]<|/det|>
+Yingjie Li Stanford University  
+
+<|ref|>text<|/ref|><|det|>[[44, 918, 133, 936]]<|/det|>
+Zhenci Xu
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 106, 102, 124]]<|/det|>
+## Article  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 144, 136, 163]]<|/det|>
+## Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 181, 302, 201]]<|/det|>
+Posted Date: June 29th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 220, 474, 239]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3053894/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 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|>[[44, 317, 531, 337]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 372, 925, 417]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on March 13th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 46491- 6.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 159, 68]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[40, 82, 950, 377]]<|/det|>
+Rescuing Sustainable Development Goals (SDGs) from failing requires understanding their interactions networks, i.e., synergies and trade- offs, at national and especially sub- national levels, where SDGs were delivered. This understanding will help identifying the key hurdles and opportunities to prioritize the 17 SDGs in a indivisible manner for a country. However, current research on SDG priorities at sub- national levels remains limited mainly due to difficulty in data collection. Here, we collect a unified annual dataset of 102 indicators covering national and 31 provinces in China over 2000–2020. We analyze the importance of the 17 SDGs at national, provincial and regional levels through synergy and trade- off networks. The key SDGs in trade- off (provincial: 12/31, regional: 1/6) differ more than synergy (provincial: 7/31, regional: 0). Nevertheless, combating climate change (SDG13) and improving gender equality (SDG5) are overall key hurdles for China to achieving 2030 agenda. Focusing on poverty eradication (SDG1) and increasing clean water and sanitation (SDG6) have highly compound positive effect. Our findings provide essential knowledge and insight on adopting common but diffrentiaed SDGs priorities and balance mattering China's sustainable development.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 400, 207, 426]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[41, 439, 930, 721]]<|/det|>
+The 2030 Agenda for Sustainable Development, consisting of the 17 Sustainable Development Goals (SDGs) and 169 targets, is a global agenda for people, the planet, and prosperity to transform the world onto a sustainable and resilient path<sup>1</sup>. However, SDGs have had a limited transformative impact<sup>2, 3</sup>. A reason for this failure of SDGs is their selective implementation without considering their complex interactions<sup>4</sup>. As a system of interacting components, SDGs have complex interconnections with synergies (a pair of SDGs improve or deteriorate together) and trade- offs (one SDG improves while the other deteriorates), which play essential roles in achieving or inhibiting their effectiveness<sup>4–6</sup>. These complex interactions largely depend on strategies to achieve an SDG. For example, infrastructure like roads are necessary for poverty alleviation (SDG1) and economic development (SDG8) but may be detrimental for coast (SDG14) and land ecosystem (SDG15)<sup>7</sup>. Thus, to rescue SDGs from failing, it is essential to understand their synergies and trade- offs for determining priorities and improving the balance and integrity of policies towards achieving the 2030 Agenda holistically<sup>4,8</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[41, 736, 940, 927]]<|/det|>
+Systems thinking and analysis to assess the complex interactions among all 17 SDGs is at the forefront of sustainability research<sup>9</sup>. Existing SDG studies qualitatively evaluate SDG interactions by literature review<sup>10,23</sup>, expert rating<sup>11–13</sup>, text mining<sup>14</sup>. The model- based analysis focuses more on environmental SDGs, less on social and economic dimensions<sup>15</sup>. With public database, some research used network analysis to quantitatively analyze the differences in SDG interaction networks at global and national levels<sup>16–18</sup>. However, due to economic, social and environmental heterogeneity, SDG interactions may vary at a local or sub- national level within a country, where SDGs were actually implemented<sup>3–4,16</sup>. Understanding variations in SDG interaction networks at different spatial levels, especially at the sub
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 952, 90]]<|/det|>
+national level, remain a fundamental research gap, which in fact are essential for identifying context- and location- specific strategies for an integrated SDG implementation, especially for big countries.  
+
+<|ref|>text<|/ref|><|det|>[[41, 105, 955, 289]]<|/det|>
+As the largest developing country in geographic area and population, China has experienced rapid economic development over the past few decades. However, it has also faced social problems and environmental challenges while striving a rapid economic development \(^{19 - 20}\) . Still, earlier studies suggested the uneven progress among the 17 SDGs at the sub- national level as a significant challenge for China's sustainable development \(^{21 - 22}\) . We fill the above- highlighted research gaps by addressing the following two questions from synergy and trade- off perspectives. (1) What are the common SDG priorities among provincial, regional and national levels? (2) How much are the differentiated priorities for synergy and trade- off?  
+
+<|ref|>text<|/ref|><|det|>[[41, 305, 955, 532]]<|/det|>
+To this end, we collected as much data as possible to cover all 17 SDGs at national and sub- national levels simultaneously on a yearly basis from 2000 to 2020. In total, a unified dataset of 102 indicators were used in our analysis, consisting of 31 provinces in China (see Methods). We proposed synergy and trade- off networks at national and sub- national levels, respectively. The synergy and trade- off intensity was set to be the weighted edge and the hub score of the 17 goals were set to be the nodes in the networks (see Methods). We analyzed the hub score to determine which goal served as the central hub in the synergy and trade- off networks. The larger the hub score represented the more important the node as the central hub in the networks. We analyzed these variations at national, provincial and regional levels among 17 goals. Our findings can provide essential knowledge and insights on the priority of the SDGs to accelerate implementing the SDGs in a holistic manner at different spatial levels in China.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 555, 144, 580]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 592, 614, 625]]<|/det|>
+## The SDGs priority at the national level  
+
+<|ref|>text<|/ref|><|det|>[[40, 638, 950, 911]]<|/det|>
+At the national level, 1023 out of 5100 indicators pairs showed synergy, and 374 pairs showed trade- off with the average ABS(R) (absolute value of Spearman Correlation coefficient R) of 0.95 and 0.94 for both indicators and goals (Bonferroni corrected \(p < 0.05\) and ABS(R) \(> 0.6\) ) (Fig. 1(a) and 1(b) for indicators, see SI for more details, Fig. 2(a) and 2(d) for goals). The average Ratio (ratio of the number of the selected indicator pairs out of the total number of all possible combinations among goals) was 0.69 and 0.31 for synergy and trade- off (Fig. 2(b) and 2(e)). Overall, we found that China faced challenges on SDG13 (Climate Change Action), SDG5 (Gender Equality), SDG17 (Partnerships for the Goals), and SDG16 (Peace, Justice and Strong Institutions), which showed highest hub scores in the trade- off network (0.96, 1, 0.86 and 0.81) and lowest in synergy (0.16, 0.46, 0.52 and 0.65) (Fig. 2(c) and 2(f)). SDG12 (Responsible Consumption and Production) showed a comparable score between synergy (0.69) and trade- off (0.71). China achieved great co- benefits on the other 12 goals with the score in synergy higher than trade- off (Fig. 2(c) and 2(f), see SI for more details).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 41, 861, 104]]<|/det|>
+## The similarity and differences of SDGs priority among provinces  
+
+<|ref|>text<|/ref|><|det|>[[40, 118, 955, 368]]<|/det|>
+Among the 158,100 indicator pairs from the 31 provinces, 19,046 pairs showed synergy and 6,067 pairs showed trade- off with the averaged ABS(R) of 0.94 and 0.92, respectively (Bonferroni corrected \(\mathsf{p}< 0.05\) and \(\mathsf{ABS(R)} > 0.6\) ) (see SI Tab. S1 and the data file for more details). Among goals, we found that SDG13 (Climate Action) and SDG5 (Gender Equality) had the lower hub scores in synergy on average (0.19 and 0.34) (Fig. 3(a), 3(c) and 3(e)) and higher in trade- off (0.76 for both) for 19 provinces (Fig. 3(b), 3(d) and 3(f), see SI for more details). The highest goal in trade- off differed among the other 12 provinces (Fig. 3(b) and 3(d), see SI for more details). We also found that most of the SDGs had the higher scores in synergy than trade- off. Among them, SDG1 (No Poverty), SDG6 (Clean Water and Sanitation), showed the high scores in synergy (0.98 and 0.97) for 24 provinces (Fig. 3(a), 3(c) and 3(e)) and lower in trade- off (0.35 and 0.42) (Fig. 3(b), 3(d) and 3(f), see SI for more details). The highest goal in synergy differed among the other 7 provinces (Fig. 3(a) and 3(c), see SI for more details).  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 368, 806, 401]]<|/det|>
+## The comparison of SDGs priority among regionals  
+
+<|ref|>text<|/ref|><|det|>[[41, 413, 952, 640]]<|/det|>
+For the 6 geographical regions in China, we found that SDG13 (Climate Action) and SDG5 (Gender Equality) had the highest average hub scores in trade- off (0.73 and 0.72) of all regions and the lowest in synergy (0.19 and 0.37). SDG14 (Life below Water) had a comparable score between synergy (0.30) and trade- off (0.35). The other 14 goals had higher synergy than trade- off. Among them, SDG1 (No Poverty) and SDG6 (Clean Water and Sanitation) had the highest synergy (Fig. 4(a) and 4(d)). At the regional level, we found that SDG1 and SDG6 dominated all the 6 regions in synergy (Fig. 4(b) and 4(c)). SDG13 and SDG5 dominated all the regions except for Northeast China, where SDG4 (Quality Education) had the highest trade- off (Fig. 4(e) and 4(f)). The trade- off in SDG5 in southern regions were also higher than the northern regions (Fig. 4(e)). The trade- off in SDG13 presented an opposite pattern between north and south, i.e. it increased from east to west in the north, while it decreased in the south (Fig. 4 (f)).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 661, 485, 690]]<|/det|>
+## Discussion and policy implication  
+
+<|ref|>text<|/ref|><|det|>[[43, 703, 925, 793]]<|/det|>
+We used social network analysis to quantitatively and systematically identify the priorities of the 17 SDGs through SDGs interaction networks using a unified dataset of 102 indicators at the sub- national and national levels in China. This understanding helps prioritize goals to implement the SDGs in an integrated and holistic way, so synergies can be reinforced and trade- offs can be mitigated.  
+
+<|ref|>text<|/ref|><|det|>[[42, 810, 936, 953]]<|/det|>
+Combatting climate change (SDG13) can reinforce all 17 SDGs \(^{23}\) . Gender equality (SDG5) is an enabler and accelerator for all the SDGs \(^{24}\) . Nevertheless, China became the world's largest emitter of carbon dioxide (CO2) in 2006 \(^{25}\) . China slipped from 63rd position in 2006 to 106th in the global gender gap rankings among 153 countries in 2019 \(^{26 - 27}\) . The gender gap in labor force participation between men and women rised from 9% to almost 15% between 1990s and 2020 \(^{26 - 27}\) . These brought serious trade- offs along with the rapid economic development. The most important is that China overall needs to take
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 883, 88]]<|/det|>
+decisive actions to mitigate the negative impact from SDG13 (Climate Action) and SDG5 (Gender Equality) (see SI for more discussions).  
+
+<|ref|>text<|/ref|><|det|>[[40, 106, 955, 319]]<|/det|>
+Poverty alleviation (SDG1) can have compound positive effects on all SDGs<sup>17</sup>. Water (SDG6) is a vital and irreplaceable resource for life and therefore underpins all SDGs<sup>28</sup>. By the end of 2020, Chinese government declared to the world that the poverty alleviation targets have been fulfilled as scheduled, lifting all 98.99 million rural people out of absolute poverty under the current standard<sup>29</sup>. The popularity rate of water supply reached 99.0% in urban area<sup>30</sup>. The centralized water supply and tap water reached 88% and 83% in rural areas<sup>30</sup>. The popularity rate of sanitary toilets in rural areas increased from 35.3% to more than 68% between 2017 and 2020<sup>30</sup>. China needs continuing their great efforts to maintain the highly compound positive impact from SDG1 (No Poverty) and SDG6 (Clean Water and Sanitation) on the whole.  
+
+<|ref|>text<|/ref|><|det|>[[40, 336, 950, 642]]<|/det|>
+Besides the common priorities, the key SDGs also differ at provincial and regional levels, especially in the trade- off network. Differentiated policies should be considered based on their own key SDGs. At the provincial level, Beijing and Chongqing needs to reduce the dominated trade- off in their rapid economic development (SDG8)<sup>31- 32</sup>. Xinjiang faces great trade- off from social dimension and the key priority is to improve the inequalities (SDG10)<sup>33</sup>. Tibet has poor health condition and needs to mitigate the highly negative impact from good health and well- being (SDG3)<sup>34</sup>. Heilongjiang and Jilin face high trade- off from their traditional industry<sup>35</sup>, the most important is to reduce the negative impact from industry (SDG9), and the consumption and production sectors (SDG12), respectively. At the regional level, Northeast China ought to mitigate the great trade- off from quality education (SDG4) through cooperation with other provinces outside the region<sup>36</sup>. East and Northwest China need to reduce the negative impact from high carbon emission per capita (SDG13)<sup>37- 38</sup> and the southern part of China should focus on mitigating the great trade- off from gender equality (SDG5) along with their rapid economic development, including East, Central South and Southwest China<sup>20,26</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[41, 659, 944, 867]]<|/det|>
+To make the results meaningful in statistics, we used Bonferroni correction to avoid many possible spurious positives when several statistical tests being performed simultaneously<sup>39</sup>. We knew that the 17 goals, as the basic needs for humanity's survival and development on the planet, were related with each other and each indicator reflected one aspect of the goal it belonged to<sup>1- 3</sup>. We further used expert knowledge to explain the association between indicators for all the selected indicator pairs (see the thematic excel file in SI for more details). SDG synergies and trade- offs may be also affected by cross- boundary interactions through flows of energy, people, technology, financial capital, etc. Future research and policy on SDGs interaction can further account for cross- boundary issues and their complex mechanisms behind them<sup>40</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[42, 886, 944, 952]]<|/det|>
+With over two decades of data over China, we provide new insights into the common but differentiated SDGs priorities at provincial, regional, and national levels through interaction networks. Although the key SDGs in trade- off differed more than synergy at both provincial and regional levels, SDG13 (Climate
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 944, 133]]<|/det|>
+Action) and SDG5 (Gender Equality) are the key hurdles for China to achieving 2030 agenda. SDG1 (No Poverty) and SDG6 (Clean Water and Sanitation) can have compound positive impact. Our study also provides China's example for determining priorities and improving the balance and integrity of measures towards achieving the SDGs to the other countries in the world.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 156, 212, 182]]<|/det|>
+## Declarations  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 198, 187, 217]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[44, 235, 525, 255]]<|/det|>
+All data are available in the supplementary information.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 273, 189, 293]]<|/det|>
+## Code availability  
+
+<|ref|>text<|/ref|><|det|>[[44, 310, 880, 332]]<|/det|>
+All R scripts used to process the data are available from the corresponding authors upon request.  
+
+<|ref|>text<|/ref|><|det|>[[42, 348, 922, 461]]<|/det|>
+Acknowledgments: We thank Prof. Mark Stafford Smith from Commonwealth Scientific and Industrial Research Organization (CSIRO), Australia for providing comments on improving the quality of the paper. This study was supported by Strategic Priority Research Program of the Chinese Academy of Sciences grant (XDA19040103), National Natural Science Foundation of China grant (42125101) and CAS Interdisciplinary Innovation Team grant (JCTD- 2020- 05).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 478, 227, 497]]<|/det|>
+## Author contributions:  
+
+<|ref|>text<|/ref|><|det|>[[42, 515, 680, 860]]<|/det|>
+Conceptualization: CYW, FC  Methodology: QX, PPYKL, XZC, AA  Investigation: QX, CYW  Visualization: QX, CYW  Funding acquisition: CYW, FC  Project administration: CYW, FC  Supervision: CYW, JGL, PP  Writing – original draft: QX, CYW, JGL  Writing – review & editing: PP, BB, TS, LRC, YKL, XZC, AG, XZD, YJL, ZCX  
+
+<|ref|>text<|/ref|><|det|>[[44, 857, 697, 878]]<|/det|>
+Competing interests: Authors declare that they have no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 900, 195, 925]]<|/det|>
+## References
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+<|ref|>text<|/ref|><|det|>[[48, 606, 923, 651]]<|/det|>
+43. China Statistics Press, "China Statistical Yearbook" (National Bureau of Statistics of the People's Republic of China, 2001-2021) [in Chinese].  
+
+<|ref|>text<|/ref|><|det|>[[48, 655, 940, 700]]<|/det|>
+44. China Financial & Economic Publishing House, "Finance Yearbook of China" (Ministry of Finance of the People's Republic of China, 2001-2021) [in Chinese].  
+
+<|ref|>text<|/ref|><|det|>[[48, 704, 944, 772]]<|/det|>
+45. China Statistics Press, "China Statistical Yearbook on Environment" (National Bureau of Statistics & State Environmental Protection Administration of the People's Republic of China, 2001-2021) [in Chinese].  
+
+<|ref|>text<|/ref|><|det|>[[48, 777, 933, 822]]<|/det|>
+46. People's Education Press, "Educational Statistics Yearbook of China" (Ministry of Education of the People's Republic of China, 2001-2021) [in Chinese].  
+
+<|ref|>text<|/ref|><|det|>[[48, 826, 943, 871]]<|/det|>
+47. China Statistics Press, "China Health and Family Planning Statistical Yearbook" (National Bureau of Statistics of the People's Republic of China, 2001-2021) [in Chinese].  
+
+<|ref|>text<|/ref|><|det|>[[48, 875, 910, 920]]<|/det|>
+48. China Statistics Press, "China Energy Statistical Yearbook" (National Bureau of Statistics of the People's Republic of China, 2001-2021) [in Chinese].
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[48, 44, 940, 480]]<|/det|>
+49. Hauke, J., & Kossowski, T. Comparison of values of Pearson's and Spearman's correlation coefficients on the same sets of data. Quaestiones Geographicae, 30(2), 87 (2011).  
+50. Warchold, A., Pradhan, P. & Kropp, J. P. Variations in sustainable development goal interactions: population, regional, and income disaggregation. Sustain. Dev. 29, 285-299 (2020).  
+51. Borgatti, Stephen P., et al. "Network analysis in the social sciences", Science 323.5916, 892-895 (2009).  
+52. Luke, Douglas A., and Jenine K. Harris. Network analysis in public health: history, methods, and applications, Annu. Rev. Public Health 28, 69 (2007).  
+53. Felipe-Lucia M R, Soliveres S, Penone C, et al. Land-use intensity alters networks between biodiversity, ecosystem functions, and services. Proc. Natl. Acad. Sci. U.S.A. 117(45): 28140-28149 (2020).  
+54. Horvath, Steve. Weighted network analysis: applications in genomics and systems biology. Springer Science & Business Media (2011).  
+55. Csardi, G. & Nepusz, T. Te igraph software package for complex network research. InterJournal https://igraph.org (2006).  
+56. J. Kleinberg. Authoritative sources in a hyperlinked environment. Proc. 9th ACM-SIAM Symposium on Discrete Algorithms, 1998. Extended version in Journal of the ACM 46(1999). Also appears as IBM Research Report RJ 10076, May 1997.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 501, 164, 526]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 543, 346, 563]]<|/det|>
+## Data collection and pre-processing  
+
+<|ref|>text<|/ref|><|det|>[[42, 580, 945, 696]]<|/det|>
+We selected indicators based on the definitions of goals, targets, and indicators in the UN official SDGs documents<sup>41</sup>, the 2022 SDG Index and Dashboards Report from the Sustainable Development Solutions Network<sup>42</sup>, and some recent studies<sup>20, 22</sup>. For each SDG, we chose as many SDG indicators as feasible from the list of recommended indicators based on available data at the sub- national and national levels simultaneously and the availability of the indicators across the temporal scale.  
+
+<|ref|>text<|/ref|><|det|>[[41, 712, 940, 900]]<|/det|>
+Data for the selected indicators in this study were obtained from the following official sources: the National Bureau of Statistics of the People's Republic of China, the China Statistical Yearbook<sup>43</sup>, the Finance Yearbook of China<sup>44</sup>, the China Statistical Yearbook on the Environment<sup>45</sup>, the Educational Statistics Yearbook of China<sup>46</sup>, the China Health Statistics Yearbook<sup>47</sup>, the China Energy Statistical Yearbook<sup>48</sup>, and other 9 Yearbooks from various ministries, such as insurance, urban construction, tourism, transportation & communications, industry, civil affairs, marine, forestry and population. See SI Tab. S2 for a list of SDGs and their corresponding indicators, data sources, and the period used in this paper.  
+
+<|ref|>text<|/ref|><|det|>[[42, 917, 895, 960]]<|/det|>
+If the indicator had different elements, the average value of all the elements was calculated for the analysis. For example, the proportion of the population covered by insurance (endowment,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 955, 180]]<|/det|>
+unemployment, and medicare) (SDG 1, Indicator 1.3.1) was calculated from the average of that covered by endowment, unemployment, and medicare insurance. The averaged SDGs' indicators included the following: 1.3.1, 1.4.1, 2.3.1, 4. a.L, 4. c.1, 8.4.2, 9.1.2 and 12.2.2 (SI Tab. S2). We originally collected data for 118 indicators at national and sub- national levels annually. Then, the data were narrowed down to 102 indicators after the averaged calculation of various elements within one indicator. These data for 102 indicators are related to 81 targets and 17 goals.  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 196, 514, 217]]<|/det|>
+## Synergy and trade-off calculation at the indicator level  
+
+<|ref|>text<|/ref|><|det|>[[41, 234, 953, 555]]<|/det|>
+The longitudinal Spearman correlation analyses covering non- linear relations were conducted between all 102 indicators at the 31 sub- national units one by one. The missing indicators data at certain years were dropped individually for each pairwise correlation by using the 'pairwise.complete.observation' mode. A Bonferroni correction was conducted to correct the P value when undertaking this many correlation tests<sup>39</sup>. The absolute value of the correlation coefficient \(|\mathbb{R}|\) more than 0.6 were applied further to select the indicator pairs<sup>5,22,49- 50</sup>. Since a higher value of an indicator did not necessarily mean a positive impact on sustainable development, we made a specific judgment based on the meaning of each indicator. For example, for the malnutrition rate of children under the age of 5 (SDG 2, Indicator 2.2.2), the lower value indicated a positive outcome. In contrast, for the proportion of GDP used to protect the biodiversity and ecosystem (SDG 15, Indicator 15. a.1), a lower value indicated a negative contribution to sustainable development. The detailed judgment table was listed in Supplementary Information, with "+1" indicating the better for sustainable development and "- 1" indicating worse (see SI Table S1). We used expert knowledge to explain the association between indicators for all the selected indicator pairs (see the excel files for more details).  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 571, 476, 592]]<|/det|>
+## Synergy and trade-off calculation at the goal level  
+
+<|ref|>text<|/ref|><|det|>[[42, 610, 911, 653]]<|/det|>
+Based on the affiliation between indicator, target and goal<sup>41</sup>, the synergy intensity was calculated as follows:  
+
+<|ref|>equation<|/ref|><|det|>[[204, 671, 825, 715]]<|/det|>
+\[I n t e n s i t y_{s y n e r g y} = \frac{E N_{s y n e r g y}}{T N_{s y n e r g y}}\times \frac{\sum_{i = 1}^{E N_{s y n e r g y}}|R_{s y n e r g y}|}{E N_{s y n e r g y}} \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[52, 730, 825, 866]]<|/det|>
+Where \(I n t e n s i t y_{s y n e r g y}\) was the synergy intensity, \(E N_{s y n e r g y}\) was the number of effective indicator pairs belonging to synergy, \(T N_{s y n e r g y}\) was the total number of indicator pairs between goals, \(R_{s y n e r g y}\) was the Spearman correlation cofficient of the effective indicator pair.  
+
+<|ref|>text<|/ref|><|det|>[[42, 892, 472, 912]]<|/det|>
+The trade- off intensity was calculated as follows:
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[190, 52, 830, 98]]<|/det|>
+\[Intensity_{trade - off} = \frac{EN_{trade - off}}{TN_{trade - off}} \times \frac{\sum_{i = 1}^{EN_{trade - off}}|R_{trade - off}|}{EN_{trade - off}} \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[58, 109, 816, 279]]<|/det|>
+Where \(Intensity_{trade - off}\) was the trade- off intensity, \(EN_{trade - off}\) was the number of effective indicator pairs belonging to trade- off, \(TN_{trade - off}\) was the total number of indicator pairs between goals, \(R_{trade - off}\) was the Spearman correlation coefficient of the effective indicator pair. If we calculated the synergy and trade- off intensity directly at the goal level, we will ignore the fact that there were both synergies and trade- offs between different SDGs.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 310, 196, 330]]<|/det|>
+## Network analysis  
+
+<|ref|>text<|/ref|><|det|>[[40, 348, 955, 650]]<|/det|>
+Network analysis, which has been applied in social science \(^{51}\) , public heath \(^{52}\) , ecology \(^{53}\) and biology \(^{54}\) to study complex systems, is a holistic approach to studying the complexity of SDG interactions to identify the importance of goals or targets. The synergy and trade- off networks were built separately for the national and 31 provinces using iGraph package in R Studio, respectively \(^{55}\) . Kleinberg's hub centrality score is defined as the principal eigenvector of A\*(A), where A is the adjacency matrix of the graph. Similarly, Kleinberg's authority centrality score is defined as the principal eigenvector of t(A)\*A, where A is the adjacency matrix of the graph. For undirected matrices the adjacency matrix is symmetric and the hub scores are the same as authority scores \(^{56}\) . The hub scores of the 17 SDGs were set as nodes, and the synergy or trade- off intensity among SDGs was set as the weighted edge in the network. These hub scores were used to calculate and assess the importance of the SDGs in the synergy and trade- off networks accounting for the direct and the indirect interactions. The larger the hub score was, the more important the node as a central hub was in the synergy or trade- off networks. The priority of the SDGs was identified based on the hub score in the networks from synergy and trade- off perspectives.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 664, 512, 686]]<|/det|>
+## The importance of the SDGs at different spatial levels  
+
+<|ref|>text<|/ref|><|det|>[[41, 701, 950, 860]]<|/det|>
+At the national level, we combined the 102 indicators in pairs, resulting in 5100 pairs in total. At the provincial level, we combined the 102 indicators in pairs for all the 31 provinces. The number of indicator pairs reached 158, 100 (5100 pairs 31 provinces) pairs in total. From indicator to goal, the importance of the SDGs was analyzed following the procedures above at national and all the provincial levels. For the detailed statistics of the number of the selected indicator pairs and Spearman correlation coefficients of the 31 provinces, please refer to SI Tab. S2. The results at the regional level were aggregated from those at provincial levels following the geographic regions divisions in China (See SI Tab. S3 for more details).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 883, 142, 910]]<|/det|>
+## Figures
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[66, 50, 940, 490]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 520, 115, 539]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 561, 949, 743]]<|/det|>
+The indicator pairs of synergy and trade- off at the national level (a): the distribution of the indicator pairs with numbering of the indicators showing the affiliation between the 102 indicators and 17 goals. The selected criteria are that Bonferroni corrected p value less than 0.05 and the absolute value of the Spearman correlation coefficient R more than 0.6. Each indicator is judged to have a positive or negative impact on sustainable development based on its own meaning. The indicator pairs are divided by 5 groups, including synergy, trade- off, weak synergy, weak trade- off and invalid indicator pairs. Different colors indicate different SDGs following the official UN color palette. (b): The averaged R and number of indicator pairs for each group.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[48, 45, 944, 475]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 494, 118, 514]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[39, 535, 949, 830]]<|/det|>
+The synergy and trade- off networks at the goal level (a) and (d): the absolute value of Spearman correlation coefficient R (short for ABS(R)) among goals at the national level. (a) is for synergy and (d) is for trade- off. Set Fig.2(a) as an example, the width of the colored line indicates the arithmetic mean of ABS(R) among goals calculated from the indicator pairs in Fig 1(a). The width of the arc represents the cumulative value of each line width for that goal. The number outside the circle is the scale of each goal. (b) and (e): the ratio of the number of the selected indicator pairs out of the total number of all possible combinations among goals (short for Ratio). (b) is for synergy and (e) is for trade- off. (c) and (f): the networks built upon ABS(R) and Ratio. The thickness of the edge in the network indicates the synergy or trade- off intensity among goals. The thicker the edge is the stronger the intensity is. The size of the circle suggests its importance as a central hub in the network. The larger the circle is, the more important the node as a central hub is. (c) is for synergy (hub score: 0.16- 1) and (f) is for trade- off (hub score: 0.14- 1). In the synergy network the edge is shown in blue and in red in the trade- off networks. Different colors indicate different SDGs following the official UN color palette.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[50, 49, 940, 587]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[43, 612, 116, 631]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 653, 955, 812]]<|/det|>
+The hubs scores of the 17 SDGs in synergy and trade- off at the provincial level (a) and (b): the hub scores in the synergy (a) and trade- off (b) networks. (c) and (d): the ranking of the 17 SDGs in the synergy (c) and trade- off (d) networks in order of its hub score. (e) and (f): the statistics of the hub score of the 17 SDGs for synergy (e) and trade- off (f). The black line in each box shows the minimum value, lower quartile, median, upper quartile and maximum value from left to right for each SDG. The solid black circle indicates the arithmetic mean value. Different colors indicate different SDGs following the official UN color palette.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[45, 52, 944, 435]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 464, 118, 483]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 504, 945, 618]]<|/det|>
+The hub score of the 17 SDGs at the regional level (a) and (d): the hub score in the synergy (a) and trade- off (d) networks. Different colors indicate different SDGs following the official UN color palette. (b) and (e): the spatial pattern of the hub score of SDG5 (Gender equality) in the synergy (b) and trade- off (e) networks. (c) and (f): the spatial pattern of the hub score of SDG13 (Climate action) in the synergy (c) and trade- off (f) networks.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 641, 312, 668]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 691, 765, 711]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[59, 729, 792, 802]]<|/det|>
+- Explanationsontheassociationbetweenindicators.xlsx- Dataforthesynergyandtradeoffamongindicatorsatnationalandprovinciallevels.xlsx- SupplementaryInformation.docx
+
+<--- Page Split --->

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+
+# Effects of introducing the WHO Labour Care Guide on Caesarean section: a pragmatic, stepped-wedge, cluster randomized trial in India  
+
+Joshua Vogel ( \(\boxed{ \begin{array}{r l} \end{array} }\) joshua.vogel@burnet.edu.au) Burnet Institute https://orcid.org/0000- 0002- 3214- 7096  
+
+Yeshita Pujar KLE Academy of Higher Education and Research  
+
+Sunil Vemekar KLE Academy of Higher Education and Research  
+
+Elizabeth Armarit Burnet Institute  
+
+Veronica Pingray Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+Fernando Althabe Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+Luz Gibbons IECS https://orcid.org/0000- 0002- 0235- 1635  
+
+Mabel Berrueta Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+Manjunath Somannavar KLE Academy of Higher Education and Research  
+
+Alvaro Ciganda Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+Rocio Rodriguez Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+Savitri Bendigeri KLE Academy of Higher Education and Research  
+
+Jayashree Ashok Kumar Gadag Institute of Medical Sciences  
+
+Shruti Bhavi Patil Gadag Institute of Medical Sciences  
+
+Aravind Karinagannanavar Gadag Institute of Medical Sciences  
+
+Raveendra Anteen
+
+<--- Page Split --->
+
+Gokak General Hospital  
+
+Pavithra M. R. Gokak General Hospital  
+
+Shukla Shetty JJM Medical College  
+
+Latha B JJM Medical College  
+
+Megha H. M. JJM Medical College  
+
+Suman Gaddi Vijayanagar Institute of Medical Sciences  
+
+Shaila Chikkagowdra Vijayanagar Institute of Medical Sciences  
+
+Bellara Raghavendra Vijayanagar Institute of Medical Sciences  
+
+Caroline Homer Burnet Institute https://orcid.org/0000- 0002- 7454- 3011  
+
+Tina Lavender Liverpool School of Tropical Medicine  
+
+Pralhad Kushtagi Manipal Academy of Higher Education  
+
+Justus Hofmeyr Department of Health, Universities of the Witwatersrand, Walter Sisulu and Fort Hare, East London, South Africa https://orcid.org/0000- 0002- 3080- 1007  
+
+Richard Derman Thomas Jefferson University  
+
+Shivaprasad Goudar Jawaharlal Nehru Medical College, India  
+
+## Article  
+
+Keywords:  
+
+Posted Date: July 28th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3175470/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 Medicine on January 30th, 2024. See the published version at https://doi.org/10.1038/s41591-023-02751-4.
+
+<--- Page Split --->
+
+# Effects of introducing the WHO Labour Care Guide on Caesarean section: a pragmatic, stepped-wedge, cluster randomized trial in India  
+
+Joshua P. Vogel \(^{1*}\) , Yeshita Pujar \(^{2}\) , Sunil S Vernekar \(^{2}\) , Elizabeth Armar \(^{1}\) , Veronica Pingray \(^{3}\) , Fernando Althabe \(^{3}\) , Luz Gibbons \(^{3}\) , Mabel Berrueta \(^{3}\) , Manjunath Somannavar \(^{2}\) , Alvaro Ciganda \(^{3}\) , Rocio Rodriguez \(^{3}\) , Savitri Bendigeri \(^{2}\) , Jayashree Ashok Kumar \(^{4}\) , Shruti Bhavi Patil \(^{4}\) , Aravind Karinagannanavar \(^{4}\) , Raveendra R Anteen \(^{5}\) , Pavithra M. R. \(^{5}\) , Shukla Shetty \(^{6}\) , Latha B. \(^{6}\) , Megha H. M. \(^{6}\) , Suman S. Gaddi \(^{7}\) , Shaila Chikkagowdra \(^{7}\) , Bellara Raghavendra \(^{7}\) , Caroline SE Homer \(^{1}\) , Tina Lavender \(^{8}\) , Pralhad Kushtagi \(^{9}\) , G. Justus Hofmeyr \(^{10,11}\) , Richard Derman \(^{12}\) , Shivaprasad Goudar \(^{3}\)  
+
+\* corresponding author – Joshua.vogel@burnet.edu.au \(^{1}\) Maternal, Child and Adolescent Health Program, Burnet Institute, Melbourne, Victoria, Australia \(^{2}\) Women's and Children's Health Research Unit, Jawaharlal Nehru Medical College, KLE Academy of Higher Education and Research, Belgaum, Karnataka, India \(^{3}\) Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina \(^{4}\) Gadag Institute of Medical Sciences, Gadag, Karnataka, India \(^{5}\) General Hospital, Gokak, Belgaum, Karnataka, India \(^{6}\) JJM Medical College, Davangere, Karnataka, India \(^{7}\) Vijayanagar Institute of Medical Sciences (VIMS), Ballari, Karnataka, India \(^{8}\) Department of International Health, Liverpool School of Tropical Medicine, Liverpool, United Kingdom \(^{9}\) Manipal Academy of Higher Education, Karnataka, India \(^{10}\) Department of Obstetrics and Gynaecology, University of Botswana, Gaborone, Botswana \(^{11}\) University of the Witwatersrand and Walter Sisulu University, East London, South Africa \(^{12}\) Thomas Jefferson University, Philadelphia, United States of America
+
+<--- Page Split --->
+
+## ABSTRACT  
+
+The World Health Organization's Labour Care Guide (LCG) is the "next generation" partograph, designed to improve the quality of intrapartum care and enhance women's experiences. However, the effects of the LCG on maternal and newborn outcomes have not been evaluated. We developed a novel strategy to introduce the LCG into routine intrapartum care, comprising a co- designed training program for labour ward clinicians, alongside monthly audit and feedback. We implemented the strategy and measured its effects using a stepped- wedge, randomised trial in four hospitals in India. We captured data from 26,331 women who gave birth at \(> = 20\) weeks' gestation, over a 54- week period. Following implementation, a \(5.5\%\) crude absolute reduction in the Caesarean section rate amongst women in Robson Group 1 was observed (45.2% vs 39.7%; relative risk 0.85, 95% confidence interval 0.54- 1.33). Maternal process- of- care measures were not significantly different, though labour augmentation with oxytocin was 18.0% lower with the LCG strategy. No differences were observed for maternal, fetal or newborn health outcomes, or women's birth experiences. This "proof of concept" study provides important evidence on the effects of introducing LCG into routine practice, suggesting a 15% relative risk reduction in Caesarean section use amongst women in Robson Group 1. Larger trials are warranted, particularly in settings where urgent reversal of the Caesarean section epidemic is needed.
+
+<--- Page Split --->
+
+## MAIN  
+
+An estimated 287,000 maternal deaths, 2.4 million neonatal deaths and 1.9 million stillbirths occur each year, the vast majority of which occur in low- and middle- income countries (LMICs).(1- 3). As many as \(45\%\) of these maternal deaths, stillbirths, and neonatal deaths occur during labour, birth, and the first 24 hours postpartum.(4) Ensuring good- quality care is available to all women during the intrapartum period is thus critical to any efforts to reduce global maternal and neonatal morbidity and mortality.(5) Caesarean section is an essential component of good- quality intrapartum care - when used appropriately, it is a life- saving intervention for women and babies. However, Caesarean section rates globally more than doubled between 2000 and 2015, driven in large part by those performed without a clear medical indication.(6)(7) While unnecessary Caesarean section causes avoidable harms to women and newborns,(8, 9) it By 2030, 38 million women each year (28.5% of births) will experience a Caesarean.(10)  
+
+The World Health Organization (WHO) has long recommended that a woman in labour should be monitored by a skilled healthcare provider using a partograph to document clinical assessments and help make decisions.(11) When completed prospectively, the partograph can help determine whether and when an intervention - such as labour augmentation, Caesarean section or episiotomy - is warranted. A WHO- led 1994 trial showed that prospective partograph use combined with intensive provider training optimized the use of intrapartum interventions, and improved maternal and newborn outcomes.(12) Consequently, the WHO simplified partograph was widely disseminated and adopted as a component of routine intrapartum care internationally.(13) While more women than ever are giving birth in health facilities,(14) partographs are often used poorly, or not at all. Inadequate provider training and skills, heavy staff workloads, a lack of clinical equipment and supplies, and restrictive hospital policies are known barriers to partograph use.(15- 17)  
+
+In 2018, WHO published 56 updated recommendations to improve quality of intrapartum care and enhance women's childbirth experiences.(8) Key recommendations included changing the definition of active first stage of labour from the widely used 3cm or 4cm to starting from 5cm of cervical dilation, and removal of the 'alert' and 'action' lines. These changes reflected a growing body of evidence that the historical '1cm per hour' rule for active labour progress is unrealistic for most women, and that slower dilation rates are not associated with adverse birth outcomes. In response to these recommendations, a "next generation" partograph known as the WHO Labour Care Guide (LCG) was developed in 2020 through expert consultations, primary research with maternity healthcare providers, and a multi- country usability study.(18- 20)
+
+<--- Page Split --->
+
+WHO states that the LCG should be globally disseminated and implemented as a component of routine clinical care.(21) However, introducing the LCG into routine care requires a strategy that can improve healthcare provider's clinical practice, thereby enhancing the quality of intrapartum care, reducing use of unnecessary interventions, and improving support to women during labour. However, as the LCG is a novel tool, no such strategy has been tested in a randomised trial. This knowledge gap was highlighted in WHO's recent global LCG research prioritization exercise, in which identifying optimal implementation strategies, as well as understanding LCG's effect on maternal and perinatal outcomes, were top research priorities.(22) We therefore conducted a multi- centre trial to evaluate the effects of implementing a strategy to promote LCG use in labour wards.  
+
+## METHODS  
+
+## Overview of study design  
+
+We designed and conducted a pragmatic, stepped- wedge, cluster- randomized trial which was conducted between \(1^{\text{st}}\) July 2021 and \(15^{\text{th}}\) July 2022. It was intended as a "proof- of- concept" study. We used an evidence- based, theory- informed approach to developing the intervention, and conducted the trial to determine whether it might have an effect on overuse of Caesarean section, or other important maternal and perinatal outcomes. The trial was preceded by a six- month formative phase, which was guided by the COM- B model of behaviour change, which recognises that individuals must have Capability, Motivation, and both physical and social Opportunity to perform a behaviour.(23) We used co- design principles and primary data collection to develop and refine the 'LCG strategy' intervention. The intervention was then introduced in a stepwise manner in four public hospitals in Karnataka State, India, in accordance with a randomisation schedule. Given the risk of cross- contamination, individual randomization was not possible. We used a stepped- wedge approach as the LCG reflects WHO's current advice regarding standard of care,(24) and it was thus not ethically feasible to use a parallel- group design.  
+
+## Trial approvals and oversight  
+
+This trial was designed and conducted in accordance with the ethical principles of the World Medical Association's Declaration of Helsinki, the Ottawa Statement for the Ethical Design and Conduct of Cluster Randomised Trials, and Good Clinical Practice (GCP) standards.(25- 27) We developed the trial protocol and reported findings in accordance with SPIRIT (Standard Protocol Items: Recommendations for Interventional Trials) guidance for randomised trials, and the CONSORT (Consolidated Standards of Reporting Trials) statement for stepped- wedge cluster- randomised trials
+
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+(CONSORT Checklist in Supplementary File S1).(28, 29) The trial protocol was pre- registered (CTRI/2021/01/030695), with the protocol and statistical analysis plan published prior to trial closure; there were no major deviations or changes.(30)  
+
+We sought permission from the head of study hospitals (gatekeepers) and individual providers before commencing the trial. The study protocol specified a waiver of individual consent for data collected on women giving birth – these data were non- identifiable, routinely- collected clinical variables in medical records and labour ward registries. For women invited to complete a postpartum survey, an informed consent was conducted. The trial was approved by the Alfred Hospital Human Ethics Committee (737/20), and the institutional ethics committees of the KLE Academy of Higher Education and Research (D- 281120003), J J M Medical College, Davanagere (IEC- 136/2020); Vijayanagar Institute of Medical Sciences (SVN IEC/20/2020- 2021) and the Gadag Institute of Medical Sciences, (IEC/01/2020- 21), as well as the State Ethics Committee, Department of Health and Family Welfare, Government of Karnataka (DD(MH)/71/2020- 21); and the Health Ministry's Screening Committee, Indian Council of Medical Research (2020- 10127). An independent, three- member Data and Safety Monitoring Committee oversaw the trial.  
+
+## Setting and Participants  
+
+We purposively selected four public maternity hospitals in Karnataka State to participate, based on their capacity to provide comprehensive emergency obstetric care (including access to caesarean section). All four hospitals attend to more than 4,000 women giving birth each year, and have an overall caesarean section rate of \(30\%\) or more. In three hospitals labour monitoring and partograph completion is primarily performed by postgraduate resident doctors, while in the remaining hospital it was performed by nurses. All hospitals had either completed or were undergoing accreditation under the Government of India's national Labour Room Quality Initiative ("LaQshya") which closely aligned with WHO intrapartum care recommendations.(31)  
+
+Each hospital was treated as a cluster (H1, H2, H3 and H4). Two senior obstetricians working at each hospital were appointed as facility investigators and were responsible for trial activities at each hospital. The target of the intervention were labour ward staff, including obstetricians, postgraduate doctors and nurses. These staff routinely use a WHO simplified partograph to make decisions about labour interventions. We hypothesized that the intervention would promote correct LCG use by these providers, changing their labour monitoring and management practices to align with WHO's
+
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+intrapartum recommendations. In turn, this could reduce overuse of Caesarean section, improve maternal and newborn outcomes, and enhance women's care experiences.  
+
+## Randomisation and blinding  
+
+Prior to trial commencement, the four clusters (hospitals) were randomly assigned to one of four sequences (H1, H2, H3, or H4, see Figure 1) using a computer- generated list of random numbers that was managed by the study statistician. The allocation sequence was concealed from the investigators and study teams and only revealed by the statistician one month prior to cross over to allow time for planning LCG implementation activities. Once the hospital had commenced the intervention, blinding of hospital staff, research staff and individual women was not possible. The intervention was commenced in hospitals according to the randomly assigned sequence, with one hospital transitioning to intervention at 2- month intervals (i.e., a step occurred every 2 months). A two- week transition period was used to allow for the intervention to be fully adopted.  
+
+## Control and intervention  
+
+The control condition for the trial was current labour monitoring and management practices ('usual clinical care'). While the WHO simplified partograph is widely used in India, the formative phase showed that its use was inconsistent and oftentimes retrospective. Training seminars were conducted at all hospitals on using the WHO simplified partograph to standardize the control condition. The WHO intrapartum care recommendations were also disseminated at all hospitals at the start of the trial.  
+
+The LCG strategy intervention included a co- designed LCG training program for doctors and nurses working on labour ward, and a monthly audit and feedback process using hospital Caesarean section data. For training, we developed and ran two- day workshops for all labour ward staff, co- ordinated by facility investigators who had undergone a "training of trainers" workshop. After this, all providers working on labour ward underwent an 8- week "low- dose, high- frequency" training program,(32) comprising of clinical cases and bedside teaching using LCG with senior clinical staff. The 8- week training was delivered in cycles to accommodate postgraduate resident rotations every 3 months. Refresher training was used if new staff arrived during the intervention period. At time of randomization, all simplified WHO partographs in the labour ward were replaced with the LCG. Senior labour ward staff were encouraged to monitor and promote consistent, accurate LCG use through supportive supervision.
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+The intervention also included monthly audit and feedback meetings on Caesarean rates, using the Robson Classification. Audit and feedback is widely used to promote evidence- based clinical practice, and is recommended by WHO for avoiding unnecessary Caesarean sections.(33, 34) WHO also recommends that countries use the Robson Classification for assessing, monitoring and comparing their Caesarean rates over time.(6) The Robson Classification organises all births in a facility into one of 10 mutually exclusive, all- inclusive groups, on the basis of parity, previous Caesarean, onset of labour, fetal presentation and lie, number of neonates and gestational age (term or preterm).(35) Providers at randomized hospitals underwent a brief training on how to interpret Robson Classification data, and how audit and feedback can help optimize Caesarean section use. Robson Classification tables were prepared using trial data, and shared directly with the study hospital on a monthly basis. These data were presented by senior clinical staff at monthly meetings, with structured discussions amongst the attendees on how to improve hospital performance. Hospitals and staff were instructed that all other aspects of clinical care during the trial should be in accordance with relevant local guidelines and protocols. In addition, facility leads were encouraged to identify and address anticipated barriers to the LCG strategy in their hospital. This included revision of hospital policies, standardisation of clinical protocols, rearrangements to the physical labour ward environment, and addressing some supply and equipment constraints. We used logbooks, tracking sheets and site visits to confirm that all eligible staff underwent LCG training activities, were using the LCG routinely, and attended monthly Caesarean audit meetings as planned.  
+
+## Primary and secondary outcomes  
+
+Trained research staff collected non- identifiable, individual- level data on all women giving birth from 20 weeks' gestation onwards and their babies. Data were collected from the time of admission for childbirth until the time of discharge, transfer, death or until 7 days after admission (whichever came first). The primary trial outcome was the use of Caesarean section amongst women in Robson Group 1. That is, women who were nulliparous, gave birth to a singleton, term pregnancy in cephalic presentation, and were in spontaneous labour. While Robson Group 1 is a subset of all women giving birth (usually around \(30\%\) of the obstetric population), it is a group of largely low- risk women in whom Caesarean is often overused.(35) Should the LCG strategy have any effect, we anticipated that it would be more easily detected amongst these women. Secondary outcomes included use of intrapartum interventions, and maternal, fetal and neonatal health outcomes. The denominator varied depending on the outcome of interest (see Supplementary Table S1 for outcome definitions).
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+We also measured women's experiences of care using a pre- tested, interviewer- administered survey, conducted in a local language (Kannada, Hindi or Marathi), that was completed by postnatal day 7 or discharge (whichever came first) in a sample of postpartum women. This sample comprised women in Robson Group 1 or 3 who gave birth in the last 15 days of each 2- month period, had a liveborn baby, were 18 years or older, and who provided informed consent. In each hospital, trained interviewers approached and invited all eligible women to complete the survey.  
+
+All data were collected into pre- designed study forms and managed using REDCap electronic data capture via tablets. Each hospital team had access to their own hospital data only, and facility investigators were responsible for checking completeness and accuracy of all collected data. To minimize errors, data validation processes were implemented in the data collection system. Statistical methods and data cleaning algorithms were utilized to identify potential errors and outliers for further investigation and correction. Regular data and trial progress review meetings and audits were conducted to identify and rectify any inconsistencies or outliers. Data monitors periodically visit the study sites to verify the accuracy and completeness of the collected data. They also provided training and guidance to study personnel, addressing any issues or concerns that might arise during the study. The trial concluded when \(15^{\text{th}}\) July 2022 was reached, as planned.  
+
+## Sample size  
+
+No previous trial using LCG has been conducted, meaning the effect size of our strategy was difficult to estimate. For the year 2020 (prior to the trial) these four hospitals collectively averaged 24,000 births per year, and their overall Caesarean rate was \(44\%\) . The Caesarean rate in women in Robson Group 1 (i.e., the primary outcome) for all four hospitals was at least \(40\%\) . The trial was designed to provide \(92\%\) power to detect a \(25\%\) reduction in the Robson Group 1 Caesarean rate from \(40\%\) to \(30\%\) , assuming an intraclass correlation coefficient (ICC) equal to 0.02, a cluster auto correlation equal to 0.90, and an average of 300 women per cluster per step with a coefficient of variation of cluster size equal to 0.60. (36)  
+
+## Statistical methods and analysis  
+
+Analyses were performed according to the intention- to- treat principle. Maternal baseline characteristics were summarized by trial arm as means and standard deviations, or numbers and percentages, as appropriate. For the primary and secondary outcomes, a generalized estimating equation (GEE) to estimate the effect of the intervention with respect to the population- average was used. A bias correction method and degree of freedom approximation due to the small number of
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+clusters was applied in the GEE models to maintain the validity of the estimations. Manck and DeRouen correction method with N- 2 degrees of freedom was selected due to being the most conservative option.(37) An exchangeable correlation structure was assumed and the modified Poisson distribution with a log link function was considered. The model was constructed considering two variables: a binary indicator for treatment - indicating whether the observation was made during the control or the intervention period - and a categorical variable indicating the step. The relative risk and the \(95\%\) confidence interval were reported as the size effect. For the secondary outcomes in which duration was measured in days, the effect size was calculated as the difference between the mean of days in the intervention group and the mean of days in the control group. The ICC was estimated under the control period using the GEE model. As no adjustment for multiplicity testing of secondary outcomes was considered, their results are reported as point estimates with \(95\%\) confidence intervals and p- values.  
+
+## RESULTS  
+
+## Characteristics of study population  
+
+Between 1 July 2021 and 15 July 2022, 26,331 women gave birth to 26,595 babies in the four hospitals during the control and intervention periods and were included for analysis (Figure 1). The total number of women giving birth differed between hospitals, ranging from 5,295 to 8,772 women per hospital. The analysis population comprised 11,517 women (11,624 babies) who gave birth in the control period and 14,814 women (14,971 babies) who gave birth in the intervention period. The main analysis did not include the 1,080 women (1,089 babies) who gave birth in the transition period.  
+
+While there were more women in intervention than control, the characteristics of women were similar (Table 1). Nearly half of included women were nulliparous (46.7% of the control group and 47.5% of the intervention group), while more than half of multiparous women had no prior Caesarean section (56.7% vs 55.0%) The distribution of women across the 10 Robson Classification groups was also similar (Supplementary Table S1). Robson Group 1 accounted for 30.8% (3,543/11,517) of women in the control group and 29.0% (4,302/14,814) of women in the intervention group. The intervention group had a slightly higher proportion of women in Group 2 and a slightly lower proportion of women in Group 3.
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+## Primary and secondary outcomes  
+
+Table 2 reports the intervention effect sizes for the primary outcome and secondary maternal process- of- care outcomes. The Caesarean section rate in Robson Group 1 for the control group was \(45.2\%\) , while in the intervention group it was \(39.7\%\) with a crude absolute difference of \(- 5.5\%\) (relative risk [RR] 0.85, \(95\%\) confidence interval [CI] 0.54- 1.33, p value 0.1088). The estimated ICC for the primary outcome during the control period was \(0.015 (0; 0.043)\) .  
+
+The Caesarean section rate in Robson Groups 1 and 3 was \(30.9\%\) for the control group, and \(26.9\%\) for the intervention group - a crude absolute difference of \(- 4.0\%\) (RR 0.81, \(95\%\) CI 0.59 - 1.11). For the outcome augmentation with oxytocin during spontaneous labour, the prevalence in control group was \(27.3\%\) and in the intervention group it was \(9.3\%\) (crude absolute difference - \(18.0\%\) ). However, the estimate of effect was not significant (RR 0.34, \(95\%\) CI 0.01 - 15.04) - the wide confidence interval was attributable to the high variability in outcome prevalence between hospitals and steps. Table 3 reports the intervention effects on maternal, fetal and newborn health outcomes. The prevalence of these outcomes was low in both intervention and control groups, and there were no clear differences.  
+
+A total of 1,438 women in the control group and 1,277 women in the intervention group consented ( \(100\%\) and \(99.9\%\) consent rate, respectively) and completed postpartum surveys. Table 4 reports the effects on women's experiences at birth, for which there were no differences between groups. In terms of adverse events, there were 5 maternal deaths, 196 neonatal deaths and 367 stillbirths in the control period, and 13 maternal deaths, 200 neonatal deaths and 449 stillbirths in the intervention period (Supplementary Tables S3 and S4). None of these deaths were assessed as being related to the intervention.  
+
+## DISCUSSION  
+
+In this stepped- wedge, cluster- randomised trial in India, we implemented a novel strategy to introduce the LCG into routine care, as well as initiating monthly audit and feedback meetings on Caesarean section data using Robson Classification. We observed a \(5.5\%\) crude absolute reduction in Caesarean rates amongst women in Robson Group 1 following introduction of the intervention, however this difference was not statistically significant. Maternal process- of- care measures were not significantly different, though the crude absolute difference for labour augmentation using oxytocin was \(- 18.0\%\) . We did not observe any clear differences in maternal, fetal or newborn health
+
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+outcomes, or women's experiences at birth. The findings do not preclude the possibility that the LCG strategy may reduce Caesarean section and augmentation of labour in larger trials.  
+
+Reversing the worldwide trend in rising Caesarean section rates, driven in large part by medically unnecessary Caesarean use, has proven to be a challenging problem - a 2018 WHO guideline identified few effective interventions to address this.(34, 38) The LCG promotes several supportive care measures which have been shown in trials to prevent Caesarean section, such as labour companionship, mobilisation during labour, and adequate pain relief.(39- 41) Also, the use of 5cm dilatation to define active first stage, as well as removal of the "1cm per hour rule" would, assumedly, lead to fewer intrapartum interventions. As the LCG is a novel clinical tool, there are few effectiveness studies available for comparison, though more trials using LCG are planned.(42, 43) In 2022, Pandey et al published findings of an individually- randomized trial of 271 low- risk women in a single hospital in India, comparing the effects of using LCG versus modified partograph.(44) They reported a dramatic reduction in Caesarean section - 1.5% in the LCG group compared with 17.8% in the control group (p- value 0.0001) - as well as significantly lower oxytocin use and shorter duration of active phase of labour with LCG. Our trial was powered to detect a 25% risk reduction for Caesarean section rate in Robson Group 1, equating to an absolute reduction of 10% (from 40% to 30%). Though we lacked power to detect a smaller magnitude of effect, our findings suggest that an effect does exist, and is probably closer to a 15% risk reduction. While we lacked power to test a superiority hypothesis for rarer adverse outcomes (such as mortality and severe morbidity of women and babies), reassuringly there was no evidence of short- term harms associated with the LCG strategy. Data on these outcomes should be monitored in future, larger- scale research.  
+
+We did not detect any differences for outcomes on women's experiences. However, these data showed women had high levels of satisfaction with the amount of time health workers spent with them, the way they were communicated with, and with their overall birth experience. It also showed that some supportive care practices, such as being offered a labour companion, were reasonably common, though other women- centred interventions were not well- implemented. For example, being offered pain relief (5.2% and 15.3%), and being asked which birth position they preferred (0.7% and 2.1%) were poorly used. This highlights that substantive gaps persist in the provision of supportive care around the time of birth - additional strategies are needed to address these gaps.  
+
+This trial was conducted in large, busy, public tertiary hospitals in India with high Caesarean use. In three hospitals, partograph completion was the responsibility of postgraduate residents only. In
+
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+India, the LaQshya national initiative and hospital accreditation process (31) has a strong emphasis on respectful maternity care, which is well- aligned with WHO's recommendations and the LCG's foundational principles. These factors mean the trial findings may not necessarily generalize to other settings that are naïve to respectful maternity care principles and policies. For example, it may be more challenging to generate provider behaviour change in settings without a national policy framework. Contextual differences around how frequently obstetric interventions are used, as well as differences in the risk profile of obstetric populations, may mean the LCG strategy has variable effects.  
+
+This study was designed as a "proof of concept" study of a novel, complex intervention. Strengths include the use of a theory- based, evidence- informed, co- design approach to developing the LCG strategy, which aimed to address factors known to impair partograph use.(17) We also used a robust, cluster- randomised design, and recruited a large number of participants in a real- world clinical setting. The stepped- wedge design means that all hospitals were implementing the LCG strategy at trial conclusion. This trial nonetheless has some limitations. The intervention did not have a specific component aimed at the antenatal period, though in retrospect it would be helpful to better prepare women for the introduction of new supportive care options. Also, women arriving at hospital in advanced labour had only a short period of time in which they could benefit from LCG, thereby diminishing any possible effects. The stepped- wedge design meant that other, secular trends – such as changes in COVID case numbers over time - could have affected the findings. However, COVID data shows that infections in these hospitals were quite infrequent. The use of the same clusters over a 54- week period means we cannot exclude the possibility that some women may have given birth twice during the study. We measured women's experiences using a survey instrument in their language of choice, however their responses may have been affected by social or courtesy biases.  
+
+## CONCLUSION  
+
+Findings from this multi- centred, stepped- wedge, cluster- randomized trial suggest that the LCG strategy is a promising intervention that can improve quality of labour and childbirth care, reducing overuse of intrapartum interventions. This study provides important evidence on the debate around introduction of LCG into routine clinical practice internationally. Further evaluation in larger scale, multi- country trials in hospital with high rates of Caesarean section are warranted.
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+## FUNDING  
+
+This study was supported by a Grand Challenges grant from the Bill & Melinda Gates Foundation (GNT INV- 023273). We received additional funding support from the Burnet Institute, via the Alastair Lucas Award. JPV and CSEH are supported by Investigator Grants from the Australian National Health and Medical Research Council (NHMRC). EA is supported by a NHMRC Postgraduate Student Award. The study funder had no role in study design, data collection, analysis, interpretation, or writing of the report. The corresponding author had full access to all the study data, and takes final responsibility for the decision to submit for publication.  
+
+## ACKNOWLEDGEMENTS  
+
+We gratefully acknowledge Ana Pilar Betran (Chair), Dr Dennis Wallace and Shuchita Mundle for their role as Data and Safety Monitoring Board members, and Olufemi T. Oladapo and Mercedes Bonet for their role as Observers to the study.  
+
+## INCLUSION AND ETHICS STATEMENT  
+
+Our study team support the principles of the Cape Town Statement, in particular the commitment to equitable international collaborations. The study was designed in partnership between three research groups (India, Argentina, Australia), building on multiple years of research collaborations and co- authored publications between several co- authors.  
+
+This study was funded by a Global Grand Challenges grant – the submission was jointly prepared by JPV, SG, YP, SV, VP, FA and LG. This grant funding went to all three of our research organisations, with the largest amount of this funding received by the JNMC- India research team. The study protocol had 14 named investigators – 12 from India, 1 from Argentina, and 1 from Australia. JPV and SG were named as co- Principal Investigators. During the study, decisions were taken by consensus amongst the steering group, during fortnightly teleconferences.  
+
+The authorship group (29 individuals) comprised 17 women and 12 men, and included late- , mid- and early- career individuals. Members of the authorship group include researchers in India (YP, SSV, MS, SB, JAK, SBP, AK, RRA, PMR, SS, LB, MHM, SSG, SC, BR), Argentina (VP, FA, LG, MB, AV, RR) and Australia (JPV, EA, CSEH). The lead author (JPV) is in Australia and the senior author (SG) is in India. Our Technical Advisory Group (TL, PK, GJH, RD) included senior researchers from India, UK, South
+
+<--- Page Split --->
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+Africa and USA, and our Data and Safety Monitoring Committee included individuals from India, Switzerland and the USA.  
+
+## DATA AND CODE AVAILABILITY STATEMENT  
+
+In keeping with the Bill & Melinda Gates Foundation Open Access Policy, the trial dataset generated during this study, the data dictionary and syntax used for analyses are hosted at the Gates Open Research- approved repository Zenodo at time of paper publication under DOI: https://doi.org/10.5281/zenodo.8140454  
+
+## REFERENCES  
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+<--- Page Split --->
+
+<table><tr><td rowspan="2">Characteristic</td><td>Intervention period<br/>(N = 14,814 women)</td><td>Control period<br/>(N = 11,517 women)</td></tr><tr><td>n (%)</td><td>n (%)</td></tr><tr><td>Maternal age (years)*</td><td>23.9 (3.6)</td><td>23.4 (3.6)</td></tr><tr><td>Maternal age</td><td></td><td></td></tr><tr><td>Less than 20</td><td>1,020 (6.9%)</td><td>1,010 (8.8%)</td></tr><tr><td>20-34</td><td>13,572 (91.6%)</td><td>10,357 (89.9%)</td></tr><tr><td>35 or more</td><td>222 (1.5%)</td><td>150 (1.3%)</td></tr><tr><td>Previous Caesarean Section**</td><td></td><td></td></tr><tr><td>0</td><td>4,282 (55.0%)</td><td>3,484 (56.7%)</td></tr><tr><td>1</td><td>2,819 (36.2%)</td><td>2,133 (34.7%)</td></tr><tr><td>2 or more</td><td>682 (8.8%)</td><td>525 (8.5%)</td></tr><tr><td>Gravida</td><td></td><td></td></tr><tr><td>1</td><td>6,394 (43.2%)</td><td>4,940 (42.9%)</td></tr><tr><td>2-4</td><td>8,160 (55.1%)</td><td>6,369 (55.3%)</td></tr><tr><td>5 or more</td><td>260 (1.8%)</td><td>208 (1.8%)</td></tr><tr><td>Parity</td><td></td><td></td></tr><tr><td>0</td><td>7,031 (47.5%)</td><td>5,375 (46.7%)</td></tr><tr><td>1-3</td><td>7,674 (51.8%)</td><td>6,022 (52.3%)</td></tr><tr><td>4 or more</td><td>109 (0.7%)</td><td>120 (1.0%)</td></tr><tr><td>Women receive antenatal care during pregnancy</td><td>14,745 (99.5%)</td><td>11,438 (99.3%)</td></tr><tr><td>Covid status at admission</td><td></td><td></td></tr><tr><td>Positive</td><td>32 (0.2%)</td><td>5 (0.0%)</td></tr><tr><td>Negative</td><td>8,208 (55.4%)</td><td>9,168 (79.6%)</td></tr><tr><td>Pending or not done</td><td>6,574 (44.4%)</td><td>2,344 (20.4%)</td></tr><tr><td>Transferred from another health facility during labour</td><td>2,102 (14.2%)</td><td>1,881 (16.3%)</td></tr><tr><td>Gestational age at time of birth*</td><td>38.3 (2.5)</td><td>38.3 (2.6)</td></tr></table>
+
+* Mean and (Standard deviation) is reported
+
+** Multiparous women only were considered
+
+Table 1. Characteristics of study population
+
+<--- Page Split --->
+
+
+Table 2. Effect of the intervention on primary outcome, and maternal process of care outcomes   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Intervention period<br>(N = 14,814 women)</td><td colspan="2">Control period<br>(N = 11,517 women)</td><td rowspan="2">Relative Risk<br>(95% CI)α</td></tr><tr><td>n/N</td><td>(%)</td><td>n/N</td><td>(%)</td></tr><tr><td>Primary outcome</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cesarean section in Robson Group 1</td><td>1709/4302</td><td>(39.7%)</td><td>1602/3543</td><td>(45.2%)</td><td>0.85 (0.54; 1.33)</td></tr><tr><td>Maternal process of care outcomes</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cesarean section in women in Robson Groups 1 and 3</td><td>2012/7485</td><td>(26.9%)</td><td>1919/6204</td><td>(30.9%)</td><td>0.81 (0.59; 1.11)</td></tr><tr><td>Cesarean section in women in Robson Groups 1, 2, 3, 4 and 5</td><td>6529/12735</td><td>(51.3%)</td><td>5028/9808</td><td>(51.3%)</td><td>0.92 (0.78; 1.10)</td></tr><tr><td>Caesarean section (all women)</td><td>7505/14814</td><td>(50.7%)</td><td>5817/11517</td><td>(50.5%)</td><td>0.91 (0.71; 1.15)</td></tr><tr><td>Augmentation with oxytocin during labourβ</td><td>912/9764</td><td>(9.3%)</td><td>2273/8318</td><td>(27.3%)</td><td>0.34 (0.01; 15.04)</td></tr><tr><td>Artificial rupture of the membranes*β</td><td>553/9764</td><td>(5.7%)</td><td>559/8318</td><td>(6.7%)</td><td>-</td></tr><tr><td>Episiotomyε</td><td>4820/7309</td><td>(65.9%)</td><td>3137/5700</td><td>(55.0%)</td><td>0.99 (0.73; 1.35)</td></tr><tr><td>Operative vaginal birthε</td><td>192/7309</td><td>(2.63%)</td><td>112/5700</td><td>(1.96%)</td><td>1.12 (0.13; 9.36)</td></tr><tr><td>Days from admission to childbirth**</td><td>0.34</td><td>(0.73)</td><td>0.30</td><td>(0.68)</td><td>0.05 (-0.31; 0.41)</td></tr><tr><td>Days from childbirth to discharge**</td><td>3.29</td><td>(1.75)</td><td>3.52</td><td>(1.88)</td><td>0.23 (-0.84; 1.30)</td></tr></table>
+
+\(\beta\) Women in spontaneous labour were considered \(\epsilon\) Women with vaginal deliveries were considered \\*\\*The mean of the days and (S.D.) is reported. The effect size was calculated as the difference between the mean of days in the intervention group and the mean of days in the control group. \(\ast \ast\) RR was not estimated since convergence of the model was not achieved \(\Omega\) The relative risk and \(95\%\) confidence interval \((95\% CI)\) was estimated with the Generalized Estimating Equation method employing the "Manck and DeRouen" bias correction method and a degree of freedom approximation.
+
+<--- Page Split --->
+
+
+Table 3. Effect of the intervention on maternal, perinatal and neonatal health outcomes   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Intervention period<br>(N = 14,814 women)</td><td colspan="2">Control period<br>(N = 11,517 women)</td><td>Relative Risk<br>(95% CI)Ω</td></tr><tr><td>n/N</td><td>(%)</td><td>n/N</td><td>(%)</td><td></td></tr><tr><td>Maternal Secondary Outcomes</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3rd or 4th degree tears</td><td>18/14814</td><td>(0.12%)</td><td>25/11517</td><td>(0.22%)</td><td>0.51 (0.01; 29.16)</td></tr><tr><td>PPH requiring uterine balloon tamponade or surgical intervention</td><td>28/14814</td><td>(0.19%)</td><td>46/11517</td><td>(0.40%)</td><td>0.38 (0.00; 84.07)</td></tr><tr><td>Suspected or confirmed maternal infection requiring therapeutic antibiotics</td><td>114/14814</td><td>(0.77%)</td><td>53/11517</td><td>(0.46%)</td><td>2.12 (0.06; 70.96)</td></tr><tr><td>Fetal/Neonatal Secondary Outcomes</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Stillbirth</td><td>449/14971</td><td>(3.00%)</td><td>367/11624</td><td>(3.16%)</td><td>0.97 (0.43; 2.19)</td></tr><tr><td>Antepartum stillbirth</td><td>279/14971</td><td>(1.86%)</td><td>286/11624</td><td>(2.46%)</td><td>0.91 (0.34; 2.47)</td></tr><tr><td>Intrapartum stillbirth</td><td>163/14971</td><td>(1.09%)</td><td>79/11624</td><td>(0.68%)</td><td>0.90 (0.49; 1.65)</td></tr><tr><td>Apgar score &amp;lt;7 at 5 minutes</td><td>670/14522</td><td>(4.61%)</td><td>567/11257</td><td>(5.04%)</td><td>1.17 (0.86; 1.59)</td></tr><tr><td>Bag and mask ventilation of newborn</td><td>424/14522</td><td>(2.92%)</td><td>256/11257</td><td>(2.27%)</td><td>1.21 (0.08; 18.75)</td></tr><tr><td>Mechanical ventilation of newborn</td><td>293/14522</td><td>(2.02%)</td><td>260/11257</td><td>(2.31%)</td><td>1.29 (0.36; 4.66)</td></tr><tr><td>Prolonged (&amp;gt;48 hour) admission in NICU</td><td>1843/14522</td><td>(12.7%)</td><td>1014/11257</td><td>(9.0%)</td><td>1.14 (0.47; 2.79)</td></tr><tr><td>Newborns requiring NICU admission for hypoxic ischaemic encephalopathy</td><td>34/14522</td><td>(0.23%)</td><td>152/11257</td><td>(1.35%)</td><td>0.40 (0.04; 3.74)</td></tr><tr><td>Composite neonatal morbidity outcome*</td><td>376/14522</td><td>(2.59%)</td><td>377/11257</td><td>(3.35%)</td><td>1.11 (0.32; 3.79)</td></tr><tr><td>Neonatal death</td><td>200/14522</td><td>(1.38%)</td><td>196/11257</td><td>(1.74%)</td><td>1.31 (0.37; 4.71)</td></tr><tr><td>Perinatal death (stillbirth or neonatal death)</td><td>649/14971</td><td>(4.34%)</td><td>563/11624</td><td>(4.84%)</td><td>1.06 (0.41; 2.73)</td></tr></table>
+
+\(\Omega\) The relative risk and \(95\%\) confidence interval \((95\% CI)\) was estimated with the Generalized Estimating Equation method employing the "Manc and DeRouen" bias correction method and a degree of freedom approximation. \\* The composite neonatal outcome was defined as one or more of the following: Mechanical ventilation of the newborn or requirement of NICU admission for hypoxic ischaemic encephalopathy of the newborn or neonatal death
+
+<--- Page Split --->
+
+
+Table 4. Effect of the intervention on women's experience outcomes (Women in Robson Group 1 or 3)   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Intervention period<br>(N=1277 women)</td><td colspan="2">Control period<br>(N=1438 women)</td><td rowspan="2">Relative Risk<br>(95% CI) a</td></tr><tr><td>n/N</td><td>(%)</td><td>n/N</td><td>(%)</td></tr><tr><td>Women reporting labour companion</td><td>982/1277</td><td>(76.9%)</td><td>1206/1438</td><td>(83.9%)</td><td>1.19 (0.89; 1.59)</td></tr><tr><td>Women reporting being offered pain relief</td><td>196/1277</td><td>(15.3%)</td><td>75/1438</td><td>(5.2%)</td><td>2.30 (0.00; 1281.82)</td></tr><tr><td>Women reporting being very satisfied or somewhat satisfied with how their pain was managed</td><td>827/1277</td><td>(64.8%)</td><td>957/1437</td><td>(66.6%)</td><td>0.94 (0.06; 16.14)</td></tr><tr><td>Women reporting being encouraged to drink water</td><td>863/1277</td><td>(67.6%)</td><td>1123/1438</td><td>(78.1%)</td><td>0.98 (0.34; 2.86)</td></tr><tr><td>Women reporting being encouraged to eat food</td><td>657/1277</td><td>(51.4%)</td><td>823/1438</td><td>(57.2%)</td><td>0.99 (0.13; 7.37)</td></tr><tr><td>Women reporting being encouraged to walk</td><td>827/1277</td><td>(64.8%)</td><td>863/1437</td><td>(60.1%)</td><td>1.10 (0.34; 3.58)</td></tr><tr><td>Women reporting being asked which birth position they preferred</td><td>27/1277</td><td>(2.11%)</td><td>10/1438</td><td>(0.70%)</td><td>1.96 (0.00; 1384.48)</td></tr><tr><td>Women reporting being very or somewhat satisfied with the amount of time health provider spent with them</td><td>1260/1277</td><td>(98.7%)</td><td>1424/1437</td><td>(99.1%)</td><td>0.99 (0.93; 1.05)</td></tr><tr><td>Women reporting being very or somewhat satisfied with the way health provider communicated with them</td><td>1262/1277</td><td>(98.8%)</td><td>1424/1438</td><td>(99.0%)</td><td>0.99 (0.91; 1.07)</td></tr><tr><td>Women who strongly agreed or agreed that their privacy was respected</td><td>1234/1277</td><td>(96.6%)</td><td>1315/1438</td><td>(91.4%)</td><td>0.99 (0.56; 1.75)</td></tr><tr><td>Women who reported being asked permission before examinations</td><td>596/1277</td><td>(46.7%)</td><td>992/1438</td><td>(69.0%)</td><td>0.84 (0.07; 10.34)</td></tr><tr><td>Women who reported being asked permission before treatments</td><td>588/1277</td><td>(46.0%)</td><td>996/1438</td><td>(69.3%)</td><td>0.85 (0.07; 10.37)</td></tr><tr><td>Women who strongly agreed or agreed that they were satisfied with their labour and birth experience</td><td>1268/1277</td><td>(99.3%)</td><td>1404/1438</td><td>(97.6%)</td><td>1.01 (0.95; 1.07)</td></tr></table>
+
+\(\Omega\) The relative risk and \(95\%\) confidence interval (95% CI) was estimated with the Generalized Estimating Equation method employing the "Manc and DeRouen" bias correction method and a degree of freedom approximation.
+
+<--- Page Split --->
+
+# FIGURES
+
+Figure 1. Trial diagram showing number of women with a gestational age &gt;20 weeks by hospital and steps
+
+<table><tr><td colspan="2" rowspan="2"></td><td colspan="5">STEP (2 months periods)</td><td rowspan="2">Total<br>(Transition<br>period)**</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>\(5^{**}\)</td></tr><tr><td rowspan="4">HOSPITAL</td><td>1</td><td>946</td><td>915<br>(240)*</td><td>1127</td><td>877</td><td>2374</td><td>6239<br>(240)</td></tr><tr><td>2</td><td>965</td><td>983</td><td>708<br>(267)*</td><td>719</td><td>1920</td><td>5295<br>(267)</td></tr><tr><td>3</td><td>1398</td><td>1677</td><td>1529</td><td>1015<br>(302)*</td><td>3153</td><td>8772<br>(302)</td></tr><tr><td>4</td><td>950</td><td>1060</td><td>1087</td><td>922</td><td>2006<br>(271)*</td><td>6025<br>(271)</td></tr><tr><td></td><td>Total<br>(Transition<br>period)</td><td>4259</td><td>4635<br>(240)</td><td>4451<br>(267)</td><td>3533<br>(302)</td><td>9453<br>(271)</td><td>26331<br>(1080)</td></tr></table>
+
+![PLACEHOLDER_23_0]
+
+Control Study period Intervention study period
+
+* Number of women recruited during the two weeks-transition period
+
+** The sample size was larger for step 4 because this step included 4 months of data, compared with 2 months for preceding steps and baseline period.
+
+<--- Page Split --->
+
+## SUPPLEMENTARY APPENDIX 
+
+### Table S1. Primary and secondary outcomes 
+
+#### Primary Outcome 
+
+CS rate amongst women in Robson Group 1 (i.e. women who are nulliparous, singleton, cephalic, ≥37 weeks' gestation, in spontaneous labour). The numerator are the women in Robson Group 1 who had a CS and the denominator the number of women in Robson group 1. 
+
+#### Maternal Secondary Outcomes 
+
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>CS rate in women in Robson Groups 1 and 3</td><td>Numerator: Number of women undergoing CS<br/>Denominator: Number of women in Robson Groups 1 and 3</td></tr><tr><td>CS rate in women in Robson Groups 1 to 5</td><td>Numerator: Number of women undergoing CS<br/>Denominator: Number of women in Robson Groups 1 to 5</td></tr><tr><td>Overall CS rate</td><td>Numerator: Number of women undergoing CS<br/>Denominator: Number of women giving birth</td></tr><tr><td>Augmentation with oxytocin during labour rate</td><td>Numerator: Number of women given oxytocin for augmentation during labour<br/>Denominator: Number of women who experienced spontaneous labour</td></tr><tr><td>Artificial rupture of the membranes rate</td><td>Numerator: Number of women who had artificial rupture of membranes<br/>Denominator: Number of women who experienced spontaneous labour</td></tr><tr><td>Episiotomy rate</td><td>Numerator: Number of women who had episiotomy<br/>Denominator: Number of women with vaginal birth</td></tr><tr><td>Operative vaginal birth rate</td><td>Numerator: Number of women who had operative vaginal birth (forceps or vacuum)<br/>Denominator: Number of women with vaginal birth</td></tr><tr><td>Days between admission to childbirth</td><td>Mean of the days between admission to childbirth</td></tr><tr><td>Days between childbirth to discharge</td><td>Mean of the days between childbirth to discharge</td></tr><tr><td>3rd or 4th degree tears</td><td>Numerator: Number of women experiencing 3rd or 4th degree tears<br/>Denominator: Number of women giving birth</td></tr><tr><td>PPH requiring uterine balloon tamponade or surgical intervention</td><td>Numerator: Number of women requiring uterine balloon tamponade OR surgical intervention for PPH<br/>Denominator: Number of women giving birth</td></tr></table>
+
+<--- Page Split --->
+
+
+<table><tr><td>Suspected or confirmed maternal<br>infection requiring therapeutic<br>antibiotics</td><td>Numerator: Number of women with clinical signs or symptoms<br>of maternal infection AND therapeutic antibiotics were required<br>Denominator: Number of women giving birth</td></tr></table>
+
+Fetal/Neonatal Secondary Outcomes
+
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>Stillbirth</td><td>Numerator: Fetal death<br>Denominator: All born babies</td></tr><tr><td>Antepartum stillbirth</td><td>Numerator: Fetal death prior to admission<br>Denominator: All born babies</td></tr><tr><td>Intrapartum stillbirth</td><td>Numerator: Fetal death after admission<br>Denominator: All born babies</td></tr><tr><td>Apgar score &lt;7 at 5 minutes</td><td>Numerator: Liveborn babies with Apgar &lt;7 at 5 minutes<br>Denominator: Liveborn babies</td></tr><tr><td>Bag and mask ventilation of newborn</td><td>Numerator: Use of continuous bag and mask ventilation of<br>newborn for &gt;1 minute<br>Denominator: Liveborn babies</td></tr><tr><td>Mechanical ventilation of newborn</td><td>Numerator: Use of mechanical ventilation of newborn<br>Denominator: Liveborn babies</td></tr><tr><td>Composite neonatal outcome</td><td>Numerator: Use of mechanical ventilation of newborn or<br>admission to NICU for suspected or confirmed or neonatal death<br>Denominator: Liveborn babies</td></tr><tr><td>Prolonged (&gt;48 hour) admission in NICU</td><td>Numerator: Admission to NICU for &gt;48 hours<br>Denominator: Liveborn babies</td></tr><tr><td>Newborns requiring NICU admission for<br>hypoxic ischaemic encephalopathy</td><td>Numerator: Admission to NICU for suspected or confirmed<br>Denominator: Liveborn babies</td></tr><tr><td>Composite neonatal outcome</td><td>Numerator: Use of mechanical ventilation of newborn or<br>admission to NICU for suspected or confirmed or neonatal death<br>Denominator: Liveborn babies</td></tr><tr><td>Neonatal death</td><td>Numerator: Neonatal death in a liveborn infant by day 7 or<br>discharge (whichever came first)<br>Denominator: All liveborn babies</td></tr><tr><td>Perinatal death</td><td>Numerator: Fetal death or neonatal death in a liveborn infant by<br>day 7 or discharge (whichever came first)<br>Denominator: All born babies</td></tr></table>
+
+<--- Page Split --->
+
+
+Women's experience outcomes   
+
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>Woman&#x27;s experience with labour companion</td><td>Numerator: Women who reported a labour companion was present during labour or birth<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of being offered pain relief</td><td>Numerator: Women who reported that they were asked whether they would like any pain relief<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Women&#x27;s satisfaction with their pain management during labour and birth</td><td>Numerator: Women who reported being very satisfied or somewhat satisfied with how their pain was managed during labour and birth<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of being encouraged to drink oral fluids</td><td>Numerator: Women who reported that a health worker encouraged them to drink water<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of being encouraged to eat food</td><td>Numerator: Women who reported that a health worker encouraged them to eat food<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of mobilising during labour</td><td>Numerator: Women who reported that a health worker encouraged them to walk around during labour<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of birth position of choice</td><td>Numerator: Women who reported that a health worker asked them which birth position they preferred<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of time health worker spent with them</td><td>Numerator: Women who reported being very satisfied or somewhat satisfied with amount of time health worker spent with them during labour<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr></table>
+
+<--- Page Split --->
+
+
+Women's experience outcomes (cont.)   
+
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>Women&#x27;s satisfaction with the way health providers communicated with them</td><td>Numerator: Women who reported being very satisfied or somewhat satisfied with the way health workers communicated with them during labour and birth<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of privacy</td><td>Numerator: Number of women who strongly agreed or agreed that their privacy was respected during examinations and treatments<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Women&#x27;s experience of being asked permission</td><td>Numerator: Number of women who said their health worker always asked permission before examinations and treatments<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s overall experience of care</td><td>Numerator: Number of women who strongly agreed or agreed that they felt satisfied with their labour and birth experience<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr></table>
+
+<--- Page Split --->
+
+Table S2. Application of Robson Classification to intervention and control groups
+
+<table><tr><td>Robson Classification Group</td><td>Intervention<br>period<br>(N=14,814<br>women)</td><td>Control period<br>(N=11,517<br>women)</td></tr><tr><td>Group 1: Nulliparous, singleton, cephalic, term, spontaneous labour</td><td>4,302 (29.0%)</td><td>3,543 (30.8%)</td></tr><tr><td>Group 2: Nulliparous, singleton, cephalic, term, induced/prelabour Caesarean</td><td>1,729 (11.7%)</td><td>1,022 (8.9%)</td></tr><tr><td>· Group 2a: Nulliparous, singleton, cephalic, term, induced</td><td>848 (5.7%)</td><td>471 (4.1%)</td></tr><tr><td>· Group 2b: Nulliparous, singleton, cephalic, term, prelabour<br>Caesarean</td><td>881 (5.9%)</td><td>551 (4.8%)</td></tr><tr><td>Group 3: Multiparous (no previous Caesarean), singleton, cephalic, term,<br>spontaneous labour</td><td>3,183 (21.5%)</td><td>2,661 (23.1%)</td></tr><tr><td>Group 4: Multiparous (no previous Caesarean), singleton, cephalic, term,<br>induced/prelabour Caesarean</td><td>450 (3.0%)</td><td>282 (2.4%)</td></tr><tr><td>· Group 4a: Multiparous (no previous Caesarean), singleton, cephalic,<br>term, induced</td><td>292 (2.0%)</td><td>212 (1.8%)</td></tr><tr><td>· Group 4a: Multiparous (no previous Caesarean), singleton, cephalic,<br>term, prelabour Caesarean</td><td>158 (1.0%)</td><td>70 (0.6%)</td></tr><tr><td>Group 5: Previous Caesarean, singleton, cephalic, term, (spontaneous labour,<br>induced labour or prelabour Caesarean)</td><td>3,071 (20.7%)</td><td>2,300 (20.0%)</td></tr><tr><td>Group 6: Nulliparous with a singleton breech</td><td>235 (1.6%)</td><td>182 (1.6%)</td></tr><tr><td>Group 7: Multiparous with a singleton breech (including previous Caesarean)</td><td>224 (1.5%)</td><td>153 (1.3%)</td></tr><tr><td>Group 8: Multiple pregnancies (including previous Caesarean)</td><td>155 (1.0%)</td><td>107 (0.9%)</td></tr><tr><td>Group 9: Single pregnancy, transverse or oblique lie (including previous<br>Caesarean)</td><td>21 (0.1%)</td><td>36 (0.3%)</td></tr><tr><td>Group 10: Singleton, cephalic, preterm (including previous Caesarean)</td><td>1,444 (9.7%)</td><td>1,231 (10.7%)</td></tr></table>
+
+<--- Page Split --->
+
+Table S3. Serious adverse events by period
+
+<table><tr><td></td><td>Intervention Period<br>(N of women = 14,814)<br>(N of liveborns=14,522)<br>(N of newborns=14,971)</td><td>Transition period<br>(N of women=1,080)<br>(N of liveborns=1,060)<br>(N of newborns: 1,089)</td><td>Control Period<br>(N of women= 11,517)<br>(N of liveborns= 11,257)<br>(N of newborns= 11,624)</td></tr><tr><td></td><td>n (%)</td><td>n (%)</td><td>n (%)</td></tr><tr><td>Maternal death</td><td>13 (0.09)</td><td>1 (0.09)</td><td>5 (0.04)</td></tr><tr><td>Neonatal death</td><td>200 (1.38)</td><td>11 (1.04)</td><td>196 (1.74)</td></tr><tr><td>Neonatal death (less than 28 weeks)</td><td>18 (0.12)</td><td>1 (0.09)</td><td>16 (0.14)</td></tr><tr><td>Neonatal death (28 weeks or more)</td><td>182 (1.25)</td><td>10 (0.94)</td><td>180 (1.60)</td></tr><tr><td>Stillbirth</td><td>449 (3.00)</td><td>29 (2.66)</td><td>367 (3.16)</td></tr><tr><td>Stillbirth (less than 28 weeks)</td><td>175 (1.17)</td><td>10 (0.92)</td><td>139 (1.20)</td></tr><tr><td>Stillbirth (28 weeks or more)</td><td>274 (1.83)</td><td>19 (1.74)</td><td>228 (1.96)</td></tr></table>
+
+Table S4. Causes of maternal deaths, by period
+
+<table><tr><td></td><td>Intervention Period<br>(N = 13)</td><td>Transition Period<br>(N = 1)</td><td>Control Period<br>(N = 5)</td></tr><tr><td>Pre-eclampsia/eclampsia</td><td>5</td><td>0</td><td>4</td></tr><tr><td>Obstructed labour</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Haemorrhage</td><td>1</td><td>0</td><td>0</td></tr><tr><td>Infection</td><td>2</td><td>1</td><td>0</td></tr><tr><td>Other*</td><td>5</td><td>0</td><td>1</td></tr></table>
+
+*The case classified as "Other" in the control period was a postpartum cardiomyopathy. The five cases classified as "Other"in the intervention period were: (1) Immediate cause: a) Hepatic encephalopathy with MODS Antecedent cause: b) Acute fatty liver of pregnancy, (2) Amniotic fluid embolism, (3) Disseminated intravascular coagulation secondary to acute fatty liver of pregnancy, (4) Cerebrovascular Accident, (5) Pulmonary embolism.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- 2SupplementaryFileS1.pdf
+
+<--- Page Split --->

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+<|ref|>title<|/ref|><|det|>[[44, 106, 944, 207]]<|/det|>
+# Effects of introducing the WHO Labour Care Guide on Caesarean section: a pragmatic, stepped-wedge, cluster randomized trial in India  
+
+<|ref|>text<|/ref|><|det|>[[44, 228, 545, 270]]<|/det|>
+Joshua Vogel ( \(\boxed{ \begin{array}{r l} \end{array} }\) joshua.vogel@burnet.edu.au) Burnet Institute https://orcid.org/0000- 0002- 3214- 7096  
+
+<|ref|>text<|/ref|><|det|>[[44, 275, 480, 316]]<|/det|>
+Yeshita Pujar KLE Academy of Higher Education and Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 322, 480, 363]]<|/det|>
+Sunil Vemekar KLE Academy of Higher Education and Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 368, 193, 408]]<|/det|>
+Elizabeth Armarit Burnet Institute  
+
+<|ref|>text<|/ref|><|det|>[[44, 414, 777, 456]]<|/det|>
+Veronica Pingray Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+<|ref|>text<|/ref|><|det|>[[44, 460, 777, 503]]<|/det|>
+Fernando Althabe Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+<|ref|>text<|/ref|><|det|>[[44, 507, 457, 548]]<|/det|>
+Luz Gibbons IECS https://orcid.org/0000- 0002- 0235- 1635  
+
+<|ref|>text<|/ref|><|det|>[[44, 554, 777, 596]]<|/det|>
+Mabel Berrueta Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+<|ref|>text<|/ref|><|det|>[[44, 600, 480, 641]]<|/det|>
+Manjunath Somannavar KLE Academy of Higher Education and Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 647, 777, 689]]<|/det|>
+Alvaro Ciganda Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+<|ref|>text<|/ref|><|det|>[[44, 693, 777, 735]]<|/det|>
+Rocio Rodriguez Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina  
+
+<|ref|>text<|/ref|><|det|>[[44, 740, 480, 781]]<|/det|>
+Savitri Bendigeri KLE Academy of Higher Education and Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 787, 371, 828]]<|/det|>
+Jayashree Ashok Kumar Gadag Institute of Medical Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 833, 371, 874]]<|/det|>
+Shruti Bhavi Patil Gadag Institute of Medical Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 880, 371, 920]]<|/det|>
+Aravind Karinagannanavar Gadag Institute of Medical Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 926, 204, 944]]<|/det|>
+Raveendra Anteen
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[52, 45, 262, 64]]<|/det|>
+Gokak General Hospital  
+
+<|ref|>text<|/ref|><|det|>[[44, 70, 262, 110]]<|/det|>
+Pavithra M. R. Gokak General Hospital  
+
+<|ref|>text<|/ref|><|det|>[[44, 116, 242, 156]]<|/det|>
+Shukla Shetty JJM Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 163, 242, 202]]<|/det|>
+Latha B JJM Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 209, 242, 248]]<|/det|>
+Megha H. M. JJM Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 255, 420, 295]]<|/det|>
+Suman Gaddi Vijayanagar Institute of Medical Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 300, 420, 341]]<|/det|>
+Shaila Chikkagowdra Vijayanagar Institute of Medical Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 347, 420, 387]]<|/det|>
+Bellara Raghavendra Vijayanagar Institute of Medical Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 393, 545, 434]]<|/det|>
+Caroline Homer Burnet Institute https://orcid.org/0000- 0002- 7454- 3011  
+
+<|ref|>text<|/ref|><|det|>[[44, 440, 387, 480]]<|/det|>
+Tina Lavender Liverpool School of Tropical Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 486, 393, 527]]<|/det|>
+Pralhad Kushtagi Manipal Academy of Higher Education  
+
+<|ref|>text<|/ref|><|det|>[[44, 533, 905, 595]]<|/det|>
+Justus Hofmeyr Department of Health, Universities of the Witwatersrand, Walter Sisulu and Fort Hare, East London, South Africa https://orcid.org/0000- 0002- 3080- 1007  
+
+<|ref|>text<|/ref|><|det|>[[44, 601, 310, 641]]<|/det|>
+Richard Derman Thomas Jefferson University  
+
+<|ref|>text<|/ref|><|det|>[[44, 648, 405, 689]]<|/det|>
+Shivaprasad Goudar Jawaharlal Nehru Medical College, India  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 732, 102, 750]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 769, 137, 788]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 806, 296, 826]]<|/det|>
+Posted Date: July 28th, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 845, 475, 864]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3175470/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 882, 909, 925]]<|/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, 923, 142]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Medicine on January 30th, 2024. See the published version at https://doi.org/10.1038/s41591-023-02751-4.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[118, 84, 852, 125]]<|/det|>
+# Effects of introducing the WHO Labour Care Guide on Caesarean section: a pragmatic, stepped-wedge, cluster randomized trial in India  
+
+<|ref|>text<|/ref|><|det|>[[117, 154, 864, 294]]<|/det|>
+Joshua P. Vogel \(^{1*}\) , Yeshita Pujar \(^{2}\) , Sunil S Vernekar \(^{2}\) , Elizabeth Armar \(^{1}\) , Veronica Pingray \(^{3}\) , Fernando Althabe \(^{3}\) , Luz Gibbons \(^{3}\) , Mabel Berrueta \(^{3}\) , Manjunath Somannavar \(^{2}\) , Alvaro Ciganda \(^{3}\) , Rocio Rodriguez \(^{3}\) , Savitri Bendigeri \(^{2}\) , Jayashree Ashok Kumar \(^{4}\) , Shruti Bhavi Patil \(^{4}\) , Aravind Karinagannanavar \(^{4}\) , Raveendra R Anteen \(^{5}\) , Pavithra M. R. \(^{5}\) , Shukla Shetty \(^{6}\) , Latha B. \(^{6}\) , Megha H. M. \(^{6}\) , Suman S. Gaddi \(^{7}\) , Shaila Chikkagowdra \(^{7}\) , Bellara Raghavendra \(^{7}\) , Caroline SE Homer \(^{1}\) , Tina Lavender \(^{8}\) , Pralhad Kushtagi \(^{9}\) , G. Justus Hofmeyr \(^{10,11}\) , Richard Derman \(^{12}\) , Shivaprasad Goudar \(^{3}\)  
+
+<|ref|>text<|/ref|><|det|>[[117, 323, 870, 675]]<|/det|>
+\* corresponding author – Joshua.vogel@burnet.edu.au \(^{1}\) Maternal, Child and Adolescent Health Program, Burnet Institute, Melbourne, Victoria, Australia \(^{2}\) Women's and Children's Health Research Unit, Jawaharlal Nehru Medical College, KLE Academy of Higher Education and Research, Belgaum, Karnataka, India \(^{3}\) Instituto de Efectividad Clínica y Sanitaria (IECS- CONICET), Buenos Aires, Argentina \(^{4}\) Gadag Institute of Medical Sciences, Gadag, Karnataka, India \(^{5}\) General Hospital, Gokak, Belgaum, Karnataka, India \(^{6}\) JJM Medical College, Davangere, Karnataka, India \(^{7}\) Vijayanagar Institute of Medical Sciences (VIMS), Ballari, Karnataka, India \(^{8}\) Department of International Health, Liverpool School of Tropical Medicine, Liverpool, United Kingdom \(^{9}\) Manipal Academy of Higher Education, Karnataka, India \(^{10}\) Department of Obstetrics and Gynaecology, University of Botswana, Gaborone, Botswana \(^{11}\) University of the Witwatersrand and Walter Sisulu University, East London, South Africa \(^{12}\) Thomas Jefferson University, Philadelphia, United States of America
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 202, 99]]<|/det|>
+## ABSTRACT  
+
+<|ref|>text<|/ref|><|det|>[[115, 107, 880, 487]]<|/det|>
+The World Health Organization's Labour Care Guide (LCG) is the "next generation" partograph, designed to improve the quality of intrapartum care and enhance women's experiences. However, the effects of the LCG on maternal and newborn outcomes have not been evaluated. We developed a novel strategy to introduce the LCG into routine intrapartum care, comprising a co- designed training program for labour ward clinicians, alongside monthly audit and feedback. We implemented the strategy and measured its effects using a stepped- wedge, randomised trial in four hospitals in India. We captured data from 26,331 women who gave birth at \(> = 20\) weeks' gestation, over a 54- week period. Following implementation, a \(5.5\%\) crude absolute reduction in the Caesarean section rate amongst women in Robson Group 1 was observed (45.2% vs 39.7%; relative risk 0.85, 95% confidence interval 0.54- 1.33). Maternal process- of- care measures were not significantly different, though labour augmentation with oxytocin was 18.0% lower with the LCG strategy. No differences were observed for maternal, fetal or newborn health outcomes, or women's birth experiences. This "proof of concept" study provides important evidence on the effects of introducing LCG into routine practice, suggesting a 15% relative risk reduction in Caesarean section use amongst women in Robson Group 1. Larger trials are warranted, particularly in settings where urgent reversal of the Caesarean section epidemic is needed.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 86, 166, 100]]<|/det|>
+## MAIN  
+
+<|ref|>text<|/ref|><|det|>[[117, 108, 879, 365]]<|/det|>
+An estimated 287,000 maternal deaths, 2.4 million neonatal deaths and 1.9 million stillbirths occur each year, the vast majority of which occur in low- and middle- income countries (LMICs).(1- 3). As many as \(45\%\) of these maternal deaths, stillbirths, and neonatal deaths occur during labour, birth, and the first 24 hours postpartum.(4) Ensuring good- quality care is available to all women during the intrapartum period is thus critical to any efforts to reduce global maternal and neonatal morbidity and mortality.(5) Caesarean section is an essential component of good- quality intrapartum care - when used appropriately, it is a life- saving intervention for women and babies. However, Caesarean section rates globally more than doubled between 2000 and 2015, driven in large part by those performed without a clear medical indication.(6)(7) While unnecessary Caesarean section causes avoidable harms to women and newborns,(8, 9) it By 2030, 38 million women each year (28.5% of births) will experience a Caesarean.(10)  
+
+<|ref|>text<|/ref|><|det|>[[117, 394, 880, 653]]<|/det|>
+The World Health Organization (WHO) has long recommended that a woman in labour should be monitored by a skilled healthcare provider using a partograph to document clinical assessments and help make decisions.(11) When completed prospectively, the partograph can help determine whether and when an intervention - such as labour augmentation, Caesarean section or episiotomy - is warranted. A WHO- led 1994 trial showed that prospective partograph use combined with intensive provider training optimized the use of intrapartum interventions, and improved maternal and newborn outcomes.(12) Consequently, the WHO simplified partograph was widely disseminated and adopted as a component of routine intrapartum care internationally.(13) While more women than ever are giving birth in health facilities,(14) partographs are often used poorly, or not at all. Inadequate provider training and skills, heavy staff workloads, a lack of clinical equipment and supplies, and restrictive hospital policies are known barriers to partograph use.(15- 17)  
+
+<|ref|>text<|/ref|><|det|>[[117, 681, 875, 891]]<|/det|>
+In 2018, WHO published 56 updated recommendations to improve quality of intrapartum care and enhance women's childbirth experiences.(8) Key recommendations included changing the definition of active first stage of labour from the widely used 3cm or 4cm to starting from 5cm of cervical dilation, and removal of the 'alert' and 'action' lines. These changes reflected a growing body of evidence that the historical '1cm per hour' rule for active labour progress is unrealistic for most women, and that slower dilation rates are not associated with adverse birth outcomes. In response to these recommendations, a "next generation" partograph known as the WHO Labour Care Guide (LCG) was developed in 2020 through expert consultations, primary research with maternity healthcare providers, and a multi- country usability study.(18- 20)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 107, 879, 317]]<|/det|>
+WHO states that the LCG should be globally disseminated and implemented as a component of routine clinical care.(21) However, introducing the LCG into routine care requires a strategy that can improve healthcare provider's clinical practice, thereby enhancing the quality of intrapartum care, reducing use of unnecessary interventions, and improving support to women during labour. However, as the LCG is a novel tool, no such strategy has been tested in a randomised trial. This knowledge gap was highlighted in WHO's recent global LCG research prioritization exercise, in which identifying optimal implementation strategies, as well as understanding LCG's effect on maternal and perinatal outcomes, were top research priorities.(22) We therefore conducted a multi- centre trial to evaluate the effects of implementing a strategy to promote LCG use in labour wards.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 352, 201, 367]]<|/det|>
+## METHODS  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 376, 315, 392]]<|/det|>
+## Overview of study design  
+
+<|ref|>text<|/ref|><|det|>[[115, 400, 880, 705]]<|/det|>
+We designed and conducted a pragmatic, stepped- wedge, cluster- randomized trial which was conducted between \(1^{\text{st}}\) July 2021 and \(15^{\text{th}}\) July 2022. It was intended as a "proof- of- concept" study. We used an evidence- based, theory- informed approach to developing the intervention, and conducted the trial to determine whether it might have an effect on overuse of Caesarean section, or other important maternal and perinatal outcomes. The trial was preceded by a six- month formative phase, which was guided by the COM- B model of behaviour change, which recognises that individuals must have Capability, Motivation, and both physical and social Opportunity to perform a behaviour.(23) We used co- design principles and primary data collection to develop and refine the 'LCG strategy' intervention. The intervention was then introduced in a stepwise manner in four public hospitals in Karnataka State, India, in accordance with a randomisation schedule. Given the risk of cross- contamination, individual randomization was not possible. We used a stepped- wedge approach as the LCG reflects WHO's current advice regarding standard of care,(24) and it was thus not ethically feasible to use a parallel- group design.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 735, 344, 751]]<|/det|>
+## Trial approvals and oversight  
+
+<|ref|>text<|/ref|><|det|>[[115, 758, 880, 895]]<|/det|>
+This trial was designed and conducted in accordance with the ethical principles of the World Medical Association's Declaration of Helsinki, the Ottawa Statement for the Ethical Design and Conduct of Cluster Randomised Trials, and Good Clinical Practice (GCP) standards.(25- 27) We developed the trial protocol and reported findings in accordance with SPIRIT (Standard Protocol Items: Recommendations for Interventional Trials) guidance for randomised trials, and the CONSORT (Consolidated Standards of Reporting Trials) statement for stepped- wedge cluster- randomised trials
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[118, 83, 820, 150]]<|/det|>
+(CONSORT Checklist in Supplementary File S1).(28, 29) The trial protocol was pre- registered (CTRI/2021/01/030695), with the protocol and statistical analysis plan published prior to trial closure; there were no major deviations or changes.(30)  
+
+<|ref|>text<|/ref|><|det|>[[116, 179, 875, 461]]<|/det|>
+We sought permission from the head of study hospitals (gatekeepers) and individual providers before commencing the trial. The study protocol specified a waiver of individual consent for data collected on women giving birth – these data were non- identifiable, routinely- collected clinical variables in medical records and labour ward registries. For women invited to complete a postpartum survey, an informed consent was conducted. The trial was approved by the Alfred Hospital Human Ethics Committee (737/20), and the institutional ethics committees of the KLE Academy of Higher Education and Research (D- 281120003), J J M Medical College, Davanagere (IEC- 136/2020); Vijayanagar Institute of Medical Sciences (SVN IEC/20/2020- 2021) and the Gadag Institute of Medical Sciences, (IEC/01/2020- 21), as well as the State Ethics Committee, Department of Health and Family Welfare, Government of Karnataka (DD(MH)/71/2020- 21); and the Health Ministry's Screening Committee, Indian Council of Medical Research (2020- 10127). An independent, three- member Data and Safety Monitoring Committee oversaw the trial.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 491, 304, 507]]<|/det|>
+## Setting and Participants  
+
+<|ref|>text<|/ref|><|det|>[[116, 513, 877, 699]]<|/det|>
+We purposively selected four public maternity hospitals in Karnataka State to participate, based on their capacity to provide comprehensive emergency obstetric care (including access to caesarean section). All four hospitals attend to more than 4,000 women giving birth each year, and have an overall caesarean section rate of \(30\%\) or more. In three hospitals labour monitoring and partograph completion is primarily performed by postgraduate resident doctors, while in the remaining hospital it was performed by nurses. All hospitals had either completed or were undergoing accreditation under the Government of India's national Labour Room Quality Initiative ("LaQshya") which closely aligned with WHO intrapartum care recommendations.(31)  
+
+<|ref|>text<|/ref|><|det|>[[117, 728, 880, 867]]<|/det|>
+Each hospital was treated as a cluster (H1, H2, H3 and H4). Two senior obstetricians working at each hospital were appointed as facility investigators and were responsible for trial activities at each hospital. The target of the intervention were labour ward staff, including obstetricians, postgraduate doctors and nurses. These staff routinely use a WHO simplified partograph to make decisions about labour interventions. We hypothesized that the intervention would promote correct LCG use by these providers, changing their labour monitoring and management practices to align with WHO's
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[118, 84, 848, 125]]<|/det|>
+intrapartum recommendations. In turn, this could reduce overuse of Caesarean section, improve maternal and newborn outcomes, and enhance women's care experiences.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 156, 338, 172]]<|/det|>
+## Randomisation and blinding  
+
+<|ref|>text<|/ref|><|det|>[[116, 179, 878, 390]]<|/det|>
+Prior to trial commencement, the four clusters (hospitals) were randomly assigned to one of four sequences (H1, H2, H3, or H4, see Figure 1) using a computer- generated list of random numbers that was managed by the study statistician. The allocation sequence was concealed from the investigators and study teams and only revealed by the statistician one month prior to cross over to allow time for planning LCG implementation activities. Once the hospital had commenced the intervention, blinding of hospital staff, research staff and individual women was not possible. The intervention was commenced in hospitals according to the randomly assigned sequence, with one hospital transitioning to intervention at 2- month intervals (i.e., a step occurred every 2 months). A two- week transition period was used to allow for the intervention to be fully adopted.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 419, 312, 435]]<|/det|>
+## Control and intervention  
+
+<|ref|>text<|/ref|><|det|>[[117, 442, 870, 579]]<|/det|>
+The control condition for the trial was current labour monitoring and management practices ('usual clinical care'). While the WHO simplified partograph is widely used in India, the formative phase showed that its use was inconsistent and oftentimes retrospective. Training seminars were conducted at all hospitals on using the WHO simplified partograph to standardize the control condition. The WHO intrapartum care recommendations were also disseminated at all hospitals at the start of the trial.  
+
+<|ref|>text<|/ref|><|det|>[[116, 608, 876, 867]]<|/det|>
+The LCG strategy intervention included a co- designed LCG training program for doctors and nurses working on labour ward, and a monthly audit and feedback process using hospital Caesarean section data. For training, we developed and ran two- day workshops for all labour ward staff, co- ordinated by facility investigators who had undergone a "training of trainers" workshop. After this, all providers working on labour ward underwent an 8- week "low- dose, high- frequency" training program,(32) comprising of clinical cases and bedside teaching using LCG with senior clinical staff. The 8- week training was delivered in cycles to accommodate postgraduate resident rotations every 3 months. Refresher training was used if new staff arrived during the intervention period. At time of randomization, all simplified WHO partographs in the labour ward were replaced with the LCG. Senior labour ward staff were encouraged to monitor and promote consistent, accurate LCG use through supportive supervision.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 80, 880, 535]]<|/det|>
+The intervention also included monthly audit and feedback meetings on Caesarean rates, using the Robson Classification. Audit and feedback is widely used to promote evidence- based clinical practice, and is recommended by WHO for avoiding unnecessary Caesarean sections.(33, 34) WHO also recommends that countries use the Robson Classification for assessing, monitoring and comparing their Caesarean rates over time.(6) The Robson Classification organises all births in a facility into one of 10 mutually exclusive, all- inclusive groups, on the basis of parity, previous Caesarean, onset of labour, fetal presentation and lie, number of neonates and gestational age (term or preterm).(35) Providers at randomized hospitals underwent a brief training on how to interpret Robson Classification data, and how audit and feedback can help optimize Caesarean section use. Robson Classification tables were prepared using trial data, and shared directly with the study hospital on a monthly basis. These data were presented by senior clinical staff at monthly meetings, with structured discussions amongst the attendees on how to improve hospital performance. Hospitals and staff were instructed that all other aspects of clinical care during the trial should be in accordance with relevant local guidelines and protocols. In addition, facility leads were encouraged to identify and address anticipated barriers to the LCG strategy in their hospital. This included revision of hospital policies, standardisation of clinical protocols, rearrangements to the physical labour ward environment, and addressing some supply and equipment constraints. We used logbooks, tracking sheets and site visits to confirm that all eligible staff underwent LCG training activities, were using the LCG routinely, and attended monthly Caesarean audit meetings as planned.  
+
+<|ref|>sub_title<|/ref|><|det|>[[119, 574, 377, 590]]<|/det|>
+## Primary and secondary outcomes  
+
+<|ref|>text<|/ref|><|det|>[[116, 597, 881, 856]]<|/det|>
+Trained research staff collected non- identifiable, individual- level data on all women giving birth from 20 weeks' gestation onwards and their babies. Data were collected from the time of admission for childbirth until the time of discharge, transfer, death or until 7 days after admission (whichever came first). The primary trial outcome was the use of Caesarean section amongst women in Robson Group 1. That is, women who were nulliparous, gave birth to a singleton, term pregnancy in cephalic presentation, and were in spontaneous labour. While Robson Group 1 is a subset of all women giving birth (usually around \(30\%\) of the obstetric population), it is a group of largely low- risk women in whom Caesarean is often overused.(35) Should the LCG strategy have any effect, we anticipated that it would be more easily detected amongst these women. Secondary outcomes included use of intrapartum interventions, and maternal, fetal and neonatal health outcomes. The denominator varied depending on the outcome of interest (see Supplementary Table S1 for outcome definitions).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 83, 878, 222]]<|/det|>
+We also measured women's experiences of care using a pre- tested, interviewer- administered survey, conducted in a local language (Kannada, Hindi or Marathi), that was completed by postnatal day 7 or discharge (whichever came first) in a sample of postpartum women. This sample comprised women in Robson Group 1 or 3 who gave birth in the last 15 days of each 2- month period, had a liveborn baby, were 18 years or older, and who provided informed consent. In each hospital, trained interviewers approached and invited all eligible women to complete the survey.  
+
+<|ref|>text<|/ref|><|det|>[[117, 250, 880, 485]]<|/det|>
+All data were collected into pre- designed study forms and managed using REDCap electronic data capture via tablets. Each hospital team had access to their own hospital data only, and facility investigators were responsible for checking completeness and accuracy of all collected data. To minimize errors, data validation processes were implemented in the data collection system. Statistical methods and data cleaning algorithms were utilized to identify potential errors and outliers for further investigation and correction. Regular data and trial progress review meetings and audits were conducted to identify and rectify any inconsistencies or outliers. Data monitors periodically visit the study sites to verify the accuracy and completeness of the collected data. They also provided training and guidance to study personnel, addressing any issues or concerns that might arise during the study. The trial concluded when \(15^{\text{th}}\) July 2022 was reached, as planned.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 515, 211, 530]]<|/det|>
+## Sample size  
+
+<|ref|>text<|/ref|><|det|>[[117, 538, 875, 723]]<|/det|>
+No previous trial using LCG has been conducted, meaning the effect size of our strategy was difficult to estimate. For the year 2020 (prior to the trial) these four hospitals collectively averaged 24,000 births per year, and their overall Caesarean rate was \(44\%\) . The Caesarean rate in women in Robson Group 1 (i.e., the primary outcome) for all four hospitals was at least \(40\%\) . The trial was designed to provide \(92\%\) power to detect a \(25\%\) reduction in the Robson Group 1 Caesarean rate from \(40\%\) to \(30\%\) , assuming an intraclass correlation coefficient (ICC) equal to 0.02, a cluster auto correlation equal to 0.90, and an average of 300 women per cluster per step with a coefficient of variation of cluster size equal to 0.60. (36)  
+
+<|ref|>sub_title<|/ref|><|det|>[[119, 754, 366, 769]]<|/det|>
+## Statistical methods and analysis  
+
+<|ref|>text<|/ref|><|det|>[[117, 777, 881, 890]]<|/det|>
+Analyses were performed according to the intention- to- treat principle. Maternal baseline characteristics were summarized by trial arm as means and standard deviations, or numbers and percentages, as appropriate. For the primary and secondary outcomes, a generalized estimating equation (GEE) to estimate the effect of the intervention with respect to the population- average was used. A bias correction method and degree of freedom approximation due to the small number of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[116, 82, 877, 365]]<|/det|>
+clusters was applied in the GEE models to maintain the validity of the estimations. Manck and DeRouen correction method with N- 2 degrees of freedom was selected due to being the most conservative option.(37) An exchangeable correlation structure was assumed and the modified Poisson distribution with a log link function was considered. The model was constructed considering two variables: a binary indicator for treatment - indicating whether the observation was made during the control or the intervention period - and a categorical variable indicating the step. The relative risk and the \(95\%\) confidence interval were reported as the size effect. For the secondary outcomes in which duration was measured in days, the effect size was calculated as the difference between the mean of days in the intervention group and the mean of days in the control group. The ICC was estimated under the control period using the GEE model. As no adjustment for multiplicity testing of secondary outcomes was considered, their results are reported as point estimates with \(95\%\) confidence intervals and p- values.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 400, 188, 415]]<|/det|>
+## RESULTS  
+
+<|ref|>sub_title<|/ref|><|det|>[[119, 424, 388, 440]]<|/det|>
+## Characteristics of study population  
+
+<|ref|>text<|/ref|><|det|>[[116, 446, 881, 608]]<|/det|>
+Between 1 July 2021 and 15 July 2022, 26,331 women gave birth to 26,595 babies in the four hospitals during the control and intervention periods and were included for analysis (Figure 1). The total number of women giving birth differed between hospitals, ranging from 5,295 to 8,772 women per hospital. The analysis population comprised 11,517 women (11,624 babies) who gave birth in the control period and 14,814 women (14,971 babies) who gave birth in the intervention period. The main analysis did not include the 1,080 women (1,089 babies) who gave birth in the transition period.  
+
+<|ref|>text<|/ref|><|det|>[[116, 637, 863, 824]]<|/det|>
+While there were more women in intervention than control, the characteristics of women were similar (Table 1). Nearly half of included women were nulliparous (46.7% of the control group and 47.5% of the intervention group), while more than half of multiparous women had no prior Caesarean section (56.7% vs 55.0%) The distribution of women across the 10 Robson Classification groups was also similar (Supplementary Table S1). Robson Group 1 accounted for 30.8% (3,543/11,517) of women in the control group and 29.0% (4,302/14,814) of women in the intervention group. The intervention group had a slightly higher proportion of women in Group 2 and a slightly lower proportion of women in Group 3.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[119, 85, 378, 100]]<|/det|>
+## Primary and secondary outcomes  
+
+<|ref|>text<|/ref|><|det|>[[117, 108, 877, 222]]<|/det|>
+Table 2 reports the intervention effect sizes for the primary outcome and secondary maternal process- of- care outcomes. The Caesarean section rate in Robson Group 1 for the control group was \(45.2\%\) , while in the intervention group it was \(39.7\%\) with a crude absolute difference of \(- 5.5\%\) (relative risk [RR] 0.85, \(95\%\) confidence interval [CI] 0.54- 1.33, p value 0.1088). The estimated ICC for the primary outcome during the control period was \(0.015 (0; 0.043)\) .  
+
+<|ref|>text<|/ref|><|det|>[[116, 250, 880, 460]]<|/det|>
+The Caesarean section rate in Robson Groups 1 and 3 was \(30.9\%\) for the control group, and \(26.9\%\) for the intervention group - a crude absolute difference of \(- 4.0\%\) (RR 0.81, \(95\%\) CI 0.59 - 1.11). For the outcome augmentation with oxytocin during spontaneous labour, the prevalence in control group was \(27.3\%\) and in the intervention group it was \(9.3\%\) (crude absolute difference - \(18.0\%\) ). However, the estimate of effect was not significant (RR 0.34, \(95\%\) CI 0.01 - 15.04) - the wide confidence interval was attributable to the high variability in outcome prevalence between hospitals and steps. Table 3 reports the intervention effects on maternal, fetal and newborn health outcomes. The prevalence of these outcomes was low in both intervention and control groups, and there were no clear differences.  
+
+<|ref|>text<|/ref|><|det|>[[116, 490, 880, 653]]<|/det|>
+A total of 1,438 women in the control group and 1,277 women in the intervention group consented ( \(100\%\) and \(99.9\%\) consent rate, respectively) and completed postpartum surveys. Table 4 reports the effects on women's experiences at birth, for which there were no differences between groups. In terms of adverse events, there were 5 maternal deaths, 196 neonatal deaths and 367 stillbirths in the control period, and 13 maternal deaths, 200 neonatal deaths and 449 stillbirths in the intervention period (Supplementary Tables S3 and S4). None of these deaths were assessed as being related to the intervention.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 688, 216, 702]]<|/det|>
+## DISCUSSION  
+
+<|ref|>text<|/ref|><|det|>[[117, 710, 878, 871]]<|/det|>
+In this stepped- wedge, cluster- randomised trial in India, we implemented a novel strategy to introduce the LCG into routine care, as well as initiating monthly audit and feedback meetings on Caesarean section data using Robson Classification. We observed a \(5.5\%\) crude absolute reduction in Caesarean rates amongst women in Robson Group 1 following introduction of the intervention, however this difference was not statistically significant. Maternal process- of- care measures were not significantly different, though the crude absolute difference for labour augmentation using oxytocin was \(- 18.0\%\) . We did not observe any clear differences in maternal, fetal or newborn health
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[118, 84, 879, 126]]<|/det|>
+outcomes, or women's experiences at birth. The findings do not preclude the possibility that the LCG strategy may reduce Caesarean section and augmentation of labour in larger trials.  
+
+<|ref|>text<|/ref|><|det|>[[115, 154, 880, 605]]<|/det|>
+Reversing the worldwide trend in rising Caesarean section rates, driven in large part by medically unnecessary Caesarean use, has proven to be a challenging problem - a 2018 WHO guideline identified few effective interventions to address this.(34, 38) The LCG promotes several supportive care measures which have been shown in trials to prevent Caesarean section, such as labour companionship, mobilisation during labour, and adequate pain relief.(39- 41) Also, the use of 5cm dilatation to define active first stage, as well as removal of the "1cm per hour rule" would, assumedly, lead to fewer intrapartum interventions. As the LCG is a novel clinical tool, there are few effectiveness studies available for comparison, though more trials using LCG are planned.(42, 43) In 2022, Pandey et al published findings of an individually- randomized trial of 271 low- risk women in a single hospital in India, comparing the effects of using LCG versus modified partograph.(44) They reported a dramatic reduction in Caesarean section - 1.5% in the LCG group compared with 17.8% in the control group (p- value 0.0001) - as well as significantly lower oxytocin use and shorter duration of active phase of labour with LCG. Our trial was powered to detect a 25% risk reduction for Caesarean section rate in Robson Group 1, equating to an absolute reduction of 10% (from 40% to 30%). Though we lacked power to detect a smaller magnitude of effect, our findings suggest that an effect does exist, and is probably closer to a 15% risk reduction. While we lacked power to test a superiority hypothesis for rarer adverse outcomes (such as mortality and severe morbidity of women and babies), reassuringly there was no evidence of short- term harms associated with the LCG strategy. Data on these outcomes should be monitored in future, larger- scale research.  
+
+<|ref|>text<|/ref|><|det|>[[117, 633, 881, 820]]<|/det|>
+We did not detect any differences for outcomes on women's experiences. However, these data showed women had high levels of satisfaction with the amount of time health workers spent with them, the way they were communicated with, and with their overall birth experience. It also showed that some supportive care practices, such as being offered a labour companion, were reasonably common, though other women- centred interventions were not well- implemented. For example, being offered pain relief (5.2% and 15.3%), and being asked which birth position they preferred (0.7% and 2.1%) were poorly used. This highlights that substantive gaps persist in the provision of supportive care around the time of birth - additional strategies are needed to address these gaps.  
+
+<|ref|>text<|/ref|><|det|>[[118, 848, 864, 891]]<|/det|>
+This trial was conducted in large, busy, public tertiary hospitals in India with high Caesarean use. In three hospitals, partograph completion was the responsibility of postgraduate residents only. In
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 83, 878, 270]]<|/det|>
+India, the LaQshya national initiative and hospital accreditation process (31) has a strong emphasis on respectful maternity care, which is well- aligned with WHO's recommendations and the LCG's foundational principles. These factors mean the trial findings may not necessarily generalize to other settings that are naïve to respectful maternity care principles and policies. For example, it may be more challenging to generate provider behaviour change in settings without a national policy framework. Contextual differences around how frequently obstetric interventions are used, as well as differences in the risk profile of obstetric populations, may mean the LCG strategy has variable effects.  
+
+<|ref|>text<|/ref|><|det|>[[116, 298, 881, 675]]<|/det|>
+This study was designed as a "proof of concept" study of a novel, complex intervention. Strengths include the use of a theory- based, evidence- informed, co- design approach to developing the LCG strategy, which aimed to address factors known to impair partograph use.(17) We also used a robust, cluster- randomised design, and recruited a large number of participants in a real- world clinical setting. The stepped- wedge design means that all hospitals were implementing the LCG strategy at trial conclusion. This trial nonetheless has some limitations. The intervention did not have a specific component aimed at the antenatal period, though in retrospect it would be helpful to better prepare women for the introduction of new supportive care options. Also, women arriving at hospital in advanced labour had only a short period of time in which they could benefit from LCG, thereby diminishing any possible effects. The stepped- wedge design meant that other, secular trends – such as changes in COVID case numbers over time - could have affected the findings. However, COVID data shows that infections in these hospitals were quite infrequent. The use of the same clusters over a 54- week period means we cannot exclude the possibility that some women may have given birth twice during the study. We measured women's experiences using a survey instrument in their language of choice, however their responses may have been affected by social or courtesy biases.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 707, 224, 721]]<|/det|>
+## CONCLUSION  
+
+<|ref|>text<|/ref|><|det|>[[117, 729, 877, 842]]<|/det|>
+Findings from this multi- centred, stepped- wedge, cluster- randomized trial suggest that the LCG strategy is a promising intervention that can improve quality of labour and childbirth care, reducing overuse of intrapartum interventions. This study provides important evidence on the debate around introduction of LCG into routine clinical practice internationally. Further evaluation in larger scale, multi- country trials in hospital with high rates of Caesarean section are warranted.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 133, 196, 148]]<|/det|>
+## FUNDING  
+
+<|ref|>text<|/ref|><|det|>[[117, 155, 875, 317]]<|/det|>
+This study was supported by a Grand Challenges grant from the Bill & Melinda Gates Foundation (GNT INV- 023273). We received additional funding support from the Burnet Institute, via the Alastair Lucas Award. JPV and CSEH are supported by Investigator Grants from the Australian National Health and Medical Research Council (NHMRC). EA is supported by a NHMRC Postgraduate Student Award. The study funder had no role in study design, data collection, analysis, interpretation, or writing of the report. The corresponding author had full access to all the study data, and takes final responsibility for the decision to submit for publication.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 348, 299, 364]]<|/det|>
+## ACKNOWLEDGEMENTS  
+
+<|ref|>text<|/ref|><|det|>[[118, 371, 848, 436]]<|/det|>
+We gratefully acknowledge Ana Pilar Betran (Chair), Dr Dennis Wallace and Shuchita Mundle for their role as Data and Safety Monitoring Board members, and Olufemi T. Oladapo and Mercedes Bonet for their role as Observers to the study.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 467, 401, 483]]<|/det|>
+## INCLUSION AND ETHICS STATEMENT  
+
+<|ref|>text<|/ref|><|det|>[[118, 490, 878, 579]]<|/det|>
+Our study team support the principles of the Cape Town Statement, in particular the commitment to equitable international collaborations. The study was designed in partnership between three research groups (India, Argentina, Australia), building on multiple years of research collaborations and co- authored publications between several co- authors.  
+
+<|ref|>text<|/ref|><|det|>[[117, 608, 870, 747]]<|/det|>
+This study was funded by a Global Grand Challenges grant – the submission was jointly prepared by JPV, SG, YP, SV, VP, FA and LG. This grant funding went to all three of our research organisations, with the largest amount of this funding received by the JNMC- India research team. The study protocol had 14 named investigators – 12 from India, 1 from Argentina, and 1 from Australia. JPV and SG were named as co- Principal Investigators. During the study, decisions were taken by consensus amongst the steering group, during fortnightly teleconferences.  
+
+<|ref|>text<|/ref|><|det|>[[117, 776, 875, 890]]<|/det|>
+The authorship group (29 individuals) comprised 17 women and 12 men, and included late- , mid- and early- career individuals. Members of the authorship group include researchers in India (YP, SSV, MS, SB, JAK, SBP, AK, RRA, PMR, SS, LB, MHM, SSG, SC, BR), Argentina (VP, FA, LG, MB, AV, RR) and Australia (JPV, EA, CSEH). The lead author (JPV) is in Australia and the senior author (SG) is in India. Our Technical Advisory Group (TL, PK, GJH, RD) included senior researchers from India, UK, South
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[118, 85, 840, 125]]<|/det|>
+Africa and USA, and our Data and Safety Monitoring Committee included individuals from India, Switzerland and the USA.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 133, 457, 149]]<|/det|>
+## DATA AND CODE AVAILABILITY STATEMENT  
+
+<|ref|>text<|/ref|><|det|>[[117, 156, 872, 245]]<|/det|>
+In keeping with the Bill & Melinda Gates Foundation Open Access Policy, the trial dataset generated during this study, the data dictionary and syntax used for analyses are hosted at the Gates Open Research- approved repository Zenodo at time of paper publication under DOI: https://doi.org/10.5281/zenodo.8140454  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 304, 217, 319]]<|/det|>
+## REFERENCES  
+
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+1. WHO, UNICEF, UNFPA, World Bank, UNDP. Trends in maternal mortality 2000 to 2020. Geneva: World Health Organization; 2023.  
+2. United Nations Inter-Agency Group for Child Mortality Estimation. Levels and trends in child mortality. New York: UNICEF; 2022.  
+3. Hug L, You D, Blencowe H, Mishra A, Wang Z, Fix MJ, et al. Global, regional, and national estimates and trends in stillbirths from 2000 to 2019: a systematic assessment. Lancet. 2021;398(10302):772-85.  
+4. Alliance for Maternal Newborn Health Improvement Mortality Study Group. Population-based rates, timing, and causes of maternal deaths, stillbirths, and neonatal deaths in south Asia and sub-Saharan Africa: a multi-country prospective cohort study. Lancet Glob Health. 2018;6(12):e1297-e308.  
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+36. Hemming K, Kasza J, Hooper R, Forbes A, Taljaard M. A tutorial on sample size calculation for multiple-period cluster randomized parallel, cross-over and stepped-wedge trials using the Shiny CRT Calculator. Int J Epidemiol. 2020;49(3):979-95.  
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+38. The Lancet. Stemming the global caesarean section epidemic. Lancet. 2018;392(10155):1279.  
+39. Bohren MA, Hofmeyr GJ, Sakala C, Fukuzawa RK, Cuthbert A. Continuous support for women during childbirth. Cochrane Database Syst Rev. 2017;7:CD003766.  
+40. Lawrence A, Lewis L, Hofmeyr GJ, Styles C. Maternal positions and mobility during first stage labour. Cochrane Database Syst Rev. 2013(10):CD003934.  
+41. Anim-Somuah M, Smyth RM, Cyna AM, Cuthbert A. Epidural versus non-epidural or no analgesia for pain management in labour. Cochrane Database Syst Rev. 2018;5(5):CD000331.  
+42. Bernitz S. The Norwegian World Health Organisation Labour Care Guide Trial (NORWEL): study protocol (NCT05791630) clinicaltrials.gov2023 [  
+43. Blomberg M. Can the Use of a Next Generation Partograph Improve Neonatal Outcomes? (PICRINO): study protocol (NCT05560802) clinicaltrials.gov [  
+44. Pandey D, Bharti R, Dabral A, Khanam Z. Impact of WHO Labor Care Guide on reducing cesarean sections at a tertiary center: an open-label randomized controlled trial. AJOG Glob Rep. 2022;2(3):100075.
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[117, 149, 874, 716]]<|/det|>
+<table><tr><td rowspan="2">Characteristic</td><td>Intervention period<br/>(N = 14,814 women)</td><td>Control period<br/>(N = 11,517 women)</td></tr><tr><td>n (%)</td><td>n (%)</td></tr><tr><td>Maternal age (years)*</td><td>23.9 (3.6)</td><td>23.4 (3.6)</td></tr><tr><td>Maternal age</td><td></td><td></td></tr><tr><td>Less than 20</td><td>1,020 (6.9%)</td><td>1,010 (8.8%)</td></tr><tr><td>20-34</td><td>13,572 (91.6%)</td><td>10,357 (89.9%)</td></tr><tr><td>35 or more</td><td>222 (1.5%)</td><td>150 (1.3%)</td></tr><tr><td>Previous Caesarean Section**</td><td></td><td></td></tr><tr><td>0</td><td>4,282 (55.0%)</td><td>3,484 (56.7%)</td></tr><tr><td>1</td><td>2,819 (36.2%)</td><td>2,133 (34.7%)</td></tr><tr><td>2 or more</td><td>682 (8.8%)</td><td>525 (8.5%)</td></tr><tr><td>Gravida</td><td></td><td></td></tr><tr><td>1</td><td>6,394 (43.2%)</td><td>4,940 (42.9%)</td></tr><tr><td>2-4</td><td>8,160 (55.1%)</td><td>6,369 (55.3%)</td></tr><tr><td>5 or more</td><td>260 (1.8%)</td><td>208 (1.8%)</td></tr><tr><td>Parity</td><td></td><td></td></tr><tr><td>0</td><td>7,031 (47.5%)</td><td>5,375 (46.7%)</td></tr><tr><td>1-3</td><td>7,674 (51.8%)</td><td>6,022 (52.3%)</td></tr><tr><td>4 or more</td><td>109 (0.7%)</td><td>120 (1.0%)</td></tr><tr><td>Women receive antenatal care during pregnancy</td><td>14,745 (99.5%)</td><td>11,438 (99.3%)</td></tr><tr><td>Covid status at admission</td><td></td><td></td></tr><tr><td>Positive</td><td>32 (0.2%)</td><td>5 (0.0%)</td></tr><tr><td>Negative</td><td>8,208 (55.4%)</td><td>9,168 (79.6%)</td></tr><tr><td>Pending or not done</td><td>6,574 (44.4%)</td><td>2,344 (20.4%)</td></tr><tr><td>Transferred from another health facility during labour</td><td>2,102 (14.2%)</td><td>1,881 (16.3%)</td></tr><tr><td>Gestational age at time of birth*</td><td>38.3 (2.5)</td><td>38.3 (2.6)</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[119, 710, 374, 721]]<|/det|>
+* Mean and (Standard deviation) is reported
+
+<|ref|>text<|/ref|><|det|>[[119, 721, 373, 731]]<|/det|>
+** Multiparous women only were considered
+
+<|ref|>table_caption<|/ref|><|det|>[[119, 734, 456, 748]]<|/det|>
+Table 1. Characteristics of study population
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[80, 155, 777, 680]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[83, 120, 602, 143]]<|/det|>
+Table 2. Effect of the intervention on primary outcome, and maternal process of care outcomes   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Intervention period<br>(N = 14,814 women)</td><td colspan="2">Control period<br>(N = 11,517 women)</td><td rowspan="2">Relative Risk<br>(95% CI)α</td></tr><tr><td>n/N</td><td>(%)</td><td>n/N</td><td>(%)</td></tr><tr><td>Primary outcome</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cesarean section in Robson Group 1</td><td>1709/4302</td><td>(39.7%)</td><td>1602/3543</td><td>(45.2%)</td><td>0.85 (0.54; 1.33)</td></tr><tr><td>Maternal process of care outcomes</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cesarean section in women in Robson Groups 1 and 3</td><td>2012/7485</td><td>(26.9%)</td><td>1919/6204</td><td>(30.9%)</td><td>0.81 (0.59; 1.11)</td></tr><tr><td>Cesarean section in women in Robson Groups 1, 2, 3, 4 and 5</td><td>6529/12735</td><td>(51.3%)</td><td>5028/9808</td><td>(51.3%)</td><td>0.92 (0.78; 1.10)</td></tr><tr><td>Caesarean section (all women)</td><td>7505/14814</td><td>(50.7%)</td><td>5817/11517</td><td>(50.5%)</td><td>0.91 (0.71; 1.15)</td></tr><tr><td>Augmentation with oxytocin during labourβ</td><td>912/9764</td><td>(9.3%)</td><td>2273/8318</td><td>(27.3%)</td><td>0.34 (0.01; 15.04)</td></tr><tr><td>Artificial rupture of the membranes*β</td><td>553/9764</td><td>(5.7%)</td><td>559/8318</td><td>(6.7%)</td><td>-</td></tr><tr><td>Episiotomyε</td><td>4820/7309</td><td>(65.9%)</td><td>3137/5700</td><td>(55.0%)</td><td>0.99 (0.73; 1.35)</td></tr><tr><td>Operative vaginal birthε</td><td>192/7309</td><td>(2.63%)</td><td>112/5700</td><td>(1.96%)</td><td>1.12 (0.13; 9.36)</td></tr><tr><td>Days from admission to childbirth**</td><td>0.34</td><td>(0.73)</td><td>0.30</td><td>(0.68)</td><td>0.05 (-0.31; 0.41)</td></tr><tr><td>Days from childbirth to discharge**</td><td>3.29</td><td>(1.75)</td><td>3.52</td><td>(1.88)</td><td>0.23 (-0.84; 1.30)</td></tr></table>
+
+<|ref|>table_footnote<|/ref|><|det|>[[82, 690, 914, 803]]<|/det|>
+\(\beta\) Women in spontaneous labour were considered \(\epsilon\) Women with vaginal deliveries were considered \\*\\*The mean of the days and (S.D.) is reported. The effect size was calculated as the difference between the mean of days in the intervention group and the mean of days in the control group. \(\ast \ast\) RR was not estimated since convergence of the model was not achieved \(\Omega\) The relative risk and \(95\%\) confidence interval \((95\% CI)\) was estimated with the Generalized Estimating Equation method employing the "Manck and DeRouen" bias correction method and a degree of freedom approximation.
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[90, 152, 907, 750]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[84, 121, 562, 143]]<|/det|>
+Table 3. Effect of the intervention on maternal, perinatal and neonatal health outcomes   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Intervention period<br>(N = 14,814 women)</td><td colspan="2">Control period<br>(N = 11,517 women)</td><td>Relative Risk<br>(95% CI)Ω</td></tr><tr><td>n/N</td><td>(%)</td><td>n/N</td><td>(%)</td><td></td></tr><tr><td>Maternal Secondary Outcomes</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3rd or 4th degree tears</td><td>18/14814</td><td>(0.12%)</td><td>25/11517</td><td>(0.22%)</td><td>0.51 (0.01; 29.16)</td></tr><tr><td>PPH requiring uterine balloon tamponade or surgical intervention</td><td>28/14814</td><td>(0.19%)</td><td>46/11517</td><td>(0.40%)</td><td>0.38 (0.00; 84.07)</td></tr><tr><td>Suspected or confirmed maternal infection requiring therapeutic antibiotics</td><td>114/14814</td><td>(0.77%)</td><td>53/11517</td><td>(0.46%)</td><td>2.12 (0.06; 70.96)</td></tr><tr><td>Fetal/Neonatal Secondary Outcomes</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Stillbirth</td><td>449/14971</td><td>(3.00%)</td><td>367/11624</td><td>(3.16%)</td><td>0.97 (0.43; 2.19)</td></tr><tr><td>Antepartum stillbirth</td><td>279/14971</td><td>(1.86%)</td><td>286/11624</td><td>(2.46%)</td><td>0.91 (0.34; 2.47)</td></tr><tr><td>Intrapartum stillbirth</td><td>163/14971</td><td>(1.09%)</td><td>79/11624</td><td>(0.68%)</td><td>0.90 (0.49; 1.65)</td></tr><tr><td>Apgar score &amp;lt;7 at 5 minutes</td><td>670/14522</td><td>(4.61%)</td><td>567/11257</td><td>(5.04%)</td><td>1.17 (0.86; 1.59)</td></tr><tr><td>Bag and mask ventilation of newborn</td><td>424/14522</td><td>(2.92%)</td><td>256/11257</td><td>(2.27%)</td><td>1.21 (0.08; 18.75)</td></tr><tr><td>Mechanical ventilation of newborn</td><td>293/14522</td><td>(2.02%)</td><td>260/11257</td><td>(2.31%)</td><td>1.29 (0.36; 4.66)</td></tr><tr><td>Prolonged (&amp;gt;48 hour) admission in NICU</td><td>1843/14522</td><td>(12.7%)</td><td>1014/11257</td><td>(9.0%)</td><td>1.14 (0.47; 2.79)</td></tr><tr><td>Newborns requiring NICU admission for hypoxic ischaemic encephalopathy</td><td>34/14522</td><td>(0.23%)</td><td>152/11257</td><td>(1.35%)</td><td>0.40 (0.04; 3.74)</td></tr><tr><td>Composite neonatal morbidity outcome*</td><td>376/14522</td><td>(2.59%)</td><td>377/11257</td><td>(3.35%)</td><td>1.11 (0.32; 3.79)</td></tr><tr><td>Neonatal death</td><td>200/14522</td><td>(1.38%)</td><td>196/11257</td><td>(1.74%)</td><td>1.31 (0.37; 4.71)</td></tr><tr><td>Perinatal death (stillbirth or neonatal death)</td><td>649/14971</td><td>(4.34%)</td><td>563/11624</td><td>(4.84%)</td><td>1.06 (0.41; 2.73)</td></tr></table>
+
+<|ref|>table_footnote<|/ref|><|det|>[[84, 747, 910, 822]]<|/det|>
+\(\Omega\) The relative risk and \(95\%\) confidence interval \((95\% CI)\) was estimated with the Generalized Estimating Equation method employing the "Manc and DeRouen" bias correction method and a degree of freedom approximation. \\* The composite neonatal outcome was defined as one or more of the following: Mechanical ventilation of the newborn or requirement of NICU admission for hypoxic ischaemic encephalopathy of the newborn or neonatal death
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[58, 150, 921, 787]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[82, 120, 590, 140]]<|/det|>
+Table 4. Effect of the intervention on women's experience outcomes (Women in Robson Group 1 or 3)   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Intervention period<br>(N=1277 women)</td><td colspan="2">Control period<br>(N=1438 women)</td><td rowspan="2">Relative Risk<br>(95% CI) a</td></tr><tr><td>n/N</td><td>(%)</td><td>n/N</td><td>(%)</td></tr><tr><td>Women reporting labour companion</td><td>982/1277</td><td>(76.9%)</td><td>1206/1438</td><td>(83.9%)</td><td>1.19 (0.89; 1.59)</td></tr><tr><td>Women reporting being offered pain relief</td><td>196/1277</td><td>(15.3%)</td><td>75/1438</td><td>(5.2%)</td><td>2.30 (0.00; 1281.82)</td></tr><tr><td>Women reporting being very satisfied or somewhat satisfied with how their pain was managed</td><td>827/1277</td><td>(64.8%)</td><td>957/1437</td><td>(66.6%)</td><td>0.94 (0.06; 16.14)</td></tr><tr><td>Women reporting being encouraged to drink water</td><td>863/1277</td><td>(67.6%)</td><td>1123/1438</td><td>(78.1%)</td><td>0.98 (0.34; 2.86)</td></tr><tr><td>Women reporting being encouraged to eat food</td><td>657/1277</td><td>(51.4%)</td><td>823/1438</td><td>(57.2%)</td><td>0.99 (0.13; 7.37)</td></tr><tr><td>Women reporting being encouraged to walk</td><td>827/1277</td><td>(64.8%)</td><td>863/1437</td><td>(60.1%)</td><td>1.10 (0.34; 3.58)</td></tr><tr><td>Women reporting being asked which birth position they preferred</td><td>27/1277</td><td>(2.11%)</td><td>10/1438</td><td>(0.70%)</td><td>1.96 (0.00; 1384.48)</td></tr><tr><td>Women reporting being very or somewhat satisfied with the amount of time health provider spent with them</td><td>1260/1277</td><td>(98.7%)</td><td>1424/1437</td><td>(99.1%)</td><td>0.99 (0.93; 1.05)</td></tr><tr><td>Women reporting being very or somewhat satisfied with the way health provider communicated with them</td><td>1262/1277</td><td>(98.8%)</td><td>1424/1438</td><td>(99.0%)</td><td>0.99 (0.91; 1.07)</td></tr><tr><td>Women who strongly agreed or agreed that their privacy was respected</td><td>1234/1277</td><td>(96.6%)</td><td>1315/1438</td><td>(91.4%)</td><td>0.99 (0.56; 1.75)</td></tr><tr><td>Women who reported being asked permission before examinations</td><td>596/1277</td><td>(46.7%)</td><td>992/1438</td><td>(69.0%)</td><td>0.84 (0.07; 10.34)</td></tr><tr><td>Women who reported being asked permission before treatments</td><td>588/1277</td><td>(46.0%)</td><td>996/1438</td><td>(69.3%)</td><td>0.85 (0.07; 10.37)</td></tr><tr><td>Women who strongly agreed or agreed that they were satisfied with their labour and birth experience</td><td>1268/1277</td><td>(99.3%)</td><td>1404/1438</td><td>(97.6%)</td><td>1.01 (0.95; 1.07)</td></tr></table>
+
+<|ref|>table_footnote<|/ref|><|det|>[[80, 784, 911, 831]]<|/det|>
+\(\Omega\) The relative risk and \(95\%\) confidence interval (95% CI) was estimated with the Generalized Estimating Equation method employing the "Manc and DeRouen" bias correction method and a degree of freedom approximation.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[118, 87, 189, 98]]<|/det|>
+# FIGURES
+
+<|ref|>table_caption<|/ref|><|det|>[[118, 111, 856, 147]]<|/det|>
+Figure 1. Trial diagram showing number of women with a gestational age &gt;20 weeks by hospital and steps
+
+<|ref|>table<|/ref|><|det|>[[118, 185, 879, 567]]<|/det|>
+
+<table><tr><td colspan="2" rowspan="2"></td><td colspan="5">STEP (2 months periods)</td><td rowspan="2">Total<br>(Transition<br>period)**</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>\(5^{**}\)</td></tr><tr><td rowspan="4">HOSPITAL</td><td>1</td><td>946</td><td>915<br>(240)*</td><td>1127</td><td>877</td><td>2374</td><td>6239<br>(240)</td></tr><tr><td>2</td><td>965</td><td>983</td><td>708<br>(267)*</td><td>719</td><td>1920</td><td>5295<br>(267)</td></tr><tr><td>3</td><td>1398</td><td>1677</td><td>1529</td><td>1015<br>(302)*</td><td>3153</td><td>8772<br>(302)</td></tr><tr><td>4</td><td>950</td><td>1060</td><td>1087</td><td>922</td><td>2006<br>(271)*</td><td>6025<br>(271)</td></tr><tr><td></td><td>Total<br>(Transition<br>period)</td><td>4259</td><td>4635<br>(240)</td><td>4451<br>(267)</td><td>3533<br>(302)</td><td>9453<br>(271)</td><td>26331<br>(1080)</td></tr></table>
+
+<|ref|>image<|/ref|><|det|>[[118, 579, 152, 598]]<|/det|>
+
+<|ref|>text<|/ref|><|det|>[[180, 583, 647, 594]]<|/det|>
+Control Study period Intervention study period
+
+<|ref|>text<|/ref|><|det|>[[118, 612, 508, 621]]<|/det|>
+* Number of women recruited during the two weeks-transition period
+
+<|ref|>text<|/ref|><|det|>[[118, 624, 861, 648]]<|/det|>
+** The sample size was larger for step 4 because this step included 4 months of data, compared with 2 months for preceding steps and baseline period.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 340, 99]]<|/det|>
+## SUPPLEMENTARY APPENDIX 
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 110, 452, 124]]<|/det|>
+### Table S1. Primary and secondary outcomes 
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 158, 258, 171]]<|/det|>
+#### Primary Outcome 
+
+<|ref|>text<|/ref|><|det|>[[118, 182, 848, 244]]<|/det|>
+CS rate amongst women in Robson Group 1 (i.e. women who are nulliparous, singleton, cephalic, ≥37 weeks' gestation, in spontaneous labour). The numerator are the women in Robson Group 1 who had a CS and the denominator the number of women in Robson group 1. 
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 276, 339, 288]]<|/det|>
+#### Maternal Secondary Outcomes 
+
+<|ref|>table<|/ref|><|det|>[[118, 287, 880, 906]]<|/det|>
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>CS rate in women in Robson Groups 1 and 3</td><td>Numerator: Number of women undergoing CS<br/>Denominator: Number of women in Robson Groups 1 and 3</td></tr><tr><td>CS rate in women in Robson Groups 1 to 5</td><td>Numerator: Number of women undergoing CS<br/>Denominator: Number of women in Robson Groups 1 to 5</td></tr><tr><td>Overall CS rate</td><td>Numerator: Number of women undergoing CS<br/>Denominator: Number of women giving birth</td></tr><tr><td>Augmentation with oxytocin during labour rate</td><td>Numerator: Number of women given oxytocin for augmentation during labour<br/>Denominator: Number of women who experienced spontaneous labour</td></tr><tr><td>Artificial rupture of the membranes rate</td><td>Numerator: Number of women who had artificial rupture of membranes<br/>Denominator: Number of women who experienced spontaneous labour</td></tr><tr><td>Episiotomy rate</td><td>Numerator: Number of women who had episiotomy<br/>Denominator: Number of women with vaginal birth</td></tr><tr><td>Operative vaginal birth rate</td><td>Numerator: Number of women who had operative vaginal birth (forceps or vacuum)<br/>Denominator: Number of women with vaginal birth</td></tr><tr><td>Days between admission to childbirth</td><td>Mean of the days between admission to childbirth</td></tr><tr><td>Days between childbirth to discharge</td><td>Mean of the days between childbirth to discharge</td></tr><tr><td>3rd or 4th degree tears</td><td>Numerator: Number of women experiencing 3rd or 4th degree tears<br/>Denominator: Number of women giving birth</td></tr><tr><td>PPH requiring uterine balloon tamponade or surgical intervention</td><td>Numerator: Number of women requiring uterine balloon tamponade OR surgical intervention for PPH<br/>Denominator: Number of women giving birth</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[118, 83, 877, 150]]<|/det|>
+
+<table><tr><td>Suspected or confirmed maternal<br>infection requiring therapeutic<br>antibiotics</td><td>Numerator: Number of women with clinical signs or symptoms<br>of maternal infection AND therapeutic antibiotics were required<br>Denominator: Number of women giving birth</td></tr></table>
+
+<|ref|>table_caption<|/ref|><|det|>[[118, 179, 381, 190]]<|/det|>
+Fetal/Neonatal Secondary Outcomes
+
+<|ref|>table<|/ref|><|det|>[[118, 197, 886, 861]]<|/det|>
+
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>Stillbirth</td><td>Numerator: Fetal death<br>Denominator: All born babies</td></tr><tr><td>Antepartum stillbirth</td><td>Numerator: Fetal death prior to admission<br>Denominator: All born babies</td></tr><tr><td>Intrapartum stillbirth</td><td>Numerator: Fetal death after admission<br>Denominator: All born babies</td></tr><tr><td>Apgar score &lt;7 at 5 minutes</td><td>Numerator: Liveborn babies with Apgar &lt;7 at 5 minutes<br>Denominator: Liveborn babies</td></tr><tr><td>Bag and mask ventilation of newborn</td><td>Numerator: Use of continuous bag and mask ventilation of<br>newborn for &gt;1 minute<br>Denominator: Liveborn babies</td></tr><tr><td>Mechanical ventilation of newborn</td><td>Numerator: Use of mechanical ventilation of newborn<br>Denominator: Liveborn babies</td></tr><tr><td>Composite neonatal outcome</td><td>Numerator: Use of mechanical ventilation of newborn or<br>admission to NICU for suspected or confirmed or neonatal death<br>Denominator: Liveborn babies</td></tr><tr><td>Prolonged (&gt;48 hour) admission in NICU</td><td>Numerator: Admission to NICU for &gt;48 hours<br>Denominator: Liveborn babies</td></tr><tr><td>Newborns requiring NICU admission for<br>hypoxic ischaemic encephalopathy</td><td>Numerator: Admission to NICU for suspected or confirmed<br>Denominator: Liveborn babies</td></tr><tr><td>Composite neonatal outcome</td><td>Numerator: Use of mechanical ventilation of newborn or<br>admission to NICU for suspected or confirmed or neonatal death<br>Denominator: Liveborn babies</td></tr><tr><td>Neonatal death</td><td>Numerator: Neonatal death in a liveborn infant by day 7 or<br>discharge (whichever came first)<br>Denominator: All liveborn babies</td></tr><tr><td>Perinatal death</td><td>Numerator: Fetal death or neonatal death in a liveborn infant by<br>day 7 or discharge (whichever came first)<br>Denominator: All born babies</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[117, 102, 886, 875]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[119, 87, 342, 99]]<|/det|>
+Women's experience outcomes   
+
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>Woman&#x27;s experience with labour companion</td><td>Numerator: Women who reported a labour companion was present during labour or birth<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of being offered pain relief</td><td>Numerator: Women who reported that they were asked whether they would like any pain relief<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Women&#x27;s satisfaction with their pain management during labour and birth</td><td>Numerator: Women who reported being very satisfied or somewhat satisfied with how their pain was managed during labour and birth<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of being encouraged to drink oral fluids</td><td>Numerator: Women who reported that a health worker encouraged them to drink water<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of being encouraged to eat food</td><td>Numerator: Women who reported that a health worker encouraged them to eat food<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of mobilising during labour</td><td>Numerator: Women who reported that a health worker encouraged them to walk around during labour<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of birth position of choice</td><td>Numerator: Women who reported that a health worker asked them which birth position they preferred<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of time health worker spent with them</td><td>Numerator: Women who reported being very satisfied or somewhat satisfied with amount of time health worker spent with them during labour<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[117, 103, 886, 525]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[119, 86, 390, 99]]<|/det|>
+Women's experience outcomes (cont.)   
+
+<table><tr><td>Outcome</td><td>Outcome definition</td></tr><tr><td>Women&#x27;s satisfaction with the way health providers communicated with them</td><td>Numerator: Women who reported being very satisfied or somewhat satisfied with the way health workers communicated with them during labour and birth<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s experience of privacy</td><td>Numerator: Number of women who strongly agreed or agreed that their privacy was respected during examinations and treatments<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Women&#x27;s experience of being asked permission</td><td>Numerator: Number of women who said their health worker always asked permission before examinations and treatments<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr><tr><td>Woman&#x27;s overall experience of care</td><td>Numerator: Number of women who strongly agreed or agreed that they felt satisfied with their labour and birth experience<br>Denominator: Women in Robson Group 1 or 3 who completed the survey</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table_caption<|/ref|><|det|>[[117, 85, 738, 99]]<|/det|>
+Table S2. Application of Robson Classification to intervention and control groups
+
+<|ref|>table<|/ref|><|det|>[[118, 108, 878, 602]]<|/det|>
+
+<table><tr><td>Robson Classification Group</td><td>Intervention<br>period<br>(N=14,814<br>women)</td><td>Control period<br>(N=11,517<br>women)</td></tr><tr><td>Group 1: Nulliparous, singleton, cephalic, term, spontaneous labour</td><td>4,302 (29.0%)</td><td>3,543 (30.8%)</td></tr><tr><td>Group 2: Nulliparous, singleton, cephalic, term, induced/prelabour Caesarean</td><td>1,729 (11.7%)</td><td>1,022 (8.9%)</td></tr><tr><td>· Group 2a: Nulliparous, singleton, cephalic, term, induced</td><td>848 (5.7%)</td><td>471 (4.1%)</td></tr><tr><td>· Group 2b: Nulliparous, singleton, cephalic, term, prelabour<br>Caesarean</td><td>881 (5.9%)</td><td>551 (4.8%)</td></tr><tr><td>Group 3: Multiparous (no previous Caesarean), singleton, cephalic, term,<br>spontaneous labour</td><td>3,183 (21.5%)</td><td>2,661 (23.1%)</td></tr><tr><td>Group 4: Multiparous (no previous Caesarean), singleton, cephalic, term,<br>induced/prelabour Caesarean</td><td>450 (3.0%)</td><td>282 (2.4%)</td></tr><tr><td>· Group 4a: Multiparous (no previous Caesarean), singleton, cephalic,<br>term, induced</td><td>292 (2.0%)</td><td>212 (1.8%)</td></tr><tr><td>· Group 4a: Multiparous (no previous Caesarean), singleton, cephalic,<br>term, prelabour Caesarean</td><td>158 (1.0%)</td><td>70 (0.6%)</td></tr><tr><td>Group 5: Previous Caesarean, singleton, cephalic, term, (spontaneous labour,<br>induced labour or prelabour Caesarean)</td><td>3,071 (20.7%)</td><td>2,300 (20.0%)</td></tr><tr><td>Group 6: Nulliparous with a singleton breech</td><td>235 (1.6%)</td><td>182 (1.6%)</td></tr><tr><td>Group 7: Multiparous with a singleton breech (including previous Caesarean)</td><td>224 (1.5%)</td><td>153 (1.3%)</td></tr><tr><td>Group 8: Multiple pregnancies (including previous Caesarean)</td><td>155 (1.0%)</td><td>107 (0.9%)</td></tr><tr><td>Group 9: Single pregnancy, transverse or oblique lie (including previous<br>Caesarean)</td><td>21 (0.1%)</td><td>36 (0.3%)</td></tr><tr><td>Group 10: Singleton, cephalic, preterm (including previous Caesarean)</td><td>1,444 (9.7%)</td><td>1,231 (10.7%)</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table_caption<|/ref|><|det|>[[117, 86, 450, 99]]<|/det|>
+Table S3. Serious adverse events by period
+
+<|ref|>table<|/ref|><|det|>[[70, 108, 930, 383]]<|/det|>
+
+<table><tr><td></td><td>Intervention Period<br>(N of women = 14,814)<br>(N of liveborns=14,522)<br>(N of newborns=14,971)</td><td>Transition period<br>(N of women=1,080)<br>(N of liveborns=1,060)<br>(N of newborns: 1,089)</td><td>Control Period<br>(N of women= 11,517)<br>(N of liveborns= 11,257)<br>(N of newborns= 11,624)</td></tr><tr><td></td><td>n (%)</td><td>n (%)</td><td>n (%)</td></tr><tr><td>Maternal death</td><td>13 (0.09)</td><td>1 (0.09)</td><td>5 (0.04)</td></tr><tr><td>Neonatal death</td><td>200 (1.38)</td><td>11 (1.04)</td><td>196 (1.74)</td></tr><tr><td>Neonatal death (less than 28 weeks)</td><td>18 (0.12)</td><td>1 (0.09)</td><td>16 (0.14)</td></tr><tr><td>Neonatal death (28 weeks or more)</td><td>182 (1.25)</td><td>10 (0.94)</td><td>180 (1.60)</td></tr><tr><td>Stillbirth</td><td>449 (3.00)</td><td>29 (2.66)</td><td>367 (3.16)</td></tr><tr><td>Stillbirth (less than 28 weeks)</td><td>175 (1.17)</td><td>10 (0.92)</td><td>139 (1.20)</td></tr><tr><td>Stillbirth (28 weeks or more)</td><td>274 (1.83)</td><td>19 (1.74)</td><td>228 (1.96)</td></tr></table>
+
+<|ref|>table_caption<|/ref|><|det|>[[117, 424, 483, 436]]<|/det|>
+Table S4. Causes of maternal deaths, by period
+
+<|ref|>table<|/ref|><|det|>[[125, 444, 872, 597]]<|/det|>
+
+<table><tr><td></td><td>Intervention Period<br>(N = 13)</td><td>Transition Period<br>(N = 1)</td><td>Control Period<br>(N = 5)</td></tr><tr><td>Pre-eclampsia/eclampsia</td><td>5</td><td>0</td><td>4</td></tr><tr><td>Obstructed labour</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Haemorrhage</td><td>1</td><td>0</td><td>0</td></tr><tr><td>Infection</td><td>2</td><td>1</td><td>0</td></tr><tr><td>Other*</td><td>5</td><td>0</td><td>1</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[117, 608, 876, 658]]<|/det|>
+*The case classified as "Other" in the control period was a postpartum cardiomyopathy. The five cases classified as "Other"in the intervention period were: (1) Immediate cause: a) Hepatic encephalopathy with MODS Antecedent cause: b) Acute fatty liver of pregnancy, (2) Amniotic fluid embolism, (3) Disseminated intravascular coagulation secondary to acute fatty liver of pregnancy, (4) Cerebrovascular Accident, (5) Pulmonary embolism.
+
+<--- 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|>[[61, 130, 317, 150]]<|/det|>
+- 2SupplementaryFileS1.pdf
+
+<--- Page Split --->

preprint/preprint__05aa0c2fc7100b1500f07e08d2628280742c5c4e1a4bf250c2c7ba23e4cc9a7a/preprint__05aa0c2fc7100b1500f07e08d2628280742c5c4e1a4bf250c2c7ba23e4cc9a7a.mmd

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+
+# TMEM16 scramblases thin the membrane to enable lipid scrambling  
+
+Alessio Accardi ( \(\boxed{ \begin{array}{r l} \end{array} }\) ala2022@med.cornell.edu) Weill Cornell Medical College https://orcid.org/0000- 0002- 6584- 0102  
+
+Maria Falzone Weill Cornell Medical College  
+
+Zhang Feng Weill Cornell Medical College  
+
+Omar Alvarenga Weill Cornell Medical College  
+
+Yangang Pang Weill Cornell Medical College  
+
+Byoung Lee Cornell University  
+
+Xiaolu Cheng Cornell University https://orcid.org/0000- 0002- 2785- 6488  
+
+Eva Fortea Weill Cornell Medical College  
+
+Simon Scheuring Weill Cornell Medicine https://orcid.org/0000- 0003- 3534- 069X  
+
+## Article  
+
+Keywords: TMEM16 scramblases, lipid scrambling, membrane thinning  
+
+Posted Date: October 8th, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 955726/v1  
+
+License: \(\circledcirc\) 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 May 11th, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 30300- z.
+
+<--- Page Split --->
+
+# TMEM16 scramblases thin the membrane to enable lipid scrambling  
+
+Maria E. Falzone \(^{1,2}\) , Zhang Feng \(^{1}\) , Omar E. Alvarenga \(^{1,3}\) , Yangang Pang \(^{1}\) , ByoungCheol Lee \(^{1,\wedge}\) , Xiaolu Cheng \(^{4}\) , Eva Fortea \(^{1,3}\) , Simon Scheuring \(^{1}\) , Alessio Accardi \(^{1,2,4*}\)  
+
+1 Department of Anesthesiology, Weill Cornell Medical College; 2 Department of Biochemistry, Weill Cornell Medical College; 3 Physiology, Biophysics and Systems Biology Graduate Program, Weill Cornell Medical College; 4 Department of Physiology and Biophysics, Weill Cornell Medical College  
+
+\* correspondence to: ala2022@med.cornell.edu  
+
+\(^{\wedge}\) ByoungCheol Lee's present address: Neurovascular Unit Research Group, Korea Brain Research Institute (KBRI), Daegu 41062, Republic of Korea.
+
+<--- Page Split --->
+
+## Abstract  
+
+AbstractTMEM16 scramblases dissipate the plasma membrane lipid asymmetry to activate multiple eukaryotic cellular pathways. It was proposed that lipid headgroups move between leaflets through a membrane- spanning hydrophilic groove. Direct information on lipid- groove interactions is lacking. We report the 2.3 Å resolution cryoEM structure of the \(\mathrm{Ca^{2 + }}\) - bound afTMEM16 scramblase in nanodiscs showing how rearrangement of individual lipids at the open pathway results in pronounced membrane thinning. Only the groove’s intracellular vestibule contacts lipids, and mutagenesis suggests scrambling does not entail specific protein- lipid interactions with the extracellular vestibule. Further, we find scrambling can occur outside a closed groove in thinner membranes and is inhibited in thicker membranes despite an open pathway. Our results show how afTMEM16 thins the membrane to enable scrambling and that an open hydrophilic pathway is not a structural requirement to allow rapid transbilayer movement of lipids. This mechanism could be extended to other scramblases lacking a hydrophilic groove.
+
+<--- Page Split --->
+
+## Introduction  
+
+Biological membranes play a fundamental role in many cellular signaling pathways as they define the physical boundaries of cellular compartments and actively modulate the function of integral and membrane- associated proteins. In eukaryotic cells, the composition and distribution of the phospholipid constituents of the membrane is tightly regulated by the activity of a variety of dedicated enzymes, lipases, lipases and scramblases \(^{1}\) . The headgroup asymmetry of the plasma membrane is established by the action of ATP- driven pumps which distribute phosphatidylethanolamine (PE) and phosphatidylserine (PS) to the inner leaflet and phosphatidylcholine (PC) to the outer leaflet \(^{1}\) . Activated phospholipid scramblases dissipate this asymmetry and expose PS on the extracellular leaflet. This is critical for multiple signaling pathways, ranging from apoptosis to blood coagulation and cell- cell fusion \(^{1,2}\) . There are two known families of scramblases, the \(\mathrm{Ca}^{2 + }\) - activated TMEM16 \(^{3 - 5}\) and the caspase- activated Xk- related (Xkr) proteins \(^{6}\) . Lipid scrambling by the TMEM16's is of critical importance for a myriad of physiological processes, including blood coagulation, bone mineralization, membrane fusion and viral entry \(^{2,4,7}\) . Dysregulation of TMEM16 scramblase activity can have disastrous consequences, as both gain- and loss- of function mutations have been associated with disorders of blood, brain, bone and muscle \(^{3,8 - 11}\) . The TMEM16 superfamily is comprised of CI channels and dual function scramblases/non- selective ion channels \(^{4}\) . Both subtypes share a common homodimeric architecture where each monomer is comprised of 10 transmembrane (TM) helices \(^{12 - 18}\) (Fig. 1A- B). In each protomer, the TM3- TM7 helices form a hydrophilic permeation pathway, or groove, that can adopt multiple conformations to allow passage of ions, lipids or to prevent movement of both substrates \(^{15 - 19}\) .
+
+<--- Page Split --->
+
+Upon activation, the TMEM16 scramblases mediate rapid lipid movement between leaflets causing the membrane asymmetry to collapse and thus initiating signaling cascades. The mechanism underlying scrambling has been investigated at the functional, computational and structural levels \(^{3,8,15 - 32}\) . The consensus proposal is a 'credit- card' like mechanism \(^{33}\) , where the lipid headgroups penetrate and traverse the open hydrophilic groove while their tails remain embedded within the hydrocarbon core of the membrane \(^{20,25,28}\) . Within this framework, lipid scrambling is enabled by specific interactions of the permeating lipids with charged and polar groove- lining residues \(^{20,25,28}\) . However, TMEM16 scramblases do not discriminate among lipids such as PS, PE, PG, PC and DOTAP with headgroups of different charge, structure and size \(^{13,21,23,26}\) . Further, PE lipids conjugated to 5 kDa cargoes are also efficiently scrambled \(^{24}\) . These observations suggest that specific interactions between the groove and the scrambled lipids are not necessary. Notably, this lack of headgroup selectivity is also shared by other scramblases that lack an explicit hydrophilic groove, such as the GPCR opsin \(^{24,34}\) and XKR8 and 9 \(^{6,35,36}\) .  
+
+Moderate resolution structures of the fungal afTMEM16 and nhTMEM16 in nanodiscs showed these scramblases than the membrane near the groove \(^{15,17}\) , suggesting that membrane thinning at an open pathway might be important for lipid scrambling \(^{15}\) . Membrane thinning was also observed near the closed pathway of mTMEM16F, leading to the proposal that scrambling can also occur outside a closed groove \(^{16}\) . Thus, it is not clear whether an open hydrophilic groove is required for scrambling. Direct structural information on how TMEM16 scramblases interact with lipids is essential to elucidate the molecular mechanisms of lipid permeation.  
+
+Here we use cryogenic electron microscopy (cryoEM) to determine the 2.3 Å resolution structure of the afTMEM16 scramblase in lipid nanodiscs. Our structure allows the direct visualization of lipids associated with the protein at the open groove and reveals that afTMEM16
+
+<--- Page Split --->
+
+thins the membrane at the open pathway by \(\sim 50\%\) . The closest point of approach of the two membrane leaflets occurs near the wide intracellular vestibule of the groove, and no lipids could be resolved inside or interacting with the extracellular portion of the pathway. Mutagenesis of groove- lining residues does not perturb function, suggesting that specific interactions of permeating lipids with groove- lining residues are not essential for scrambling. We show that in thicker membranes scrambling is inhibited, while the groove remains in an open conformation. Conversely, in thinner membranes scrambling is enhanced although the groove is closed. Thus, lipid permeation is not always enabled by an open groove or prevented by a closed pathway. Based on these findings we propose that when the groove is open, the thinned membrane and the hydrophilic nature of the pathway synergistically lower the energy barrier for lipid scrambling. When the groove is closed, scrambling can occur, but at reduced rates in bilayers with plasma- membrane like thickness. In thinner membranes, closed- groove scrambling is enhanced allowing for lipid transport in the absence of \(\mathrm{Ca^{2 + }}\) .  
+
+## Results  
+
+## Structural basis of lipid reorganization by the afTMEM16 scramblase  
+
+To gain insight into how the afTMEM16 scramblase alters the organization of the membrane and interacts with the surrounding lipids we used cryo- EM to determine its structure in the \(\mathrm{Ca^{2 + }}\) - bound conformation in nanodiscs at 2.3 Å (Fig. 1, Supp. Fig. 1). Nanodiscs were comprised of a mixture of \(70\%\) 1,2- Dioleoyl- sn- glycero- 3- phosphocholine (DOPC, or 18:1 PC) and \(30\%\) 1,2- Dioleoyl- sn- Glycero- 3- Phosphatidylglycerol (DOPG, 18:1 PG), which we will refer to as C18 lipids. In these conditions, referred to as \(\mathrm{C18 / Ca^{2 + }}\) , afTMEM16 is maximally active \(^{15}\) , therefore we hypothesize this represents the active state of the scramblase. The present structure is nearly superimposable to
+
+<--- Page Split --->
+
+the previously determined \(\mathrm{Ca^{2 + }}\) - bound structure of afTMEM16 in 3 1- palmitoyl- 2- oleoyl- sn- glycero- 3- phosphoethanolamine (POPE): 1 1- palmitoyl- 2- oleoyl- sn- glycero- 3- phospho- (1'- racglycerol) POPG nanodiscs \(^{15}\) , \(\mathrm{Ca}\) rmsd \(\sim 0.8 \mathrm{\AA}\) , indicating that headgroup choice and acyl- chain saturation do not influence the conformation of the protein. The significantly improved resolution of the C18/Ca \(^{2 + }\) map allowed us to resolve 4 water molecules in the \(\mathrm{Ca^{2 + }}\) binding sites which coordinate two bound ions (Supp. Fig. 2B). The presence of these water molecules brings the coordination number of bound \(\mathrm{Ca^{2 + }}\) ions to 7 and 8, consistent with the high affinity of these sites \(^{26}\) (Supp. Fig. 2B). The map also contains non- protein densities that could be modeled as lipids associated with the protein (Fig. 1C- H, Supp. Fig. 2). To improve the quality of the density of the lipids near the pathway, we carried out symmetry expansion and additional rounds of 3D classification, which yielded one class with an additional four resolved lipids (Supp. Fig. 1E), for a total of 32 resolved lipids, 16 in each monomer (Fig. 1F- H, Supp. Fig. 2). The observed lipids define nearly continuous interfaces of the scramblase with the inner and outer membrane leaflets near the dimer interface (lipids D1- D9) and illustrate how the poses adopted by individual lipids result in the profound remodeling of the membrane induced by afTMEM16 near the lipid pathway (lipids P1- P7) (Fig. 1F- H).
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 Lipid-protein interactions in \(\mathbf{Ca^{2 + }}\) -bound afTMEM16. A: Structural model of afTMEM16 in \(0.5\mathrm{mM}\mathrm{Ca}^{2 + }\) in C18 lipid nanodiscs. B: View of the open permeation pathway. C-E: Unsharpened maps of the protein (grey) and associated lipids (red) viewed from the membrane </center>
+
+<--- Page Split --->
+
+plane (C), extracellular side (D) and close- up of the open groove (E). The map showing the density of the nanodisc membrane low- pass filtered to \(10 \mathrm{\AA}\) and shown in transparent red (C- D). F- H: Views of the afTMEM16 dimer from the plane of the membrane (F), extra- (G) and intra- cellular (H) sides with modeled lipids shown in stick representation. Lipids at the dimer interface are labeled D1- 9 and those at the permeation pathway are labeled P1- 7. Lipids from the inner and outer leaflets are colored in yellow and blue, respectively. The cytosolic domain of afTMEM16 was omitted for clarity. I: Close up view of the density map at the dimer interface showing the two afTMEM16 monomers (gray and cyan) and intercalated lipid tails (red). \* denotes the symmetry axis. J: The dimer interface salt bridge between TM9 and 10 (in cartoon representation) is formed by E618 and H619 (in stick representation) and is shielded from the intra- and extra- cellular solutions by lipids D3, D4, D6, and D7 (in spheres and colored as in F- H).  
+
+## Lipids form a cap around the transmembrane dimer interface  
+
+The transmembrane dimer interface of afTMEM16 is formed by the extracellular half of TM10 from each monomer (Fig. 1I- J, Supp. Fig. 2D- E). This minimal interface contains several hydrophobic residues and two membrane- embedded salt bridges formed by E618 and H619 of opposite subunits positioned \(\sim 1 / 3\) of the way through the membrane from the extracellular leaflet (Fig. 1I- J). In the \(\mathrm{C18 / Ca^{2 + }}\) structure, these salt bridges appear to be isolated from the intra- and extra- cellular solutions by eight well- defined lipids (D3, D4, D6 and D7 from each subunit), four above and four below the interacting residues (Fig. 1J). On the extracellular side, the D3 lipids from opposite subunits straddle the N terminal region of TM10 with their heads positioned by the side chains of C607 and W608 to make direct contact above the symmetry axis (Supp. Fig. 2D). A second lipid, D4, is wedged between TM9 and TM10 with its head coordinated by polar and charged residues in the TM9- 10 linker (N593, P598, T604 and R606; Supp. Fig. 2D). On the intracellular side, the heads of D6 from each subunit make contact across the symmetry axis and are wedged between the C- termini of the TM10s (Supp. Fig. 2E). They are coordinated by D571, G574 and W578 on the TM9 from one subunit and by R625, Y626 and R629 from TM10 on the other (Supp. Fig. 2E). Additionally, the head of D7 is coordinated by Y626, S630 and K634 from TM10 of one subunit and by Q364 on TM5 and D571 on TM9 from the opposite subunit (Supp.
+
+<--- Page Split --->
+
+Fig. 2E). The tails of these 8 lipids are accommodated in hydrophobic grooves between TM2, 9, 10 from both subunits (Fig. 1I, Supp. Fig. 2D- E). The intercalated organization of the lipid tails and helices gives rise to densely packed hydrophobic regions that shield the interacting E618 and H619 residues from water access, possibly strengthening their electrostatic interaction (Fig. 1J). These observations, together with the evolutionary conservation of the E618/H619 pair (Supp. Fig. 2C) and of the TMEM16 fold suggests these lipids might play a structural role in stabilizing the dimeric architecture of all TMEM16s.  
+
+## Structural basis of membrane thinning at the scrambling pathway  
+
+The C18/Ca \(^{2 + }\) structure reveals how the scramblase reorients the lipids that approach the open scrambling pathway (Fig. 1F, 2A). Near the dimer interface, the planes of the outer (OL) and inner (IL) leaflets are respectively defined by lipids D1- 4 and D8- 9, in good agreement with the outline visualized in the low pass filtered nanodisc map (Fig. 1C). The downward slope of the OL starts at D5, a well- defined PG lipid (Fig. 1F, 2B, Fig. Supp. 2A), and progresses towards the open groove as P1 and P2 adopt distorted poses with their headgroups becoming increasingly tilted (Fig. 2A- B). The IL bends upwards and P5- P7 become increasingly tilted as their heads climb around the intracellular portions of TM3 and TM4, coordinated by the hydrophilic side chains of T341, K345 and T334 (Fig. 2A,C). Within the pathway, P3 is sandwiched between TM4 and TM6 near the constriction formed by T325 and Y432 and its headgroup points towards the extracellular side such that it is contiguous to other OL lipids (Fig. 2A). The distance between the phosphate atoms of the headgroups of P3 and P4 in the OL and IL is \(< 22 \text{Å}\) (Fig. 2A), showing that the hydrocarbon core of the membrane is thinned by \(\sim 50\%\) at the open pathway. A similar thinning is seen in the low- pass filtered nanodiscs map near the pathway (Fig. 1C- D).
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Coordination of lipids outside the permeation pathway. A: View of the seven pathway lipids (in sticks, colored as in Fig. 1F). T325 and Y423 are shown as green sticks. Dashed arrow indicates the distance between the phosphate atoms of the last lipid from the inner (P4) and outer (P3) leaflets. B-C: Coordination of P1-P2 (B) and of P4-P7 (C). Side chains are shown in green sticks. D-E: forward \((\alpha)\) and reverse \((\beta)\) scrambling rate constants for indicated quadruple mutants of residues coordinating lipids outside the pathway (P1-2 and P4-7). Bars are average values for \(\alpha\) (black) and \(\beta\) (grey), error bars are S. Dev., and red circles are values from individual repeats. </center>  
+
+## Lipids outside the open pathway define the distorted membrane interface  
+
+The identification of sites where lipids bind at or near the open groove raises the possibility that scrambling could occur via a 'conveyor belt' mechanism, where lipids translocate between leaflets by moving from site to site. Alternatively, the observed lipids could define the protein- membrane boundary but not necessarily be translocated, with the possible exception of P3 within the pathway
+
+<--- Page Split --->
+
+(Fig. 2A). To distinguish between these hypotheses, we investigated how mutating residues coordinating the headgroups of P1- 2 and P4- 6 impacts scrambling. We found that mutations aimed at disrupting the headgroup interactions of P1- P2 (W202A/R427A/I431A/W529A), P4- P5- P6 (R279A/T334A/K345A/Y349A) or P2- P5- P6 (R279A/K345A/R427A/K428A) have minimal functional effects (Fig. 2D- E, Supp. Fig. 3). This suggests that these lipid association sites are not obligatory on the path taken by scrambled lipids. Rather, other factors, such as tail interactions with interhelical grooves, contribute to their association with afTMEM16 (Supp. Fig 2F- G) and stabilize the distorted membrane- protein interface that results in thinning at the pathway.  
+
+Scrambling does not require specific interactions with extracellular groove- lining residuesOne unexpected feature of our structure is that the extracellular vestibule of the groove does not directly interact with the membrane and no lipids could be resolved (Fig. 1C- D), as they traverse the groove below this region (Fig. 2A). We mutated side chains lining the extracellular vestibule or the central constriction of the groove and assessed their impact on scrambling. Single or multiple simultaneous alanine substitutions of I298, F302, E305 and E310 on TM3, of K317, Y319, F322, T325 and I332 on TM4, of T373 and S374 on TM5 and of R425, K428, Q429, Y432 and F433 on TM6 have no effects on lipid scrambling (Fig. 3, Supp. Fig. 3). Thus, scrambling does not entail specific interactions of lipids with residues lining the extracellular vestibule or the central constriction of the groove.  
+
+In contrast, the wide intracellular vestibule is embedded in the nanodisc membrane, and the resolved P3 and P4 lipids at the open pathway have opposite orientations (Fig. 2A). This suggests lipid headgroups only need to traverse the wide intracellular vestibule of the pathway, below the constriction formed by T325 and Y432 (Fig. 2A). The pronounced membrane thinning
+
+<--- Page Split --->
+
+at the pathway lowers the energy barrier for transbilayer lipid movement and the hydrophilic environment of the open groove allows water access to this thinned membrane region, synergistically lower the energy barrier for scrambling. Scrambling by afTMEM16 and hTMEM16K is modulated by lipid acyl chain length \(^{15,23}\) , supporting the idea that membrane thinning is critical for scrambling. Our proposal predicts that this modulation should reflect whether the scramblase can sufficiently thin these membranes, rather than arise from lipid-dependent changes in the conformation of the groove.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3. Functional role of groove-lining residues in lipid scrambling. A-C: Residues lining the extracellular vestibule (A), coordinating P3 (B) and lining the central constriction (C) are shown as green sticks. D-E: forward \((\alpha)\) and reverse \((\beta)\) scrambling rate constants of single and multiple alanine substitutions at the indicated positions. Bars are average values for \(\alpha\) (black) and \(\beta\) (grey), error bars are S. Dev., and red circles are values from individual repeats. </center>
+
+<--- Page Split --->
+
+## Regulation of lipid scrambling by membrane thickness  
+
+We measured how systematic variation of lipid acyl chain length affects lipid scrambling by afTMEM16. We kept the lipid headgroup composition at a constant ratio of 7 PC: 3 PG and used acyl chains with a single unsaturation and 16- 22 carbons, C16- C22 lipids (Table 1). Liposomes formed from this mix of 14:1 lipids were not stable in our scrambling assay (Supp Fig. 4C), therefore we generated thinner membranes using a mixture comprised of \(50\%\) 1,2- dimyristoyl- sn- glycero- 3- phosphocholine (DMPC) and 1,2- dimyristoyl- sn- glycero- 3- phospho- (1'-rac- glycerol) (DMPG) in a 7:3 ratio and \(50\%\) of POPC and POPG in a 7:3 ratio \(^{23}\) ; we will refer to this mix as C14 (Table 1). Atomic force microscopy (AFM) measurements show that membrane thickness varies between \(\sim 3.2 \mathrm{nm}\) and \(\sim 4.1 \mathrm{nm}\) , with near- linear scaling with acyl chain length (Table 1, Supp. Fig. 4A- B).  
+
+In the presence of saturating \(0.5 \mathrm{mM Ca^{2 + }}\) the scrambling rate constants do not depend on membrane thickness between \(\sim 3.2 \mathrm{nm}\) (C14 lipids) and \(\sim 3.9 \mathrm{nm}\) (C20 lipids) (Fig. 4A). In contrast, scrambling is nearly completely inhibited in C22 lipids (Fig. 4A) \(^{15}\) . Thus, in saturating \(\mathrm{Ca^{2 + }}\) there is chain length selectivity with a threshold for activity below membrane thickness of \(\sim 4.1 \mathrm{nm}\) . In contrast, in \(0 \mathrm{Ca^{2 + }}\) scrambling displays a nearly exponential inverse dependence on membrane thickness (Fig. 4B). Remarkably, in C14 lipid membranes scrambling by afTMEM16 is nearly \(\mathrm{Ca^{2 + }}\) - independent, with rate constants only \(\sim 3\) - fold lower in \(0 \mathrm{Ca^{2 + }}\) compared to the \(\sim 20\) - fold reduction seen in C18 membranes (Fig. 4A- B, Supp. Fig. 4). To test whether the long C22 acyl chains inhibit scrambling in saturating \(\mathrm{Ca^{2 + }}\) by occluding the pathway \(^{37}\) we measured scrambling in membranes formed by \(70\%\) C22 lipids and \(30\%\) C18 lipids, which are \(\sim 4 \mathrm{nm}\) thick (Table 1). In saturating \(\mathrm{Ca^{2 + }}\) scrambling activity is similar to that seen in \(100\%\) C18 lipids (Fig. 4A), while in \(0 \mathrm{Ca^{2 + }}\) there is a \(\sim 17\) - fold reduction, consistent with the reduction expected for membranes of
+
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+this thickness (Fig. 4B). This behavior does not depend on whether the mixed chain lengths were segregated by headgroup. Thus, the tails of C22 lipids are not ‘blockers’ of the afTMEM16 permeation pathway. These results suggest that in \(0 \mathrm{Ca}^{2 + }\) scrambling rates are proportional to the energetic cost of lipid headgroups crossing the hydrophobic core of the membrane, while in the presence of \(\mathrm{Ca}^{2 + }\) other factors contribute to scrambling.  
+
+## \(\mathrm{Ca}^{2 + }\) -bound afTMEM16 has an open groove in C22 membranes  
+
+To determine whether the C22 lipids inhibit scrambling by inducing groove closure we determined the cryo- EM structure of nanodisc- reconstituted afTMEM16 in the presence of saturating \(\mathrm{Ca}^{2 + }\) to 2.7 Å (Supp. Fig. 5A- G). Despite a \(\sim 500\) - fold reduction in scrambling activity the groove remains open in a conformation nearly identical to that seen in C18 lipids, \(\mathrm{Ca}\) r.m.s.d. \(\sim 0.35 \mathrm{\AA}\) (Fig. 4D). Importantly, neither the \(\mathrm{C18 / Ca}^{2 + }\) nor the \(\mathrm{C22 / Ca}^{2 + }\) datasets display structural heterogeneity as no additional classes could be identified using multiple rounds of iterative 3D classifications on afTMEM16 dimers and monomers using different classification parameters and software (see Methods, Supp. Fig. 1,5, 7, 8, 10). Further, The \(\mathrm{C22 / Ca}^{2 + }\) structure of afTMEM16 in the larger MSP2N2 nanodiscs at 3.5 Å resolution (Supp. Fig. 5H- N) shows an open permeation pathway in all 3D reconstructions, with \(\mathrm{Ca}\) r.m.s.d. \(\sim 0.5 \mathrm{\AA}\) to \(\mathrm{C18 / Ca}^{2 + }\) and \(\sim 0.4 \mathrm{\AA}\) to \(\mathrm{C22 / Ca}^{2 + }\) MSP1E3 (Fig. 4D). Thus, in afTMEM16 an open groove is not sufficient to enable lipid scrambling and nanodisc size does not influence the conformation.  
+
+In the \(\mathrm{C22 / Ca}^{2 + }\) maps we resolved several of the lipids near the dimer interface corresponding to D2, D3, D6, and D7 (in MSP1E3 map) and to D2 and D6 (in MSP2N2 map) seen in the \(\mathrm{C18 / Ca}^{2 + }\) map (Supp. Fig. 6). In the MSP1E3 map we detected strong density for P6 and P7, located near the intracellular loop connecting TM3 and TM4 (Supp. Fig. 6). However, despite
+
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+the high resolution of the \(\mathrm{C22 / Ca^{2 + }}\) MSP1E3 map, we detect only weak signals for lipids associated with the pathway- delimiting helices TM4 and TM6. This suggests that the interactions of C22 lipids with the pathway helices are weaker than those of C18 lipids, likely reflecting the higher energy cost associated with distorting these longer acyl chain lipids.  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Functional and structural regulation of lipid scrambling by membrane thickness. A-B: Forward \((\alpha ,\) black circles) and reverse \((\beta ,\) red circles) scrambling rate constants as a function of membrane thickness in the presence of \(0.5\mathrm{mM}\) (A) or \(0\mathrm{Ca}^{2 + }\) (B). Values are the mean and error bars represent standard deviation. Corresponding lipid compositions are noted above. C-E: Alignment of the permeation pathway of afTMEM16 in (C) C18 nanodiscs in \(0.5\mathrm{mM}\) (grey) or 0 </center>
+
+<--- Page Split --->
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+\(\mathrm{Ca}^{2 + }\) (pink), (D) in \(0.5\mathrm{mM}\mathrm{Ca}^{2 + }\) and C18 (grey) or C22 MSP1E3 nanodiscs (light pink) or C22 MSP2N2 nanodiscs (orange), (E) in \(0\mathrm{Ca}^{2 + }\) in C18 (red) and C14 nanodiscs (cyan).  
+
+## Scrambling in \(0\mathrm{Ca}^{2 + }\) does not require groove opening  
+
+These finding that an open groove is not sufficient to allow lipid movement raises the question of whether a closed groove prevents lipid scrambling entirely. Many proteins that scramble lipids lack explicit membrane- exposed hydrophilic grooves \(^{34 - 36,38}\) and most purified TMEM16's scramble lipids in \(0\mathrm{Ca}^{2 + }\) when the groove is predominantly closed (Fig. 4B) \(^{13,23,26}\) . This basal activity could reflect transient openings of the pathway, however an open groove \(\mathrm{Ca}^{2 + }\) - free conformation has not been observed in a membrane environment \(^{15 - 18}\) . Alternatively, these scramblases could thin the membrane enough to enable slow lipid scrambling outside of a closed groove, as proposed for the mammalian TMEM16F \(^{16}\) .  
+
+To elucidate the structural bases of scrambling in the absence of \(\mathrm{Ca}^{2 + }\) , we determined the 3.1 Å resolution structure of afTMEM16 in C18 lipids in \(0\mathrm{Ca}^{2 + }\) (Supp. Fig. 7). Extensive classification of afTMEM16 dimers and of symmetry- expanded monomers (see Methods) revealed only reconstructions corresponding to a closed groove conformation (Fig 4C, Supp. Fig. 7). However, in C18 lipids the basal scrambling activity of afTMEM16 is modest, \(\sim 4.5\%\) of that in saturating \(\mathrm{Ca}^{2 + }\) (Fig. 4A- B, Supp. Fig. 4), suggesting that the fraction of particles that could adopt a \(\mathrm{Ca}^{2 + }\) - free open groove conformation could be too small to be detected. In contrast, in C14 lipids scrambling in \(0\mathrm{Ca}^{2 + }\) is only \(\sim 3\) - fold slower than in saturating \(\mathrm{Ca}^{2 + }\) (Fig. 4A- B, Supp. Fig 4) so that a significant portion of the particles should adopt a \(\mathrm{Ca}^{2 + }\) - free open- groove conformation. Analysis of a C14/0 \(\mathrm{Ca}^{2 + }\) afTMEM16 dataset yields only classes with a closed groove (Fig. 4E), \(\mathrm{Ca}\) r.m.s.d. \(\sim 0.9\mathrm{\AA}\) to C18/0 \(\mathrm{Ca}^{2 + }\) , the highest of which reached 3.3 Å average resolution (Supp. Fig. 8). Thus, in \(0\mathrm{Ca}^{2 + }\) there is a \(\sim 30\) - fold increase in scrambling between C14 and C18 lipid
+
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+membranes that is not accompanied by an increase in the probability of opening of the groove. This suggests that the basal, \(\mathrm{Ca}^{2 + }\) independent activity is due to closed- groove scrambling.  
+
+This hypothesis is further supported by the analysis of the D511A/E514A mutant of afTMEM16 that disrupts the \(\mathrm{Ca}^{2 + }\) - binding site. This mutation impairs TMEM16 activity by preventing opening of the pathway \(^{8,26,39,40}\) and scrambles lipids in a \(\mathrm{Ca}^{2 + }\) - independent manner at rates comparable to those of the WT protein in \(0 \mathrm{Ca}^{2 + }\) . Scrambling by D511A/E514A afTMEM16 is modulated by membrane thickness like the WT protein in \(0 \mathrm{Ca}^{2 + }\) (Fig. 5A, Supp. Fig. 9), so that in C14 membranes its activity is \(\sim 30\%\) of that of the WT protein in C18 lipids and saturating \(\mathrm{Ca}^{2 + }\) . To test whether the D511A/E514A afTMEM16 adopts an open- pathway conformation in conditions of high activity, we determined its structure in C14 nanodiscs with 0.5 mM \(\mathrm{Ca}^{2 + }\) to 3.1 Å resolution (Supp. Fig. 10). As expected, despite the presence of 0.5 mM \(\mathrm{Ca}^{2 + }\) , the protein adopts the same conformation as in the WT apo structure and there is no density in the \(\mathrm{Ca}^{2 + }\) binding site. In all reconstructions the permeation pathway is closed, with \(\mathrm{Ca}\) r.m.s.d. \(\sim 1.1 \mathrm{\AA}\) to C18/0 \(\mathrm{Ca}^{2 + }\) and \(\sim 0.4 \mathrm{\AA}\) to C14/0 \(\mathrm{Ca}^{2 + }\) (Supp. Fig. 10), indicating that increased scrambling is not accompanied by higher open probability of the groove. Together, our results suggest that scrambling of afTMEM16 in \(0 \mathrm{Ca}^{2 + }\) occurs outside of a closed groove. Calcium- independent openings of the lipid permeation pathway, if they occur, are transient and cannot account for the observed increase in activity. Thus, an open groove is not necessary for lipid scrambling.  
+
+In the three datasets for apo afTMEM16 (C18/0 \(\mathrm{Ca}^{2 + }\) , C14/0 \(\mathrm{Ca}^{2 + }\) and DA/EA in 0.5 mM \(\mathrm{Ca}^{2 + }\) ) we could resolve 4- 9 lipids per monomer, all localized near the dimer interface in positions closely resembling those seen in C18/ \(\mathrm{Ca}^{2 + }\) structure (Supp. Fig. 11), supporting the notion that these lipids interact strongly with the protein. No lipids could be resolved near the closed pathway
+
+<--- Page Split --->
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+in these structures. The average resolution of these datasets is lower than that of the two \(\mathrm{Ca^{2 + }}\) - bound structures, preventing us from drawing mechanistic inferences from this observation.  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5. Functional and structural characterization of afTMEM16 D511A/E514A. A-B: Forward \((\alpha ,\) black circles) and reverse \((\beta ,\) red circles) scrambling rate constants of D511A/E514A afTMEM16 in \(0.5\mathrm{mM}\) (filled symbols) or \(0\mathrm{Ca}^{2 + }\) (empty symbols). Values are the mean and error bars represent standard deviation. Corresponding lipid compositions are noted above. B: Alignment of afTMME16 D511A/E514A in the presence of \(\mathrm{Ca^{2 + }}\) (green) in C14 lipids with wildtype afTMEM16 in \(0\mathrm{Ca}^{2 + }\) in C18 lipids (grey) with close up view of the permeation pathway. </center>  
+
+## Scrambling activity correlates with membrane thinning at the pathway  
+
+Our proposal that afTMEM16 enables scrambling by thinning the membrane at the permeation pathway predicts there should be a correlation between thinning and function. Although a quantitative evaluation of thinning is precluded by the different resolutions of the maps, a qualitative analysis of the nanodisc density maps supports this notion (Fig. 6). Far from the protein, membrane thickness of C14, C18 and C22 nanodiscs is comparable to that determined by AFM (Table 1). Near the open groove, in the \(\mathrm{C18 / Ca^{2 + }}\) map the membrane appears significantly thinned (Fig. 6B), closely tracking the position of individual lipids (Fig. 2A). Thinning is reduced near the open pathway of the \(\mathrm{C22 / Ca^{2 + }}\) map (Fig. 6A) and near the closed pathway of the \(\mathrm{C18 / 0 Ca^{2 + }}\) map (Fig. 6C), consistent with the reduced scrambling activity (Fig. 4A-B). In the \(\mathrm{C14 / 0 Ca^{2 + }}\) map, thickness at the closed pathway qualitatively approaches that at the open pathway of the \(\mathrm{C18 / Ca^{2 + }}\)
+
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+map (Fig. 6D), consistent with enhanced scrambling (Fig. 4B). These qualitative observations suggest there is a direct correlation between the thickness of the membrane near the pathway and scrambling activity. This supports the idea that in C22 membranes scrambling could be inhibited because of the reduced thinning despite an open groove, and that the closed groove conformation of afTMEM16 is scrambling competent because it thins the membrane enough to enable lipid flipping.  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6. Membrane thinning at the afTMEM16 pathway as a function of acyl chain length. A-D: Views of the density maps for afTMEM16 in C22/Ca \(^{2 + }\) (A), C18/Ca \(^{2 + }\) (B), C18/0 Ca \(^{2 + }\) (C) and C14/0 Ca \(^{2 + }\) (D) from the extracellular (top panels) and intracellular (bottom panel) side. The C1 final unsharpened maps containing nanodisc densities were aligned, resampled on the same grid, and colored according to the Z coordinate using UCSF Chimera. The density corresponding to the protein is segmented and shown in gray. Nanodisc densities are colored by displacement along the Z axis and the 0 Å reference height is the same for all structures in each view. Negative values represent membrane thinning relative to the overall nanodisc. The position of the permeation pathway is denoted with arrows. </center>  
+
+## Discussion  
+
+Activation of scramblases catalyzes the rapid movement of phospholipids between membrane leaflets and results in the externalization of charged and polar lipids that trigger a variety of
+
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+fundamental physiological processes \(^{1,2,4}\) . The current consensus is that TMEM16 scramblases mediate lipid transport via a credit- card like mechanism \(^{33}\) , with the headgroups forming specific interactions with polar and charged residues lining the full length of the hydrophilic groove \(^{20,23,25,28}\) . This predicts that scramblases should discriminate among lipids based on their headgroups but not their tails, and that mutations of groove- lining residues should affect lipid scrambling. Notably, neither scramblases like the TMEM16's \(^{13,18,21,24,26}\) or the Xkr's \(^{6,41}\) nor GPCR's moonlighting as scramblases \(^{34}\) , show selectivity among lipids with different headgroups. Further, both the Xkr's and GPCR's lack explicit hydrophilic grooves \(^{34- 36}\) , bringing the structural requisites of the credit card mechanism into question. However, the modes of lipid- protein interactions of TMEM16 scramblases had not been structurally resolved \(^{15- 18}\) .  
+
+Here, we combined structural and functional experiments to investigate the mechanism of lipid scrambling by the TMEM16's. The 2.3 Å structure of afTMEM16 reconstituted in C18 nanodiscs shows how individual lipids interact with the scramblase to define the thinned and distorted profile of the membrane near the open pathway (Fig. 1C- H). Lipids mainly localize to the periphery of the groove, interacting with the intracellular portions of TM3- 4 and with the extracellular portions of TM6- 7. The position of the last lipids from the intra- and extra- cellular leaflets suggests that headgroup flipping occurs in the intracellular vestibule. No density for lipids was visible near the extracellular vestibule (Fig. 1, 2A) and mutations of residues lining this narrow constriction or the groove interior have no functional effects (Fig. 2, 3). Reconstituting afTMEM16 in membranes formed from lipids with longer acyl chains dramatically inhibits scrambling although the groove remains open (Fig. 4). Conversely, reconstitution in thinner membranes facilitates scrambling even when the groove is closed (Fig. 4- 5).
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+Together, these results have three important implications; first, lipid scrambling does not entail specific interactions with the groove's hydrophilic interior or its extracellular vestibule. Second, acyl chains rather than headgroups are key determinants of scrambling activity (Fig. 4A- B). Third, an open groove is neither sufficient nor necessary for scrambling (Fig. 4, 5). These findings are inconsistent with a credit- card mechanism. Rather, we propose that lipid scrambling is primarily determined by the ability of afTMEM16 to thin the membrane near the pathway, so that lipids only interact with the surface of the groove without penetrating deep within its narrow and hydrophilic interior (Fig. 7). The membrane- thinning mechanism readily explains evolutionarily conserved properties of TMEM16 scramblases that are difficult to reconcile with the credit card mechanism, such as the lack of discrimination based on headgroup size, chemistry or charge \(^{13,18,21,23,26,42}\) and scrambling of lipids conjugated to large cargoes \(^{24}\) . Thus, we propose this mechanism applies to other TMEM16's.  
+
+Two lines of evidence support the credit card hypothesis: mutating groove- lining residues impairs lipid scrambling by nhTMEM16 and TMEM16F \(^{25,28}\) and MD simulations show lipid headgroups penetrating and traversing the whole length of the groove \(^{20,23,25,28,43,44}\) . Strikingly we find that mutating similar residues in afTMEM16 does not impair scrambling (Fig. 2,3). This contradiction could be explained if the mutants impair scrambling by favoring groove closure rather than by impairing lipid movement through an open groove. In afTMEM16 only the \(\mathrm{Ca^{2 + }}\) - bound open conformation has been observed \(^{15}\) (Fig. 1, 4). In contrast, \(\mathrm{Ca^{2 + }}\) - bound nhTMEM16 adopts both open and closed groove conformations \(^{17}\) and in mTMEM16F only the \(\mathrm{Ca^{2 + }}\) - bound closed groove conformation has been observed \(^{16,18}\) , suggesting in these homologues the \(\mathrm{Ca^{2 + }}\) - bound open conformation is less stable than in afTMEM16. Further, several scrambling- incompetent nhTMEM16 mutants retain measurable channel activity \(^{25}\) , suggesting stabilization
+
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+of an ion channel- like groove conformation \(^{19}\) . Discrepancies with molecular dynamics simulations could be due to incomplete relaxation of the membrane during the equilibration, especially if the chosen initial conditions for the protein- lipid arrangements are far from equilibrium. Indeed, recent work suggests extended equilibration protocols are needed to capture the full extent of membrane deformations induced by some proteins \(^{45}\) . Further, our structures show several lipids with tails tightly intercalated with TM helices at the dimer cavity (Fig. 1) that might affect the dynamic rearrangements of afTMEM16 in MD simulations. It will be interesting to see how incorporating new information on the modes of lipid interactions with the afTMEM16 scramblase affects these results.  
+
+The implications of our proposed membrane- thinning mechanism for scrambling (Fig. 7) can be appreciated if we make the simplifying assumptions that (i) the energy barrier for lipid scrambling is due to the polar head and (ii) that the head can be modeled with a sphere of radius \(r\) and charge \(q\) , then the energy barrier for scrambling, \(\Delta G_{scramb}\) would be given by \(^{46}\)  
+
+\[\Delta G_{scramb} = \frac{q^{2}}{2\epsilon_{m}r} -\frac{q^{2}}{\epsilon_{m}L} ln\left(\frac{2\epsilon_{w}}{\epsilon_{m} + \epsilon_{w}}\right)\]  
+
+Where \(\epsilon_{\mathrm{m,w}}\) are the dielectric constants of the membrane and of water and L is the thickness of the membrane. Membrane thinning decreases \(\Delta G_{scramb}\) as L is reduced and the dielectric constant \(\epsilon_{\mathrm{m}}\) is increased because of higher water access to the hydrocarbon core of the membrane \(^{47}\) . When the pathway is open scrambling is fast because thinning is pronounced, and the hydrophilic interior of the open groove further decreases \(\epsilon_{\mathrm{m}}\) (Fig. 7A). In thicker or more rigid membranes (Fig. 4) \(^{15}\) , scrambling is impaired because their deformation cost is higher thus preventing lipids to reach positions conducive to scrambling (Fig. 7B). When the groove is closed membrane thinning is diminished, but not absent, which allows for slow scrambling activity (Fig. 7C), that is enhanced in membranes formed from shorter chain length lipids (Fig. 7D). Notably, the proposed membrane
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+thinning mechanism could naturally explain how proteins lacking hydrophilic grooves, such as GPCR's and Xkr's, can scramble lipids and share functional properties with the structurally unrelated TMEM16's \(^{24,34 - 36,38,48}\) .  
+
+![](images/Figure_7.jpg)
+
+<center>Figure 7. TMEM16 scramblases enable scrambling by thinning the membrane. A-D: Schematic representation of the open (A-B, colored in green) and closed pathways (C-D, colored in red) in membranes of different thickness. Cyan denotes regions accessible to water. Arrows denote high (solid line), low (dashed line) or no (no line) scrambling. </center>  
+
+In sum, our results support a mechanism where during scrambling, lipids interact with the surface of the groove without having to penetrate and interact with its narrow and hydrophilic interior. Scrambling by the TMEM16's is modulated by two signals, binding of \(\mathrm{Ca}^{2 + }\) facilitates opening of the groove while the properties of the membrane determine whether the scramblase can thin the membrane enough to enable lipid flipping. This dual control of scrambling activity, by ligand binding and membrane properties, could constitute a secondary layer of regulation that
+
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+prevents undesired lipid flipping by the TMEM16's during fluctuations in cellular cytosolic \(\mathrm{Ca}^{2 + }\) levels or when family members that reside in intracellular membranes are transiently localized to the plasma membrane. Similarly, rigidifying or thickening bilayer constituents, such as cholesterol, could silence the scrambling activity of other scramblases such as GPCR's in cellular membranes.
+
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+## Data Availability  
+
+Data AvailabilityAll constructs are available on request. All models and associated cryoEM maps have been deposited into the Electron Microscopy Data Bank (EMDB) and the Protein Data Bank (PDB). The depositions include final maps, unsharpened maps, and associated FSC curves.  
+
+Table 5: Data Availability   
+
+<table><tr><td>Structure</td><td>PDB</td><td>EMDB</td></tr><tr><td>C18/Ca2+ dimer</td><td>7RXH</td><td>EMD-24730</td></tr><tr><td>C18/Ca2+ monomer</td><td>7RXG</td><td>EMD-24731</td></tr><tr><td>C22/Ca2+ MSP1E3</td><td>7RX2</td><td>EMD-24722</td></tr><tr><td>C22/Ca2+ MSP2N2</td><td>7RWJ</td><td>EMD-24717</td></tr><tr><td>C18/0Ca2+</td><td>7RXB</td><td>EMD-24727</td></tr><tr><td>C14/0Ca2+</td><td>7RX3</td><td>EMD-24723</td></tr><tr><td>D511A/E514A C14/Ca2+</td><td>7RXA</td><td>EMD-24726</td></tr></table>  
+
+## Acknowledgements  
+
+AcknowledgementsThe authors thank members of the Accardi lab and Richard Hite for helpful discussions. The work was supported by National Institutes of Health (NIH) Grant R01GM106717 (to A.A.), by a Margaret and Herman Sokol Fellowship from Weill Cornell Medicine (M.E.F.), by the KBRI Basic Research Program through Korea Brain Research Institute funded by Ministry of Science and ICT (21- BR- 01- 08 to B.- C. L.) and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1C1C1002699 to B.- C. L.). Some of this work was performed at the Simons Electron Microscopy Center and National Resource for Automated Molecular Microscopy located at the New York Structural Biology Center, supported by grants from the Simons Foundation (SF349247), NYSTAR, and the NIH National Institute of General Medical Sciences (GM103310). Part of the work was performed at the Cryo- EM Core Facility at University of Massachusetts Chan Medical School with the help of Dr. Kangkang Song and Dr. Chen Xu. Initial screening was performed at NYU Langone Health's Cryo- Electron Microscopy Laboratory (RRID: SCR_019202).
+
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+## Author contributions  
+
+M.F., Z.F. and A.A. designed the experiments; M.F., Z.F., O.E.A., Y.P. and B.- C.L. performed experiments; M.F., Z.F., O.E.A., Y.P., B.- C.L., X.C., E.F., S.S. and A.A. analyzed the data; M.F., S.S. and A.A. wrote the paper. All authors edited the manuscript.  
+
+## Competing Interests statement  
+
+The authors declare no competing interests.
+
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+## References
+
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+37 Khelashvili, G. et al. Membrane lipids are both the substrates and a mechanistically responsive environment of TMEM16 scramblase proteins. Journal of computational chemistry 41, 538- 551, doi:10.1002/jcc.26105 (2020).38 Goren, M. A. et al. Constitutive phospholipid scramblase activity of a G protein- coupled receptor. Nat Commun 5, 5115, doi:10.1038/ncomms6115 (2014).39 Yu, K., Duran, C., Qu, Z., Cui, Y.- Y. & Hartzell, H. C. Explaining Calcium- Dependent Gating of Anoctamin- 1 Chloride Channels Requires a Revised Topology. Circulation Research 110, 990- 999, doi:10.1161/CIRCRESAHA.112.264440 (2012).40 Tien, J. et al. A comprehensive search for calcium binding sites critical for TMEM16A calcium- activated chloride channel activity. Elife, e02772, doi:10.7554/eLife.02772 (2014).41 Suzuki, J., Imanishi, E. & Nagata, S. Xkr8 phospholipid scrambling complex in apoptotic phosphatidylserine exposure. Proc Natl Acad Sci USA 113, 9509- 9514 (2016).42 Watanabe, R., Sakuragi, T., Noji, H. & Nagata, S. Single- molecule analysis of phospholipid scrambling by TMEM16F. Proceedings of the National Academy of Sciences 115, 3066- 3071, doi:10.1073/pnas.1717956115 (2018).43 Stansfeld, P. J. et al. MemProtMD: automated insertion of membrane protein structures into explicit lipid membranes. Structure 23, 1350- 1361, doi:10.1016/j.str.2015.05.006 (2015).44 Kostritskii, A. Y. & Machtens, J.- P. Molecular mechanisms of ion conduction and ion selectivity in TMEM16 lipid scramblases. Nature Communications 12, 2826, doi:10.1038/s41467- 021- 22724- w (2021).45 Stix, R., Song, J., Banerjee, A. & Faraldo- Gómez, J. D. DHHC20 Palmitoyl- Transferase Reshapes the Membrane to Foster Catalysis. Biophys J 118, 980- 988, doi:10.1016/j.bpj.2019.11.003 (2020).46 Parsegian, A. Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature 221, 844- 846, doi:10.1038/221844a0 (1969).47 Bennett, W. F. D. & Tieleman, D. P. The Importance of Membrane Defects—Lessons from Simulations. Accounts of Chemical Research 47, 2244- 2251, doi:10.1021/ar4002729 (2014).48 Wang, L. et al. Scrambling of natural and fluorescently tagged phosphatidylinositol by reconstituted G protein- coupled receptor and TMEM16 scramblases. Journal of Biological Chemistry 293, 18318- 18327, doi:10.1074/jbc.RA118.004213 (2018).
+
+<--- Page Split --->
+
+
+<table><tr><td>Name</td><td>Lipid Component Chain Length (70% PC:30%PG)</td><td>Height from AFM (nm)</td><td>Height estimated from EM maps (nm)</td></tr><tr><td>C14</td><td>50% 14:0, 50% 16:0-18:1</td><td>3.2 ± 0.29</td><td>3.0 ± 1.5</td></tr><tr><td>C16</td><td>100% 16:1</td><td>3.2 ± 0.22</td><td>N.d.</td></tr><tr><td rowspan="2">C18</td><td rowspan="2">100% 18:1</td><td rowspan="2">3.4 ± 0.19</td><td>(0 Ca2+) 3.1 ± 3.5</td></tr><tr><td>(0.5 mM Ca2+) 3.3 ± 0.95</td></tr><tr><td>C20</td><td>100% 20:1</td><td>3.7 ± 0.22</td><td>N.d.</td></tr><tr><td>70% C22</td><td>70% 22:1, 30% 18:1</td><td>4.0 ± 0.26</td><td>N.d.</td></tr><tr><td>70% C22</td><td>70% 22:1 PC, 30% 18:1 PG</td><td>4.0 ± 0.19</td><td>N.d.</td></tr><tr><td>C22</td><td>100% 22:1</td><td>4.1 ± 0.19</td><td>3.9 ± 0.85</td></tr></table>
+
+Table 1: AFM and cryoEM determination of membrane thickness for considered lipid compositions. Heights were estimated using AFM tomography, reported values indicate the peak FWHH ± of the value distribution (see Supp. Fig. 4A-B and Methods). For cryoEM membrane height was determined from C1 unsharpened EM maps using the difference in z coordinate for the inner and outer leaflet at (x,y) far from the protein. Reported values are the average ± S.Dev of 3 different points. N.d. indicates compositions for which no cryoEM data was determined.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- FalzoneetalSI.pdf- FalzoneetalMethods.pdf- Falzonenrreportingsummary.pdf- nreditorialpolicychecklist.pdf- FalzoneetalValidationReports.pdf
+
+<--- Page Split --->

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+<|ref|>title<|/ref|><|det|>[[44, 107, 950, 177]]<|/det|>
+# TMEM16 scramblases thin the membrane to enable lipid scrambling  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 666, 238]]<|/det|>
+Alessio Accardi ( \(\boxed{ \begin{array}{r l} \end{array} }\) ala2022@med.cornell.edu) Weill Cornell Medical College https://orcid.org/0000- 0002- 6584- 0102  
+
+<|ref|>text<|/ref|><|det|>[[44, 243, 310, 283]]<|/det|>
+Maria Falzone Weill Cornell Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 290, 310, 330]]<|/det|>
+Zhang Feng Weill Cornell Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 336, 310, 376]]<|/det|>
+Omar Alvarenga Weill Cornell Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 382, 310, 422]]<|/det|>
+Yangang Pang Weill Cornell Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 428, 208, 468]]<|/det|>
+Byoung Lee Cornell University  
+
+<|ref|>text<|/ref|><|det|>[[44, 474, 566, 515]]<|/det|>
+Xiaolu Cheng Cornell University https://orcid.org/0000- 0002- 2785- 6488  
+
+<|ref|>text<|/ref|><|det|>[[44, 521, 310, 561]]<|/det|>
+Eva Fortea Weill Cornell Medical College  
+
+<|ref|>text<|/ref|><|det|>[[44, 567, 608, 608]]<|/det|>
+Simon Scheuring Weill Cornell Medicine https://orcid.org/0000- 0003- 3534- 069X  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 650, 102, 667]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 687, 660, 707]]<|/det|>
+Keywords: TMEM16 scramblases, lipid scrambling, membrane thinning  
+
+<|ref|>text<|/ref|><|det|>[[44, 725, 313, 744]]<|/det|>
+Posted Date: October 8th, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 763, 463, 782]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 955726/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 801, 910, 844]]<|/det|>
+License: \(\circledcirc\) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 879, 909, 922]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on May 11th, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 30300- z.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[207, 194, 789, 213]]<|/det|>
+# TMEM16 scramblases thin the membrane to enable lipid scrambling  
+
+<|ref|>text<|/ref|><|det|>[[120, 296, 875, 353]]<|/det|>
+Maria E. Falzone \(^{1,2}\) , Zhang Feng \(^{1}\) , Omar E. Alvarenga \(^{1,3}\) , Yangang Pang \(^{1}\) , ByoungCheol Lee \(^{1,\wedge}\) , Xiaolu Cheng \(^{4}\) , Eva Fortea \(^{1,3}\) , Simon Scheuring \(^{1}\) , Alessio Accardi \(^{1,2,4*}\)  
+
+<|ref|>text<|/ref|><|det|>[[113, 540, 885, 667]]<|/det|>
+1 Department of Anesthesiology, Weill Cornell Medical College; 2 Department of Biochemistry, Weill Cornell Medical College; 3 Physiology, Biophysics and Systems Biology Graduate Program, Weill Cornell Medical College; 4 Department of Physiology and Biophysics, Weill Cornell Medical College  
+
+<|ref|>text<|/ref|><|det|>[[113, 750, 493, 769]]<|/det|>
+\* correspondence to: ala2022@med.cornell.edu  
+
+<|ref|>text<|/ref|><|det|>[[113, 820, 819, 875]]<|/det|>
+\(^{\wedge}\) ByoungCheol Lee's present address: Neurovascular Unit Research Group, Korea Brain Research Institute (KBRI), Daegu 41062, Republic of Korea.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 91, 191, 108]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[112, 123, 886, 530]]<|/det|>
+AbstractTMEM16 scramblases dissipate the plasma membrane lipid asymmetry to activate multiple eukaryotic cellular pathways. It was proposed that lipid headgroups move between leaflets through a membrane- spanning hydrophilic groove. Direct information on lipid- groove interactions is lacking. We report the 2.3 Å resolution cryoEM structure of the \(\mathrm{Ca^{2 + }}\) - bound afTMEM16 scramblase in nanodiscs showing how rearrangement of individual lipids at the open pathway results in pronounced membrane thinning. Only the groove’s intracellular vestibule contacts lipids, and mutagenesis suggests scrambling does not entail specific protein- lipid interactions with the extracellular vestibule. Further, we find scrambling can occur outside a closed groove in thinner membranes and is inhibited in thicker membranes despite an open pathway. Our results show how afTMEM16 thins the membrane to enable scrambling and that an open hydrophilic pathway is not a structural requirement to allow rapid transbilayer movement of lipids. This mechanism could be extended to other scramblases lacking a hydrophilic groove.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[114, 90, 224, 108]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[112, 120, 886, 844]]<|/det|>
+Biological membranes play a fundamental role in many cellular signaling pathways as they define the physical boundaries of cellular compartments and actively modulate the function of integral and membrane- associated proteins. In eukaryotic cells, the composition and distribution of the phospholipid constituents of the membrane is tightly regulated by the activity of a variety of dedicated enzymes, lipases, lipases and scramblases \(^{1}\) . The headgroup asymmetry of the plasma membrane is established by the action of ATP- driven pumps which distribute phosphatidylethanolamine (PE) and phosphatidylserine (PS) to the inner leaflet and phosphatidylcholine (PC) to the outer leaflet \(^{1}\) . Activated phospholipid scramblases dissipate this asymmetry and expose PS on the extracellular leaflet. This is critical for multiple signaling pathways, ranging from apoptosis to blood coagulation and cell- cell fusion \(^{1,2}\) . There are two known families of scramblases, the \(\mathrm{Ca}^{2 + }\) - activated TMEM16 \(^{3 - 5}\) and the caspase- activated Xk- related (Xkr) proteins \(^{6}\) . Lipid scrambling by the TMEM16's is of critical importance for a myriad of physiological processes, including blood coagulation, bone mineralization, membrane fusion and viral entry \(^{2,4,7}\) . Dysregulation of TMEM16 scramblase activity can have disastrous consequences, as both gain- and loss- of function mutations have been associated with disorders of blood, brain, bone and muscle \(^{3,8 - 11}\) . The TMEM16 superfamily is comprised of CI channels and dual function scramblases/non- selective ion channels \(^{4}\) . Both subtypes share a common homodimeric architecture where each monomer is comprised of 10 transmembrane (TM) helices \(^{12 - 18}\) (Fig. 1A- B). In each protomer, the TM3- TM7 helices form a hydrophilic permeation pathway, or groove, that can adopt multiple conformations to allow passage of ions, lipids or to prevent movement of both substrates \(^{15 - 19}\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 528]]<|/det|>
+Upon activation, the TMEM16 scramblases mediate rapid lipid movement between leaflets causing the membrane asymmetry to collapse and thus initiating signaling cascades. The mechanism underlying scrambling has been investigated at the functional, computational and structural levels \(^{3,8,15 - 32}\) . The consensus proposal is a 'credit- card' like mechanism \(^{33}\) , where the lipid headgroups penetrate and traverse the open hydrophilic groove while their tails remain embedded within the hydrocarbon core of the membrane \(^{20,25,28}\) . Within this framework, lipid scrambling is enabled by specific interactions of the permeating lipids with charged and polar groove- lining residues \(^{20,25,28}\) . However, TMEM16 scramblases do not discriminate among lipids such as PS, PE, PG, PC and DOTAP with headgroups of different charge, structure and size \(^{13,21,23,26}\) . Further, PE lipids conjugated to 5 kDa cargoes are also efficiently scrambled \(^{24}\) . These observations suggest that specific interactions between the groove and the scrambled lipids are not necessary. Notably, this lack of headgroup selectivity is also shared by other scramblases that lack an explicit hydrophilic groove, such as the GPCR opsin \(^{24,34}\) and XKR8 and 9 \(^{6,35,36}\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 541, 886, 771]]<|/det|>
+Moderate resolution structures of the fungal afTMEM16 and nhTMEM16 in nanodiscs showed these scramblases than the membrane near the groove \(^{15,17}\) , suggesting that membrane thinning at an open pathway might be important for lipid scrambling \(^{15}\) . Membrane thinning was also observed near the closed pathway of mTMEM16F, leading to the proposal that scrambling can also occur outside a closed groove \(^{16}\) . Thus, it is not clear whether an open hydrophilic groove is required for scrambling. Direct structural information on how TMEM16 scramblases interact with lipids is essential to elucidate the molecular mechanisms of lipid permeation.  
+
+<|ref|>text<|/ref|><|det|>[[113, 784, 885, 876]]<|/det|>
+Here we use cryogenic electron microscopy (cryoEM) to determine the 2.3 Å resolution structure of the afTMEM16 scramblase in lipid nanodiscs. Our structure allows the direct visualization of lipids associated with the protein at the open groove and reveals that afTMEM16
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 530]]<|/det|>
+thins the membrane at the open pathway by \(\sim 50\%\) . The closest point of approach of the two membrane leaflets occurs near the wide intracellular vestibule of the groove, and no lipids could be resolved inside or interacting with the extracellular portion of the pathway. Mutagenesis of groove- lining residues does not perturb function, suggesting that specific interactions of permeating lipids with groove- lining residues are not essential for scrambling. We show that in thicker membranes scrambling is inhibited, while the groove remains in an open conformation. Conversely, in thinner membranes scrambling is enhanced although the groove is closed. Thus, lipid permeation is not always enabled by an open groove or prevented by a closed pathway. Based on these findings we propose that when the groove is open, the thinned membrane and the hydrophilic nature of the pathway synergistically lower the energy barrier for lipid scrambling. When the groove is closed, scrambling can occur, but at reduced rates in bilayers with plasma- membrane like thickness. In thinner membranes, closed- groove scrambling is enhanced allowing for lipid transport in the absence of \(\mathrm{Ca^{2 + }}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 578, 179, 595]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 611, 703, 632]]<|/det|>
+## Structural basis of lipid reorganization by the afTMEM16 scramblase  
+
+<|ref|>text<|/ref|><|det|>[[113, 646, 886, 876]]<|/det|>
+To gain insight into how the afTMEM16 scramblase alters the organization of the membrane and interacts with the surrounding lipids we used cryo- EM to determine its structure in the \(\mathrm{Ca^{2 + }}\) - bound conformation in nanodiscs at 2.3 Å (Fig. 1, Supp. Fig. 1). Nanodiscs were comprised of a mixture of \(70\%\) 1,2- Dioleoyl- sn- glycero- 3- phosphocholine (DOPC, or 18:1 PC) and \(30\%\) 1,2- Dioleoyl- sn- Glycero- 3- Phosphatidylglycerol (DOPG, 18:1 PG), which we will refer to as C18 lipids. In these conditions, referred to as \(\mathrm{C18 / Ca^{2 + }}\) , afTMEM16 is maximally active \(^{15}\) , therefore we hypothesize this represents the active state of the scramblase. The present structure is nearly superimposable to
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 81, 886, 636]]<|/det|>
+the previously determined \(\mathrm{Ca^{2 + }}\) - bound structure of afTMEM16 in 3 1- palmitoyl- 2- oleoyl- sn- glycero- 3- phosphoethanolamine (POPE): 1 1- palmitoyl- 2- oleoyl- sn- glycero- 3- phospho- (1'- racglycerol) POPG nanodiscs \(^{15}\) , \(\mathrm{Ca}\) rmsd \(\sim 0.8 \mathrm{\AA}\) , indicating that headgroup choice and acyl- chain saturation do not influence the conformation of the protein. The significantly improved resolution of the C18/Ca \(^{2 + }\) map allowed us to resolve 4 water molecules in the \(\mathrm{Ca^{2 + }}\) binding sites which coordinate two bound ions (Supp. Fig. 2B). The presence of these water molecules brings the coordination number of bound \(\mathrm{Ca^{2 + }}\) ions to 7 and 8, consistent with the high affinity of these sites \(^{26}\) (Supp. Fig. 2B). The map also contains non- protein densities that could be modeled as lipids associated with the protein (Fig. 1C- H, Supp. Fig. 2). To improve the quality of the density of the lipids near the pathway, we carried out symmetry expansion and additional rounds of 3D classification, which yielded one class with an additional four resolved lipids (Supp. Fig. 1E), for a total of 32 resolved lipids, 16 in each monomer (Fig. 1F- H, Supp. Fig. 2). The observed lipids define nearly continuous interfaces of the scramblase with the inner and outer membrane leaflets near the dimer interface (lipids D1- D9) and illustrate how the poses adopted by individual lipids result in the profound remodeling of the membrane induced by afTMEM16 near the lipid pathway (lipids P1- P7) (Fig. 1F- H).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[202, 80, 789, 840]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 850, 884, 905]]<|/det|>
+<center>Figure 1 Lipid-protein interactions in \(\mathbf{Ca^{2 + }}\) -bound afTMEM16. A: Structural model of afTMEM16 in \(0.5\mathrm{mM}\mathrm{Ca}^{2 + }\) in C18 lipid nanodiscs. B: View of the open permeation pathway. C-E: Unsharpened maps of the protein (grey) and associated lipids (red) viewed from the membrane </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 282]]<|/det|>
+plane (C), extracellular side (D) and close- up of the open groove (E). The map showing the density of the nanodisc membrane low- pass filtered to \(10 \mathrm{\AA}\) and shown in transparent red (C- D). F- H: Views of the afTMEM16 dimer from the plane of the membrane (F), extra- (G) and intra- cellular (H) sides with modeled lipids shown in stick representation. Lipids at the dimer interface are labeled D1- 9 and those at the permeation pathway are labeled P1- 7. Lipids from the inner and outer leaflets are colored in yellow and blue, respectively. The cytosolic domain of afTMEM16 was omitted for clarity. I: Close up view of the density map at the dimer interface showing the two afTMEM16 monomers (gray and cyan) and intercalated lipid tails (red). \* denotes the symmetry axis. J: The dimer interface salt bridge between TM9 and 10 (in cartoon representation) is formed by E618 and H619 (in stick representation) and is shielded from the intra- and extra- cellular solutions by lipids D3, D4, D6, and D7 (in spheres and colored as in F- H).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 316, 635, 334]]<|/det|>
+## Lipids form a cap around the transmembrane dimer interface  
+
+<|ref|>text<|/ref|><|det|>[[112, 345, 886, 895]]<|/det|>
+The transmembrane dimer interface of afTMEM16 is formed by the extracellular half of TM10 from each monomer (Fig. 1I- J, Supp. Fig. 2D- E). This minimal interface contains several hydrophobic residues and two membrane- embedded salt bridges formed by E618 and H619 of opposite subunits positioned \(\sim 1 / 3\) of the way through the membrane from the extracellular leaflet (Fig. 1I- J). In the \(\mathrm{C18 / Ca^{2 + }}\) structure, these salt bridges appear to be isolated from the intra- and extra- cellular solutions by eight well- defined lipids (D3, D4, D6 and D7 from each subunit), four above and four below the interacting residues (Fig. 1J). On the extracellular side, the D3 lipids from opposite subunits straddle the N terminal region of TM10 with their heads positioned by the side chains of C607 and W608 to make direct contact above the symmetry axis (Supp. Fig. 2D). A second lipid, D4, is wedged between TM9 and TM10 with its head coordinated by polar and charged residues in the TM9- 10 linker (N593, P598, T604 and R606; Supp. Fig. 2D). On the intracellular side, the heads of D6 from each subunit make contact across the symmetry axis and are wedged between the C- termini of the TM10s (Supp. Fig. 2E). They are coordinated by D571, G574 and W578 on the TM9 from one subunit and by R625, Y626 and R629 from TM10 on the other (Supp. Fig. 2E). Additionally, the head of D7 is coordinated by Y626, S630 and K634 from TM10 of one subunit and by Q364 on TM5 and D571 on TM9 from the opposite subunit (Supp.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 885, 319]]<|/det|>
+Fig. 2E). The tails of these 8 lipids are accommodated in hydrophobic grooves between TM2, 9, 10 from both subunits (Fig. 1I, Supp. Fig. 2D- E). The intercalated organization of the lipid tails and helices gives rise to densely packed hydrophobic regions that shield the interacting E618 and H619 residues from water access, possibly strengthening their electrostatic interaction (Fig. 1J). These observations, together with the evolutionary conservation of the E618/H619 pair (Supp. Fig. 2C) and of the TMEM16 fold suggests these lipids might play a structural role in stabilizing the dimeric architecture of all TMEM16s.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 367, 671, 388]]<|/det|>
+## Structural basis of membrane thinning at the scrambling pathway  
+
+<|ref|>text<|/ref|><|det|>[[112, 400, 886, 878]]<|/det|>
+The C18/Ca \(^{2 + }\) structure reveals how the scramblase reorients the lipids that approach the open scrambling pathway (Fig. 1F, 2A). Near the dimer interface, the planes of the outer (OL) and inner (IL) leaflets are respectively defined by lipids D1- 4 and D8- 9, in good agreement with the outline visualized in the low pass filtered nanodisc map (Fig. 1C). The downward slope of the OL starts at D5, a well- defined PG lipid (Fig. 1F, 2B, Fig. Supp. 2A), and progresses towards the open groove as P1 and P2 adopt distorted poses with their headgroups becoming increasingly tilted (Fig. 2A- B). The IL bends upwards and P5- P7 become increasingly tilted as their heads climb around the intracellular portions of TM3 and TM4, coordinated by the hydrophilic side chains of T341, K345 and T334 (Fig. 2A,C). Within the pathway, P3 is sandwiched between TM4 and TM6 near the constriction formed by T325 and Y432 and its headgroup points towards the extracellular side such that it is contiguous to other OL lipids (Fig. 2A). The distance between the phosphate atoms of the headgroups of P3 and P4 in the OL and IL is \(< 22 \text{Å}\) (Fig. 2A), showing that the hydrocarbon core of the membrane is thinned by \(\sim 50\%\) at the open pathway. A similar thinning is seen in the low- pass filtered nanodiscs map near the pathway (Fig. 1C- D).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 120, 872, 540]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 556, 883, 700]]<|/det|>
+<center>Figure 2. Coordination of lipids outside the permeation pathway. A: View of the seven pathway lipids (in sticks, colored as in Fig. 1F). T325 and Y423 are shown as green sticks. Dashed arrow indicates the distance between the phosphate atoms of the last lipid from the inner (P4) and outer (P3) leaflets. B-C: Coordination of P1-P2 (B) and of P4-P7 (C). Side chains are shown in green sticks. D-E: forward \((\alpha)\) and reverse \((\beta)\) scrambling rate constants for indicated quadruple mutants of residues coordinating lipids outside the pathway (P1-2 and P4-7). Bars are average values for \(\alpha\) (black) and \(\beta\) (grey), error bars are S. Dev., and red circles are values from individual repeats. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 732, 730, 752]]<|/det|>
+## Lipids outside the open pathway define the distorted membrane interface  
+
+<|ref|>text<|/ref|><|det|>[[113, 767, 884, 893]]<|/det|>
+The identification of sites where lipids bind at or near the open groove raises the possibility that scrambling could occur via a 'conveyor belt' mechanism, where lipids translocate between leaflets by moving from site to site. Alternatively, the observed lipids could define the protein- membrane boundary but not necessarily be translocated, with the possible exception of P3 within the pathway
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 354]]<|/det|>
+(Fig. 2A). To distinguish between these hypotheses, we investigated how mutating residues coordinating the headgroups of P1- 2 and P4- 6 impacts scrambling. We found that mutations aimed at disrupting the headgroup interactions of P1- P2 (W202A/R427A/I431A/W529A), P4- P5- P6 (R279A/T334A/K345A/Y349A) or P2- P5- P6 (R279A/K345A/R427A/K428A) have minimal functional effects (Fig. 2D- E, Supp. Fig. 3). This suggests that these lipid association sites are not obligatory on the path taken by scrambled lipids. Rather, other factors, such as tail interactions with interhelical grooves, contribute to their association with afTMEM16 (Supp. Fig 2F- G) and stabilize the distorted membrane- protein interface that results in thinning at the pathway.  
+
+<|ref|>text<|/ref|><|det|>[[112, 401, 886, 736]]<|/det|>
+Scrambling does not require specific interactions with extracellular groove- lining residuesOne unexpected feature of our structure is that the extracellular vestibule of the groove does not directly interact with the membrane and no lipids could be resolved (Fig. 1C- D), as they traverse the groove below this region (Fig. 2A). We mutated side chains lining the extracellular vestibule or the central constriction of the groove and assessed their impact on scrambling. Single or multiple simultaneous alanine substitutions of I298, F302, E305 and E310 on TM3, of K317, Y319, F322, T325 and I332 on TM4, of T373 and S374 on TM5 and of R425, K428, Q429, Y432 and F433 on TM6 have no effects on lipid scrambling (Fig. 3, Supp. Fig. 3). Thus, scrambling does not entail specific interactions of lipids with residues lining the extracellular vestibule or the central constriction of the groove.  
+
+<|ref|>text<|/ref|><|det|>[[113, 750, 885, 876]]<|/det|>
+In contrast, the wide intracellular vestibule is embedded in the nanodisc membrane, and the resolved P3 and P4 lipids at the open pathway have opposite orientations (Fig. 2A). This suggests lipid headgroups only need to traverse the wide intracellular vestibule of the pathway, below the constriction formed by T325 and Y432 (Fig. 2A). The pronounced membrane thinning
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 319]]<|/det|>
+at the pathway lowers the energy barrier for transbilayer lipid movement and the hydrophilic environment of the open groove allows water access to this thinned membrane region, synergistically lower the energy barrier for scrambling. Scrambling by afTMEM16 and hTMEM16K is modulated by lipid acyl chain length \(^{15,23}\) , supporting the idea that membrane thinning is critical for scrambling. Our proposal predicts that this modulation should reflect whether the scramblase can sufficiently thin these membranes, rather than arise from lipid-dependent changes in the conformation of the groove.  
+
+<|ref|>image<|/ref|><|det|>[[118, 330, 875, 775]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 790, 883, 884]]<|/det|>
+<center>Figure 3. Functional role of groove-lining residues in lipid scrambling. A-C: Residues lining the extracellular vestibule (A), coordinating P3 (B) and lining the central constriction (C) are shown as green sticks. D-E: forward \((\alpha)\) and reverse \((\beta)\) scrambling rate constants of single and multiple alanine substitutions at the indicated positions. Bars are average values for \(\alpha\) (black) and \(\beta\) (grey), error bars are S. Dev., and red circles are values from individual repeats. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[114, 90, 575, 110]]<|/det|>
+## Regulation of lipid scrambling by membrane thickness  
+
+<|ref|>text<|/ref|><|det|>[[113, 123, 886, 459]]<|/det|>
+We measured how systematic variation of lipid acyl chain length affects lipid scrambling by afTMEM16. We kept the lipid headgroup composition at a constant ratio of 7 PC: 3 PG and used acyl chains with a single unsaturation and 16- 22 carbons, C16- C22 lipids (Table 1). Liposomes formed from this mix of 14:1 lipids were not stable in our scrambling assay (Supp Fig. 4C), therefore we generated thinner membranes using a mixture comprised of \(50\%\) 1,2- dimyristoyl- sn- glycero- 3- phosphocholine (DMPC) and 1,2- dimyristoyl- sn- glycero- 3- phospho- (1'-rac- glycerol) (DMPG) in a 7:3 ratio and \(50\%\) of POPC and POPG in a 7:3 ratio \(^{23}\) ; we will refer to this mix as C14 (Table 1). Atomic force microscopy (AFM) measurements show that membrane thickness varies between \(\sim 3.2 \mathrm{nm}\) and \(\sim 4.1 \mathrm{nm}\) , with near- linear scaling with acyl chain length (Table 1, Supp. Fig. 4A- B).  
+
+<|ref|>text<|/ref|><|det|>[[112, 472, 886, 877]]<|/det|>
+In the presence of saturating \(0.5 \mathrm{mM Ca^{2 + }}\) the scrambling rate constants do not depend on membrane thickness between \(\sim 3.2 \mathrm{nm}\) (C14 lipids) and \(\sim 3.9 \mathrm{nm}\) (C20 lipids) (Fig. 4A). In contrast, scrambling is nearly completely inhibited in C22 lipids (Fig. 4A) \(^{15}\) . Thus, in saturating \(\mathrm{Ca^{2 + }}\) there is chain length selectivity with a threshold for activity below membrane thickness of \(\sim 4.1 \mathrm{nm}\) . In contrast, in \(0 \mathrm{Ca^{2 + }}\) scrambling displays a nearly exponential inverse dependence on membrane thickness (Fig. 4B). Remarkably, in C14 lipid membranes scrambling by afTMEM16 is nearly \(\mathrm{Ca^{2 + }}\) - independent, with rate constants only \(\sim 3\) - fold lower in \(0 \mathrm{Ca^{2 + }}\) compared to the \(\sim 20\) - fold reduction seen in C18 membranes (Fig. 4A- B, Supp. Fig. 4). To test whether the long C22 acyl chains inhibit scrambling in saturating \(\mathrm{Ca^{2 + }}\) by occluding the pathway \(^{37}\) we measured scrambling in membranes formed by \(70\%\) C22 lipids and \(30\%\) C18 lipids, which are \(\sim 4 \mathrm{nm}\) thick (Table 1). In saturating \(\mathrm{Ca^{2 + }}\) scrambling activity is similar to that seen in \(100\%\) C18 lipids (Fig. 4A), while in \(0 \mathrm{Ca^{2 + }}\) there is a \(\sim 17\) - fold reduction, consistent with the reduction expected for membranes of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 885, 249]]<|/det|>
+this thickness (Fig. 4B). This behavior does not depend on whether the mixed chain lengths were segregated by headgroup. Thus, the tails of C22 lipids are not ‘blockers’ of the afTMEM16 permeation pathway. These results suggest that in \(0 \mathrm{Ca}^{2 + }\) scrambling rates are proportional to the energetic cost of lipid headgroups crossing the hydrophobic core of the membrane, while in the presence of \(\mathrm{Ca}^{2 + }\) other factors contribute to scrambling.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 298, 648, 318]]<|/det|>
+## \(\mathrm{Ca}^{2 + }\) -bound afTMEM16 has an open groove in C22 membranes  
+
+<|ref|>text<|/ref|><|det|>[[112, 330, 886, 736]]<|/det|>
+To determine whether the C22 lipids inhibit scrambling by inducing groove closure we determined the cryo- EM structure of nanodisc- reconstituted afTMEM16 in the presence of saturating \(\mathrm{Ca}^{2 + }\) to 2.7 Å (Supp. Fig. 5A- G). Despite a \(\sim 500\) - fold reduction in scrambling activity the groove remains open in a conformation nearly identical to that seen in C18 lipids, \(\mathrm{Ca}\) r.m.s.d. \(\sim 0.35 \mathrm{\AA}\) (Fig. 4D). Importantly, neither the \(\mathrm{C18 / Ca}^{2 + }\) nor the \(\mathrm{C22 / Ca}^{2 + }\) datasets display structural heterogeneity as no additional classes could be identified using multiple rounds of iterative 3D classifications on afTMEM16 dimers and monomers using different classification parameters and software (see Methods, Supp. Fig. 1,5, 7, 8, 10). Further, The \(\mathrm{C22 / Ca}^{2 + }\) structure of afTMEM16 in the larger MSP2N2 nanodiscs at 3.5 Å resolution (Supp. Fig. 5H- N) shows an open permeation pathway in all 3D reconstructions, with \(\mathrm{Ca}\) r.m.s.d. \(\sim 0.5 \mathrm{\AA}\) to \(\mathrm{C18 / Ca}^{2 + }\) and \(\sim 0.4 \mathrm{\AA}\) to \(\mathrm{C22 / Ca}^{2 + }\) MSP1E3 (Fig. 4D). Thus, in afTMEM16 an open groove is not sufficient to enable lipid scrambling and nanodisc size does not influence the conformation.  
+
+<|ref|>text<|/ref|><|det|>[[113, 749, 885, 876]]<|/det|>
+In the \(\mathrm{C22 / Ca}^{2 + }\) maps we resolved several of the lipids near the dimer interface corresponding to D2, D3, D6, and D7 (in MSP1E3 map) and to D2 and D6 (in MSP2N2 map) seen in the \(\mathrm{C18 / Ca}^{2 + }\) map (Supp. Fig. 6). In the MSP1E3 map we detected strong density for P6 and P7, located near the intracellular loop connecting TM3 and TM4 (Supp. Fig. 6). However, despite
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 214]]<|/det|>
+the high resolution of the \(\mathrm{C22 / Ca^{2 + }}\) MSP1E3 map, we detect only weak signals for lipids associated with the pathway- delimiting helices TM4 and TM6. This suggests that the interactions of C22 lipids with the pathway helices are weaker than those of C18 lipids, likely reflecting the higher energy cost associated with distorting these longer acyl chain lipids.  
+
+<|ref|>image<|/ref|><|det|>[[113, 230, 850, 770]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 787, 883, 878]]<|/det|>
+<center>Figure 4. Functional and structural regulation of lipid scrambling by membrane thickness. A-B: Forward \((\alpha ,\) black circles) and reverse \((\beta ,\) red circles) scrambling rate constants as a function of membrane thickness in the presence of \(0.5\mathrm{mM}\) (A) or \(0\mathrm{Ca}^{2 + }\) (B). Values are the mean and error bars represent standard deviation. Corresponding lipid compositions are noted above. C-E: Alignment of the permeation pathway of afTMEM16 in (C) C18 nanodiscs in \(0.5\mathrm{mM}\) (grey) or 0 </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 127]]<|/det|>
+\(\mathrm{Ca}^{2 + }\) (pink), (D) in \(0.5\mathrm{mM}\mathrm{Ca}^{2 + }\) and C18 (grey) or C22 MSP1E3 nanodiscs (light pink) or C22 MSP2N2 nanodiscs (orange), (E) in \(0\mathrm{Ca}^{2 + }\) in C18 (red) and C14 nanodiscs (cyan).  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 160, 568, 179]]<|/det|>
+## Scrambling in \(0\mathrm{Ca}^{2 + }\) does not require groove opening  
+
+<|ref|>text<|/ref|><|det|>[[113, 193, 886, 457]]<|/det|>
+These finding that an open groove is not sufficient to allow lipid movement raises the question of whether a closed groove prevents lipid scrambling entirely. Many proteins that scramble lipids lack explicit membrane- exposed hydrophilic grooves \(^{34 - 36,38}\) and most purified TMEM16's scramble lipids in \(0\mathrm{Ca}^{2 + }\) when the groove is predominantly closed (Fig. 4B) \(^{13,23,26}\) . This basal activity could reflect transient openings of the pathway, however an open groove \(\mathrm{Ca}^{2 + }\) - free conformation has not been observed in a membrane environment \(^{15 - 18}\) . Alternatively, these scramblases could thin the membrane enough to enable slow lipid scrambling outside of a closed groove, as proposed for the mammalian TMEM16F \(^{16}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 472, 886, 878]]<|/det|>
+To elucidate the structural bases of scrambling in the absence of \(\mathrm{Ca}^{2 + }\) , we determined the 3.1 Å resolution structure of afTMEM16 in C18 lipids in \(0\mathrm{Ca}^{2 + }\) (Supp. Fig. 7). Extensive classification of afTMEM16 dimers and of symmetry- expanded monomers (see Methods) revealed only reconstructions corresponding to a closed groove conformation (Fig 4C, Supp. Fig. 7). However, in C18 lipids the basal scrambling activity of afTMEM16 is modest, \(\sim 4.5\%\) of that in saturating \(\mathrm{Ca}^{2 + }\) (Fig. 4A- B, Supp. Fig. 4), suggesting that the fraction of particles that could adopt a \(\mathrm{Ca}^{2 + }\) - free open groove conformation could be too small to be detected. In contrast, in C14 lipids scrambling in \(0\mathrm{Ca}^{2 + }\) is only \(\sim 3\) - fold slower than in saturating \(\mathrm{Ca}^{2 + }\) (Fig. 4A- B, Supp. Fig 4) so that a significant portion of the particles should adopt a \(\mathrm{Ca}^{2 + }\) - free open- groove conformation. Analysis of a C14/0 \(\mathrm{Ca}^{2 + }\) afTMEM16 dataset yields only classes with a closed groove (Fig. 4E), \(\mathrm{Ca}\) r.m.s.d. \(\sim 0.9\mathrm{\AA}\) to C18/0 \(\mathrm{Ca}^{2 + }\) , the highest of which reached 3.3 Å average resolution (Supp. Fig. 8). Thus, in \(0\mathrm{Ca}^{2 + }\) there is a \(\sim 30\) - fold increase in scrambling between C14 and C18 lipid
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 144]]<|/det|>
+membranes that is not accompanied by an increase in the probability of opening of the groove. This suggests that the basal, \(\mathrm{Ca}^{2 + }\) independent activity is due to closed- groove scrambling.  
+
+<|ref|>text<|/ref|><|det|>[[112, 156, 886, 704]]<|/det|>
+This hypothesis is further supported by the analysis of the D511A/E514A mutant of afTMEM16 that disrupts the \(\mathrm{Ca}^{2 + }\) - binding site. This mutation impairs TMEM16 activity by preventing opening of the pathway \(^{8,26,39,40}\) and scrambles lipids in a \(\mathrm{Ca}^{2 + }\) - independent manner at rates comparable to those of the WT protein in \(0 \mathrm{Ca}^{2 + }\) . Scrambling by D511A/E514A afTMEM16 is modulated by membrane thickness like the WT protein in \(0 \mathrm{Ca}^{2 + }\) (Fig. 5A, Supp. Fig. 9), so that in C14 membranes its activity is \(\sim 30\%\) of that of the WT protein in C18 lipids and saturating \(\mathrm{Ca}^{2 + }\) . To test whether the D511A/E514A afTMEM16 adopts an open- pathway conformation in conditions of high activity, we determined its structure in C14 nanodiscs with 0.5 mM \(\mathrm{Ca}^{2 + }\) to 3.1 Å resolution (Supp. Fig. 10). As expected, despite the presence of 0.5 mM \(\mathrm{Ca}^{2 + }\) , the protein adopts the same conformation as in the WT apo structure and there is no density in the \(\mathrm{Ca}^{2 + }\) binding site. In all reconstructions the permeation pathway is closed, with \(\mathrm{Ca}\) r.m.s.d. \(\sim 1.1 \mathrm{\AA}\) to C18/0 \(\mathrm{Ca}^{2 + }\) and \(\sim 0.4 \mathrm{\AA}\) to C14/0 \(\mathrm{Ca}^{2 + }\) (Supp. Fig. 10), indicating that increased scrambling is not accompanied by higher open probability of the groove. Together, our results suggest that scrambling of afTMEM16 in \(0 \mathrm{Ca}^{2 + }\) occurs outside of a closed groove. Calcium- independent openings of the lipid permeation pathway, if they occur, are transient and cannot account for the observed increase in activity. Thus, an open groove is not necessary for lipid scrambling.  
+
+<|ref|>text<|/ref|><|det|>[[113, 715, 885, 842]]<|/det|>
+In the three datasets for apo afTMEM16 (C18/0 \(\mathrm{Ca}^{2 + }\) , C14/0 \(\mathrm{Ca}^{2 + }\) and DA/EA in 0.5 mM \(\mathrm{Ca}^{2 + }\) ) we could resolve 4- 9 lipids per monomer, all localized near the dimer interface in positions closely resembling those seen in C18/ \(\mathrm{Ca}^{2 + }\) structure (Supp. Fig. 11), supporting the notion that these lipids interact strongly with the protein. No lipids could be resolved near the closed pathway
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 883, 144]]<|/det|>
+in these structures. The average resolution of these datasets is lower than that of the two \(\mathrm{Ca^{2 + }}\) - bound structures, preventing us from drawing mechanistic inferences from this observation.  
+
+<|ref|>image<|/ref|><|det|>[[115, 160, 884, 348]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 367, 883, 476]]<|/det|>
+<center>Figure 5. Functional and structural characterization of afTMEM16 D511A/E514A. A-B: Forward \((\alpha ,\) black circles) and reverse \((\beta ,\) red circles) scrambling rate constants of D511A/E514A afTMEM16 in \(0.5\mathrm{mM}\) (filled symbols) or \(0\mathrm{Ca}^{2 + }\) (empty symbols). Values are the mean and error bars represent standard deviation. Corresponding lipid compositions are noted above. B: Alignment of afTMME16 D511A/E514A in the presence of \(\mathrm{Ca^{2 + }}\) (green) in C14 lipids with wildtype afTMEM16 in \(0\mathrm{Ca}^{2 + }\) in C18 lipids (grey) with close up view of the permeation pathway. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 508, 710, 528]]<|/det|>
+## Scrambling activity correlates with membrane thinning at the pathway  
+
+<|ref|>text<|/ref|><|det|>[[113, 541, 884, 878]]<|/det|>
+Our proposal that afTMEM16 enables scrambling by thinning the membrane at the permeation pathway predicts there should be a correlation between thinning and function. Although a quantitative evaluation of thinning is precluded by the different resolutions of the maps, a qualitative analysis of the nanodisc density maps supports this notion (Fig. 6). Far from the protein, membrane thickness of C14, C18 and C22 nanodiscs is comparable to that determined by AFM (Table 1). Near the open groove, in the \(\mathrm{C18 / Ca^{2 + }}\) map the membrane appears significantly thinned (Fig. 6B), closely tracking the position of individual lipids (Fig. 2A). Thinning is reduced near the open pathway of the \(\mathrm{C22 / Ca^{2 + }}\) map (Fig. 6A) and near the closed pathway of the \(\mathrm{C18 / 0 Ca^{2 + }}\) map (Fig. 6C), consistent with the reduced scrambling activity (Fig. 4A-B). In the \(\mathrm{C14 / 0 Ca^{2 + }}\) map, thickness at the closed pathway qualitatively approaches that at the open pathway of the \(\mathrm{C18 / Ca^{2 + }}\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 283]]<|/det|>
+map (Fig. 6D), consistent with enhanced scrambling (Fig. 4B). These qualitative observations suggest there is a direct correlation between the thickness of the membrane near the pathway and scrambling activity. This supports the idea that in C22 membranes scrambling could be inhibited because of the reduced thinning despite an open groove, and that the closed groove conformation of afTMEM16 is scrambling competent because it thins the membrane enough to enable lipid flipping.  
+
+<|ref|>image<|/ref|><|det|>[[115, 295, 884, 595]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 610, 883, 770]]<|/det|>
+<center>Figure 6. Membrane thinning at the afTMEM16 pathway as a function of acyl chain length. A-D: Views of the density maps for afTMEM16 in C22/Ca \(^{2 + }\) (A), C18/Ca \(^{2 + }\) (B), C18/0 Ca \(^{2 + }\) (C) and C14/0 Ca \(^{2 + }\) (D) from the extracellular (top panels) and intracellular (bottom panel) side. The C1 final unsharpened maps containing nanodisc densities were aligned, resampled on the same grid, and colored according to the Z coordinate using UCSF Chimera. The density corresponding to the protein is segmented and shown in gray. Nanodisc densities are colored by displacement along the Z axis and the 0 Å reference height is the same for all structures in each view. Negative values represent membrane thinning relative to the overall nanodisc. The position of the permeation pathway is denoted with arrows. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 803, 205, 820]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[115, 836, 884, 891]]<|/det|>
+Activation of scramblases catalyzes the rapid movement of phospholipids between membrane leaflets and results in the externalization of charged and polar lipids that trigger a variety of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 86, 886, 423]]<|/det|>
+fundamental physiological processes \(^{1,2,4}\) . The current consensus is that TMEM16 scramblases mediate lipid transport via a credit- card like mechanism \(^{33}\) , with the headgroups forming specific interactions with polar and charged residues lining the full length of the hydrophilic groove \(^{20,23,25,28}\) . This predicts that scramblases should discriminate among lipids based on their headgroups but not their tails, and that mutations of groove- lining residues should affect lipid scrambling. Notably, neither scramblases like the TMEM16's \(^{13,18,21,24,26}\) or the Xkr's \(^{6,41}\) nor GPCR's moonlighting as scramblases \(^{34}\) , show selectivity among lipids with different headgroups. Further, both the Xkr's and GPCR's lack explicit hydrophilic grooves \(^{34- 36}\) , bringing the structural requisites of the credit card mechanism into question. However, the modes of lipid- protein interactions of TMEM16 scramblases had not been structurally resolved \(^{15- 18}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 436, 886, 842]]<|/det|>
+Here, we combined structural and functional experiments to investigate the mechanism of lipid scrambling by the TMEM16's. The 2.3 Å structure of afTMEM16 reconstituted in C18 nanodiscs shows how individual lipids interact with the scramblase to define the thinned and distorted profile of the membrane near the open pathway (Fig. 1C- H). Lipids mainly localize to the periphery of the groove, interacting with the intracellular portions of TM3- 4 and with the extracellular portions of TM6- 7. The position of the last lipids from the intra- and extra- cellular leaflets suggests that headgroup flipping occurs in the intracellular vestibule. No density for lipids was visible near the extracellular vestibule (Fig. 1, 2A) and mutations of residues lining this narrow constriction or the groove interior have no functional effects (Fig. 2, 3). Reconstituting afTMEM16 in membranes formed from lipids with longer acyl chains dramatically inhibits scrambling although the groove remains open (Fig. 4). Conversely, reconstitution in thinner membranes facilitates scrambling even when the groove is closed (Fig. 4- 5).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 494]]<|/det|>
+Together, these results have three important implications; first, lipid scrambling does not entail specific interactions with the groove's hydrophilic interior or its extracellular vestibule. Second, acyl chains rather than headgroups are key determinants of scrambling activity (Fig. 4A- B). Third, an open groove is neither sufficient nor necessary for scrambling (Fig. 4, 5). These findings are inconsistent with a credit- card mechanism. Rather, we propose that lipid scrambling is primarily determined by the ability of afTMEM16 to thin the membrane near the pathway, so that lipids only interact with the surface of the groove without penetrating deep within its narrow and hydrophilic interior (Fig. 7). The membrane- thinning mechanism readily explains evolutionarily conserved properties of TMEM16 scramblases that are difficult to reconcile with the credit card mechanism, such as the lack of discrimination based on headgroup size, chemistry or charge \(^{13,18,21,23,26,42}\) and scrambling of lipids conjugated to large cargoes \(^{24}\) . Thus, we propose this mechanism applies to other TMEM16's.  
+
+<|ref|>text<|/ref|><|det|>[[112, 506, 886, 878]]<|/det|>
+Two lines of evidence support the credit card hypothesis: mutating groove- lining residues impairs lipid scrambling by nhTMEM16 and TMEM16F \(^{25,28}\) and MD simulations show lipid headgroups penetrating and traversing the whole length of the groove \(^{20,23,25,28,43,44}\) . Strikingly we find that mutating similar residues in afTMEM16 does not impair scrambling (Fig. 2,3). This contradiction could be explained if the mutants impair scrambling by favoring groove closure rather than by impairing lipid movement through an open groove. In afTMEM16 only the \(\mathrm{Ca^{2 + }}\) - bound open conformation has been observed \(^{15}\) (Fig. 1, 4). In contrast, \(\mathrm{Ca^{2 + }}\) - bound nhTMEM16 adopts both open and closed groove conformations \(^{17}\) and in mTMEM16F only the \(\mathrm{Ca^{2 + }}\) - bound closed groove conformation has been observed \(^{16,18}\) , suggesting in these homologues the \(\mathrm{Ca^{2 + }}\) - bound open conformation is less stable than in afTMEM16. Further, several scrambling- incompetent nhTMEM16 mutants retain measurable channel activity \(^{25}\) , suggesting stabilization
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 86, 885, 388]]<|/det|>
+of an ion channel- like groove conformation \(^{19}\) . Discrepancies with molecular dynamics simulations could be due to incomplete relaxation of the membrane during the equilibration, especially if the chosen initial conditions for the protein- lipid arrangements are far from equilibrium. Indeed, recent work suggests extended equilibration protocols are needed to capture the full extent of membrane deformations induced by some proteins \(^{45}\) . Further, our structures show several lipids with tails tightly intercalated with TM helices at the dimer cavity (Fig. 1) that might affect the dynamic rearrangements of afTMEM16 in MD simulations. It will be interesting to see how incorporating new information on the modes of lipid interactions with the afTMEM16 scramblase affects these results.  
+
+<|ref|>text<|/ref|><|det|>[[113, 402, 885, 527]]<|/det|>
+The implications of our proposed membrane- thinning mechanism for scrambling (Fig. 7) can be appreciated if we make the simplifying assumptions that (i) the energy barrier for lipid scrambling is due to the polar head and (ii) that the head can be modeled with a sphere of radius \(r\) and charge \(q\) , then the energy barrier for scrambling, \(\Delta G_{scramb}\) would be given by \(^{46}\)  
+
+<|ref|>equation<|/ref|><|det|>[[338, 541, 658, 583]]<|/det|>
+\[\Delta G_{scramb} = \frac{q^{2}}{2\epsilon_{m}r} -\frac{q^{2}}{\epsilon_{m}L} ln\left(\frac{2\epsilon_{w}}{\epsilon_{m} + \epsilon_{w}}\right)\]  
+
+<|ref|>text<|/ref|><|det|>[[112, 596, 886, 899]]<|/det|>
+Where \(\epsilon_{\mathrm{m,w}}\) are the dielectric constants of the membrane and of water and L is the thickness of the membrane. Membrane thinning decreases \(\Delta G_{scramb}\) as L is reduced and the dielectric constant \(\epsilon_{\mathrm{m}}\) is increased because of higher water access to the hydrocarbon core of the membrane \(^{47}\) . When the pathway is open scrambling is fast because thinning is pronounced, and the hydrophilic interior of the open groove further decreases \(\epsilon_{\mathrm{m}}\) (Fig. 7A). In thicker or more rigid membranes (Fig. 4) \(^{15}\) , scrambling is impaired because their deformation cost is higher thus preventing lipids to reach positions conducive to scrambling (Fig. 7B). When the groove is closed membrane thinning is diminished, but not absent, which allows for slow scrambling activity (Fig. 7C), that is enhanced in membranes formed from shorter chain length lipids (Fig. 7D). Notably, the proposed membrane
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 883, 176]]<|/det|>
+thinning mechanism could naturally explain how proteins lacking hydrophilic grooves, such as GPCR's and Xkr's, can scramble lipids and share functional properties with the structurally unrelated TMEM16's \(^{24,34 - 36,38,48}\) .  
+
+<|ref|>image<|/ref|><|det|>[[113, 193, 881, 582]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 597, 883, 670]]<|/det|>
+<center>Figure 7. TMEM16 scramblases enable scrambling by thinning the membrane. A-D: Schematic representation of the open (A-B, colored in green) and closed pathways (C-D, colored in red) in membranes of different thickness. Cyan denotes regions accessible to water. Arrows denote high (solid line), low (dashed line) or no (no line) scrambling. </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 702, 884, 898]]<|/det|>
+In sum, our results support a mechanism where during scrambling, lipids interact with the surface of the groove without having to penetrate and interact with its narrow and hydrophilic interior. Scrambling by the TMEM16's is modulated by two signals, binding of \(\mathrm{Ca}^{2 + }\) facilitates opening of the groove while the properties of the membrane determine whether the scramblase can thin the membrane enough to enable lipid flipping. This dual control of scrambling activity, by ligand binding and membrane properties, could constitute a secondary layer of regulation that
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 214]]<|/det|>
+prevents undesired lipid flipping by the TMEM16's during fluctuations in cellular cytosolic \(\mathrm{Ca}^{2 + }\) levels or when family members that reside in intracellular membranes are transiently localized to the plasma membrane. Similarly, rigidifying or thickening bilayer constituents, such as cholesterol, could silence the scrambling activity of other scramblases such as GPCR's in cellular membranes.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 261, 108]]<|/det|>
+## Data Availability  
+
+<|ref|>text<|/ref|><|det|>[[114, 124, 884, 214]]<|/det|>
+Data AvailabilityAll constructs are available on request. All models and associated cryoEM maps have been deposited into the Electron Microscopy Data Bank (EMDB) and the Protein Data Bank (PDB). The depositions include final maps, unsharpened maps, and associated FSC curves.  
+
+<|ref|>table<|/ref|><|det|>[[115, 226, 501, 364]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[115, 364, 323, 380]]<|/det|>
+Table 5: Data Availability   
+
+<table><tr><td>Structure</td><td>PDB</td><td>EMDB</td></tr><tr><td>C18/Ca2+ dimer</td><td>7RXH</td><td>EMD-24730</td></tr><tr><td>C18/Ca2+ monomer</td><td>7RXG</td><td>EMD-24731</td></tr><tr><td>C22/Ca2+ MSP1E3</td><td>7RX2</td><td>EMD-24722</td></tr><tr><td>C22/Ca2+ MSP2N2</td><td>7RWJ</td><td>EMD-24717</td></tr><tr><td>C18/0Ca2+</td><td>7RXB</td><td>EMD-24727</td></tr><tr><td>C14/0Ca2+</td><td>7RX3</td><td>EMD-24723</td></tr><tr><td>D511A/E514A C14/Ca2+</td><td>7RXA</td><td>EMD-24726</td></tr></table>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 414, 280, 432]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[113, 447, 886, 888]]<|/det|>
+AcknowledgementsThe authors thank members of the Accardi lab and Richard Hite for helpful discussions. The work was supported by National Institutes of Health (NIH) Grant R01GM106717 (to A.A.), by a Margaret and Herman Sokol Fellowship from Weill Cornell Medicine (M.E.F.), by the KBRI Basic Research Program through Korea Brain Research Institute funded by Ministry of Science and ICT (21- BR- 01- 08 to B.- C. L.) and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1C1C1002699 to B.- C. L.). Some of this work was performed at the Simons Electron Microscopy Center and National Resource for Automated Molecular Microscopy located at the New York Structural Biology Center, supported by grants from the Simons Foundation (SF349247), NYSTAR, and the NIH National Institute of General Medical Sciences (GM103310). Part of the work was performed at the Cryo- EM Core Facility at University of Massachusetts Chan Medical School with the help of Dr. Kangkang Song and Dr. Chen Xu. Initial screening was performed at NYU Langone Health's Cryo- Electron Microscopy Laboratory (RRID: SCR_019202).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 125, 296, 143]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[114, 158, 884, 250]]<|/det|>
+M.F., Z.F. and A.A. designed the experiments; M.F., Z.F., O.E.A., Y.P. and B.- C.L. performed experiments; M.F., Z.F., O.E.A., Y.P., B.- C.L., X.C., E.F., S.S. and A.A. analyzed the data; M.F., S.S. and A.A. wrote the paper. All authors edited the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 299, 375, 317]]<|/det|>
+## Competing Interests statement  
+
+<|ref|>text<|/ref|><|det|>[[115, 333, 460, 352]]<|/det|>
+The authors declare no competing interests.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 209, 106]]<|/det|>
+## References
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 90, 886, 895]]<|/det|>
+19 Khelashvili, G. et al. Dynamic modulation of the lipid translocation groove generates a conductive ion channel in \(\mathrm{Ca2 + }\) - bound nhTMEM16. Nature Communications 10, 4972, doi:10.1038/s41467- 019- 12865- 4 (2019). 20 Bethel, N. P. & Grabe, M. Atomistic insight into lipid translocation by a TMEM16 scramblase. Proc Natl Acad Sci USA 113, 14049- 14054 (2016). 21 Suzuki, J. et al. Calcium- dependent phospholipid scramblase activity of TMEM16 protein family members. J Biol Chem 288, 13305- 13316, doi:10.1074/jbc.M113.457937 (2013). 22 Segawa, K., Suzuki, J. & Nagata, S. Constitutive exposure of phosphatidylserine on viable cells. PNAS 108, 19246- 19251 (2011). 23 Bushell, S. R. et al. The structural basis of lipid scrambling and inactivation in the endoplasmic reticulum scramblase TMEM16K. Nature Communications 10, 3956, doi:10.1038/s41467- 019- 11753- 1 (2019). 24 Malvezzi, M. et al. Out- of- the- groove transport of lipids by TMEM16 and GPCR scramblases. Proc Natl Acad Sci U S A 115, E7033- E7042, doi:10.1073/pnas.1806721115 (2018). 25 Lee, B.- C. et al. Gating mechanism of the extracellular entry to the lipid pathway in a TMEM16 scramblase. Nature Communications 9, 3251, doi:10.1038/s41467- 018- 05724- 1 (2018). 26 Malvezzi, M. et al. \(\mathrm{Ca2 + }\) - dependent phospholipid scrambling by a reconstituted TMEM16 ion channel. Nature Communications 4, 2367, doi:10.1038/ncomms3367 https://www.nature.com/articles/ncomms3367#supplementary- information (2013). 27 Brunner, J. D., Schenck, S. & Dutzler, R. Structural basis for phospholipid scrambling in the TMEM16 family. Curr Opin Struct Biol 39, 61- 70, doi:10.1016/j.sbi.2016.05.020 (2016). 28 Jiang, T., Yu, K., Hartzell, H. C. & Tajkhorshid, E. Lipids and ions traverse the membrane by the same physical pathway in the nhTMEM16 scramblase. Elife 6, doi:10.7554/eLife.28671 (2017). 29 Griffin, D. A. et al. Defective membrane fusion and repair in Anoctamin5- deficient muscular dystrophy. Hum Mol Genet 25, 1900- 1911, doi:10.1093/hmg/ddw063 (2016). 30 Yu, K. et al. Identification of a lipid scrambling domain in ANO6/TMEM16F. eLife 4, 1- 23, doi:10.7554/eLife.06901 (2015). 31 Peters, C. J. et al. The Sixth Transmembrane Segment Is a Major Gating Component of the TMEM16A Calcium- Activated Chloride Channel. Neuron 97, 1063- 1077. e1064, doi:https://doi.org/10.1016/j.neuron.2018.01.048 (2018). 32 Le, T. et al. An inner activation gate controls TMEM16F phospholipid scrambling. Nature Communications 10, 1846, doi:10.1038/s41467- 019- 09778- 7 (2019). 33 Pomorski, T. & Menon, A. K. Lipid flippases and their biological functions. Cell Mol Life Sci 63, 2908- 2921 (2006). 34 Menon, I. et al. Opsin is a phospholipid flippase. Current Biology 21, 149- 153, doi:10.1016/j.cub.2010.12.031 (2011). 35 Straub, M. S., Alvadia, C., Sawicka, M. & Dutzler, R. Cryo- EM structures of the caspase- activated protein XKR9 involved in apoptotic lipid scrambling. eLife 10, e69800, doi:10.7554/eLife.69800 (2021). 36 Sakuragi, T. et al. An intramolecular scrambling path controlled by a gatekeeper in Xkr8 phospholipid scramblase. bioRxiv, 2021.2005.2006.442885, doi:10.1101/2021.05.06.442885 (2021).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 886, 669]]<|/det|>
+37 Khelashvili, G. et al. Membrane lipids are both the substrates and a mechanistically responsive environment of TMEM16 scramblase proteins. Journal of computational chemistry 41, 538- 551, doi:10.1002/jcc.26105 (2020).38 Goren, M. A. et al. Constitutive phospholipid scramblase activity of a G protein- coupled receptor. Nat Commun 5, 5115, doi:10.1038/ncomms6115 (2014).39 Yu, K., Duran, C., Qu, Z., Cui, Y.- Y. & Hartzell, H. C. Explaining Calcium- Dependent Gating of Anoctamin- 1 Chloride Channels Requires a Revised Topology. Circulation Research 110, 990- 999, doi:10.1161/CIRCRESAHA.112.264440 (2012).40 Tien, J. et al. A comprehensive search for calcium binding sites critical for TMEM16A calcium- activated chloride channel activity. Elife, e02772, doi:10.7554/eLife.02772 (2014).41 Suzuki, J., Imanishi, E. & Nagata, S. Xkr8 phospholipid scrambling complex in apoptotic phosphatidylserine exposure. Proc Natl Acad Sci USA 113, 9509- 9514 (2016).42 Watanabe, R., Sakuragi, T., Noji, H. & Nagata, S. Single- molecule analysis of phospholipid scrambling by TMEM16F. Proceedings of the National Academy of Sciences 115, 3066- 3071, doi:10.1073/pnas.1717956115 (2018).43 Stansfeld, P. J. et al. MemProtMD: automated insertion of membrane protein structures into explicit lipid membranes. Structure 23, 1350- 1361, doi:10.1016/j.str.2015.05.006 (2015).44 Kostritskii, A. Y. & Machtens, J.- P. Molecular mechanisms of ion conduction and ion selectivity in TMEM16 lipid scramblases. Nature Communications 12, 2826, doi:10.1038/s41467- 021- 22724- w (2021).45 Stix, R., Song, J., Banerjee, A. & Faraldo- Gómez, J. D. DHHC20 Palmitoyl- Transferase Reshapes the Membrane to Foster Catalysis. Biophys J 118, 980- 988, doi:10.1016/j.bpj.2019.11.003 (2020).46 Parsegian, A. Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature 221, 844- 846, doi:10.1038/221844a0 (1969).47 Bennett, W. F. D. & Tieleman, D. P. The Importance of Membrane Defects—Lessons from Simulations. Accounts of Chemical Research 47, 2244- 2251, doi:10.1021/ar4002729 (2014).48 Wang, L. et al. Scrambling of natural and fluorescently tagged phosphatidylinositol by reconstituted G protein- coupled receptor and TMEM16 scramblases. Journal of Biological Chemistry 293, 18318- 18327, doi:10.1074/jbc.RA118.004213 (2018).
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[114, 88, 699, 375]]<|/det|>
+
+<table><tr><td>Name</td><td>Lipid Component Chain Length (70% PC:30%PG)</td><td>Height from AFM (nm)</td><td>Height estimated from EM maps (nm)</td></tr><tr><td>C14</td><td>50% 14:0, 50% 16:0-18:1</td><td>3.2 ± 0.29</td><td>3.0 ± 1.5</td></tr><tr><td>C16</td><td>100% 16:1</td><td>3.2 ± 0.22</td><td>N.d.</td></tr><tr><td rowspan="2">C18</td><td rowspan="2">100% 18:1</td><td rowspan="2">3.4 ± 0.19</td><td>(0 Ca2+) 3.1 ± 3.5</td></tr><tr><td>(0.5 mM Ca2+) 3.3 ± 0.95</td></tr><tr><td>C20</td><td>100% 20:1</td><td>3.7 ± 0.22</td><td>N.d.</td></tr><tr><td>70% C22</td><td>70% 22:1, 30% 18:1</td><td>4.0 ± 0.26</td><td>N.d.</td></tr><tr><td>70% C22</td><td>70% 22:1 PC, 30% 18:1 PG</td><td>4.0 ± 0.19</td><td>N.d.</td></tr><tr><td>C22</td><td>100% 22:1</td><td>4.1 ± 0.19</td><td>3.9 ± 0.85</td></tr></table>
+
+<|ref|>table_caption<|/ref|><|det|>[[114, 376, 883, 480]]<|/det|>
+Table 1: AFM and cryoEM determination of membrane thickness for considered lipid compositions. Heights were estimated using AFM tomography, reported values indicate the peak FWHH ± of the value distribution (see Supp. Fig. 4A-B and Methods). For cryoEM membrane height was determined from C1 unsharpened EM maps using the difference in z coordinate for the inner and outer leaflet at (x,y) far from the protein. Reported values are the average ± S.Dev of 3 different points. N.d. indicates compositions for which no cryoEM data was determined.
+
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+## 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, 375, 257]]<|/det|>
+- FalzoneetalSI.pdf- FalzoneetalMethods.pdf- Falzonenrreportingsummary.pdf- nreditorialpolicychecklist.pdf- FalzoneetalValidationReports.pdf
+
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+
+# LARP3, LARP7, and MePCE are Involved in the Early Stage of Human Telomerase RNA Biogenesis  
+
+Chi- Kang Tseng ( ckt0513@ntu.edu.tw) Department of Microbiology, College of Medicine, National Taiwan University Tsai- Ling Kao ( tsailing0905@gmail.com) College of Medicine, National Taiwan University, Yi- Hsuan Chen ( yihsuan1chen@gmail.com) College of Medicine, National Taiwan University, https://orcid.org/0000- 0002- 1029- 7632 Yu- Cheng Huang ( lilyhuang901102@gmail.com) College of Medicine, National Taiwan University, Peter Baumann ( peter@baumannlab.org) Gutenberg University https://orcid.org/0000- 0003- 4892- 1485  
+
+## Article  
+
+# Keywords:  
+
+DOI: https://doi.org/  
+
+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 --->
+
+# LARP3, LARP7, and MePCE are Involved in the Early Stage of Human Telomerase RNA Biogenesis  
+
+Tsai- Ling Kao<sup>1</sup>, Yi- Hsuan Chen<sup>1</sup>, Yu- Cheng Huang<sup>1</sup>, Peter Baumann<sup>2,3</sup>, and Chi- Kang Tseng<sup>1\*</sup>  
+
+<sup>1</sup>Department of Microbiology, College of Medicine, National Taiwan University, Taipei 100, Taiwan  
+
+<sup>2</sup>Institute of Developmental Biology and Neurobiology, Johannes Gutenberg University, 55099 Mainz, Germany  
+
+<sup>3</sup>Institute of Molecular Biology, 55128 Mainz, Germany  
+
+\* Corresponding authors
+
+<--- Page Split --->
+
+## Abstract  
+
+Human telomerase assembly is a highly dynamic process. Using biochemical approaches, we found that LARP3 and LARP7/MePCE are involved in the early stage and that their binding to hTR is destabilized when the mature hTR is produced. LARP7 and MePCE knockdown inhibits the conversion of the 3'- extended short (exS) form into mature hTR and the cytoplasmic accumulation of hTR, resulting in telomere shortening. LARP3 plays a negative role in preventing the processing of the 3'- extended long (exL) form and binding of LARP7 and MePCE. Interestingly, the tertiary structure of the exL form prevents LARP3 binding and facilitates hTR biogenesis. Supporting this process, LARP3 at low levels promotes hTR maturation, increases telomerase activity, and elongates telomeres. Our data suggest that LARP3 and LARP7/MePCE mediate the processing of hTR precursors and thus control the production of functional telomerase.
+
+<--- Page Split --->
+
+Telomerase is a ribonucleoprotein complex that contains two highly conserved components in its catalytic core. In humans, one core component is a noncoding RNA called human telomerase RNA (hTR); the other is a protein enzyme called human telomerase reverse transcriptase (hTERT). hTERT copies the template region within hTR to replenish telomeric DNA sequences. Thus, the ends of chromosomes are protected, and the lengths of telomeres are maintained \(^{1}\) . hTR is transcribed by RNA polymerase II and accumulates in a cell as a 451- nt- long RNA \(^{2}\) . Longer forms of this transcript have been reported \(^{3,4}\) . Accumulating evidence suggests that the longer transcripts are predominantly degraded by RNA exosomes in a process mediated by CBC and NEXT \(^{5}\) . However, a fraction of the long transcripts may be processed into the mature form \(^{5}\) . During hTR maturation, 3'- end processing is mediated in concert with multiple 3'- to- 5' exonucleases \(^{3,6,7}\) . A 3'- extended long form (exL, \(\geq 460\) - nt hTR) of hTR is first trimmed by the exosomal component RRP6 to produce the 3'- extended short form (exS, \(\geq 452\) - nt and \(\leq 460\) - nt hTR) \(^{3}\) . The exS of hTR is then processed by two other exonucleases (PARN and TOE1) that function in parallel and/or sequentially to produce mature 451- nt hTR \(^{5 - 8}\) . Given that PARN is detected mainly in the nucleolus and that TOE1 is located in Cajal bodies \(^{7}\) , the formation of mature hTR has been suggested to couple to 3'- end processing with RNA trafficking.  
+
+Human telomerase assembly proceeds via precise stepwise binding of protein components to hTR during 3'- end maturation \(^{3,5,9}\) . The structure of hTR is highly organized and plays a role in mediating its stability, trafficking, and maturation \(^{10}\) . The 3'- domain of hTR folds into a box H/ACA- like domain \(^{11}\) , which is bound by the box H/ACA complex \(^{12}\) . The assembly of the pre- H/ACA complex on hTR via cotranscription is thought to be critical for protecting longer transcripts from rapid degradation \(^{5,9}\) . A biochemical study showed that the exL form of hTR folds into a triple- helix structure \(^{3}\) . Although how the triple helix conformation transiently protects the
+
+<--- Page Split --->
+
+exL form of hTR from rapid degradation remains unclear, it creates an opportunity for the H/ACA complex to bind<sup>3</sup>. The binding of the H/ACA complex is not only critical for hTR stability but also attenuates processing by PARN at position \(451^{3}\) . Mutations in most well- characterized components of human telomerase and telomeres, as well as their accessory factors, have been reported in premature- ageing diseases, such as dyskeratosis congenita, Hoyeral- Hreidarsson syndrome, aplastic anaemia, and idiopathic pulmonary fibrosis<sup>13- 16</sup>.  
+
+At the molecular level, patients with these telomere biology disorders (TBDs) have characteristic accelerated telomere shortening. In addition to canonical TBDs, mutations in several other genes are associated with dysregulation of telomere maintenance in human diseases<sup>17</sup>. One of these dysregulated gene products is in the La- related protein (LARP) family, which is an important RNA- binding protein family that emerged early in eukaryote evolution and engaging in a large range of crucial functions in a cell involving both coding and noncoding RNAs<sup>18,19</sup>. Seven distinct LARP- encoding genes have been identified in humans. Among human LARPs, LARP3 (a genuine La protein) and LARP7 have previously been implicated in human telomere maintenance<sup>20,21</sup>. Aberrantly expression of LARP3 has been found in various cancer types, including chronic myelogenous leukaemia (CML)<sup>22</sup>. LARP3 has been shown to interact directly with hTR and cause telomere shortening when exogenous LARP3 is overexpressed in certain cell lines<sup>20</sup>. Whether LARP3 is involved in hTR biogenesis remains unclear.  
+
+A total of 52 pathogenic variants in the LARP7 gene have been identified in patients with Alazami syndrome<sup>23</sup>. Patients with Alazami syndrome exhibit very short telomeres, and LARP7 knockdown in cancer cells causes a reduction in telomerase activity and telomere shortening<sup>21</sup>. In ciliated protozoa and fission yeast, LARP family protein p65 in Tetrahymena thermophila<sup>24</sup>, p43 in Euplotes aediculatus<sup>25</sup>, and Pof8 in S. pombe<sup>26- 28</sup> are constitutive components of active
+
+<--- Page Split --->
+
+telomerase. In addition to LARP7, MePCE, a LARP7- interacting protein, has been implicated in neurodevelopment<sup>29</sup>. The heterozygous MePCE nonsense variant c.1552C>T/p. (Arg518\*) has been identified<sup>29</sup>. Patients with MePCE mutations exhibit a neurodevelopmental disorder phenotype similar to that of patients with loss- of- function mutations in LARP7. Bmc1, a human MePCE homologue, is a fission yeast telomerase holoenzyme<sup>30,31</sup>. Bmc1 cooperates with Pof8 to recognize correctly folded TER1<sup>30</sup>. Whether human LARP7 and MePCE are involved in hTR and biological functions in a manner analogous to that in other species remains unclear.  
+
+In this study, we established in vitro systems that allowed us to monitor hTR 3'- end maturation and protein component assembly. Telomerase assembled in vitro was functional. Using these systems, we found that LARP3, LARP7, and MePCE participate in the early stage of human telomerase biogenesis. LARP3 binds to the exL form of hTR before H/ACA complex binding and prevents 3'- end processing. The triple- helix structure of the exL form of hTR prevents binding by LARP3 and facilitates 3'- end processing. Supporting these observations, LARP3 knockdown facilitated the maturation of hTR and caused increases in telomerase activity. Consistent with the expression levels of LARP3 increasing during CML progression<sup>32</sup> and CML patients normally exhibiting short telomeres<sup>33</sup>, our data showed that reducing LARP3 expression caused an increase in telomerase activity and telomere elongation in K562 cells. LARP7 and MePCE binding then increases as LARP3 decreases during the conversion of the exS form into the mature form. LARP7 and MePCE knockdown caused telomere shortening by affecting both hTR maturation and localization. Our data suggest that human telomerase assembly is a highly dynamic process that involves compositional and conformational rearrangement, which leads to the production of a functional telomerase.
+
+<--- Page Split --->
+
+## Results  
+
+## The establishment of in vitro systems to examine the biogenesis of human telomerase  
+
+Establishing research to study the fates of human hTR precursors is challenging due to the extremely low abundance of endogenous pre- telomerase complexes in a cell. To overcome these limitations and to dissect the molecular mechanisms involved in hTR maturation, in vitro systems of human telomerase biogenesis are established. The in vitro systems we established to study hTR can be classified into 3 major parts: the examination of \(3^{\prime}\) - end maturation of hTR, telomerase component assembly, and telomerase activity (Supplementary Fig. 1a). To analyse the \(3^{\prime}\) - end processing of hTR, we synthesized the H/ACA domain of hTR (starting with nucleotide 206) of the exL form in vitro with oligo A tails in the presence of \(\alpha\) - \(^{32}\mathrm{P}\) - UTP. The oligoadenylated exL form of hTR was incubated in whole- 293T cell extract. During the incubation period, deadenylation neared completion within 10 min (Fig. 1a, lane 2). The exS and mature forms of hTR were produced after a 30\~60- min and 2- hour incubation, respectively (Fig. 1a, lanes 4 and 5). Consistent with previous observations indicating that more than \(80\%\) of the exL form is degraded in vivo \(^5\) , only \(20\%\) of the exL form was converted into the mature form of hTR in our assay (Fig. 1b and Supplementary Fig. 1b). These data indicate that the \(3^{\prime}\) - end processing of hTR was successful in vitro.  
+
+To examine the assembly of telomerase components on hTR, telomerase complexes assembled on the biotinylated exL form of hTR (nucleotides from 1 to 461 with an oligo A tail) with a monoguanosine cap (MMG) were purified at different time points by pulling RNP's down with streptavidin beads (Supplementary Fig. 1a). The purified telomerase complexes were subjected to western blotting (Fig. 1c). DHX36, which has been shown to interact with the \(5^{\prime}\) -
+
+<--- Page Split --->
+
+guanosine tracts of hTR \(^{34}\) , was pulled down. The binding of DHX36 to hTR exerted a minor effect on the maturation of the hTR 3' end (Fig. 1c, lanes 8- 12). All H/ACA complex components (DKC1, NHP2, NOP10, NAF1, and GAR1) were detected. This finding supports in vivo observations \(^{9,35}\) suggesting that NAF1 in the pre- H/ACA complex (NAF1- DKC1- NOP10- NHP2) binds to hTR and is subsequently replaced with GAR1 to produce a functional H/ACA complex. NAF1 was associated mainly with the exL form of hTR in the early maturation stage (Fig. 1c, lanes 9 and 10). In contrast, GAR1 was associated with hTR in the late stage, while NAF1 disassociated from the exL form of hTR (lanes 10- 12). TCAB1 appeared to associate with hTR after NAF1 disassociated along with GAR1 binding (lanes 10- 12).  
+
+To measure the catalytic effect of the in vitro assembled telomerase with either the mature or exL forms of hTR, a direct primer extension assay was performed to measure telomerase activity (Fig. 1d). The telomerase assembled with the exL and mature forms showed enzymatic activity (Fig. 1d). However, the enzymatic activity of the purified telomerase with mature hTR (lanes 5- 8) was higher than that of the exL- containing telomerase (lanes 1- 4). We further examined the processivity of the purified telomerase and plotted the normalized intensity of each telomere- extended species against the repeat number (Fig. 1e). Quantification analysis showed that the telomerase with the mature hTR showed higher processivity than that with the exL form (Fig. 1e). These data suggest that telomerase assembly undergoes compositional rearrangement during 3'- end maturation and that the removal of 3'- extended sequences from hTR may increase telomerase activity and processivity.  
+
+LARP3, LARP7, and MePCE are involved in the early stage of telomerase assemblyBiochemical and structural studies of telomerases from ciliated protozoa and fission yeast revealed
+
+<--- Page Split --->
+
+that an La- related protein and its interacting partners are the constitutive components of a telomerase holoenzyme and are critical for the assembly and activity of this telomerase<sup>26,30,36</sup>. Therefore, we examined the associations of all human La- related proteins with hTR. LARP3, LARP7 and MePCE were found to be significantly associated with hTR (Fig. 2a). A time course analysis revealed that LARP3 associated with the exL form of hTR before the binding of LARP7, MePCE, and the pre- H/ACA complex (Fig. 2a, lane 8). LARP7 and MePCE appeared to bind to hTR after LARP3 association and concurrently with binding of the pre- H/ACA complex (Fig. 2a, lane 9). All component binding in the telomerase complexes was destabilized when the mature hTR forms were produced (Fig. 2a, lanes 11- 12). To examine how the 3'- extended sequence affects component binding. The different forms of hTR species were individually generated, including the exL, exS, and mature forms, and the pseudoknot plus the 5' stem loop (3' ST del) and the pseudoknot domain of hTR (Fig. 2b). Western blotting of telomerase complexes assembled with the different hTR species revealed that DHX36 bound to all the forms of hTR. Consistent with previous studies showing that the 3' stem loop is critical for H/ACA complex assembly<sup>37</sup>, deletion of the 3' stem loop abolished the binding of DKC1 (Fig. 2b, lane 11). LARP7 and MePCE preferentially associated with the 3'- extended forms (exL and exS forms) of hTR (Fig. 2b, lanes 8- 10). The extension of the 451- nt hTR- end by 5 nucleotides (nucleotides 1- 455 in the exS form) and 10 nucleotides (nucleotides 1- 461 in the exL form) stabilized the binding of LARP7/MePCE and LARP3, respectively (Fig. 2b, lanes 8 and 9), suggesting that a 3'- extended sequence is required for the stable binding of LARP3, LARP7, and MePCE to hTR. Taken together, these data suggest that LARP3, LARP7, and MePCE are involved in the early stage of telomerase assembly and disassociate from each other when the functional telomerase is produced. Supporting these observations, purified LARP3-, LARP7-, and MePCE- associated endogenous telomerases were
+
+<--- Page Split --->
+
+produced and showed only low levels of telomerase activity (Fig. 2c).  
+
+## The LARP3 binding competes with tertiary structure formation  
+
+LARP3 preferentially associated with the exL form of hTR (Fig. 2b). The exL form of hTR is a highly organized structure that contains two stem- loop conformations and a 3'- terminal UUU stretch. The 3'- terminal UUU stretch in the exL form has been proposed to form a triple helix structure in concert with box H and the UCU sequence between the P4.2 and P5 stems \(^3\) (Fig. 3a). In addition, the 3'- terminal U stretch, which is commonly in the 3'- end of RNA polymerase III transcripts, is the binding target of LARP3 \(^{38}\) . This prompted us to speculate that the preferential binding of LARP3 to the exL form is due to either the 3'- terminal UUU stretch or the structure of the triple helix (Fig. 3a). First, we investigated the effect of the 3'- terminal UUU sequence on LARP3 binding. First, we generated U460C mutant hTR. The U460C mutant lacked the 3'- terminal UUU stretch but showed a strengthened triple- base interaction \(^3\) . If the exL form is normally bound by LARP3 via the triple helix structure, then the U460C mutant would recruit more LARP3 than if LARP3 binds the UUU stretch. In contrast, if the 3'- terminal UUU stretch of exL is the binding site of LARP3, then the U460C mutant will destabilize the association of LARP3 with the exL form of hTR. The results showed that the U460C hTR mutant pulled down less recombinant LARP3 than wild- type hTR, suggesting that LARP3 binding to hTR relied on the terminal UUU stretch in the exL form of hTR, while LARP3 binding to the exL form appeared to be attenuated by the triple helix structure (Fig. 3b).  
+
+The triple helix structure of the exL form plays a role in transiently protecting it from rapid degradation and creates an opportunity for the exL form to enter the biogenesis process that yields the mature form \(^3\) . Consistent with previous observations \(^3\) , the U460C hTR mutant, which
+
+<--- Page Split --->
+
+stabilized the tertiary structure in our study, affected the dynamics of 3'- end processing (Fig. 3c and Supplementary Fig. 2a). Incubation of the U460C mutant for 60 min led to the production of large quantities of the mature form (lane 9) compared to the amount of mature form obtained from wild- type hTR (lane 4). Analysis of in vitro telomerase assembly with the U460C mutant showed a decrease in the binding of LARP3 compared to its binding on wild- type hTR (Fig. 3d). Taken together, these data suggest that LARP3 binding to the exL form of hTR competes with the formation of tertiary structures in the exL form, determining the efficiency of mature hTR production.  
+
+## LARP3 plays a negative role in telomerase biogenesis  
+
+Our results suggest a role for tertiary RNA interactions in the exL form of hTR which promotes 3'- end processing via a mechanism that leads to competition between 3'- end processing and LARP3 binding (Fig. 3). We wondered whether LARP3 plays a negative role in hTR biogenesis. To examine the role of LARP3 in the processing of the exL form, LARP3 was either knocked down or overexpressed in 293T cells (Fig. 4a). There was a minor effect on the steady- state levels of hTR in LARP3- knockdown cells (Fig. 4b). LARP3 knockdown, however, did not substantially affect the assembly of DKC1 with hTR in vitro (Fig. 4c, lanes 1- 12). However, the telomerase activity was increased by 20% when the telomerase was purified by immunoprecipitation based on DKC1 pulldown (Fig. 4d, lane 4). Subjecting LARP3 knockdown- containing extracts to in vitro 3' processing facilitated the biogenesis of hTR (Fig. 4e, lanes 7- 12 and Supplementary Fig. 3a) in contrast to the outcome with control extracts (Fig. 4e, lanes 1- 6). These observations mimicked the effects of the U460C mutant (Fig. 3) and suggested that LARP3 plays a role in preventing 3'- end maturation.
+
+<--- Page Split --->
+
+To confirm the negative role of LARP3 in hTR 3'- end processing, we overexpressed LARP3 in 293T cells (Fig. 4a, lanes 3\~4). LARP3 overexpression caused a 1.2-fold and 3.1-fold increase in all forms and the 3'- exL form of hTR, respectively (Fig. 4b). In addition, a 40% decrease in telomerase activity was observed (Fig. 4d, lanes 5\~8). An in vitro telomerase assembly assay revealed that although it exerted minor effects on DKC1 binding, LARP3 overexpression markedly blocked the binding of LARP7 and MePCE to hTR (Fig. 4c, lanes 20\~24). Supporting the observations that LARP3 overexpression caused an increase in the fraction of the exL form, the 3'- end processing of exL was profoundly blocked (Fig. 4f and Supplementary Fig. 3b). These data indicated that the binding of LARP3 to hTR prevented the 3'- end processing of the exL form and may lead to exL targeted for degradation. In addition, the binding of LARP7/MePCE to hTR was blocked by LARP3 binding, suggesting that a switch from LARP3 binding to LARP7/MePCE binding is required for telomerase biogenesis.  
+
+## Reducing the expression level of LARP3 increases telomerase function and causes telomere elongation  
+
+Aberrant expression of LARP3 has been found in various cancers, including CML<sup>22</sup>. CML patients normally exhibit short telomeres<sup>33</sup>. Since LARP3 overexpression blocked the 3'- end processing of the exL form hTR (Fig. 4f), we speculated that reducing LARP3 expression levels would rescue the defects caused by LARP3 and may lead to increased telomere length. To evaluate this possibility, LARP3 was depleted in K562 cells (Fig. 5a and Supplementary Fig. 4a). The levels of both the mature and 3'- extended forms of hTR were increased in LARP3- knockdown cells (Fig. 5b). Consistent with this observation, an in vitro 3'- end processing assay indicated that relatively more of the exL from was converted into mature hTR (Fig. 5c and Supplementary Fig. 4b). In
+
+<--- Page Split --->
+
+addition, more telomerase was formed in vitro, as determined by more DKC1 molecules binding to hTR (Fig. 5d, lanes 8\~10). Supporting these findings, increased levels of telomerase activity were observed (Fig. 5e and Supplementary Fig. 4c). We measured telomere length by a telomere restriction fragment (TRF) assay (Fig. 5f). Telomeres were elongated in LARP3- knockdown cells (Fig. 5f, lanes 4\~6).  
+
+In aggregate, our data suggest that LARP3 plays a negative role in controlling telomere length by affecting telomerase biogenesis. LARP3 binds to the exL form of hTR, which prevents not only the binding of LARP7 and MePCE but also the processing of the exL form. As a result, telomerase assembly was impaired, which led to telomere shortening.  
+
+## LARP7 and MePCE knockdown impairs the processing of the exS form and causes cytoplasmic localization of hTR  
+
+LARP7 and MePCE were associated mainly with the exS form (Fig. 2). How LARP7 and MePCE affect exS processing or degradation remains unclear. To evaluate the requirements of LARP7 and MePCE for telomerase biogenesis, we prepared extracts from cells that had been subjected to LARP7 or MePCE knockdown (Fig. 6a and Supplementary Fig. 5a). LARP7 and MePCE knockdown did not affect the steady- state levels of hTR (Fig. 6b). An in vitro telomerase assembly assay showed that MePCE bound the exS form of hTR in the absence of LARP7 (Fig. 6c, lanes 5\~8) and vice versa. In the absence of LARP7 or MePCE, LARP3 bound to hTR relatively longer than it did in the shRNA- treated control cell extracts (Fig. 6c). We investigated the effect of LARP7 and MePCE knockdown on the processing of the exS form. Although exS was processed into mature hTR in the extracts from cells with LARP7 and MePCE knocked down (Fig. 6d, lanes 5, 10, and 15 and Supplementary Fig. 5b), the conversion rate of the exS form into the mature form
+
+<--- Page Split --->
+
+was reduced in extracts from cells with both LARP7 and MePCE knocked down (Fig. 6d, lanes 9 and 14) compared to that in the control extracts (Fig. 6d, lane 4).  
+
+LARP7 and MePCE knockdown mimicked the effect of inhibited PARN activity on the exS form processing<sup>3</sup>, which substantially impaired the conversion of exS into the mature form in vitro (Fig. 6d). Cytoplasmic localization of hTR has been previously observed in PARN- knockdown cells<sup>39</sup>. Induced pluripotent stem (iPS) cells from patients with PARN mutations produced short telomeres<sup>8</sup>. Supporting these observations, PARN- knockdown cells produced shorter telomeres (Fig. 6e, lanes 7 and 8), and 46% of hTR localized to the cytoplasm in PARN- knockdown cells, which was higher than that in control cells (32%) (Fig. 6f and g). We measured telomere length in LARP7- and MePCE- knockdown cells (Fig. 6e and Supplementary Fig. 5d). Telomeres in the LARP7- and MePCE- knockdown cells (Fig. 6e, lanes 3- 6) were shorter than those in the control cells (Fig. 6e, lanes 1- 2). In addition, the fraction of cytoplasmic hTR was increased (Fig. 6f and g). Taken together, these results indicated that LARP7 and MePCE were involved in the conversion of the exS form into the mature form. Defects in LARP7 and MePCE proteins caused the accumulation of hTR in the cytoplasm and telomere shortening.  
+
+## Discussion  
+
+Human telomerase biogenesis is a highly dynamic process that is initiated by the precise stepwise binding of protein components to the RNA subunit hTR/TERC. Each step serves as a checkpoint for quality control and plays a decisive role in the production of a mature telomerase versus the elimination of improper products<sup>3,5</sup>. Deficiency in telomerase components, including proteins and RNA, leads to degenerative human disease. Therefore, understanding telomerase biogenesis is critical for determining its medical relevance and elucidates the cause of telomere disorder
+
+<--- Page Split --->
+
+syndrome. Unfortunately, the low abundance of endogenous telomerase pre- complexes in cells makes it difficult to characterize the molecular mechanisms involved in vivo. To overcome these limitations, we established in vitro cell- free systems that allowed us to investigate telomerase assembly and 3'- end processing of hTR. Using these systems, we uncovered LARP3, LARP7, and MePCE as previously unknown players that are sequentially involved in the early stage of hTR biogenesis (Fig. 7).  
+
+LARP3 has been shown to bind with high affinity to 3' uridylate residues of RNA polymerase III transcripts immediately upon transcription termination; these precursors include 5S rRNA \(^{40}\) , tRNA \(^{40}\) and 7SK RNA \(^{41,42}\) . Similarly, our data indicated that LARP3 preferentially bound to the hTR precursor form exL prior to the binding of LARP7, MePCE, and the H/ACA complex (Fig. 2). The association of LARP3 with the exL form was stabilized by a terminal U stretch (Fig. 3). LARP3 knockdown facilitated the maturation of hTR and telomerase activity (Fig. 4). In contrast, LARP3 overexpression clearly prevented both the processing and degradation of the exL form in vitro and caused a reduction in telomerase activity (Fig. 4). Our data suggest that LARP3 negatively regulates telomerase activity at the level of telomerase biogenesis. Interestingly, the terminal U stretch is also essential for the tertiary structure conformations in the exL form, protecting it from rapid degradation and creating an opportunity for hTR maturation \(^{3}\) . The biogenesis pathway was highly activated when the tertiary structure of the exL form is stabilized after the introduction of a U460C mutation that attenuated LARP3 binding (Fig. 3). These data suggest that the amount of mature hTR is determined by kinetic competition between LARP3 binding to the exL form and the formation of the tertiary exL structure (Fig. 7). Excessive LARP3 blocked the maturation of hTR, and the disassociation of LARP3 was essential for the assembly of functional RNPs with hTR. LARP3 acts as an RNA chaperone to prevent pre- tRNA
+
+<--- Page Split --->
+
+misfolding<sup>43,44</sup>. However, whether LARP3 specifically recognizes the exL form hTR that fails to fold into the triple helix and targets this faulty hTR for degradation is unclear.  
+
+The average telomere length is normally shorter in CML patients than in healthy individuals<sup>33</sup>. Additionally, CML patients with long telomeres have been suggested to have a lower clinical risk profile than patients with short telomeres<sup>45</sup>. The study of the correlation between telomere length and CML progression suggests that patients in later phases (the accelerated phase and blast phase) present with considerably shorter telomeres than patients in the early phase (chronic phase)<sup>33</sup>. Notably, LARP3 expression correlates with poor clinical prognosis of CML and increases during CML progression<sup>32</sup>. Our studies established a link between LARP3 expression and human telomerase biogenesis. We showed that reducing the expression level of LARP3 in a CML cell line increased telomere length by promoting telomerase biogenesis and activity (Fig. 5). Together with the observations that the tertiary structure of the exL form attenuates LARP3 binding and facilitates telomerase biogenesis, our data suggest a novel drug intervention point. The development of a small molecule that either directly inhibits LARP3 binding to hTR or specifically targets hTR structure to prevent LARP3 binding may be an important strategy to increase telomerase function and improve the prognosis of CML.  
+
+Previous study suggested that RRP6 processes the terminal U tract and irreversibly disrupts the triple helix and generates the exS form and subsequently dyskerin precisely establishes the 451- nt end by attenuating the 3'- end processing of the exS form via PARN, suggesting that structural rearrangements of hTR is required for efficient maturation<sup>3</sup>. Our data indicated that the compositional exchange of protein components occurs in this process (Fig. 7). NAF1 is replaced with GAR1. LARP3 appears to disassociate from the exL form of hTR. The mutually exclusive interaction of 7SK RNP with LARP3 or LARP7 has been suggested, and LARP3 needs to be
+
+<--- Page Split --->
+
+replaced by LARP7 for the maturation of 7SK RNPs<sup>41</sup>. This may be the case with hTR. The binding of LARP7 and MePCE to hTR was attenuated by LARP3 overexpression (Fig. 4c). Notably, LARP3 maintained the association with the exS form longer in the absence of LARP7 and MePCE (Fig. 6c), suggesting that LARP7 and MePCE bind instead of LARP3. We found that LARP7 and MePCE knockdown impaired the PARN-mediated processing of the exS form into the mature form and, like PARN knockdown cells, caused cytoplasmic accumulation of hTR. Together with these observations, these data support a model in which LARP7 and MePCE promote the transition of a LARP3- associated pre- telomerase to a H/ACA complex- associated telomerase that promotes the conversion of the exS form into the mature form. Once this conversion is impaired, hTR would be exported to the cytoplasm and degraded by DCP2- XRN1. Loss of function in LARP7 and MePCE has been shown to cause Alazami syndrome<sup>21</sup> and neurodevelopmental disorders<sup>29</sup>, respectively. Reduced expression of LARP7 has been shown to cause a reduction in telomerase activity and result in progressively shorter telomeres in human cancer cell lines<sup>21</sup>. Previous works with S. pombe demonstrated that Pof8 plays a key role in S. pombe telomerase RNA folding quality control and forms a complex with Bmc1, the orthologue of MePCE, and Telomerase Holoenzyme Component 1 (Thc1), which promotes the assembly of a functional telomerase<sup>26- 28,30,31,46</sup>. Similar to that associated with S. pombe Bmc1, telomere shortening has been observed in MePCE- deficient human cells. Interestingly, Thc1 shares structural similarity with the nuclear cap- binding complex and PARN<sup>30</sup>. LARP7 and MePCE knockdown impaired the conversion of the exS form into the mature form. LARP7 bound hTR in a MePCE- independent manner and was required to stabilize the interaction of MePCE with hTR (Fig. 6c). Although LARP7 and MePCE contribute to the conversion of the exS form into the mature form, they do not remain stably associated with the active telomerase (Fig. 7). Compared
+
+<--- Page Split --->
+
+to S. pombe telomerase RNA, an additional 3'- end processing step is required for the 3' end maturation of telomerase RNA after spliceosomal cleavage in other species<sup>47,48</sup>. An investigation into the requirement of Pof8 for 3'- end processing in these species may yield interesting results. Our data not only suggest an evolutionary link in the biogenesis of telomerase among distant organisms but also provide new insights into the mechanisms underlying the pathogenesis of LARP3 and LARP7/MePCE deficiencies.  
+
+## Online methods  
+
+## Preparation of hTR RNA substrates  
+
+In vitro transcription reactions were carried out in 1X transcription buffer (Promega), \(0.5\mathrm{mM}\) ATP (CROYEZ), CTP (CROYEZ), and GTP (CROYEZ); \(0.1\mathrm{mM}\) UTP (CROYEZ); \(\alpha\) - 32P- UTP (3000 Ci mmol<sup>- 1</sup>, \(10\mathrm{mCi}\mathrm{ml}^{- 1}\) , PerkinElmer), \(0.2\mu \mathrm{g}\) of DNA template, \(40\mathrm{U}\) of RNasin (TOOLs), and 1 unit \(\mu \mathrm{l}^{- 1}\) T7 RNA polymerase (Promega). The reaction mixtures ( \(10\mu \mathrm{l}\) ) were incubated at \(37^{\circ}\mathrm{C}\) for 30 min followed by the addition of an equal volume of formamide dye. The RNA products were purified on a \(6\%\) polyacrylamide (19:1) gel containing \(8\mathrm{M}\) urea. The primers used to generate the DNA templates are listed in Supplementary Table 1. The loading control actin- 1 RNA was expressed via the Sp6 RNA polymerase (Promega).  
+
+## In vitro hTR 3'-end processing assay  
+
+In vitro hTR processing reactions ( \(10\mu \mathrm{l}\) ) were carried out at \(37^{\circ}\mathrm{C}\) in a buffer containing \(20\mathrm{mM}\) Tris- HCl (pH 7.5), \(50\mathrm{mM}\) KCl, \(2.5\mathrm{mM}\) \(\mathrm{MgCl}_2\) , \(40\mathrm{U}\) RNasin, \(2\mathrm{nM}\) 32P- labelled hTR RNA, and \(40\mu \mathrm{g}\) of whole- cell extracts. Reactions were stopped by the addition of stop buffer ( \(10\mathrm{mg}\mathrm{ml}^{- 1}\)
+
+<--- Page Split --->
+
+proteinase K in \(0.5\%\) SDS; \(40\mathrm{mM}\) EDTA; \(20\mathrm{mM}\) Tris- HCl, pH 7.5; and \(1000\mathrm{c.p.m.}\mu \mathrm{l}^{- 1}32\mathrm{P}\) - labelled actin mRNA) and incubation at \(37^{\circ}\mathrm{C}\) for \(30\mathrm{min}\) followed by extraction with phenol/chloroform preequilibrated with \(50\mathrm{mM}\) NaOAc (pH 5.0) and ethanol precipitation. The RNA was dissolved in \(80\%\) formamide dye and analysed on a \(6\%\) polyacrylamide (19:1) gel containing \(8\mathrm{M}\) urea.  
+
+## Preparation of capped hTR RNA substrates  
+
+In vitro transcription reactions were performed in 1X transcription buffer (Promega), \(0.5\mathrm{mM}\) nucleoside 5- triphosphates (NTPs), \(25\mu \mathrm{M}\) Bio11 UTP, \(\alpha - 32\mathrm{P}\) - UTP (3000 Ci mmol \(^{- 1}\) , \(10\mathrm{mCi}\mathrm{ml}^{- 1}\) , PerkinElmer), \(0.1\mu \mathrm{g}\) of DNA template, \(40\mathrm{U}\) of RNasin, and \(1\mathrm{U}\) of SP6 RNA polymerase (RiboMAX™, Promega). The reaction mixtures ( \(100\mu \mathrm{l}\) ) were incubated at \(37^{\circ}\mathrm{C}\) for 4 hours and then treated with DNase I (New England Biolabs) at \(37^{\circ}\mathrm{C}\) for 1 hour, followed by extraction with phenol/chloroform preequilibrated with \(50\mathrm{mM}\) NaOAc (pH 5.0) and ethanol precipitation. RNA was dissolved in \(80\%\) formamide dye and purified on a \(4\%\) polyacrylamide (29:1) gel containing \(8\mathrm{M}\) urea. The capping reactions were carried out in 1X capping buffer (New England Biolabs), \(0.5\mathrm{mM}\) GTP, \(0.1\mathrm{mM}\) SAM, and \(1\mathrm{U}\) of vaccinia virus capping enzyme (New England Biolabs). Reaction mixtures were incubated at \(37^{\circ}\mathrm{C}\) for 2 hours, followed by extraction with phenol/chloroform preequilibrated with \(50\mathrm{mM}\) NaOAc (pH 5.0) and ethanol precipitation. The RNA was dissolved in \(\mathrm{ddH_2O}\) .  
+
+## Telomerase pulldown  
+
+Telomerase was assembled in a buffer containing \(20\mathrm{mM}\) Tris- HCl (pH 7.5), \(50\mathrm{mM}\) KCl, \(2.5\mathrm{mM}\) \(\mathrm{MgCl}_2\) , \(40\mathrm{U}\) RNasin, \(50\mathrm{mM}\) capped hTR RNA, and \(10\mu \mathrm{g}\) of whole- cell extracts. The reaction
+
+<--- Page Split --->
+
+mixture (25 μl) was incubated at \(37^{\circ}\mathrm{C}\) for the desired times, followed by centrifugation at 15,000 r.p.m. at \(4^{\circ}\mathrm{C}\) for 2 min. The supernatant was incubated with streptavidin beads at \(4^{\circ}\mathrm{C}\) for 1 hour. The precipitants were washed with NET- 2 buffer (50 mM Tris- HCl pH 7.5, 150 mM NaCl, and \(0.05\%\) NP- 40) and then subjected to Western blotting.  
+
+## Immunoblotting  
+
+The human cell pellets were lysed in CHAPS lysis buffer containing \(0.5\%\) CHAPS, \(50\mathrm{mM}\) Tris- HCl (pH 8), \(50\mathrm{mM}\) KCl, \(1\mathrm{mM}\) MgCl2, \(1\mathrm{mM}\) EGTA, \(10\%\) glycerol, \(5\mathrm{mM}\) DTT, and \(1\mathrm{mM}\) PMSF. Cell extracts were diluted in \(2\times \mathrm{LDS}\) sample buffer. Proteins in cell lysate were loaded onto a 4- \(20\%\) Tris- glycine protein gel (mPAGE™ \(4 - 20\%\) Bis- Tris, Millipore) and transferred to a PVDF blot membrane (Bio- Rad). Low- fat milk (5%) in wash buffer ( \(10\mathrm{mM}\) Tris- HCl, pH 8.0; \(150\mathrm{mM}\) NaCl; \(1\mathrm{mM}\) EDTA; and \(10\%\) Triton X- 100) was used as a blocking reagent. The antibodies used in this study are listed in Supplementary Table 3.  
+
+## Cell culture and transduction  
+
+293T cells (ATCC® CRL- 3216TM) were maintained in DMEM (Gibco) supplemented with \(10\%\) heat- inactivated foetal bovine serum (Corning) and \(2\mathrm{mM}\) L- glutamine (Gibco) at \(37^{\circ}\mathrm{C}\) in a humidified atmosphere containing \(5\%\) CO2. HeLa cells (ATCC® CCL- 2TM) were maintained in DMEM (Gibco) supplemented with \(10\%\) heat- inactivated foetal bovine serum. K562 cells (horizon, HD PAR- 131) were maintained in IMEM medium (HyClone™) supplemented with \(10\%\) heat- inactivated foetal bovine serum. The cells were subcultured when the confluency reached \(80\%\) . The cells were transfected with \(15\mu \mathrm{g}\) of plasmid DNA using TransIT® LT1 (Mirus) for \(24\mathrm{hr}\) . The plasmids used for transfection are listed in Supplementary Table 2. Cells were transduced with
+
+<--- Page Split --->
+
+shRNAs for 24 hr. Medium containing \(2 \mu \mathrm{g} \mathrm{ml}^{- 1}\) puromycin was used to select the knockdown cells. Information on the shRNAs used for transduction is presented in Supplementary Table 4.  
+
+## Genomic DNA extraction  
+
+Genomic DNA was prepared from pellets (5×10<sup>6</sup> cells) with a GenElute<sup>TM</sup> Mammalian Genomic DNA Miniprep Kit (Sigma–Aldrich, Cat. No: G1N350- 1KT) according to the manufacturer's instructions.  
+
+## Terminal restriction fragment (TRF) analysis  
+
+Genomic DNA (1 \(\mu \mathrm{g}\) ) from 293T cells was digested with Hinf I (New England Biolabs) and Rsa I (New England Biolabs) restriction enzymes in 10X CutSmart® Buffer (NEB) at 37°C overnight. The digested gDNA fragments were separated on a 1% SeaKem® LE agarose gel (Lonza) by electrophoresis at 120 V for 12 hours, followed by capillary transfer to a Hybond- N<sup>+</sup> nylon transfer membrane (GE Healthcare) in 10X saline sodium citrate (SSC) for 14 hours. DNA was subsequently crosslinked twice to the membrane at 120 mJ in a UV Stratalinker 1800 (Stratagene, 254 nm, 120 mJ). The blot was prehybridized in Church buffer at 65°C for 1 hour and then hybridized with <sup>32</sup>P- dCTP- labelled (TTAGGG)<sub>3</sub> overnight. The blot was exposed to a phosphor imaging screen (Fujifilm) at room temperature overnight. Phosphor images were scanned by an Amersham Typhoon 5 scanner (Cytiva). The telomere length images were quantified and analysed by ImageQuantTL software (Cytiva).  
+
+## Telomerase activity assay
+
+<--- Page Split --->
+
+Telomerase activity reactions were performed in a \(10 - \mu \mathrm{l}\) reaction volume consisting of \(50~\mathrm{mM}\) Tris- HCl, \(\mathrm{pH}8.0\) ; \(50~\mathrm{mM}\) KCl; \(1\mathrm{mM}\) \(\mathrm{MgCl}_2\) ; \(1\mathrm{mM}\) spermidine; \(5\mathrm{mM}\) DTT; \(1\mathrm{mM}\) dATP; \(1\mathrm{mM}\) dTTP; \(10\mu \mathrm{M}\) dGTP; \(0.75\mu \mathrm{M}^{32}\mathrm{P}\) - \(\alpha\) - dGTP (3000 Ci mmol \(^{- 1}\) ); \(1\mu \mathrm{M}\) telomeric primer (TTAGGG) \(_3\) and \(2\mu \mathrm{g}\) of cell extract at \(37^{\circ}\mathrm{C}\) for 2 hours. Reactions were stopped with \(10~\mu \mathrm{l}\) of \(1\mathrm{mgml}^{- 1}\) proteinase K. DNA was extracted with phenol/chloroform equilibrated with \(50\mathrm{mM}\) NaOAc (pH 7.0) and ethanol precipitated with \(2.5\mathrm{M}\) ammonium acetate and \(10\mu \mathrm{g}\) of glycogen at \(- 80^{\circ}\mathrm{C}\) overnight. Reactions were then centrifuged for \(20\mathrm{min}\) at 14,000 r.p.m., and the pellets were washed with \(1\mathrm{ml}\) of \(70\%\) ethanol. The dried pellets were then resuspended in \(5\mu \mathrm{l}\) of \(80\%\) formamide loading buffer. Reaction products were analysed on a \(10\%\) polyacrylamide (19:1) gel containing \(8\mathrm{M}\) urea. All blots were prepared with products obtained from the same experiment and processed in parallel.  
+
+## qRT-PCR  
+
+Quantitative reverse transcription(qRT)- PCR was performed via the SYBR Green method. The 50- fold diluted random hexamer priming cDNA was amplified with the primers shown in Supplementary Table 5 and was performed with a CFX384TM Real- Time PCR System in a C1000 Touch™ Thermal Cycler (Bio- Rad) using iQ™ SYBR® Green Supermix (Bio- Rad, Cat. No. 1708882). The results were normalized to the GAPDH, ATP5β, and HPRT reference gene levels and measured by CFX Maestro software (Bio- Rad). Graphing and statistical analysis of the qRT- PCR results were performed using Prism 9 (GraphPad).  
+
+In situ hybridization (FISH) and immunofluorescence (IF)
+
+<--- Page Split --->
+
+Cells were fixed on coverslips with \(4\%\) paraformaldehyde (Thermo Scientific, Cat. No. 047317) and permeabilized with \(0.1\%\) Triton- X- 100. The cells were hybridized with hybridization buffer (2X SSC, \(10\%\) formamide, \(0.2\mathrm{mgml}^{- 1}\) , \(10\%\) dextran sulfate, \(0.4\mathrm{U}\) RNase inhibitor, \(1\mathrm{mgml}^{- 1}E\) coli tRNA). The cells were incubated with 7 Cy3- conjugated hTR oligos (Supplementary Table 6) at \(37^{\circ}\mathrm{C}\) overnight. For immunofluorescence experiments, cells were incubated with anti- Coilin primary antibody (Abcam, Cat. No. ab11822, \(0.5\mu \mathrm{gml}^{- 1}\) ) in \(1\%\) bovine serum albumin (BSA) for 2 hours, followed by FITC- conjugated AffiniPure goat anti- mouse IgG (H+L) (Jackson ImmunoResearch, Cat. No. 115- 095- 003, 1:100 dilution) secondary antibody for 1 hour. Cells were stained with Hoechst 33258 (Sigma- Aldrich, Cat. No. B2883- 1g, 1:1000 dilution) in \(1\%\) BSA for 10 min. Coverslips were mounted with Fluoromount™ Aqueous Mounting Medium (Sigma- Aldrich, Cat. No. F4680- 25ML). The images were photographed with a Carl Zeiss LSM880 microscope.
+
+<--- Page Split --->
+
+## References  
+
+1. Nandakumar, J. & Cech, T.R. Finding the end: recruitment of telomerase to telomeres. Nat. Rev. Mol. Cell Biol. 14, 69–82 (2013).  
+2. Feng, J. et al. The RNA component of human telomerase. Science 269, 1236–41 (1995).  
+3. Tseng, C.K., Wang, H.F., Schroeder, M.R. & Baumann, P. The H/ACA complex disrupts triplex in hTR precursor to permit processing by RRP6 and PARN. Nat. Commun. 9, 5430 (2018).  
+4. Theimer, C.A. et al. Structural and functional characterization of human telomerase RNA processing and cajal body localization signals. Mol. Cell 27, 869–81 (2007).  
+5. Tseng, C.K. et al. Human telomerase RNA processing and quality control. Cell Rep. 13, 2232–43 (2015).  
+6. Deng, T. et al. TOE1 acts as a 3' exonuclease for telomerase RNA and regulates telomere maintenance. Nucleic Acids Res. 47, 391–405 (2019).  
+7. Son, A., Park, J.E. & Kim, V.N. PARN and TOE1 constitute a 3' end maturation module for nuclear non-coding RNAs. Cell Rep. 23, 888–898 (2018).  
+8. Moon, D.H. et al. Poly(A)-specific ribonuclease (PARN) mediates 3'-end maturation of the telomerase RNA component. Nat. Genet. 47, 1482–8 (2015).  
+9. Darzacq, X. et al. Stepwise RNP assembly at the site of H/ACA RNA transcription in human cells. J. Cell Biol. 173, 207–18 (2006).  
+10. Qin, J. & Autexier, C. Regulation of human telomerase RNA biogenesis and localization. RNA Biol. 18, 305–315 (2021).  
+11. Mitchell, J.R., Cheng, J. & Collins, K. A box H/ACA small nucleolar RNA-like domain at the human telomerase RNA 3' end. Mol. Cell. Biol. 19, 567–76 (1999).  
+12. Fu, D. & Collins, K. Distinct biogenesis pathways for human telomerase RNA and H/ACA small nucleolar RNAs. Mol. Cell 11, 1361–72 (2003).  
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+
+## Acknowledgements  
+
+We thank all members of the Tseng laboratory for helpful discussions. This work was supported by MOST 111- 2636- B- 002- 026 - and NTU- 112V1403- 5.  
+
+## Figure legends  
+
+Fig. 1 The establishment of in vitro systems to examine the biogenesis of human telomerase. (a) The in vitro 3' end processing assay with \(^{32}\mathrm{P}\) - labeled hTR fragments (nucleotides 206 to 461 with oligo A tails) were carried out in 293T cell extracts at \(37^{\circ}\mathrm{C}\) for the indicated times. RNA was purified and resolved by a \(6\%\) polyacrylamide gel containing \(8\mathrm{M}\) urea. Actin acted as the loading control. (b) The exL and mature forms of hTR signals were quantified by ImageQuantTL and normalized to \(0\mathrm{min}\) , respectively. (c) Western blotting analysis of telomerase assembled on biotin
+
+<--- Page Split --->
+
+labelled hTR pulled down with streptavidin beads for the indicated times. (d) Telomerase activity of the in vitro purified telomerase assembled on exL and mature forms of hTR. (e) The intensity of each major band \((+4, + 10, + 16, + 22, + 28\) , and so on) from the telomerase activity assay in d was quantitated by phosphorimager analysis.  
+
+Fig. 2 LARP3, LARP7, and MePCE are involved in the early stage of telomerase assembly. (a) Western blotting analysis of in vitro assembled telomerase purified from the indicated times. (b) Western blotting analysis of in vitro assembled telomerase assembled on the different hTR species as shown in the schematic (exL, exS, mature, \(3^{\prime}\) stem loop- deleted, and pseudoknot). (c) Endogenous LARP3, LARP7, MePCE, and DKC1 were immunoprecipitated and subjected to telomerase activity assay.  
+
+Fig. 3 The LARP3 binding competes with tertiary structure formation. (a) Schematic showing the proposed mechanism of how the tertiary structure of exL affects the binding of LARP3. (b) Western blotting analysis of recombinant LARP3 pulled down with biotinylated wild type or the U460C mutant hTR. (c) The in vitro \(3^{\prime}\) end processing assay with \(^{32}\mathrm{P}\) - labeled wild type or U460C mutant hTR fragments (nucleotides 206 to 461 with oligo A tails) were carried out in 293T cell extracts at \(37^{\circ}\mathrm{C}\) for the indicated times. RNA was purified and resolved by a \(6\%\) polyacrylamide gel containing 8 M urea. Actin acted as the loading control. (d) Western blotting analysis of telomerase assembled on biotin- labeled wild type or U460C mutant hTR pulled down with streptavidin beads for the indicated times.  
+
+Fig. 4 LARP3 plays a negative role in telomerase biogenesis. (a) Western blots of cell extracts prepared from 293T cells treated with either shRNA targeting LARP3 or transfected with an LARP3 plasmid. Endogenous TUBULIN served as a loading control. (b) Total RNA prepared from 293T cells treated with either shRNA targeting LARP3 or transfected with an LARP3
+
+<--- Page Split --->
+
+plasmid was subjected to qRT- PCR for total hTR, \(3^{\prime}\) - extended hTR, GAPDH, ATP5β, and HPRT. Bar graph of mean fold change for hTR relative to the control samples and normalized to GAPDH, ATP5β, and HPRT. Mean values were calculated from triplicate qRT- PCR experiments of three biological replicates with bars representing SE. (c) Western blotting analysis of telomerase assembled on biotin- labelled hTR in the indicated extracts, followed by pulldown with streptavidin beads for the indicated times. (d) LARP3 was immunoprecipitated from cell extracts prepared from 293T cells either treated with either shRNA targeting LARP3 or transfected with an LARP3 plasmid and subjected to telomerase activity assay. (e and f) The in vitro \(3^{\prime}\) end processing assay with \(^{32}\mathrm{P}\) - labeled hTR fragments (nucleotides 206 to 461 with oligo A tails) were carried out in cell extracts prepared from 293T cells either treated with either shRNA targeting LARP3 (e) or transfected with an LARP3 plasmid (f) at \(37^{\circ}\mathrm{C}\) for the indicated times. RNA was purified and resolved by a \(6\%\) polyacrylamide gel containing \(8\mathrm{M}\) urea. Actin acted as the loading control.  
+
+Fig. 5 Reducing the expression level of LARP3 increases telomerase function and causes telomere elongation. (a) Western blots of cell extracts prepared from K562 cells treated with shRNA targeting Luciferase or LARP3. Endogenous TUBULIN served as a loading control. (b) Total RNA from LARP3- knockdown K562 cells was subjected to qRT- PCR for the measurement of the levels of total hTR, \(3^{\prime}\) - extended hTR, GAPDH, ATP5β, and HPRT. Bar graph of mean fold change for \(3^{\prime}\) - extended hTR relative to the control samples and normalized to GAPDH, ATP5β, and HPRT. Mean values were calculated from triplicate qRT- PCR experiments of three biological replicates with bars representing SE. (c) The in vitro \(3^{\prime}\) end processing assay with \(^{32}\mathrm{P}\) - labeled hTR fragments (nucleotides 206 to 461 with oligo A tails) were carried out in the indicated cell extracts. RNA was purified and resolved by a \(6\%\) polyacrylamide gel containing \(8\mathrm{M}\) urea. Actin acted as the loading control. (d) Western blotting analysis of telomerase assembled on biotin- labeled hTR in the
+
+<--- Page Split --->
+
+indicated extracts, followed by pulldown with streptavidin beads for the indicated times. (e) Endogenous DKC1 was immunoprecipitated and subjected to telomerase activity assay. (f) Telomere lengths determined by TRF analysis of gDNA prepared from K562 cells treated with the shRNA targeting Luciferase or LARP3.  
+
+Fig. 6 LARP7 and MePCE knockdown impairs the processing of the exS form and causes cytoplasmic localization of hTR. (a) Western blots of cell extracts prepared from 293T cells treated with shRNAs targeting LARP7 or MePCE. (b) Total RNA prepared from 293T cells treated with the shRNA targeting Luciferase, LARP7, or MePCE was subjected to qRT- PCR for the total hTR, 3'- extended hTR, GAPDH, ATP5β, and HPRT. Bar graph of mean fold change for 3'- extended hTR relative to the control samples and normalized to GAPDH, ATP5β, and HPRT. Mean values were calculated from triplicate qRT- PCR experiments of three biological replicates with bars representing SE. (c) Western blots of telomerase assembled on biotin- labeled hTR in the indicated extracts, followed by pulldown with streptavidin beads for the indicated times. (d) The in vitro 3' end processing assay with \(^{32}\mathrm{P}\) - labeled hTR fragments (nucleotides 206 to 461 with oligo A tails) were carried out in the indicated cell extracts. RNA was purified and resolved by a 6% polyacrylamide gel containing 8 M urea. Actin acted as the loading control. (e) Telomere lengths determined by TRF analysis of gDNA prepared from 293T cells treated with the shRNA targeting Luciferase, LARP7, MePCE, or PARN. (f) In situ hybridization and immunofluorescence data after sh- Luc, sh- PARN, sh- LARP7, and sh- MePCE treatment in HeLa cells. Coilin served as a Cajal body marker. The scale bar represents 5 μm. (g) Bar graph illustrating the distribution of hTR in the cytosolic and nuclear fractions.  
+
+Fig. 7 Schematic showing the working model.
+
+<--- Page Split --->
+
+## Figures  
+
+图  
+
+Figure 1  
+
+Figure 1- 7  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+Supplementary materials.pdf.pdfSupplementary materials.pdf.pdf
+
+<--- Page Split --->

preprint/preprint__05f1891193c1720f597ee19876aa1d2b3d061937d2a7931dcff717edf288996f/images_list.json

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+    "caption": "Figure 1. Behavioural task and model explanation. (a) Example trials from a representative participant, showing the true probability of high (H) and low (L) stimuli given current stimuli, trial stimulation given, and participant rated probabilities. Arrows pointing to jump points of true probabilities, where a large change happens. (b) Participant rating screens during the task, where they were asked to estimate the identity of the upcoming stimulus given the current one. For example, after a low stimulus participants would be asked to rate the probability of the upcoming stimulus being low (L -> L) or high (L -> H). (c) Markovian generative process of the sequence of low and high intensity stimuli, depicted in a. The transition probability matrix was resampled at change points, determined by a fixed probability of a jump.",
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+    "caption": "Figure 2. Behavioural results. (a) True vs rated probabilities for \\(\\mathrm{p(H|H)}\\) and \\(\\mathrm{p(H|L)}\\) from an example participant, a positive correlation suggests the participant correctly learned the stimuli probability, (b) Pearson's r for true vs rated probabilities for \\(\\mathrm{p(H|H)}\\) and \\(\\mathrm{p(H|L)}\\) within individual participants.",
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+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Model comparison results. (a) Bayesian model comparison based on model fitting evidence, in fMRI sessions. Subjects' predictive ratings of next trial's pain intensity were fitted with posterior means from Bayesian models, values from Rescorla-Wagner (reinforcement learning) model, and random fixed probabilities. Bayesian jump frequency model (assuming jumps in sequence and inference with stimuli frequency) was the winning model in both cases. (b) Individual subject model evidence.",
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+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Brain responses to noxious stimuli (high \\(>\\) low pain stimuli) in (a) sagittal, (b) axial and (c) coronal views (colorbar shows Z scores thresholded at \\(z > 3.3\\) , FWE corrected \\(p< 0.05\\) ).",
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+    "caption": "Figure 5. Posterior probability mean of high pain in Bayesian jump frequency model showed activations in the bilateral primary and secondary somatosensory cortex, primary motor cortex and right caudate (FDR corrected p&lt;0.001, colorbar shows Z scores &gt;3.3). (a) sagittal (b) axial and (c) coronal view.",
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+    "caption": "Figure 6. Uncertainty (SD) of the posterior probability of high pain in Bayesian jump frequency model was associated with activations in the right superior parietal cortex (FDR corrected \\(\\mathrm{p}< 0.001\\) , colorbar shows Z scores \\(>3.3\\) ). (a) sagittal (b) axial and (c) coronal view.",
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+    "caption": "Figure 7. Neural activity associated with the model update, i.e. the KL divergence between posteriors from successive trials (positive contrast), in (a) sagittal, (b) coronal, and (c) axial views (FDR corrected \\(p< 0.001\\) , colorbar shows Z scores \\(>3.3\\) ).",
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+    "caption": "Figure 8. Overlaying the temporal prediction of high pain (mean posterior probability, red-yellow), its uncertainty (SD posterior probability, blue) and the model update (KL divergence between successive posterior distributions, green); (FDR corrected \\(p< 0.001\\) , colorbar shows Z scores \\(>3.3\\) )",
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preprint/preprint__05f1891193c1720f597ee19876aa1d2b3d061937d2a7931dcff717edf288996f/preprint__05f1891193c1720f597ee19876aa1d2b3d061937d2a7931dcff717edf288996f.mmd

@@ -0,0 +1,332 @@
+
+# Learning the statistics of pain: computational and neural mechanisms  
+
+Flavia Mancini ( fm456@cam.ac.uk) University of Cambridge https://orcid.org/0000- 0001- 8441- 9236  
+
+Suyi Zhang University of Oxford  
+
+Ben Seymour University of Oxford https://orcid.org/0000- 0003- 1724- 5832  
+
+## Article  
+
+Keywords: pain, Bayesian models, sensory pain pathways  
+
+Posted Date: November 8th, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1003293/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Version of Record: A version of this preprint was published at Nature Communications on November 3rd, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 34283- 9.
+
+<--- Page Split --->
+
+## Learning the statistics of pain: computational and neural mechanisms  
+
+Flavia Mancini \(^{1}\) , Suyi Zhang \(^{2}\) , and Ben Seymour \(^{2}\)  
+
+\(^{1}\) Department of Engineering, University of Cambridge, Trumpington Street, Cambridge \(^{2}\) CB2 1PZ, United Kingdom \(^{2}\) Wellcome Centre for Integrative Neuroimaging, John Radcliffe Hospital, Headington, Oxford OX3 9DU, United Kingdom  
+
+\(^{8}\) Corresponding author: \(^{9}\) Flavia Mancini \(^{1}\) \(^{10}\) Email address: flavia.mancini@eng.cam.ac.uk  
+
+## ABSTRACT  
+
+\(^{12}\) Pain invariably changes over time, and these temporal fluctuations are riddled with uncertainty about body safety. In theory, statistical regularities of pain through time contain useful information that can be learned, allowing the brain to generate expectations and inform behaviour. To investigate this, we exposed healthy participants to probabilistic sequences of low and high- intensity electrical stimuli to the left hand, containing sudden changes in stimulus frequencies. We demonstrate that humans can learn to extract these regularities, and explicitly predict the likelihood of forthcoming pain intensities in a manner consistent with optimal Bayesian models with dynamic update of beliefs. We studied brain activity using functional MRI whilst subjects performed the task, which allowed us to dissect the underlying neural correlates of these statistical inferences from their uncertainty and update. We found that the inferred frequency (posterior probability) of high intensity pain correlated with activity in bilateral sensorimotor cortex, secondary somatosensory cortex and right caudate. The uncertainty of statistical inferences of pain was encoded in the right superior parietal cortex. An intrinsic part of this hierarchical Bayesian model is the way that unexpected changes in frequency lead to shift beliefs and update the internal model. This is reflected by the KL divergence between consecutive posterior distributions and associated with brain responses in the premotor cortex, dorsolateral prefrontal cortex, and posterior parietal cortex. In conclusion, this study extends what is conventionally considered a sensory pain pathway dedicated to process pain intensity, to include the generation of Bayesian internal models of temporal statistics of pain intensity levels in sensorimotor regions, which are updated dynamically through the engagement of premotor, prefrontal and parietal regions.  
+
+## INTRODUCTION  
+
+\(^{32}\) In recent years, our understanding of pain has shifted from viewing it as a simple responsive system to a complex predictive system, that interprets incoming inputs based on past experience and future goals (Fields, 2018). Indeed, all types of pain response, including perception, judgement and decision- making, are invariably and often strongly shaped by what pain is being predicted, and the nature of this influence gives clues regarding the fundamental architecture of the pain system in the brain (Buchel et al., 2014; Seymour and Mancini, 2020; Roy et al., 2014; Wiech, 2016). To date, most experimental strategies to study prediction have come from explicit cue- based paradigms, in which a learned or given cue, such as visual image, contains the relevant information about an upcoming pain stimulus. (Atlas et al., 2010; Buchel et al., 2014; Fazeli and Buchel, 2018; Geuter et al., 2017; Zhang et al., 2016). However, a much more general route to generate predictions relates to the background statistics of pain over time - the underlying base- rate of getting pain, and of different pain intensities, at any one moment. In principle, the pain system should be able to generate predictions based on how pain changes over time, in absence of external cues. This possibility is suggested by research in other sensory domains, showing that the temporal statistics of sequences of inputs are learned and inferred through experience - a process termed temporal statistical learning (Dehaene et al., 2015; Frost et al., 2015; Fiser and Aslin, 2002; Kourtzi and Welchman, 2019; Turk- Browne et al., 2005; Wang et al., 2017). We hypothesise that temporal statistical
+
+<--- Page Split --->
+
+learning also occurs in the pain system, allowing the brain to infer the prospective likelihood of pain by keeping track of ongoing temporal statistics and patterns. In this way, pain should effectively act as the cue for itself, instead of utilising a cue from a different sensory modality. This may be especially important in clinical contexts, in which pain typically comes in streams of inputs changing over time (Kajander and Bennett, 1992).  
+
+Here, we tested this hypothesis by designing a frequency learning paradigm involving long, probabilistic sequences of noxious stimuli of two intensities (low and high) that could suddenly change. We tested people's ability to generate explicit predictions about the probability of forthcoming pain, and probed the underlying neural mechanisms. In particular, following evidence in other sensory domains (Meyniel et al., 2016), we proposed that the brain uses a optimal Bayesian strategy to infer the background temporal statistics of pain. Importantly, this approach may allow us to map core regions of the pain system to specific functional information processing operations: the temporal prediction of pain, its uncertainty and update. Our hypothesis predicts that the predictive inference of pain stimuli should be encoded largely within pain processing brain regions (Conway and Christiansen, 2005). The uncertainty of the prediction is expected to implicate multisensory, intraparietal regions, as shown previously using visual and auditory stimuli (Meyniel and Dehaene, 2017).  
+
+## RESULTS  
+
+Thirty- five participants (17 females; mean age 27.4 years old; age range 18- 45 years) completed an experiment with concurrent brain fMRI scanning. They received continuous sequences of low and high intensity painful electrical stimuli, wherein they were required to intermittently judge the likelihood that the next stimulus was of high versus low intensity (figure 2 a). We designed the task such that the statistics of the sequence could occasionally and suddenly change, which meant that the the sequences effectively incorporated sub- sequences of stimuli. The statistics themselves incorporated two types of information. First, they varied in terms of the relative frequency of high and low intensity stimuli, to test the primary hypothesis that frequency statistics can be learned. Second, sequences also contained an additional aspect of predictability, in which the conditional probability of a stimulus depended on the identity of the previous stimulus (i.e. its transition probability). By having different transition probabilities between high and low stimuli within subsequences, it is possible to make a more accurate prediction of a forthcoming stimulus intensity over- and- above simply learning the general background statistics. For instance, if low pain tends to predict low pain, and high predicts high, then one tends to get 'clumping' patterns of pain (runs of high or low stimuli); or conversely if high predicts low and vice versa, one tends to get alternating patterns. Both might have the same overall frequency of high and low pain, but better predictions can be made by learning the temporal patterns within. Thus we were able to test the supplementary hypothesis that humans can learn the specific transition probabilities between different intensities, as shown previously with visual stimuli (Meyniel et al., 2016).  
+
+At the beginning of the experiment, participants were informed that the sequence was set by the computer and could occasionally change at any point in time. This design mirrored a well- studied task used to probe statistical learning with visual stimuli (Meyniel and Dehaene, 2017); participants were explicitly and occasionally asked to estimate the probability of forthcoming stimuli (figure 2 b). The sequence was thus defined by a set of transition probabilities: the probability of high or low pain following a high pain stimulus; and the probability of high or low pain following a low pain stimulus (i.e. a Markovian transition matrix; see example in figure 2 c). Occasionally, these probabilities were suddenly resampled, such that in fact the total task length of 1300 stimuli (split into 5 blocks) comprised typically about 50 subsequences (mean \(25 \pm 4\) stimuli per subsequence). Participants were not explicitly informed when these changes happened. Within these subsequences, the frequency of high (versus low) stimuli varied from 15% to 85%, and figure 2 a illustrates an example of a snapshot of a typical sequence, showing a couple of 'jump' points where the probabilities change. Figure 2 b shows the rating screen, with ratings being required on 4.8% of stimuli. Before the main experimental scanning session, subjects practiced the task for an average of roughly 1200 trials before the MRI sessions.  
+
+## Behavioural results  
+
+Participants were able to successfully learn to predict the intensity (high versus low) of the upcoming painful stimulus within the sequence. Fig 2a shows the positive correlation between stimulus rated and true probabilities for low and high pain respectively for an example individual (Pearson correlation for
+
+<--- Page Split --->
+
+this participant \(\mathrm{p(H|H)}\) \(\mathrm{r = 0.567}\) \(\mathrm{p = 4.61e - 4}\) \(\mathrm{p(H|L)}\) \(\mathrm{r = 0.348}\) \(\mathrm{p = 0.075}\) ; see supplementary figs 1- 2 for plots from all subjects). Across subjects, the within- individual Pearson's r between true and rated probabilities was significantly above zero. (Fig 2b, 26 out of 35 subjects had \(\mathrm{r > 0}\) : \(\mathrm{p(H|H)}\) \(\mathrm{r = 0.138\pm 0.225}\) \(\mathrm{t(34) = 3.65}\) \(\mathrm{p = 0.00088}\) , Cohen's \(\mathrm{d = 0.871}\) ; \(\mathrm{p(H|L)}\) \(\mathrm{r = 0.117\pm 0.220}\) \(\mathrm{t(34) = 3.15}\) \(\mathrm{p = 0.0034}\) , Cohen's \(\mathrm{d = 0.752}\) ; see also supplementary figures 1- 2; note that \(\mathrm{p(H|L)}\) and \(\mathrm{p(L|L)}\) are reciprocal, as well as \(\mathrm{p(H|L)}\) and \(\mathrm{p(L|L)}\) ).  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Behavioural task and model explanation. (a) Example trials from a representative participant, showing the true probability of high (H) and low (L) stimuli given current stimuli, trial stimulation given, and participant rated probabilities. Arrows pointing to jump points of true probabilities, where a large change happens. (b) Participant rating screens during the task, where they were asked to estimate the identity of the upcoming stimulus given the current one. For example, after a low stimulus participants would be asked to rate the probability of the upcoming stimulus being low (L -> L) or high (L -> H). (c) Markovian generative process of the sequence of low and high intensity stimuli, depicted in a. The transition probability matrix was resampled at change points, determined by a fixed probability of a jump. </center>  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Behavioural results. (a) True vs rated probabilities for \(\mathrm{p(H|H)}\) and \(\mathrm{p(H|L)}\) from an example participant, a positive correlation suggests the participant correctly learned the stimuli probability, (b) Pearson's r for true vs rated probabilities for \(\mathrm{p(H|H)}\) and \(\mathrm{p(H|L)}\) within individual participants. </center>
+
+<--- Page Split --->
+
+## Behavioural data modelling  
+
+## Model choice  
+
+Based on previous evidence in other sensory domains, we hypothesised that subjects use an optimal Bayesian strategy to infer the statistics over time (Meyniel, 2020; Meyniel et al., 2016). We fit subjects' ratings to four variations of a Bayesian model, according to two factors: first, sequence inference through stimulus frequency (by assuming the sequence as generated by a Bernoulli process, where subjects track how often they encountered previous stimuli), versus inference through transition probability (by assuming the sequence follows a Markov transition probability between successive stimuli, where the subject tracks such transition of previous stimuli). This distinguishes between whether participants learn simple statistics (our primary hypothesis), or are able to learn the full transition probabilities (supplementary hypothesis). The second factor was to whether the model incorporates the possibility of sudden changes (jumps) in stimuli probability, as occurs in the task paradigm, or ignores such possibilities (fixed). To compare against alternative models, we also fit a basic reinforcement learning model (Rescorla- Wagner with fixed learning rate, which is an established model of Pavlovian conditioning; (Rescorla et al., 1972)) and a baseline random model that assumes constant probabilities throughout the experiment for high and low pain respectively.  
+
+## Model fitting  
+
+The selected models estimate the probability of a pain stimulus' identity in each trial. The values predicted by the model can be fitted to actual subject predictive ratings gathered during the experiment. A model is considered a good fit to the data if the total difference between the model predicted values and the subjects' predictions is small. Within each model, free parameters were allowed to differ for individual subjects in order to minimise prediction differences. For Bayesian 'jump' models, the free parameter is the prior probability of sequence jump occurrence. For Bayesian fixed models, the free parameters are the window length for stimuli history tracking, and an exponential decay parameter that discounts increasingly distant previous stimuli. The RL model's free parameter is the initial learning rate, and random model assumes a fixed high pain probability that varies across subjects. The model fitting procedure minimises each subject's negative log likelihood for each model, based on residuals from a linear model that predicts subject's ratings using learning model predictors. The smaller the sum residual, the better fit a model's predictions are to the subject's ratings.  
+
+## Model comparison  
+
+We compared the different models using the likelihood calculated during fitting as model evidence. Fig 3a showed model frequency, model exceedance probability, and protected exceedance probability for each model, fitted for fMRI sessions of the experiment. Both comparisons showed the winning model was the 'Bayesian jump frequency' model inferring both the frequency of pain states and their volatility, producing predictions significantly better than alternative models (Bayesian jump frequency model frequency=0.563, exceedance probability=0.923, protected exceedance=0.924). Fig 3b reports the model evidence for each subject; it shows that, although the majority (n=23) of participants were best fit by the model that infers the background frequency, some participants (n=12) were better fit by the more sophisticated model that infers specific transition probabilities.  
+
+## Neuroimaging results  
+
+We used the winning computational model to generate trial- by- trial regressors for the neuroimaging analyses. The rationale of this approach is that neural correlation of core computational components of a specific model provides evidence that and how the model is implemented in the brain (Cohen et al., 2017).  
+
+First, a simple high>low pain contrast identified BOLD responses in the right thalamus, sensorimotor, premotor and supplementary motor cortex, insula, anterior cingulate cortex and left cerebellum (with peaks in laminae V- VI), consistent with the known neuroanatomy of pain responses (fig 4, table 1). The opposite contrast (low>high pain) is reported in Supplementary Figure 3 and Supplementary Table 1.  
+
+Next, we looked at BOLD correlations with the modelled posterior probability of high pain. For any pain stimulus, this reflects the newly calculated probability that the next stimulus will be high, i.e. the dynamic and probabilistic inference of high pain. This analysis identified BOLD responses in the bilateral primary and secondary somatosensory cortex, primary motor cortex and right caudate (fig 5, table 2). We report the opposite contrasts (posterior probability of low pain) in Supplementary Figure 3 and Supplementary Table 2.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. Model comparison results. (a) Bayesian model comparison based on model fitting evidence, in fMRI sessions. Subjects' predictive ratings of next trial's pain intensity were fitted with posterior means from Bayesian models, values from Rescorla-Wagner (reinforcement learning) model, and random fixed probabilities. Bayesian jump frequency model (assuming jumps in sequence and inference with stimuli frequency) was the winning model in both cases. (b) Individual subject model evidence. </center>  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Brain responses to noxious stimuli (high \(>\) low pain stimuli) in (a) sagittal, (b) axial and (c) coronal views (colorbar shows Z scores thresholded at \(z > 3.3\) , FWE corrected \(p< 0.05\) ). </center>
+
+<--- Page Split --->
+
+<table><tr><td></td><td>Cluster ID</td><td>X</td><td>Y</td><td>Z</td><td>Peak Stat</td><td>Cluster Size (mm3)</td></tr><tr><td>0</td><td>1</td><td>13</td><td>-17</td><td>5</td><td>6.886</td><td>2587</td></tr><tr><td>1</td><td>1a</td><td>13</td><td>-22</td><td>-3</td><td>4.957</td><td></td></tr><tr><td>2</td><td>2</td><td>33</td><td>-22</td><td>58</td><td>6.524</td><td>5247</td></tr><tr><td>3</td><td>2a</td><td>30</td><td>-19</td><td>49</td><td>5.953</td><td></td></tr><tr><td>4</td><td>2b</td><td>16</td><td>-17</td><td>68</td><td>5.524</td><td></td></tr><tr><td>5</td><td>3</td><td>37</td><td>-17</td><td>15</td><td>5.742</td><td>1186</td></tr><tr><td>6</td><td>4</td><td>6</td><td>-7</td><td>49</td><td>5.128</td><td>3486</td></tr><tr><td>7</td><td>4a</td><td>0</td><td>-2</td><td>43</td><td>4.967</td><td></td></tr><tr><td>8</td><td>4b</td><td>4</td><td>-19</td><td>49</td><td>4.333</td><td></td></tr><tr><td>9</td><td>4c</td><td>11</td><td>-14</td><td>49</td><td>4.289</td><td></td></tr><tr><td>10</td><td>5</td><td>-17</td><td>-60</td><td>-19</td><td>4.851</td><td>1707</td></tr><tr><td>11</td><td>5a</td><td>-10</td><td>-55</td><td>-16</td><td>4.651</td><td></td></tr><tr><td>12</td><td>5b</td><td>-7</td><td>-62</td><td>-22</td><td>4.217</td><td></td></tr></table>
+
+Table 1. High pain &gt; low pain stimuli activation clusters (FWE p<0.05).
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5. Posterior probability mean of high pain in Bayesian jump frequency model showed activations in the bilateral primary and secondary somatosensory cortex, primary motor cortex and right caudate (FDR corrected p&lt;0.001, colorbar shows Z scores &gt;3.3). (a) sagittal (b) axial and (c) coronal view.</center>
+
+<--- Page Split --->
+
+
+Table 2. Activation clusters associated with the posterior mean \(\mathrm{p(H)}\) of the Bayesian jump frequency model.   
+
+<table><tr><td>Cluster ID</td><td>X</td><td>Y</td><td>Z</td><td>Peak Stat</td><td>Cluster Size (mm3)</td></tr><tr><td>0</td><td>1</td><td>66</td><td>-7</td><td>27</td><td>6.477</td></tr><tr><td>1</td><td>1a</td><td>52</td><td>-7</td><td>33</td><td>5.787</td></tr><tr><td>2</td><td>2</td><td>-62</td><td>-7</td><td>33</td><td>5.924</td></tr><tr><td>3</td><td>2a</td><td>-46</td><td>-12</td><td>43</td><td>4.002</td></tr><tr><td>4</td><td>3</td><td>21</td><td>-12</td><td>24</td><td>4.885</td></tr><tr><td>5</td><td>3a</td><td>11</td><td>-2</td><td>15</td><td>4.197</td></tr><tr><td>6</td><td>3b</td><td>13</td><td>-7</td><td>21</td><td>4.140</td></tr></table>  
+
+In contrast, a right superior parietal region, bordering with the supramarginal gyrus, was implicated in the computation of the uncertainty (SD) of the posterior probability of high pain, a measure that reflects the uncertainty of pain predictions (figure 6 and table 3). The negative contrast of the posterior SD did not yield any significant cluster.  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6. Uncertainty (SD) of the posterior probability of high pain in Bayesian jump frequency model was associated with activations in the right superior parietal cortex (FDR corrected \(\mathrm{p}< 0.001\) , colorbar shows Z scores \(>3.3\) ). (a) sagittal (b) axial and (c) coronal view. </center>  
+
+A key aspect of the Bayesian model is that it provides a metric of the model update, quantified as the KL divergence between successive trial's posterior distribution. The KL divergence increases when the two successive posteriors are more different from each other, and the opposite when the posteriors are similar. We found that the KL divergence was associated with BOLD responses in left premotor cortex, bilateral dorsolateral prefrontal cortex, superior parietal lobe, supramarginal gyrus, and left somatosensory cortex (fig 7, table 4). For completeness, we report the negative contrast in Supplementary Figure 5 and
+
+<--- Page Split --->
+
+
+Table 3. Activation clusters associated with the uncertainty of the Bayesian jump frequency model.   
+
+<table><tr><td>Cluster ID</td><td>X</td><td>Y</td><td>Z</td><td>Peak Stat</td><td>Cluster Size (mm3)</td></tr><tr><td>0</td><td>1</td><td>40</td><td>-48</td><td>58</td><td>4.311</td></tr><tr><td>1</td><td>1a</td><td>47</td><td>-38</td><td>58</td><td>4.168</td></tr><tr><td>2</td><td>1b</td><td>33</td><td>-41</td><td>43</td><td>3.745</td></tr><tr><td>3</td><td>2</td><td>28</td><td>-58</td><td>49</td><td>4.084</td></tr></table>  
+
+Supplementary Table 3. Figure 8 overlays the posterior probability with its uncertainty and update (KL divergence). This shows that the temporal prediction of high pain and its update activate distinct, although neighbouring regions in the sensorimotor and premotor cortex, bilaterally. In contrast, the uncertainty of pain predictions activates a right superior parietal region that partially overlaps with the neural correlates of model update.  
+
+![](images/Figure_7.jpg)
+
+<center>Figure 7. Neural activity associated with the model update, i.e. the KL divergence between posteriors from successive trials (positive contrast), in (a) sagittal, (b) coronal, and (c) axial views (FDR corrected \(p< 0.001\) , colorbar shows Z scores \(>3.3\) ). </center>  
+
+## DISCUSSION  
+
+Pain is typically uncertain, and this is most often true when pain persists after injury. When pain persists, the brain needs to be able to track changes in intensity and patterns over time, in order to predict what will happen next and what to do about it. Here we investigated whether, in absence of external cues, the human brain can generate explicit (conscious) predictions about the likelihood of forthcoming pain, as these are central to the generation of internal models of pain and can be formally compared to normative models of statistical learning (Dehaene et al., 2015; Meyniel et al., 2016). This study provides evidence that humans can learn and predict the background temporal statistics of pain using optimal
+
+<--- Page Split --->
+
+
+Table 4. Activation clusters positively associated with the update (KL divergence) of the Bayesian jump frequency model.   
+
+<table><tr><td>Cluster ID</td><td>X</td><td>Y</td><td>Z</td><td>Peak Stat</td><td>Cluster Size (mm3)</td></tr><tr><td>0</td><td>1</td><td>-58</td><td>6</td><td>36</td><td>6.191</td></tr><tr><td>1</td><td>1a</td><td>-26</td><td>-2</td><td>49</td><td>5.945</td></tr><tr><td>2</td><td>1b</td><td>-60</td><td>4</td><td>21</td><td>4.935</td></tr><tr><td>3</td><td>1c</td><td>-43</td><td>0</td><td>55</td><td>4.516</td></tr><tr><td>4</td><td>2</td><td>-46</td><td>-41</td><td>40</td><td>6.098</td></tr><tr><td>5</td><td>2a</td><td>-36</td><td>-50</td><td>52</td><td>5.438</td></tr><tr><td>6</td><td>2b</td><td>-50</td><td>-41</td><td>55</td><td>3.789</td></tr><tr><td>7</td><td>3</td><td>59</td><td>11</td><td>24</td><td>5.308</td></tr><tr><td>8</td><td>4</td><td>47</td><td>-41</td><td>58</td><td>5.295</td></tr><tr><td>9</td><td>4a</td><td>37</td><td>-50</td><td>52</td><td>4.972</td></tr><tr><td>10</td><td>4b</td><td>37</td><td>-58</td><td>61</td><td>4.460</td></tr><tr><td>11</td><td>4c</td><td>30</td><td>-65</td><td>61</td><td>4.255</td></tr><tr><td>12</td><td>5</td><td>-62</td><td>-17</td><td>33</td><td>4.814</td></tr><tr><td>13</td><td>5a</td><td>-50</td><td>-24</td><td>33</td><td>4.584</td></tr><tr><td>14</td><td>5b</td><td>-46</td><td>-29</td><td>27</td><td>3.849</td></tr></table>  
+
+![](images/Figure_8.jpg)
+
+<center>Figure 8. Overlaying the temporal prediction of high pain (mean posterior probability, red-yellow), its uncertainty (SD posterior probability, blue) and the model update (KL divergence between successive posterior distributions, green); (FDR corrected \(p< 0.001\) , colorbar shows Z scores \(>3.3\) ) </center>
+
+<--- Page Split --->
+
+Bayesian inference with dynamic update of beliefs, allowing explicit prediction of the probability of forthcoming pain at any moment in time. Using neuroimaging, we reveal the neural correlates of the internal models of pain predictions. We found distinct neural correlates for the probabilistic, predictive inference of pain and its update. Pain predictions (i.e. mean posterior probability) are encoded in the bilateral, primary somatosensory and motor regions, secondary somatosensory cortex and right caudate, whereas the signal representing the update of the probabilistic model localises in adjacent premotor and superior parietal cortex. The superior parietal cortex is also implicated in the computation of the uncertainty of the probabilistic inference of pain. Overall, the results show that cortical regions typically associated with the sensory processing of pain (primary and secondary somatosensory cortices) encode how likely different pain intensities are to occur at any moment in time, in the absence of any other cues or information; the uncertainty of this inference is encoded in superior parietal cortex and used by a network of parietal- prefrontal regions to update the temporal statistical representation of pain intensity.  
+
+The ability of the brain to extract regularities from temporal sequences is well- documented in other sensory domains such as vision and audition (Kourtzi and Welchman, 2019; Dehaene et al., 2015), but pain is a fundamentally different system with intrinsic motivational value and direct impact on the state of the body (Baliki and Apkarian, 2015; Fields, 2018; Seymour, 2019). Despite this fundamental difference, we show that temporal inferences of pain are generated using optimal Bayesian inference - tracking the frequency of low and high intensity pain states and their volatility (i.e. how likely they are to change) based on past experience. A more complex strategy involves trying to infer higher level statistical patterns within these sequences, namely representing all the transition probabilities between different states (Meyniel et al., 2016). Although this model fits 1/3 of our subjects best, overall it was not favoured over the simpler frequency learning model, which best describes the behaviour of approximately 2/3 of our sample (figure 3). At this stage it is not clear whether this is because of stable inter- individual differences, or whether given more time, more participants would be able to learn specific transition probabilities. However, it is worth noting that stable, individual differences in learning strategy have been previously reported in visual statistical learning (Karlaftis et al., 2019; Wang et al., 2017).  
+
+The Bayesian frequency model is consistent with many other tasks that involve cognitive model learning or acquisition of explicit contingency knowledge across modalities, including pain (Yoshida et al., 2013; Jepma et al., 2018; Hoskin et al., 2019). This reflects a fundamentally different process to pain response learning - either in Pavlovian conditioning where simple autonomic, physiological or motor responses are acquired, or basic stimulus- response (instrumental / operant) avoidance or escape response learning. These behaviours are usually best captured by reinforcement learning models such as temporal difference learning (Seymour, 2019), and reflect a computationally different process (Carter et al., 2006). Having said that, such error- driven learning models have been applied to statistical learning paradigms in other domains before (Orpella et al., 2021), and so here we were able to directly demonstrate that it provided a less accurate model than Bayesian models (figure 3). In contrast to simple reinforcement learning models, Bayesian models allow building an internal, hierarchical model of the temporal statistics of the environment that can support a range of cognitive functions (Honey et al., 2012; Meyniel et al., 2016; Weiss et al., 2021).  
+
+A key benefit of the computational approach is that it allows us to accurately map underlying operations of pain information processing to their neural substrates. Our study shows that the probabilistic inference of high pain frequency is encoded in the bilateral sensorimotor cortex, secondary somatosensory cortex, and right caudate (figure 5). The neural correlates of pain predictions arising from predictive Bayesian inference seem to contrast to a certain extent with those arising from value- based learning, which is typically characterised by non- probabilistic model- free learning and involves insula, anterior cingulate and ventromedial prefrontal cortices (Seymour and Mancini, 2020). An exception to this is the observation that the caudate nucleus correlates well with the posterior probability of high pain (i.e. its temporal inference). Although it is difficult to interpret this without an accompanying experimentally- matched value learning task, and without measuring conditioned responses such as autonomic responses, it may represent the parallel or integrative role of caudate in multiple divergent learning processes.  
+
+A specific facet of the Bayesian model is the representation of an uncertainty signal, i.e. the posterior SD, and a model update signal, defined as the statistical KL divergence between consecutive posterior distributions. This captures the extent to which a model is updated when an incoming pain stimulus deviates from that expected, taking into account the uncertainty inherent in the original prediction. In our task, the uncertainty of the prediction was encoded in a right superior parietal region, which partially
+
+<--- Page Split --->
+
+overlapped with a wider parietal region associated with the encoding of the model update (figures 6, 8). This emphasises the close relationship between uncertainty and learning in Bayesian inference (Koblinger et al., 2021). A previous study on statistical learning in other sensory domains reported that a more posterior, intraparietal region, was associated with the precision of the temporal inference (Meyniel and Dehaene, 2017). The role of the superior parietal cortex in uncertainty representation is also evident in other memory- based decision- making tasks, as the superior parietal cortex is more active for low vs. high confidence judgements (Hutchinson et al., 2014; Moritz et al., 2006; Sestieri et al., 2010). In addition to the parietal cortex, the model update signal was encoded in the left premotor cortex and bilateral dorsolateral prefrontal cortex (figure 7), neighbouring regions activated by pain statistical inferences (figure 8). This is particularly interesting, as the premotor cortex sits along a hierarchy of reciprocally and highly interconnected regions within the sensorimotor cortex. The premotor cortex has also been implicated in the computation of an update signal in visual and auditory statistical learning tasks (Meyniel and Dehaene, 2017).  
+
+In conclusion, our study demonstrates that the pain system generates probabilistic predictions about the background temporal statistics of pain states, in absence of external cues and using Bayesian- like inference strategy. This extends both current anatomical and functional concepts of what is conventionally considered a 'sensory pain pathway', to include encoding not just stimulus intensity (Segerdahl et al., 2015; Wager et al., 2013) and location (Mancini et al., 2012), but the generation of more sophisticated and dynamic internal models of temporal statistics of pain intensity levels. Future studies will need to determine whether temporal statistical predictions modulate pain perception, similarly to other kinds of pain expectations (Büchel et al., 2014; Wiech, 2016; Wager et al., 2004). More broadly, temporal statistical learning is likely to be most important after injury, when continuous streams of fluctuating pain signals ascend nociceptive afferents to the brain, and their underlying pattern may hold important clues as to the nature of the injury, its future evolution, and its broader semantic meaning in terms of the survival and prospects of the individual. It is therefore possible that the underlying computational process might go awry in certain instances of chronic pain, especially when instrumental actions can be performed that might influence the pattern of pain intensity (Jepma et al., 2018; Jung et al., 2017). Thus, future studies could explore both how temporal statistical learning interacts with pain perception and controllability, as well as its application to clinical pain.  
+
+## METHODS  
+
+## Code and data availability  
+
+Raw functional imaging data is deposited at OpenNEURO https://openneuro.org/datasets/ds003836 and derived statistical maps are available at NeuroVault (upon acceptance]). Sequence generation, task instructions and behavioural data can be found at https://github.com/NoxLab- cam/pain_statistics_3tfrmri. Analysis code can be found at https://github.com/syzhang/tsl_paper.  
+
+## Participants  
+
+Thirty- five healthy participants (17 females; mean age 27.4 years old; age range 18- 45 years) took part in two experimental sessions, 2- 3 days apart: a pain- tuning and training session and an MRI session. Each participant gave informed consent according to procedures approved by University of Cambridge ethics committee (PRE.2018.046).  
+
+## Protocol  
+
+The electrical stimuli were generated using a DS5 isolated bipolar current stimulator (Digitimer), delivered to surface electrodes placed on the index and middle fingers of the left hand. All participants underwent a standardised intensity work- up procedure at the start of each testing day, in order to match subjective pain levels across sessions to a low- intensity level (just above pain detection threshold) and a high- intensity level that was reported to be painful but bearable (>4 out of 10 on a VAS ranging from 0 ['no pain'] to 10 ['worst imaginable pain']). The pain delivery setup was identical for lab- based and MR sessions. After identifying appropriate intensity levels, we checked that discrimination accuracy was >95% in a short sequence of 20 randomised stimuli. This was done to ensure that uncertainty in the sequence task would derive from the temporal order of the stimuli rather than their current intensity level or discriminability. If needed, we tweaked the stimulus intensities to achieve our target discriminability. Next, we gave the task instructions to each participants (openly available https://github.com/NoxLab- cam/pain_statistics_3tfrmri).
+
+<--- Page Split --->
+
+After receiving a shock on trial t, subjects were asked to predict the probability of receiving a stimulus of the same or different intensity on the upcoming trial (trial t+1). We informed participants that in the task they "would receive two kinds of stimuli, a low intensity shock and a high intensity shock. The L and H stimuli would be presented in a sequence, in an order set by the computer. After each stimulus, the following stimulus could be either the same or different than the previous one. The computer sets the probability that after a given stimulus (for example L) there would be either L or H" (we showed a visual representation of this example). We asked participants to "always try to guess the probability that after each stimulus there will the same or a different one" and we informed them that "the computer sometimes changes its settings and sets new probabilities", so to pay attention all the time. We also told them the sequence would be paused occasionally in order to collect probability estimates from participants using the scale depicted in Fig 1. A white fixation cross was displayed on a dark screen throughout the trial, except when a response was requested every 12- 18 trials. The interstimulus interval was 2.8- 3 seconds. There were 300 stimuli in each block, lasting approx. 8 minutes. Average intensity ratings for each stimulus level were collected after each block during a short break. Low intensity stimuli were felt by participants as barely painful, rated on average 1.39 (SD 0.77) on a scale ranging from 0 (no pain) to 10 (worst pain imaginable). In contrast, high intensity stimuli were rated as more than 4 times higher than low intensity stimuli (mean 5.74, SD 4.85). Participants were given 4 blocks of practice, 2- 3 days prior the imaging sessions, and 5 blocks (1500 stimuli in total) during task fMRI.  
+
+The sequence of stimuli was unique and generated as in (Meynie et al., 2016). L and H stimuli were drawn randomly from a 2x2 transition probability matrix, which remained constant for a number of trials (chunks). The probability of a change was 0.014. Chunks had to be \(>5\) and \(< 200\) trials long. In each chunk, transition probabilities were sampled independently and uniformly in the 0.15- 0.85 range (in steps of 0.05), with the constraint that at least one of the two transition probabilities must be \(> / < 0.2\) than in the previous chunk. Participants were not informed when the matrix was resampled, and a new chunk started.  
+
+Behavioural data analysis were conducted with Python packages pandas (pypi version 1.1.3) and scipy (pypi version 1.5.3). Effect size was calculated as Cohen's d for t- tests.  
+
+## Computational modelling of temporal statistical learning  
+
+Learning models The models used in comparison are listed as followed:  
+
+Random (baseline model) Probabilities are assumed fixed and reciprocal for high and low stimuli, where \(p_{h} = 1 - p_{l}\) ( \(p_{l}\) as free parameter). Uncertainty are also assumed fixed for high/low pain.  
+
+Rescorla- Wagner (RW model) Rated probabilities are assumed to be state values, which were updated as  
+
+\[V_{t + 1}\gets V_{t} + \alpha (R_{t} - V_{t})\]  
+
+, where \(R_{t} = 1\) if stimulus was low, and O otherwise. \(\alpha\) was fitted as free parameter (see (Rescorla et al., 1972)).  
+
+Bayesian models Bayesian models update each trial with stimulus identity information to obtain upcoming trial probability from posterior distribution (Meynie et al., 2016). Using Bayes' rule, the model parameters \(\theta_{t}\) is estimated at each trial \(t\) provided previous observations \(y_{1:t}\) (sequence of high or low pain), given a model \(M\) .  
+
+\[p(\theta_t|y_{1:t},M)\sim p(y_{1:t}|\theta_t,M)p(\theta_t,M)\]  
+
+Stimulus information can either be frequency or transition of the binary sequence. There are 'fixed' models that assume no sudden jump in stimuli probabilities, and 'jump' models that assume the opposite. The four combinations were fitted and compared.  
+
+1. Fixed frequency model For fixed models, the likelihood of parameters \(\theta\) follows a Beta distribution with parameters \(N_{h} + 1\) and \(N_{l} + 1\) , where \(N_{h}\) and \(N_{l}\) are the numbers of high and low pain in the sequence \(y_{1:t}\) . Given that the prior is also a flat Beta distribution with parameters [1,1], the posterior can be analytically obtained with:  
+
+\[p(\theta |y_{1:t}) = Beta(\theta |N_{h} + 1,N_{l} + 1)\]
+
+<--- Page Split --->
+
+The likelihood of a sequence \(y_{1:t}\) given model parameters \(\theta\) can be calculated as:  
+
+\[p(y_{1:t}|\theta) = p(y_{1}|\theta)\prod_{t = 2}^{t}p(y_{i}|\theta ,y_{i - 1})\]  
+
+Finally, the posterior probability of a stimulus occurring in the next trial can be estimated with Bayes' rule:  
+
+\[p(y_{t + 1}|y_{1:t}) = \int p(y_{t + 1}|\theta ,y_{t})p(\theta |y_{1:t})d\theta\]  
+
+Priors window and decay were fitted as free parameters, where window is the previous \(n\) trials where frequency of stimuli were estimated, and decay is the previous \(n\) trials where the frequency of stimuli further from current trial were discounted following an exponential decay.  
+
+When window \(= w\) is applied, then \(N_{h}\) and \(N_{l}\) are counted within the window of \(w\) trials \(y_{t - w,t}\) . When decay \(= d\) is applied, an exponential decay factor \(e^{(-\frac{k}{d})}\) is applied to the \(k\) trials before their sum is calculated. Both window and decay were used simultaneously.  
+
+2. Fixed transition model Priors window and decay were fitted as free parameters as Fixed frequency model above, however, the transition probability was estimated instead of frequency. The likelihood of a stimuli now depends on the estimated transition probability vector \(\theta \sim [\theta_{h|l},\theta_{l|h}]\) and the previous stimulus pairs \(N\sim [N_{h|l},N_{l|h}]\) . Given that both likelihood and prior can be represented using Beta distributions as before, the posterior result can be analytically obtained as:  
+
+\[p(\theta |y_{1:t}) = Beta(\theta_{h|l}|N_{h|l} + 1,N_{l|l} + 1)Beta(\theta_{l|h}|N_{l|h} + 1,N_{h|h} + 1)\]  
+
+3. Jump frequency model In jump models, parameter \(\theta\) is no longer fixed, instead it can change from one trial to another with a probability of \(p_{jump}\) . Prior \(p_{jump}\) was fitted as a free parameter, representing the subject's assumed probability of a jump occurring during the sequence of stimuli (e.g. a high \(p_{jump}\) assumes the sequence can reverse quickly from a low pain majority to a high pain majority). The model can be approximated as a Hidden Markov Model (HMM) in order to compute the joint distribution of \(\theta\) and observed stimuli iteratively,  
+
+\[p(\theta_{t + 1},y_{1:t + 1}) = p(y_{t + 1}|\theta_{t + 1},y_{t})\int p(\theta_{t},y_{1:t})p(\theta_{t + 1}|\theta_{t})d\theta_{t}\]  
+
+where the integral term captures the change in \(\theta\) from one observation \(t\) to the next \(t + 1\) , with probability \((1 - p_{jump})\) of staying the same and probability \(p_{jump}\) of changing. This integral can be calculated numerically within a discretised grid. The posterior probability of a stimulus occurring in the next trial can then be calculated using Bayes' rule as  
+
+\[p(y_{t + 1}|y_{1:t}) = \int p(y_{t + 1}|\theta_{t + 1})p(\theta_{t + 1}|y_{1:t}\theta_{t + 1})\] \[\qquad = \int p(y_{t + 1}|\theta_{t + 1})\left[\int p(\theta_{t}|y_{1:t})p(\theta_{t + 1}|\theta_{t})d\theta_{t}\right]d\theta_{t + 1}\] \[\qquad = \int p(y_{t + 1}|\theta_{t + 1})\left[(1 - p_{jump})p(\theta_{t + 1} = \theta_{t}|y_{1:t}) + p_{jump}p(\theta_{0})\right]d\theta_{t + 1}\]  
+
+4. Jump transition model Similar to jump frequency model above, prior \(p_{jump}\) was fitted as a free parameter, but estimating transition instead of frequency. The difference is the stimulus at trial \(y_{t + 1}\) now dependent of stimulus at the previous trial, hence the addition of the term \(y_{t}\) in the joint distribution term, shown below.  
+
+\[p(y_{t + 1}|y_{1:t}) = \int p(y_{t + 1}|\theta_{t + 1},y_{t})\left[(1 - p_{jump})p(\theta_{t + 1} = \theta_{t}|y_{1:t}) + p_{jump}p(\theta_{0})\right]d\theta_{t + 1}\]
+
+<--- Page Split --->
+
+KL divergence Kullback- Leibler (KL) divergence quantifies the distance between two probability distributions. In the current context, it measures the difference between the posterior probability distributions of successive trials. It is calculated as  
+
+\[D_{K L}(P\parallel Q) = \sum_{x\in \mathcal{X}}P(x)l o g\left(\frac{P(x)}{Q(x)}\right)\]  
+
+330 , where \(P\) and \(Q\) represents the two discrete posterior probability distributions calculated in discretised 331 grids \(\mathcal{X}\) . KL divergence can be used to represent information gains when updating after successive trials 332 (Meyniel and Dehaene, 2017).  
+
+Subject rated probability For each individual subject, model predicted probabilities \(p_{k}\) from the trial \(k\) was used as predictors in the regression:  
+
+\[y_{k}\sim \beta_{0} + \beta_{1}\cdot p_{k}(M_{i},\theta_{i}) + \beta_{2}\cdot N_{s} + \epsilon\]  
+
+333 where \(y_{k}\) is the subject rated probabilities, \(M_{i}\) is the \(i\) th candidate model, \(N_{s}\) is the session number within subject, \(\beta_{0}\) , \(\beta_{1}\) , \(\beta_{2}\) and \(\theta_{i}\) are free parameters to be fitted, and \(\epsilon\) is normally distributed noise added 335 to avoid fitting errors (Maheu et al., 2019).  
+
+## Model fitting  
+
+337 To estimate the model free parameters from data, Bayesian information criteria (BIC) values were 338 calculated as:  
+
+\[\mathrm{BIC} = n\cdot \log \hat{\sigma}_{\epsilon}^{2} + k\cdot \log n\]  
+
+\[\hat{\sigma}_{\epsilon}^{2} = \min_{n}\frac{1}{n}\sum_{k = 1}^{n}\left(y_{k} - \hat{y}_{k}\right)\]  
+
+339 where \(\hat{\sigma}^{2}\) is the squared residual from the linear model above that relates subject ratings to model predicted 340 probabilities, and \(n\) is the number of free parameters fitted.  
+
+341 We use fmincon in MATLAB to minimise the BIC (as approximate for negative log likelihood, Maheu 342 et al. (2019)) for each subject/model. The procedure was repeated 100 times with different parameter 343 initialisation, and the mean results of these repetitions were taken as the fitted parameters and minimised 344 log likelihoods.  
+
+## Model comparison  
+
+346 In general, the best fit model was defined as the candidate model with the lowest averaged BIC. We 347 conducted a random effect analysis with VBA toolbox (Daunizeau et al., 2014), where fitted log likelihoods 348 from each subject/model pair was used as model evidence. With this approach, model was treated as 349 random effects that could differ between individuals. This comparison produces model frequency (how 350 often a given model is used by individuals), model exceedance probability (how likely it is that any given 351 model is more frequent than all other models in the comparison set), and protected exceedance probability 352 (corrected exceedance probability for observations due to chance) (Stephan et al., 2009; Rigoux et al., 353 2014). These values are correlated and would be considered together when selecting the best fit model.  
+
+## Neuroimaging data  
+
+## Data acquisition  
+
+356 First, we collected a T1- weighted MPRAGE structural scan (voxel size 1 mm isotropic) on a 3T Siemens 357 Magnetom Skyra (Siemens Healthcare), equipped with a 32- channel head coil (Wolfson Brain Imaging 358 Centre, Cambridge). Then we collected 5 task fMRI sessions of 246 volumes using a gradient echo 359 planar imaging (EPI) sequence (TR = 2000 ms, TE = 23 ms, flip angle = 78°, slices per volume = 31, 360 Grappa 2, voxel size 2.4 mm isotropic, A>P phase- encoding; this included four dummy volumes, in 361 addition to those pre- discarded by the scanner). In order to correct for inhomogeneities in the static 362 magnetic field, we imaged 4 volumes using an EPI sequence identical to that used in task fMRI, inverted 363 in the posterior- to- anterior phase encoding direction. Full sequence metadata are available at OpenNeuro 364 (https://openneuro.org/datasets/ds003836).
+
+<--- Page Split --->
+
+## Preprocessing  
+
+Imaging data were preprocessed using fmriprep (pypi version: 20.1.1, RRID:SCR_016216) with Freesurfer option disabled, within its Docker container. Processed functional images had first four dummy scans removed, and then smoothed in an 8mm Gaussian filter in SPM12.  
+
+## GLM analysis  
+
+Nipype (pypi version: 1.5.1) was used for all fMRI processing and analysis within its published Docker container. Nipype is a python package that wraps around fMRI analysis tools including SPM12 and FLS in a Debian environment.  
+
+First and second level GLM analyses were conducted using SPM12 through nipype. In all first level analyses, 25 regressors of no interest were included from fmriprep confounds output: CSF, white matter, global signal, dvars, std_dvars, framewise displacement, rmsd, 6 a_comp_cor with corresponding cosine components, translation in 3 axis and rotation in 3 axis. Sessions within subject are not concatenated.  
+
+In second level analyses, all first level contrasts were entered into a one- sample T- test, with group subject mask applied. The default FDR threshold used was 0.001 (set in Nipype threshold node height_threshold=0.001).  
+
+For visualisation and cluster statistics extraction, nilearn (pypi version: 1.6.1) was used. A cluster extent of 10 voxels was applied. Visualised slice coordinates were chosen based on cluster peaks identified. Activation clusters were overlayed on top of a subject averaged anatomical scan normalised to MNI152 space as output by fmriprep.  
+
+## GLM design  
+
+All imaging results were obtained from a single GLM model. We investigated neural correlates using the winning Bayesian jump frequency model. All model predictors were generated with the group mean fitted parameters in order to minimise noise. First level regressors include the onset times for all trials, high pain trials, and low pain trials (duration=0). The all trial regressor was parametrically modulated by model- predicted posterior mean of high pain, the KL divergence between successive posterior distributions on jump probability, and the posterior SD of high pain.  
+
+For second level analysis, both positive and negative T- contrasts were obtained for posterior mean, KL divergence and uncertainty parametric modulators, across all the first level contrast images from all subjects. A group mean brain mask was applied to exclude activations outside the brain. Given that high and low pain are reciprocal in probabilities, a negative contrast of posterior mean of low pain would be equivalent to the posterior mean of high pain. In addition, high and low pain comparisons were done using a subtracting T- contrast between high and low pain trial regressors. We corrected for multiple comparisons with a cluster- wise FDR threshold of \(p< 0.001\) for both parametric modulator analyses, reporting only clusters that survived this.  
+
+## ACKNOWLEDGEMENTS  
+
+The study was funded by a Medical Research Council Career Development Award to Flavia Mancini (MR/T010614/1) and Wellcome Trust grants to Ben Seymour (097490). We are grateful to Professor Zoe Kourtzi and Dr Michael Lee for helpful discussions about the concept of the study, and to the staff of the Wolfson Brain Imaging Centre for their support during data collection. The authors declare no competing interest.  
+
+## AUTHOR CONTRIBUTIONS  
+
+FM and BS designed the study. FM collected the data and SZ analysed the data. All authors wrote the paper.  
+
+## REFERENCES  
+
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+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- tslfrmisupplementary.pdf- rs.pdf
+
+<--- Page Split --->

preprint/preprint__06076107a582a7db1a993272bc8d0902287719a4fcc5b06c29c18d0dc685d84a/preprint__06076107a582a7db1a993272bc8d0902287719a4fcc5b06c29c18d0dc685d84a.mmd

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+
+# Pan-cancer copy number variant analysis identifies optimized size thresholds and co-occurrence models for individualized risk-stratification  
+
+David Raleigh  
+
+david.raleigh@ucsf.edu  
+
+University of California San Francisco https://orcid.org/0000- 0001- 9299- 8864  
+
+Minh Nguyen University of California San Francisco  
+
+William Chen UCSF https://orcid.org/0000- 0001- 8924- 5853  
+
+Naomi Zakimi Univeristy of California San Francisco  
+
+Kanish Mirchia Univeristy of California San Francisco https://orcid.org/0000- 0002- 7371- 7059  
+
+Calixto- Hope Lucas  
+
+Johns Hopkins University https://orcid.org/0000- 0002- 8347- 9592  
+
+## Brief Communication  
+
+Keywords:  
+
+Posted Date: January 11th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3443805/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 2nd, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 61063- y.
+
+<--- Page Split --->
+
+## Abstract  
+
+Chromosome instability leading to accumulation of copy number gains or losses is a hallmark of cancer. Copy number variant (CNV) signatures are increasingly used for clinical risk- stratification, but size thresholds for defining CNVs are variable and the biological or clinical implications of CNV size heterogeneity or co- occurrence patterns are incompletely understood. Here we analyze CNV and clinical data from 565 meningiomas and 9,885 tumors from The Cancer Genome Atlas (TCGA) to develop tumor- and chromosome- specific CNV size- dependent and co- occurrence models for clinical outcomes. Our results reveal prognostic CNVs with optimized size thresholds and co- occurrence patterns that refine risk- stratification across a diversity of human cancers.  
+
+## Main  
+
+Chromosome instability contributes to the genomic complexity of cancer<sup>1</sup> and is implicated in tumorigenesis, progression, metastasis, and resistance to therapy<sup>2- 4</sup>. As a marker of chromosome instability, CNV signatures are increasingly used for clinical risk- stratification of diverse cancer types<sup>5,6</sup>, and pan- cancer databases such as TCGA<sup>7</sup> have been used to derive prognostic models based on CNVs<sup>6,8</sup>. There is no consensus on the optimal size threshold for defining or reporting CNVs, and CNV co- occurrence patterns that may improve risk- stratification models are incompletely understood.  
+
+To test the hypothesis that size- dependent CNV models and co- occurrence patterns may improve clinical risk- stratification, CNV size- dependence was investigated in meningiomas, a tumor that is not represented in TCGA datasets but is associated with recurrent CNVs that can be used for risk- stratification<sup>9,10</sup>. Loss of chromosomes 1p, 6q, and others distinguish biologically aggressive meningiomas<sup>9,10</sup>, but published models have applied inconsistent size thresholds ranging from 5–80% of individual chromosome arms to define meningioma CNVs<sup>9–12</sup>. Using a previously described cohort of 565 meningiomas with long- term clinical outcomes data<sup>11</sup>, we used DNA methylation arrays to define CNVs ranging from individual CpG loci to entire chromosome arms (Extended Data Fig. 1). Next, we used CNVs ranging from 5–95% of each chromosome arm to generate univariate Cox proportional hazards models for postoperative local freedom from recurrence (LFFR) or overall survival (OS). These analyses revealed “size- dependent” CNVs (Fig. 1a), defined as having a maximum area under the curve (AUC) for 5- year LFFR or OS of at least 0.60 that decreased by at least 5% from the maximum AUC as CNV threshold varied (Supplementary Table 1).  
+
+The implications of CNV size- dependence for meningioma risk- stratification were investigated using 2 robust models that rely on CNVs to predict postoperative meningioma LFFR. The first, integrated grade, is based on copy number losses of chromosomes 1p, 3p, 4p/q, 6p/q, 10p/q, 14q, 18p/q, and 19p/q at a uniform threshold of 50% of each chromosome arm plus CDKN2A loss and mitotic count from histology<sup>9</sup>. The second, integrated score, is based on copy number losses of chromosomes 1p, 6q, and 14q at a uniform threshold of 5% of each chromosome arm plus DNA methylation family<sup>13</sup> and World
+
+<--- Page Split --->
+
+Health Organization (WHO) histological grade \(^{10}\) . We tested each model on our cohort of 565 meningiomas using CNV thresholds ranging from 5–95% (Fig. 1b). Integrated grade reached a maximum AUC for 5- year LFFR of 0.78 at a uniform CNV threshold of 20%, and a maximum AUC for OS of 0.77 at a uniform threshold of 30%. Integrated score reached a maximum AUC for LFFR or OS of 0.76 at a uniform CNV threshold of 5%. The performance of each model degraded with varying CNV size thresholds (Fig. 1b), suggesting that CNV size heterogeneity influences risk- stratification for the most common primary intracranial tumor \(^{14}\) .  
+
+To determine if models based on chromosome- specific CNV size thresholds could improve meningioma risk- stratification, LASSO and elastic net regularized Cox models were trained using optimized CNVs thresholds across the 565 meningiomas in our cohort (Extended Data Fig. 2). Cross- validated AUCs for 5- year LFFR or OS were 0.76 for LASSO models and 0.77–0.78 for elastic net models. CNV size- dependent models identified prognostic chromosome arms that were not included in either integrated grade or integrated score, such as gain of 1q or 17q and loss of 4p, 9p, 10q, or 12q for LFFR, and gain of 1q, 9q, or 10p and loss of 3q, 5p/q, 6p, 9p, 10q, 11p, 13q, 14q, or 18p/q for OS (Fig. 1c), many of which have been previously associated with biologically aggressive meningiomas \(^{11}\) . There were numerous areas of focal deletion across chromosome arms with size- dependent CNVs that correlated with decreased expression of genes mapping to these loci from RNA sequencing of 502 meningiomas (Fig. 1d, e and Supplementary Table 2). Ontology analysis of genes mapping to focal CNVs revealed dysregulation of metabolic and hormone signaling pathways (Fig. 1f), both of which have been implicated in meningiomas through mechanisms that are poorly understood \(^{15–18}\) .  
+
+Prognostic CNVs from integrated grade, integrated score, and size- dependent LASSO or elastic net models (Fig. 1c) tended to co- occur in individual meningiomas (Fig. 2a). Regularized Cox regression models using co- occurrent CNV pairs identified 1p/22q and 9p/14q co- deletion as important predictors of postoperative LFFR or OS, respectively (Extended Data Fig. 3a). These findings remained significant when accounting for the total number of CNVs per meningioma ("CNV burden") on multivariate modeling (Supplementary Table 3), and meningiomas with 1p/22q or 9p/14q co- deletion, as defined using optimized CNV size- thresholds, had significantly worse clinical outcomes than meningiomas with these CNVs in isolation of one another (Fig. 2b).  
+
+Chromosome 22q loss is a common early alteration in meningiomas \(^{19}\) , but the prognostic significance of this CNV is limited as subsequent genomic alterations lead to divergent meningioma phenotypes, such as immune infiltration or cell cycle misactivation \(^{11}\) . Thus, we hypothesized that CNV accumulation in meningiomas may occur sequentially, with some CNVs like loss of chromosome 22q occurring early during tumorigenesis and other CNVs developing later in tumor progression. In support of this hypothesis, hierarchical clustering of meningiomas, binned by CNV burden using optimized size- thresholds, revealed 3 clusters (Fig. 2c, Extended Data Fig. 3b, c). "Early" cluster CNVs, such as loss of 22q, 1p, and 14q, were prevalent regardless of total CNV burden. "Late" cluster CNVs, such as loss of 9p or gain of 1q, were prevalent in samples with higher CNV burden. The third cluster contained uncommon
+
+<--- Page Split --->
+
+CNVs that did not correlate with total CNV burden. Meningioma CNV burden was associated with worse clinical outcomes, suggesting that progressive destabilization and development of late CNVs is associated with worse prognosis (Extended Data Fig. 3d, e).  
+
+To test the broader implications of CNV size thresholds and co- occurrence patterns on cancer risk- stratification, SNP array- derived CNV profiles and clinical outcome data were obtained for 9,885 tumors in TCGA<sup>7</sup>. Nine cancer types, comprising approximately half of TCGA samples analyzed, were identified with CNV size- dependence, which was again defined using prognostic CNV- based models with a maximum AUC for 5- year local PFS or OS of at least 0.60 that decreased by at least 5% from the maximum AUC as CNV threshold varied (Fig. 3a, Supplementary Table 4). There were areas of focal deletion or amplification on size- dependent CNVs across these 9 cancer types, such as gain of 1q and loss of 17q or 21q that were not identified in size- independent cancers (Supplementary Table 5). Ontology analysis of genes mapping to focal CNVs across these 9 cancer types revealed dysregulation of metabolic, developmental, differentiation, biosynthetic, cytoskeletal, and enzymatic pathways (Extended Data Fig. 4).  
+
+As in meningioma, size- dependent CNVs for 2 cancer types, glioblastoma (GBM) and cervical squamous cell carcinoma and endocervical adenocarcinoma (CESC), were used as inputs for co- occurrence models (Fig. 3b). In GBM, concurrent 16q loss and 7p gain was associated with worse OS than these CNVs in isolation (Fig. 3c, d). In CESC, concurrent 13q gain and 19p loss, as well as 19p/21q co- deletion, were both significant predictors of OS (Fig. 3c, d). These CNV co- occurrences remained significant predictors for GBM or CESC outcomes in multivariate models that accounted for total CNV burden (Supplementary Table 6). These findings support the clinical relevance of CNV size- dependence and co- occurrence in developing risk- stratification models for human cancer.  
+
+In sum, our results demonstrate that CNVs exhibit size- dependence with respect to their prognostic value across multiple cancer types. We find cancer risk- stratification systems using CNVs with chromosome- specific size thresholds and co- occurrence patterns may refine risk- stratification across a diversity of human cancers.  
+
+## Methods  
+
+## Inclusion and ethics  
+
+This study complied with all relevant ethical regulations and was approved by the UCSF Institutional Review Board (13- 12587, 17- 22324, 17- 23196 and 18- 24633). As part of routine clinical practice at UCSF, all patients included in this study signed a waiver of informed consent to contribute deidentified data to research.  
+
+## Meningioma samples and clinical data
+
+<--- Page Split --->
+
+Meningioma samples were collected from two sites, UCSF and Hong Kong University. Samples from the UCSF cohort \((n = 200)\) were selected from the UCSF Brain Tumor Center Biorepository and Pathology Core in 2017, and comprised all available WHO grade 2 and 3 meningioma frozen samples, WHO grade 1 frozen samples with clinical follow- up of greater than 10 years \((n = 40)\) or those with the longest available clinical follow- up less than 10 years \((n = 47)\) . The electronic medical record was reviewed for all patients in late 2018, and paper charts were reviewed in early 2019 for patients treated before the advent of the electronic medical record. The Hong Kong University cohort \((n = 365)\) comprised consecutive meningiomas from patients treated at Hong Kong University from 2000 to 2019 with frozen tissue that was sufficient for DNA methylation profiling. The medical record was reviewed for all patients in late 2019. For both cohorts, meningioma recurrence was defined as new radiographic tumor on magnetic resonance imaging after gross total resection, or progression of residual meningioma on magnetic resonance imaging after subtotal resection.  
+
+## Meningioma DNA methylation profiling and analysis  
+
+DNA methylation profiling was performed as previously described \(^{11}\) using the Illumina Methylation EPIC 850k Beadchip (WG- 317- 1003, Illumina) according to manufacturer instructions. Pre- processing and \(\beta\) - value calculations were performed using the SeSAME (v1.12.9) pipeline (BioConductor 3.13) with default settings. All DNA methylation profiling was performed at the Molecular Genomics Core at the University of Southern California. Assignment of meningiomas to DNA methylation groups or DNA methylation subgroups was performed using support vector models (https://william- cchen.shinyapps.io/MeninMethylClassApp/) \(^{11,20}\) .  
+
+## TCGA CNV and clinical outcomes data  
+
+TCGA data was collected from the TCGA PanCanAtlas (https://gdc.cancer.gov/about- data/publications/pancanatlas) \(^{21}\) . Copy number information was obtained using the Copy Number dataset (broad.mit.edu_PANCAN_Genome_Wide_SNP_6_whitelisted.seg). Only primary tumor samples were included by filtering TCGA Biospecimen Core Resource (BCR) barcodes for sample numbers containing the "01" designator. Clinical information was obtained from the TCGA- Clinical Data Resource (CDR) Outcome dataset (TCGA- CDR- SupplementalTableS1.xlsx) and was matched to CNV data by BCR barcode.  
+
+## CNV analysis  
+
+CNV profiles were generated from DNA methylation data using the SeSaMe package as previously described \(^{11}\) . The "cnSegmentation" command with default settings and the 'EPIC.5. normal' dataset as a copy- number normal control were used.  
+
+For both meningioma methylation data and TCGA SNP array data, chromosome segments with mean intensity values less than - 0.1 were defined as lost. Mean intensity values greater than 0.15 were defined as gained. CNV profiling excluded sex chromosomes and p arms of acrocentric chromosomes (13p, 14p, 15p, 21p and 22p). CNV threshold analysis for each CNV profile was performed by measuring
+
+<--- Page Split --->
+
+the mean intensity value at intervals of 30000 bases along each chromosome arm and summing nonconsecutive gains and losses. The total number of CNV profiles which met each threshold of gain or loss from \(5 - 95\%\) by \(5\%\) increments of the chromosome arm were counted. 5- year AUC for meningioma LFFR and OS, and TCGA PFS and OS, were calculated for each threshold using the survivalROC package (v1.0.3.1) in R, and the optimal threshold for each CNV was chosen based on the highest AUC for each clinical endpoint. Size- dependent CNVs were defined as those with a maximum 5- year AUC of at least 0.6 with another threshold of less than \(95\%\) of that maximum AUC.  
+
+CNV network plots were constructed using the igraph package (v1.5.1) in R. Plots were constructed using the CNVs selected from regression models, as well as from those identified in the previously published integrated grade \(^{9}\) and integrated score \(^{10}\) models for meningioma. CNVs were called using their optimal thresholds. In the case of TCGA cancer data, network plots were constructed using size- dependent CNVs and the most important predictors identified in LASSO and Elastic Net Cox regression co- occurrence models. Co- occurrence analysis was limited to pairs of CNVs as sample size was insufficient to analyze the high number of predictors involved when using 3 or more CNVs.  
+
+Cluster analysis was performed using CNVs defined with the optimal size- threshold for predicting LFFR. Clustering was done using the factoextra (v1.0.7) and cluster (v2.1.4) packages in R and visualized with the ComplexHeatmap package (v2.15.4).  
+
+## Survival analysis and modelling  
+
+CNV profiles using the optimal threshold for each CNV were used to train regression models on all available meningioma samples, and for all TCGA samples for size- dependent cancer types (BRCA, CESC, GBM, HNSCC, LGG, LUAD, OV, PRAD, and UCEC). LASSO and Elastic net regularized Cox regression models were trained with the concordance index (c- index) for each target endpoint, using the glmnet and cv.glmnet functions from the glmnet package (v4.1- 8) in R. Elastic net model selection was performed by selecting an optimal alpha value from a range of 0.05 to 0.95 (0.6 for meningioma LFFR, 0.2 for meningioma OS, 0.85 for TCGA PFS, 0.9 for TCGA OS). Model training was performed using 10- fold cross validation. CNV predictors for each model were identified within 1 standard error of the model achieving maximal c- index to reduce over- fitting. A risk metric was calculated for each sample, defined as the product of the regression coefficients and the normalized counts. Model performance was measured with 5- year cross- validation AUC for each model's respective clinical endpoint using the same training dataset with no hold out validation cohort.  
+
+Integrated grade \(^{9}\) was assigned to meningioma samples using CNV calls for each threshold, mitoses per 10 high- power fields, and CDKN2A/B loss. Integrated score \(^{10}\) was assigned using CNV calls for each threshold, WHO grade, and methylation family \(^{13}\) , the latter which had been previously assigned independently by the authors who developed of this system.  
+
+Multivariate Cox proportional hazards analysis was performed using the survival package (v3.5- 7) in R. Focal genomic and ontology analysis
+
+<--- Page Split --->
+
+CNV pileup plots demonstrating the proportion of tumors with gains or losses at each position along the chromosome arm were constructed using the ggplot2 (v3.4.3) package in R. Focal regions of loss were selected by selecting loci along the chromosome arm with a higher proportion of samples demonstrating deletion compared to the surrounding regions. Genes present in regions of interest were identified by cross- referencing positions along the chromosome with the Ensembl (release 109)22 database using the biomaRt (v2.54.1) package in R.  
+
+Meningioma gene expression analysis was performed using RNA- Seq data as previously described16. Briefly, RNA sequencing was performed on all 200 of the UCSF samples and 302 of the HKU samples meeting quality metrics. For UCSF samples, library preparation was performed using either the TruSeq RNA Library Prep Kit v2 (RS- 122- 2001, Illumina), sequencing was done on an Illumina HiSeq 4000 to a mean of 42 million reads per sample at the UCSF IHG Genomics Core, Quality control of FASTQ files was performed with FASTQC (v0.11.9), and 50 bp single- end reads were mapped to the human reference genome GRCh38 using HISAT2 (v2.1.0) with default parameters. For HKU samples, library preparation was performed using the TruSeq Standard mRNA Kit (20020595, Illumina) and 150 bp paired- end reads were sequenced on an Illumina NovaSeq 6000 to a mean of 100 million reads per sample at MedGenome Inc. Analysis was performed using a pipeline comprised of FastQC for quality control, and Kallisto for reading pseudo alignment and transcript abundance quantification using the default settings (v0.46.2).  
+
+Gene ontology and interaction analysis were performed using Cytoscape. In brief, Gene Set Enrichment Analysis (GSEA, v4.3.2) was performed and gene rank scores were calculated using the formula \(\mathrm{sign}(\log_2\mathrm{fold - change})\times -\log 10(\mathrm{p - value})\) . Pathways were defined using the gene set file Human_GOBP_AllPathways_no_GO_iea_December_01_2022_symbol.gmt, which is maintained by the Bader laboratory. Gene set size was limited to range between 15 and 500, and positive and negative enrichment files were generated using 2000 permutations. The EnrichmentMap App (v3.3.4) in Cytoscape (v3.7.2) was used to visualize the results of pathway analysis. Nodes with FDR q value \(< 0.05\) and p- value \(< 0.05\) , and nodes sharing gene overlaps with Jaccard + Overlap Combined (JOC) threshold of 0.375 were connected by blue lines (edges) to generate network maps. Clusters of related pathways were identified and annotated using the AutoAnnotate app (v1.3.5) in Cytoscape that uses a Markov Cluster algorithm to connect pathways by shared keywords in the description of each pathway. The resulting groups of pathways were designated as the consensus pathways in a circle.  
+
+## Statistics  
+
+All experiments were performed with independent biological replicates and repeated, and statistics were derived from biological replicates. Biological replicates are indicated in each figure panel or figure legend. No statistical methods were used to predetermine sample sizes, but sample sizes in this study are similar or larger to those reported in previous publications. Data distribution was assumed to be normal, but this was not formally tested. Investigators were blinded to conditions during clinical data collection and analysis. Bioinformatic analyses were performed blind to clinical features, outcomes or
+
+<--- Page Split --->
+
+molecular characteristics. The clinical samples used in this study were retrospective and nonrandomized with no intervention, and all samples were interrogated equally. Thus, controlling for covariates among clinical samples is not relevant. No data points were excluded from the analyses. Statistical analyses were conducted in R (v4.2.2).  
+
+## Declarations  
+
+## Reporting summary  
+
+Further information on research design is available in the Nature Research Reporting Summary linked to this article.  
+
+## Data availability  
+
+DNA methylation (n=565) and RNA sequencing (n=502) of the meningiomas analyzed in this manuscript have been deposited in the NCBI Gene Expression Omnibus under the accessions GSE183656 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE183656), GSE101638 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc= GSE101638), and GSE212666 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE212666). The publicly available GRCh38 (hg38, https://www.ncbi.nlm.nih.gov/assembly/GCF_000001405.39/), and Kallisto index v10 (https://github.com/pachterlab/kallisto-transcriptome-indices/releases) datasets were used in this study. TCGA data was collected from the publicly available TCGA PanCanAtlas (https://gdc.cancer.gov/about-data/publications/pancanatlas). Copy number information was obtained using the Copy Number dataset (broad.mit.edu_PANCAN_Genome_Wide_SNP_6_whitelisted.seg). Clinical information was obtained from the TCGA- Clinical Data Resource (CDR) Outcome dataset (TCGA- CDR-SupplementalTableS1.xlsx). Source data are provided with this paper.  
+
+## Code availability  
+
+No custom software, tools, or packages were used. The open- source software, tools, and packages used for data analysis in this study are referenced in the methods where applicable and include R (v4.2.2), FASTQC (v0.11.9), HISAT2 (v2.1.0), Kallisto (v0.46.2), SeSAME (v1.12.9) (BioConductor 3.13), survival R package (v3.5- 7), survivalROC R package (v1.0.3.1), biomaRt R package (v2.54.1), glmnet R package (v4.1- 8), igraph R package (v1.5.1), factoextra R package (v1.0.7), cluster R package (v2.1.4), ComplexHeatmap R package (v2.15.4), GSEA (v4.3.2), and EnrichmentMap App (v3.3.4) and AutoAnnotate app (v1.3.5) in Cytoscape (v3.7.2).  
+
+## Acknowledgements  
+
+This study was supported by funding from American Brain Tumor Association Jack & Fay Netchin Medical Student Summer Fellowship in memory of Rose Digang to M.P.N., K12 CA260225 and the Chan Zuckerburg Biohub Physician Scientist Fellowship to W.C.C., and R01 CA262311, P50 CA097257, the UCSF Wolfe Meningioma Program Project and the Trenchard Family Charitable Fund, to D.R.R. The
+
+<--- Page Split --->
+
+results shown here are in part based upon data generated by the TCGA Research Network (https://www.cancer.gov/tcga).  
+
+## Author contributions statement  
+
+All authors made substantial contributions to the conception or design of the study; the acquisition, analysis, or interpretation of data; or drafting or revising the manuscript. All authors approved the manuscript. All authors agree to be personally accountable for individual contributions and to ensure that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved and the resolution documented in the literature. M.P.N. and W.C.C. conceived and designed the study and analyzed bioinformatic data with supervision from D.R.R. N.Z. performed gene ontology analyses with supervision from D.R.R. K.M. and C-H.G.L. provided guidance and feedback on study design, analysis, and presentation.  
+
+## Competing interests statement  
+
+The authors declare no competing interests.  
+
+## References  
+
+1. Hanahan, D. Hallmarks of Cancer: New Dimensions. Cancer Discov 12, 31–46 (2022).  
+2. Nguyen, B. et al. Genomic characterization of metastatic patterns from prospective clinical sequencing of 25,000 patients. Cell 185, 563-575.e11 (2022).  
+3. Lukow, D. A. et al. Chromosomal instability accelerates the evolution of resistance to anti-cancer therapies. Dev Cell 56, 2427-2439.e4 (2021).  
+4. Bakhoum, S. F. et al. Numerical chromosomal instability mediates susceptibility to radiation treatment. Nat Commun 6, 5990 (2015).  
+5. Beroukhim, R. et al. The landscape of somatic copy-number alteration across human cancers. Nature 463, 899–905 (2010).  
+6. Steele, C. D. et al. Signatures of copy number alterations in human cancer. Nature 606, 984���991 (2022).  
+7. Weinstein, J. N. et al. The Cancer Genome Atlas Pan-Cancer analysis project. Nat Genet 45, 1113–1120 (2013).  
+8. van Dijk, E. et al. Chromosomal copy number heterogeneity predicts survival rates across cancers. Nat Commun 12, 3188 (2021).  
+9. Driver, J. et al. A molecularly integrated grade for meningioma. Neuro Oncol 24, 796–808 (2022).  
+10. Maas, S. L. N. et al. Integrated Molecular-Morphologic Meningioma Classification: A Multicenter Retrospective Analysis, Retrospectively and Prospectively Validated. J Clin Oncol 39, 3839–3852 (2021).
+
+<--- Page Split --->
+
+11. Choudhury, A. et al. Meningioma DNA methylation groups identify biological drivers and therapeutic vulnerabilities. Nat Genet 54, 649–659 (2022).  
+
+12. Youngblood, M. W. et al. Associations of meningioma molecular subgroup and tumor recurrence. Neuro Oncol 23, 783–794 (2021).  
+
+13. Sahm, F. et al. DNA methylation-based classification and grading system for meningioma: a multicentre, retrospective analysis. Lancet Oncol 18, 682–694 (2017).  
+
+14. Ostrom, Q. T. et al. CBTRUS Statistical Report: Primary Brain and Other Central Nervous System Tumors Diagnosed in the United States in 2015-2019. Neuro Oncol 24, v1–v95 (2022).  
+
+15. Nassiri, F. et al. A clinically applicable integrative molecular classification of meningiomas. Nature 597, 119–125 (2021).  
+
+16. Choudhury, A. et al. Hypermitotic meningiomas harbor DNA methylation subgroups with distinct biological and clinical features. Neuro-Oncology 25, 520–530 (2023).  
+
+17. Miyagishima, D. F., Moliterno, J., Claus, E. & Günel, M. Hormone therapies in meningioma-where are we? J Neurooncol 161, 297–308 (2023).  
+
+18. Walsh, K. M. et al. Pleiotropic MLLT10 variation confers risk of meningioma and estrogen-mediated cancers. Neurooncol Adv 4, vdac044 (2022).  
+
+19. Magill, S. T. et al. Multiplatform genomic profiling and magnetic resonance imaging identify mechanisms underlying intratumor heterogeneity in meningioma. Nat Commun 11, 4803 (2020).  
+
+20. Chang, C.-W. et al. Identification of Human Housekeeping Genes and Tissue-Selective Genes by Microarray Meta-Analysis. PLoS One 6, e22859 (2011).  
+
+21. Smith, J. C. & Sheltzer, J. M. Genome-wide identification and analysis of prognostic features in human cancers. Cell Reports 38, (2022).  
+
+22. Cunningham, F. et al. Ensembl 2022. Nucleic Acids Research 50, D988–D995 (2022).  
+
+## Figures
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+Meningioma risk- stratification models demonstrate CNV size- dependence. a, Heatmaps showing area under the curve for univariate Cox models of LFFR or OS based on individual copy number gains (left, red) or individual copy number losses (right, blue). Models were trained using sequential size thresholds requiring \(\geq 5\%\) to \(\geq 95\%\) of chromosome arms to be gained or lost to define CNVs. Boxes show peak AUCs for "size- dependent" CNVs, defined as having a maximum area under the curve (AUC) for 5- year LFFR or OS of at least 0.60 that decreased by at least \(5\%\) from the maximum AUC as CNV threshold was varied. n=565 meningiomas. b, Previously published meningioma risk- stratification models incorporating CNVs (integrated grade based on histology and a \(\geq 50\%\) CNV threshold, or integrated score based on histology,
+
+<--- Page Split --->
+
+DNA methylation profiling, and a \(\geq 5\%\) CNV threshold) show decreasing AUC with varying size-thresholds. n=565 meningiomas. c, CNVs from previously published meningioma risk-stratification models or from newly-derived size-dependent LASSO or elastic net models for meningioma LFFR or OS. n=565 meningiomas. d, CNV profile plots demonstrating focal copy number losses in size-dependent CNVs from LASSO or elastic net models. Chromosomes 14 and 20 are shown as examples of broad/non-focal CNVs. n=565 meningiomas. e, Average RNA sequencing expression of genes mapping to regions of focal copy number loss on size-dependent CNVs from LASSO or elastic net models versus genes mapping to other regions on the same chromosomes. n=502 meningiomas. Error bars show standard error of the mean. Student's t test, p≤0.0001. f, Network of gene circuits distinguishing genes mapping to regions of focal copy number loss. Nodes represent pathways and edges represent shared genes between pathways (p≤0.05, FDR≤0.05). n=502 meningiomas.  
+
+![](images/Figure_3.jpg)
+
+
+<--- Page Split --->
+
+Size- dependent CNV co- occurrence is prognostic for meningioma outcomes. a, Network diagrams demonstrating co- occurrence of prognostic size- dependent CNVs from Fig. 1c. b, Kaplan- Meier curves comparing meningioma LFFR or OS according to individual CNVs versus co- occurrent CNV pairs identified as the most important predictors of postoperative outcomes in LASSO Cox models from Extended Data Fig. 3a using optimized thresholds for defining CNVs from Fig. 1a. Log- rank tests. n=565 meningiomas. c, Heatmap showing unsupervised hierarchical clustering of individual CNVs according to the total number of CNVs per meningioma. CNVs were defined using optimal size thresholds for LFFR or OS models from Fig. 1a.  
+
+![PLACEHOLDER_12_0]
+
+<center>Figure 3 </center>  
+
+Pan- cancer analyses reveal size- dependent CNV co- occurrence risk- stratification models for half of human cancers. a, TCGA SNP- array and clinical outcomes data used in pan- cancer analyses. Cancers with size- dependent prognostic CNVs were defined as having a CNV with a univariate Cox AUC for either PFS or OS of at least 0.60 that dropped by at least \(5\%\) from the maximum AUC when varying the size threshold for defining CNVs. b, Network diagrams demonstrating co- occurrence of prognostic size- dependent CNVs for GBM or CESC from Supplementary Table 4. c, LASSO Cox model coefficients using
+
+<--- Page Split --->
+
+size- dependent CNV co- occurrence to predict postoperative OS in GBM or CESC. d, Kaplan- Meier curves comparing OS for GBM or CESC with individual CNVs versus co- occurrent CNV pairs identified as the most important predictors of postoperative outcomes in LASSO Cox models. Log- rank tests. \(n = 571\) GBM and 294 CESC.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- NguyenChenNatGenetEDFigv7.docx- NguyenChenNatGenetSupplementaryTablesv7.xlsx
+
+<--- Page Split --->

preprint/preprint__06076107a582a7db1a993272bc8d0902287719a4fcc5b06c29c18d0dc685d84a/preprint__06076107a582a7db1a993272bc8d0902287719a4fcc5b06c29c18d0dc685d84a_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 930, 208]]<|/det|>
+# Pan-cancer copy number variant analysis identifies optimized size thresholds and co-occurrence models for individualized risk-stratification  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 156, 248]]<|/det|>
+David Raleigh  
+
+<|ref|>text<|/ref|><|det|>[[54, 257, 300, 274]]<|/det|>
+david.raleigh@ucsf.edu  
+
+<|ref|>text<|/ref|><|det|>[[50, 303, 741, 323]]<|/det|>
+University of California San Francisco https://orcid.org/0000- 0001- 9299- 8864  
+
+<|ref|>text<|/ref|><|det|>[[44, 328, 383, 368]]<|/det|>
+Minh Nguyen University of California San Francisco  
+
+<|ref|>text<|/ref|><|det|>[[44, 374, 465, 415]]<|/det|>
+William Chen UCSF https://orcid.org/0000- 0001- 8924- 5853  
+
+<|ref|>text<|/ref|><|det|>[[44, 420, 383, 460]]<|/det|>
+Naomi Zakimi Univeristy of California San Francisco  
+
+<|ref|>text<|/ref|><|det|>[[44, 466, 741, 507]]<|/det|>
+Kanish Mirchia Univeristy of California San Francisco https://orcid.org/0000- 0002- 7371- 7059  
+
+<|ref|>text<|/ref|><|det|>[[44, 512, 202, 530]]<|/det|>
+Calixto- Hope Lucas  
+
+<|ref|>text<|/ref|><|det|>[[52, 534, 639, 553]]<|/det|>
+Johns Hopkins University https://orcid.org/0000- 0002- 8347- 9592  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 595, 230, 614]]<|/det|>
+## Brief Communication  
+
+<|ref|>text<|/ref|><|det|>[[44, 634, 136, 652]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 671, 330, 691]]<|/det|>
+Posted Date: January 11th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 710, 475, 728]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3443805/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 746, 914, 789]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 807, 535, 826]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 862, 904, 906]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on July 2nd, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 61063- y.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 158, 68]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[41, 82, 954, 264]]<|/det|>
+Chromosome instability leading to accumulation of copy number gains or losses is a hallmark of cancer. Copy number variant (CNV) signatures are increasingly used for clinical risk- stratification, but size thresholds for defining CNVs are variable and the biological or clinical implications of CNV size heterogeneity or co- occurrence patterns are incompletely understood. Here we analyze CNV and clinical data from 565 meningiomas and 9,885 tumors from The Cancer Genome Atlas (TCGA) to develop tumor- and chromosome- specific CNV size- dependent and co- occurrence models for clinical outcomes. Our results reveal prognostic CNVs with optimized size thresholds and co- occurrence patterns that refine risk- stratification across a diversity of human cancers.  
+
+<|ref|>sub_title<|/ref|><|det|>[[43, 287, 111, 312]]<|/det|>
+## Main  
+
+<|ref|>text<|/ref|><|det|>[[41, 327, 940, 472]]<|/det|>
+Chromosome instability contributes to the genomic complexity of cancer<sup>1</sup> and is implicated in tumorigenesis, progression, metastasis, and resistance to therapy<sup>2- 4</sup>. As a marker of chromosome instability, CNV signatures are increasingly used for clinical risk- stratification of diverse cancer types<sup>5,6</sup>, and pan- cancer databases such as TCGA<sup>7</sup> have been used to derive prognostic models based on CNVs<sup>6,8</sup>. There is no consensus on the optimal size threshold for defining or reporting CNVs, and CNV co- occurrence patterns that may improve risk- stratification models are incompletely understood.  
+
+<|ref|>text<|/ref|><|det|>[[39, 488, 951, 792]]<|/det|>
+To test the hypothesis that size- dependent CNV models and co- occurrence patterns may improve clinical risk- stratification, CNV size- dependence was investigated in meningiomas, a tumor that is not represented in TCGA datasets but is associated with recurrent CNVs that can be used for risk- stratification<sup>9,10</sup>. Loss of chromosomes 1p, 6q, and others distinguish biologically aggressive meningiomas<sup>9,10</sup>, but published models have applied inconsistent size thresholds ranging from 5–80% of individual chromosome arms to define meningioma CNVs<sup>9–12</sup>. Using a previously described cohort of 565 meningiomas with long- term clinical outcomes data<sup>11</sup>, we used DNA methylation arrays to define CNVs ranging from individual CpG loci to entire chromosome arms (Extended Data Fig. 1). Next, we used CNVs ranging from 5–95% of each chromosome arm to generate univariate Cox proportional hazards models for postoperative local freedom from recurrence (LFFR) or overall survival (OS). These analyses revealed “size- dependent” CNVs (Fig. 1a), defined as having a maximum area under the curve (AUC) for 5- year LFFR or OS of at least 0.60 that decreased by at least 5% from the maximum AUC as CNV threshold varied (Supplementary Table 1).  
+
+<|ref|>text<|/ref|><|det|>[[41, 807, 940, 947]]<|/det|>
+The implications of CNV size- dependence for meningioma risk- stratification were investigated using 2 robust models that rely on CNVs to predict postoperative meningioma LFFR. The first, integrated grade, is based on copy number losses of chromosomes 1p, 3p, 4p/q, 6p/q, 10p/q, 14q, 18p/q, and 19p/q at a uniform threshold of 50% of each chromosome arm plus CDKN2A loss and mitotic count from histology<sup>9</sup>. The second, integrated score, is based on copy number losses of chromosomes 1p, 6q, and 14q at a uniform threshold of 5% of each chromosome arm plus DNA methylation family<sup>13</sup> and World
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 45, 953, 205]]<|/det|>
+Health Organization (WHO) histological grade \(^{10}\) . We tested each model on our cohort of 565 meningiomas using CNV thresholds ranging from 5–95% (Fig. 1b). Integrated grade reached a maximum AUC for 5- year LFFR of 0.78 at a uniform CNV threshold of 20%, and a maximum AUC for OS of 0.77 at a uniform threshold of 30%. Integrated score reached a maximum AUC for LFFR or OS of 0.76 at a uniform CNV threshold of 5%. The performance of each model degraded with varying CNV size thresholds (Fig. 1b), suggesting that CNV size heterogeneity influences risk- stratification for the most common primary intracranial tumor \(^{14}\) .  
+
+<|ref|>text<|/ref|><|det|>[[40, 223, 950, 522]]<|/det|>
+To determine if models based on chromosome- specific CNV size thresholds could improve meningioma risk- stratification, LASSO and elastic net regularized Cox models were trained using optimized CNVs thresholds across the 565 meningiomas in our cohort (Extended Data Fig. 2). Cross- validated AUCs for 5- year LFFR or OS were 0.76 for LASSO models and 0.77–0.78 for elastic net models. CNV size- dependent models identified prognostic chromosome arms that were not included in either integrated grade or integrated score, such as gain of 1q or 17q and loss of 4p, 9p, 10q, or 12q for LFFR, and gain of 1q, 9q, or 10p and loss of 3q, 5p/q, 6p, 9p, 10q, 11p, 13q, 14q, or 18p/q for OS (Fig. 1c), many of which have been previously associated with biologically aggressive meningiomas \(^{11}\) . There were numerous areas of focal deletion across chromosome arms with size- dependent CNVs that correlated with decreased expression of genes mapping to these loci from RNA sequencing of 502 meningiomas (Fig. 1d, e and Supplementary Table 2). Ontology analysis of genes mapping to focal CNVs revealed dysregulation of metabolic and hormone signaling pathways (Fig. 1f), both of which have been implicated in meningiomas through mechanisms that are poorly understood \(^{15–18}\) .  
+
+<|ref|>text<|/ref|><|det|>[[41, 538, 953, 717]]<|/det|>
+Prognostic CNVs from integrated grade, integrated score, and size- dependent LASSO or elastic net models (Fig. 1c) tended to co- occur in individual meningiomas (Fig. 2a). Regularized Cox regression models using co- occurrent CNV pairs identified 1p/22q and 9p/14q co- deletion as important predictors of postoperative LFFR or OS, respectively (Extended Data Fig. 3a). These findings remained significant when accounting for the total number of CNVs per meningioma ("CNV burden") on multivariate modeling (Supplementary Table 3), and meningiomas with 1p/22q or 9p/14q co- deletion, as defined using optimized CNV size- thresholds, had significantly worse clinical outcomes than meningiomas with these CNVs in isolation of one another (Fig. 2b).  
+
+<|ref|>text<|/ref|><|det|>[[41, 735, 950, 943]]<|/det|>
+Chromosome 22q loss is a common early alteration in meningiomas \(^{19}\) , but the prognostic significance of this CNV is limited as subsequent genomic alterations lead to divergent meningioma phenotypes, such as immune infiltration or cell cycle misactivation \(^{11}\) . Thus, we hypothesized that CNV accumulation in meningiomas may occur sequentially, with some CNVs like loss of chromosome 22q occurring early during tumorigenesis and other CNVs developing later in tumor progression. In support of this hypothesis, hierarchical clustering of meningiomas, binned by CNV burden using optimized size- thresholds, revealed 3 clusters (Fig. 2c, Extended Data Fig. 3b, c). "Early" cluster CNVs, such as loss of 22q, 1p, and 14q, were prevalent regardless of total CNV burden. "Late" cluster CNVs, such as loss of 9p or gain of 1q, were prevalent in samples with higher CNV burden. The third cluster contained uncommon
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 945, 111]]<|/det|>
+CNVs that did not correlate with total CNV burden. Meningioma CNV burden was associated with worse clinical outcomes, suggesting that progressive destabilization and development of late CNVs is associated with worse prognosis (Extended Data Fig. 3d, e).  
+
+<|ref|>text<|/ref|><|det|>[[40, 128, 940, 378]]<|/det|>
+To test the broader implications of CNV size thresholds and co- occurrence patterns on cancer risk- stratification, SNP array- derived CNV profiles and clinical outcome data were obtained for 9,885 tumors in TCGA<sup>7</sup>. Nine cancer types, comprising approximately half of TCGA samples analyzed, were identified with CNV size- dependence, which was again defined using prognostic CNV- based models with a maximum AUC for 5- year local PFS or OS of at least 0.60 that decreased by at least 5% from the maximum AUC as CNV threshold varied (Fig. 3a, Supplementary Table 4). There were areas of focal deletion or amplification on size- dependent CNVs across these 9 cancer types, such as gain of 1q and loss of 17q or 21q that were not identified in size- independent cancers (Supplementary Table 5). Ontology analysis of genes mapping to focal CNVs across these 9 cancer types revealed dysregulation of metabolic, developmental, differentiation, biosynthetic, cytoskeletal, and enzymatic pathways (Extended Data Fig. 4).  
+
+<|ref|>text<|/ref|><|det|>[[40, 394, 953, 575]]<|/det|>
+As in meningioma, size- dependent CNVs for 2 cancer types, glioblastoma (GBM) and cervical squamous cell carcinoma and endocervical adenocarcinoma (CESC), were used as inputs for co- occurrence models (Fig. 3b). In GBM, concurrent 16q loss and 7p gain was associated with worse OS than these CNVs in isolation (Fig. 3c, d). In CESC, concurrent 13q gain and 19p loss, as well as 19p/21q co- deletion, were both significant predictors of OS (Fig. 3c, d). These CNV co- occurrences remained significant predictors for GBM or CESC outcomes in multivariate models that accounted for total CNV burden (Supplementary Table 6). These findings support the clinical relevance of CNV size- dependence and co- occurrence in developing risk- stratification models for human cancer.  
+
+<|ref|>text<|/ref|><|det|>[[42, 592, 945, 680]]<|/det|>
+In sum, our results demonstrate that CNVs exhibit size- dependence with respect to their prognostic value across multiple cancer types. We find cancer risk- stratification systems using CNVs with chromosome- specific size thresholds and co- occurrence patterns may refine risk- stratification across a diversity of human cancers.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 703, 163, 728]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 742, 351, 772]]<|/det|>
+## Inclusion and ethics  
+
+<|ref|>text<|/ref|><|det|>[[42, 789, 951, 876]]<|/det|>
+This study complied with all relevant ethical regulations and was approved by the UCSF Institutional Review Board (13- 12587, 17- 22324, 17- 23196 and 18- 24633). As part of routine clinical practice at UCSF, all patients included in this study signed a waiver of informed consent to contribute deidentified data to research.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 879, 632, 910]]<|/det|>
+## Meningioma samples and clinical data
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 44, 955, 315]]<|/det|>
+Meningioma samples were collected from two sites, UCSF and Hong Kong University. Samples from the UCSF cohort \((n = 200)\) were selected from the UCSF Brain Tumor Center Biorepository and Pathology Core in 2017, and comprised all available WHO grade 2 and 3 meningioma frozen samples, WHO grade 1 frozen samples with clinical follow- up of greater than 10 years \((n = 40)\) or those with the longest available clinical follow- up less than 10 years \((n = 47)\) . The electronic medical record was reviewed for all patients in late 2018, and paper charts were reviewed in early 2019 for patients treated before the advent of the electronic medical record. The Hong Kong University cohort \((n = 365)\) comprised consecutive meningiomas from patients treated at Hong Kong University from 2000 to 2019 with frozen tissue that was sufficient for DNA methylation profiling. The medical record was reviewed for all patients in late 2019. For both cohorts, meningioma recurrence was defined as new radiographic tumor on magnetic resonance imaging after gross total resection, or progression of residual meningioma on magnetic resonance imaging after subtotal resection.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 316, 835, 348]]<|/det|>
+## Meningioma DNA methylation profiling and analysis  
+
+<|ref|>text<|/ref|><|det|>[[41, 362, 951, 520]]<|/det|>
+DNA methylation profiling was performed as previously described \(^{11}\) using the Illumina Methylation EPIC 850k Beadchip (WG- 317- 1003, Illumina) according to manufacturer instructions. Pre- processing and \(\beta\) - value calculations were performed using the SeSAME (v1.12.9) pipeline (BioConductor 3.13) with default settings. All DNA methylation profiling was performed at the Molecular Genomics Core at the University of Southern California. Assignment of meningiomas to DNA methylation groups or DNA methylation subgroups was performed using support vector models (https://william- cchen.shinyapps.io/MeninMethylClassApp/) \(^{11,20}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 522, 630, 553]]<|/det|>
+## TCGA CNV and clinical outcomes data  
+
+<|ref|>text<|/ref|><|det|>[[42, 570, 942, 727]]<|/det|>
+TCGA data was collected from the TCGA PanCanAtlas (https://gdc.cancer.gov/about- data/publications/pancanatlas) \(^{21}\) . Copy number information was obtained using the Copy Number dataset (broad.mit.edu_PANCAN_Genome_Wide_SNP_6_whitelisted.seg). Only primary tumor samples were included by filtering TCGA Biospecimen Core Resource (BCR) barcodes for sample numbers containing the "01" designator. Clinical information was obtained from the TCGA- Clinical Data Resource (CDR) Outcome dataset (TCGA- CDR- SupplementalTableS1.xlsx) and was matched to CNV data by BCR barcode.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 730, 248, 760]]<|/det|>
+## CNV analysis  
+
+<|ref|>text<|/ref|><|det|>[[42, 776, 945, 844]]<|/det|>
+CNV profiles were generated from DNA methylation data using the SeSaMe package as previously described \(^{11}\) . The "cnSegmentation" command with default settings and the 'EPIC.5. normal' dataset as a copy- number normal control were used.  
+
+<|ref|>text<|/ref|><|det|>[[42, 861, 944, 952]]<|/det|>
+For both meningioma methylation data and TCGA SNP array data, chromosome segments with mean intensity values less than - 0.1 were defined as lost. Mean intensity values greater than 0.15 were defined as gained. CNV profiling excluded sex chromosomes and p arms of acrocentric chromosomes (13p, 14p, 15p, 21p and 22p). CNV threshold analysis for each CNV profile was performed by measuring
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 947, 201]]<|/det|>
+the mean intensity value at intervals of 30000 bases along each chromosome arm and summing nonconsecutive gains and losses. The total number of CNV profiles which met each threshold of gain or loss from \(5 - 95\%\) by \(5\%\) increments of the chromosome arm were counted. 5- year AUC for meningioma LFFR and OS, and TCGA PFS and OS, were calculated for each threshold using the survivalROC package (v1.0.3.1) in R, and the optimal threshold for each CNV was chosen based on the highest AUC for each clinical endpoint. Size- dependent CNVs were defined as those with a maximum 5- year AUC of at least 0.6 with another threshold of less than \(95\%\) of that maximum AUC.  
+
+<|ref|>text<|/ref|><|det|>[[41, 218, 940, 378]]<|/det|>
+CNV network plots were constructed using the igraph package (v1.5.1) in R. Plots were constructed using the CNVs selected from regression models, as well as from those identified in the previously published integrated grade \(^{9}\) and integrated score \(^{10}\) models for meningioma. CNVs were called using their optimal thresholds. In the case of TCGA cancer data, network plots were constructed using size- dependent CNVs and the most important predictors identified in LASSO and Elastic Net Cox regression co- occurrence models. Co- occurrence analysis was limited to pairs of CNVs as sample size was insufficient to analyze the high number of predictors involved when using 3 or more CNVs.  
+
+<|ref|>text<|/ref|><|det|>[[42, 394, 944, 461]]<|/det|>
+Cluster analysis was performed using CNVs defined with the optimal size- threshold for predicting LFFR. Clustering was done using the factoextra (v1.0.7) and cluster (v2.1.4) packages in R and visualized with the ComplexHeatmap package (v2.15.4).  
+
+<|ref|>sub_title<|/ref|><|det|>[[42, 461, 525, 492]]<|/det|>
+## Survival analysis and modelling  
+
+<|ref|>text<|/ref|><|det|>[[41, 507, 951, 779]]<|/det|>
+CNV profiles using the optimal threshold for each CNV were used to train regression models on all available meningioma samples, and for all TCGA samples for size- dependent cancer types (BRCA, CESC, GBM, HNSCC, LGG, LUAD, OV, PRAD, and UCEC). LASSO and Elastic net regularized Cox regression models were trained with the concordance index (c- index) for each target endpoint, using the glmnet and cv.glmnet functions from the glmnet package (v4.1- 8) in R. Elastic net model selection was performed by selecting an optimal alpha value from a range of 0.05 to 0.95 (0.6 for meningioma LFFR, 0.2 for meningioma OS, 0.85 for TCGA PFS, 0.9 for TCGA OS). Model training was performed using 10- fold cross validation. CNV predictors for each model were identified within 1 standard error of the model achieving maximal c- index to reduce over- fitting. A risk metric was calculated for each sample, defined as the product of the regression coefficients and the normalized counts. Model performance was measured with 5- year cross- validation AUC for each model's respective clinical endpoint using the same training dataset with no hold out validation cohort.  
+
+<|ref|>text<|/ref|><|det|>[[42, 797, 952, 892]]<|/det|>
+Integrated grade \(^{9}\) was assigned to meningioma samples using CNV calls for each threshold, mitoses per 10 high- power fields, and CDKN2A/B loss. Integrated score \(^{10}\) was assigned using CNV calls for each threshold, WHO grade, and methylation family \(^{13}\) , the latter which had been previously assigned independently by the authors who developed of this system.  
+
+<|ref|>text<|/ref|><|det|>[[42, 908, 936, 960]]<|/det|>
+Multivariate Cox proportional hazards analysis was performed using the survival package (v3.5- 7) in R. Focal genomic and ontology analysis
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 946, 181]]<|/det|>
+CNV pileup plots demonstrating the proportion of tumors with gains or losses at each position along the chromosome arm were constructed using the ggplot2 (v3.4.3) package in R. Focal regions of loss were selected by selecting loci along the chromosome arm with a higher proportion of samples demonstrating deletion compared to the surrounding regions. Genes present in regions of interest were identified by cross- referencing positions along the chromosome with the Ensembl (release 109)22 database using the biomaRt (v2.54.1) package in R.  
+
+<|ref|>text<|/ref|><|det|>[[40, 199, 950, 472]]<|/det|>
+Meningioma gene expression analysis was performed using RNA- Seq data as previously described16. Briefly, RNA sequencing was performed on all 200 of the UCSF samples and 302 of the HKU samples meeting quality metrics. For UCSF samples, library preparation was performed using either the TruSeq RNA Library Prep Kit v2 (RS- 122- 2001, Illumina), sequencing was done on an Illumina HiSeq 4000 to a mean of 42 million reads per sample at the UCSF IHG Genomics Core, Quality control of FASTQ files was performed with FASTQC (v0.11.9), and 50 bp single- end reads were mapped to the human reference genome GRCh38 using HISAT2 (v2.1.0) with default parameters. For HKU samples, library preparation was performed using the TruSeq Standard mRNA Kit (20020595, Illumina) and 150 bp paired- end reads were sequenced on an Illumina NovaSeq 6000 to a mean of 100 million reads per sample at MedGenome Inc. Analysis was performed using a pipeline comprised of FastQC for quality control, and Kallisto for reading pseudo alignment and transcript abundance quantification using the default settings (v0.46.2).  
+
+<|ref|>text<|/ref|><|det|>[[40, 488, 944, 761]]<|/det|>
+Gene ontology and interaction analysis were performed using Cytoscape. In brief, Gene Set Enrichment Analysis (GSEA, v4.3.2) was performed and gene rank scores were calculated using the formula \(\mathrm{sign}(\log_2\mathrm{fold - change})\times -\log 10(\mathrm{p - value})\) . Pathways were defined using the gene set file Human_GOBP_AllPathways_no_GO_iea_December_01_2022_symbol.gmt, which is maintained by the Bader laboratory. Gene set size was limited to range between 15 and 500, and positive and negative enrichment files were generated using 2000 permutations. The EnrichmentMap App (v3.3.4) in Cytoscape (v3.7.2) was used to visualize the results of pathway analysis. Nodes with FDR q value \(< 0.05\) and p- value \(< 0.05\) , and nodes sharing gene overlaps with Jaccard + Overlap Combined (JOC) threshold of 0.375 were connected by blue lines (edges) to generate network maps. Clusters of related pathways were identified and annotated using the AutoAnnotate app (v1.3.5) in Cytoscape that uses a Markov Cluster algorithm to connect pathways by shared keywords in the description of each pathway. The resulting groups of pathways were designated as the consensus pathways in a circle.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 763, 189, 790]]<|/det|>
+## Statistics  
+
+<|ref|>text<|/ref|><|det|>[[41, 808, 949, 943]]<|/det|>
+All experiments were performed with independent biological replicates and repeated, and statistics were derived from biological replicates. Biological replicates are indicated in each figure panel or figure legend. No statistical methods were used to predetermine sample sizes, but sample sizes in this study are similar or larger to those reported in previous publications. Data distribution was assumed to be normal, but this was not formally tested. Investigators were blinded to conditions during clinical data collection and analysis. Bioinformatic analyses were performed blind to clinical features, outcomes or
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 955, 134]]<|/det|>
+molecular characteristics. The clinical samples used in this study were retrospective and nonrandomized with no intervention, and all samples were interrogated equally. Thus, controlling for covariates among clinical samples is not relevant. No data points were excluded from the analyses. Statistical analyses were conducted in R (v4.2.2).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 156, 210, 182]]<|/det|>
+## Declarations  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 198, 218, 218]]<|/det|>
+## Reporting summary  
+
+<|ref|>text<|/ref|><|det|>[[42, 235, 949, 278]]<|/det|>
+Further information on research design is available in the Nature Research Reporting Summary linked to this article.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 296, 183, 316]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[40, 333, 950, 605]]<|/det|>
+DNA methylation (n=565) and RNA sequencing (n=502) of the meningiomas analyzed in this manuscript have been deposited in the NCBI Gene Expression Omnibus under the accessions GSE183656 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE183656), GSE101638 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc= GSE101638), and GSE212666 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE212666). The publicly available GRCh38 (hg38, https://www.ncbi.nlm.nih.gov/assembly/GCF_000001405.39/), and Kallisto index v10 (https://github.com/pachterlab/kallisto-transcriptome-indices/releases) datasets were used in this study. TCGA data was collected from the publicly available TCGA PanCanAtlas (https://gdc.cancer.gov/about-data/publications/pancanatlas). Copy number information was obtained using the Copy Number dataset (broad.mit.edu_PANCAN_Genome_Wide_SNP_6_whitelisted.seg). Clinical information was obtained from the TCGA- Clinical Data Resource (CDR) Outcome dataset (TCGA- CDR-SupplementalTableS1.xlsx). Source data are provided with this paper.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 621, 188, 641]]<|/det|>
+## Code availability  
+
+<|ref|>text<|/ref|><|det|>[[42, 659, 950, 815]]<|/det|>
+No custom software, tools, or packages were used. The open- source software, tools, and packages used for data analysis in this study are referenced in the methods where applicable and include R (v4.2.2), FASTQC (v0.11.9), HISAT2 (v2.1.0), Kallisto (v0.46.2), SeSAME (v1.12.9) (BioConductor 3.13), survival R package (v3.5- 7), survivalROC R package (v1.0.3.1), biomaRt R package (v2.54.1), glmnet R package (v4.1- 8), igraph R package (v1.5.1), factoextra R package (v1.0.7), cluster R package (v2.1.4), ComplexHeatmap R package (v2.15.4), GSEA (v4.3.2), and EnrichmentMap App (v3.3.4) and AutoAnnotate app (v1.3.5) in Cytoscape (v3.7.2).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 833, 218, 852]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[42, 871, 944, 958]]<|/det|>
+This study was supported by funding from American Brain Tumor Association Jack & Fay Netchin Medical Student Summer Fellowship in memory of Rose Digang to M.P.N., K12 CA260225 and the Chan Zuckerburg Biohub Physician Scientist Fellowship to W.C.C., and R01 CA262311, P50 CA097257, the UCSF Wolfe Meningioma Program Project and the Trenchard Family Charitable Fund, to D.R.R. The
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 824, 90]]<|/det|>
+results shown here are in part based upon data generated by the TCGA Research Network (https://www.cancer.gov/tcga).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 106, 319, 125]]<|/det|>
+## Author contributions statement  
+
+<|ref|>text<|/ref|><|det|>[[41, 144, 950, 323]]<|/det|>
+All authors made substantial contributions to the conception or design of the study; the acquisition, analysis, or interpretation of data; or drafting or revising the manuscript. All authors approved the manuscript. All authors agree to be personally accountable for individual contributions and to ensure that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved and the resolution documented in the literature. M.P.N. and W.C.C. conceived and designed the study and analyzed bioinformatic data with supervision from D.R.R. N.Z. performed gene ontology analyses with supervision from D.R.R. K.M. and C-H.G.L. provided guidance and feedback on study design, analysis, and presentation.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 340, 317, 360]]<|/det|>
+## Competing interests statement  
+
+<|ref|>text<|/ref|><|det|>[[44, 379, 428, 398]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 421, 193, 447]]<|/det|>
+## References  
+
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+
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+21. Smith, J. C. & Sheltzer, J. M. Genome-wide identification and analysis of prognostic features in human cancers. Cell Reports 38, (2022).  
+
+<|ref|>text<|/ref|><|det|>[[48, 586, 816, 608]]<|/det|>
+22. Cunningham, F. et al. Ensembl 2022. Nucleic Acids Research 50, D988–D995 (2022).  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 630, 143, 656]]<|/det|>
+## Figures
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[40, 37, 950, 714]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 725, 115, 743]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 765, 952, 946]]<|/det|>
+Meningioma risk- stratification models demonstrate CNV size- dependence. a, Heatmaps showing area under the curve for univariate Cox models of LFFR or OS based on individual copy number gains (left, red) or individual copy number losses (right, blue). Models were trained using sequential size thresholds requiring \(\geq 5\%\) to \(\geq 95\%\) of chromosome arms to be gained or lost to define CNVs. Boxes show peak AUCs for "size- dependent" CNVs, defined as having a maximum area under the curve (AUC) for 5- year LFFR or OS of at least 0.60 that decreased by at least \(5\%\) from the maximum AUC as CNV threshold was varied. n=565 meningiomas. b, Previously published meningioma risk- stratification models incorporating CNVs (integrated grade based on histology and a \(\geq 50\%\) CNV threshold, or integrated score based on histology,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 45, 950, 291]]<|/det|>
+DNA methylation profiling, and a \(\geq 5\%\) CNV threshold) show decreasing AUC with varying size-thresholds. n=565 meningiomas. c, CNVs from previously published meningioma risk-stratification models or from newly-derived size-dependent LASSO or elastic net models for meningioma LFFR or OS. n=565 meningiomas. d, CNV profile plots demonstrating focal copy number losses in size-dependent CNVs from LASSO or elastic net models. Chromosomes 14 and 20 are shown as examples of broad/non-focal CNVs. n=565 meningiomas. e, Average RNA sequencing expression of genes mapping to regions of focal copy number loss on size-dependent CNVs from LASSO or elastic net models versus genes mapping to other regions on the same chromosomes. n=502 meningiomas. Error bars show standard error of the mean. Student's t test, p≤0.0001. f, Network of gene circuits distinguishing genes mapping to regions of focal copy number loss. Nodes represent pathways and edges represent shared genes between pathways (p≤0.05, FDR≤0.05). n=502 meningiomas.  
+
+<|ref|>image<|/ref|><|det|>[[40, 290, 940, 960]]<|/det|>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 84, 950, 264]]<|/det|>
+Size- dependent CNV co- occurrence is prognostic for meningioma outcomes. a, Network diagrams demonstrating co- occurrence of prognostic size- dependent CNVs from Fig. 1c. b, Kaplan- Meier curves comparing meningioma LFFR or OS according to individual CNVs versus co- occurrent CNV pairs identified as the most important predictors of postoperative outcomes in LASSO Cox models from Extended Data Fig. 3a using optimized thresholds for defining CNVs from Fig. 1a. Log- rank tests. n=565 meningiomas. c, Heatmap showing unsupervised hierarchical clustering of individual CNVs according to the total number of CNVs per meningioma. CNVs were defined using optimal size thresholds for LFFR or OS models from Fig. 1a.  
+
+<|ref|>image<|/ref|><|det|>[[42, 268, 952, 768]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 781, 116, 800]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[40, 825, 949, 960]]<|/det|>
+Pan- cancer analyses reveal size- dependent CNV co- occurrence risk- stratification models for half of human cancers. a, TCGA SNP- array and clinical outcomes data used in pan- cancer analyses. Cancers with size- dependent prognostic CNVs were defined as having a CNV with a univariate Cox AUC for either PFS or OS of at least 0.60 that dropped by at least \(5\%\) from the maximum AUC when varying the size threshold for defining CNVs. b, Network diagrams demonstrating co- occurrence of prognostic size- dependent CNVs for GBM or CESC from Supplementary Table 4. c, LASSO Cox model coefficients using
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 945, 134]]<|/det|>
+size- dependent CNV co- occurrence to predict postoperative OS in GBM or CESC. d, Kaplan- Meier curves comparing OS for GBM or CESC with individual CNVs versus co- occurrent CNV pairs identified as the most important predictors of postoperative outcomes in LASSO Cox models. Log- rank tests. \(n = 571\) GBM and 294 CESC.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 157, 312, 185]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 207, 768, 227]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[59, 245, 528, 292]]<|/det|>
+- NguyenChenNatGenetEDFigv7.docx- NguyenChenNatGenetSupplementaryTablesv7.xlsx
+
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+# 4000-year-old Mycobacterium lepromatosis genomes from Chile reveal long-establishment of Hansen's Disease in the Americas  
+
+Dario Ramirez Universidad Nacional de Cordoba https://orcid.org/0000- 0001- 8982- 2550  
+
+T. Sitter Max Planck Institute for Evolutionary Anthropology https://orcid.org/0000- 0002- 7160- 6240  
+
+Sanni Oversti Max Planck Institute for Geoanthropology  
+
+Maria Herrera-Soto Universidad de Buenos Aires  
+
+Nicolás Pastor Instituto de Antropología de Córdoba, Consejo Nacional de Investigaciones Científicas y Técnicas, Córdoba, Argentina https://orcid.org/0000- 0001- 8971- 7910  
+
+Oscar Fontana Silva Museo Arqueológico de La Serena  
+
+Casey Kirkpatrick Simon Fraser University https://orcid.org/0000- 0001- 9755- 6459  
+
+José Castelleti Dellepiane Independent researcher  
+
+Rodrigo Nores Instituto de Antropología de Córdoba https://orcid.org/0000- 0002- 9153- 0626  
+
+Kirsten Bos  
+
+kirsten_bos@eva.mpg.de  
+
+Max Planck Institute for Evolutionary Anthropology https://orcid.org/0000- 0003- 2937- 3006  
+
+Article  
+
+Keywords:  
+
+Posted Date: May 28th, 2025  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 5776739/v1
+
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+License: © ① 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 Ecology & Evolution on June 30th, 2025. See the published version at https://doi.org/10.1038/s41559-025-02771- y.
+
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+
+# 4000-year-old Mycobacterium lepromatosis genomes from Chile reveal long- establishment of Hansen's Disease in the Americas 
+
+Darío A. Ramirez*1, T. Lesley Sitter*2, Sanni Översti3, María José Herrera-Soto4, Nicolás Pastor5, Oscar Eduardo Fontana Silva6, Casey L. Kirkpatrick2,7,8, José Castelletti Dellepiane9, Rodrigo Nores1, and Kirsten Bos2 
+
+1 Instituto de Antropología de Córdoba CONICET-UNC, Museo de Antropologías, Departamento de Antropología, Facultad de Filosofía y Humanidades, Universidad Nacional de Córdoba. Av. Hipólito Yrigoyen 174, Córdoba, Argentina. 
+
+2 Max Planck Institute for Evolutionary Anthropology. Deutscher Platz 6, Leipzig, Germany. 
+
+3 Max Planck Institute of Geoanthropology. Kahlaische Strasse 10, Jena, Germany. 
+
+4 Facultad de Filosofía y Letras, Universidad de Buenos Aires, Argentina. 
+
+5 Instituto de Antropología de Córdoba CONICET-UNC, Museo de Antropologías, Facultad de Filosofía y Humanidades y Departamento de Diversidad Biológica y Ecología, Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba. Av. Hipólito Yrigoyen 174, Córdoba, Argentina. 
+
+6 Museo Arqueológico de La Serena. Gregorio Cordovez esquina Cienfuegos, S/N, La Serena, Chile. 
+
+7 Simon Fraser University, Dept. of Archaeology, 8888 University Drive, Burnaby, B.C., Canada 
+
+8 Western University, Dept. of Anthropology, 1151 Richmond St., London, Ontario, Canada. 
+
+9 Independent researcher, Chile. 
+
+*These authors contributed equally to this work 
+
+Address correspondence to: kirsten_bos@eva.mpg.de, or rodrigonores@ffyh.unc.edu.ar
+
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+1 Abstract2 Mycobacterium lepromatosis is a recently identified cause of Hansen's Disease, and3 is associated with the more severe and potentially lethal presentations of diffuse4 lepromatous leprosy (DLL) and Lucio's phenomenon (LP). Detection of this infection5 has been limited to a small number of individuals, leaving much to be learned about6 its global distribution and transmissibility. Its discovery in wild rodent populations in the7 United Kingdom and Ireland also raises questions about its zoonotic potential. Here8 we raise further awareness of this disease via analyses of two exceptionally well9 preserved M. lepromatosis genomes obtained from 4000- year- old human remains of10 two adult males from the archaeological sites of El Cerrito and La Herradura in11 Northern Chile. This formed the basis of genomic comparisons between ancient and12 modern forms of the pathogen. We demonstrate an unexpected long history of M.13 lepromatosis in the Americas, which contrasts with the more recent Eurasian history14 of the closely related Mycobacterium leprae. We offer relevant perspectives on its15 evolution while providing an incentive for further disease monitoring in both humans16 and other potential reservoir species in the Americas and elsewhere.17
+
+<--- Page Split --->
+
+## Introduction  
+
+Hansen's disease, more commonly known as leprosy, is caused by the unculturable bacteria Mycobacterium leprae and the recently described Mycobacterium lepromatosis<sup>1</sup>. Transmission occurs via prolonged exposure to respiratory droplets from of an infected person<sup>2</sup>. Untreated individuals can develop a chronic peripheral neuropathy with associated physical impairment<sup>3</sup>. Many infected remain asymptomatic, which can obscure diagnoses and control measures<sup>4</sup>. The availability of curative multidrug treatments has decreased worldwide prevalence<sup>5</sup>; regardless, the disease persists in more than 100 countries, with up to 174,000 new cases reported globally in 2022 alone<sup>6</sup>. Risk of infection is closely correlated with conditions of overcrowding, poverty, malnutrition and an immunocompromised state<sup>7</sup>.  
+
+Written accounts describe the impact of disfiguring diseases presumed to be Hansen's Disease on Eurasian populations throughout the historic period<sup>8</sup>. As skeletal involvement occurs in advanced stages, past infections have been identified in archaeological tissues as early as 5,000 years ago in Europe, Asia, and Oceania<sup>9- 14</sup>. For M. leprae, analyses of ancient genomic data provide further support for its infectious potential having spanned several millennia<sup>16</sup>. While humans are regarded as the principal host of Hansen's Disease, maintenance of the causative bacteria in other animal species have raised concerns over their potential as zoonotic reservoirs from a One Health perspective. Nine- banded armadillos are known sources of M. leprae, where transmission may occur through human consumption<sup>16</sup>. Red squirrels in Britain and Ireland can harbour both M. leprae and M. lepromatosis<sup>17</sup>, and recent identification of M. leprae in archaeological rodent bone demonstrates cross- species infectivity in historical periods<sup>18</sup>. Detection of M. leprae in several species of non- human primates further demonstrates the broad host range of this pathogen<sup>19- 21</sup>. Viability of M. leprae in ticks and amoebae for several months opens the possibility of environmental reservoirs as well<sup>22,23</sup>. Unlike many bacterial diseases, presentation of symptoms and the development of its more severe multibacillary or lepromatous forms seem highly dependent on host immunological status<sup>2,24</sup>. While the few available reports tend to associate M. lepromatosis with severe disease presentation such as Diffuse Lepromatous Leprosy (DLL) and the potentially fatal Lucio's phenomenon (LP), a set of clinically defined criteria that distinguish it from M. leprae infection has yet to be established<sup>25</sup>.  
+
+Understanding of M. lepromatosis distribution and evolutionary history is limited as few examples of the infection have been molecularly confirmed. PCR- based detections demonstrate its presence in the Americas (Mexico, the Caribbean)<sup>1,26</sup>, as well as Southeast Asia (Myanmar, Singapore)<sup>27</sup>, consistent with the global occurrence of DLL<sup>25,28</sup>. Genome- level analyses are limited in scope: the available modern genomes suggest a deep divergence of M. lepromatosis and M. leprae, though with retention of genomic features that contribute to some similarities in disease presentation<sup>29</sup>. While investigations that draw upon both modern and ancient genomic data consistently support an origin for M. leprae outside the Americas<sup>15</sup>, the identification of M. lepromatosis in archaeological contexts has not been reported, though its modern association with Latin American contexts could suggest its endemicity in the continent in the pre- colonial period<sup>28,29</sup>.  
+
+Paleogenomic investigations of this disease are currently restricted to the recovery of M. leprae genomes, and are dominated by investigations that are limited to a Eurasian
+
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+context. Here we present two high- coverage M. lepromatosis genomes reconstructed from skeletal remains of individuals from distinct archaeological contexts from Chile, both dated to ca. 4,000 years ago. These data indicate a long and previously undocumented history of this infectious disease in the Americas.  
+
+## Archaeological context, morphology, and molecular recovery  
+
+To investigate infectious disease in the American pre- colonial period from a molecular perspective, we sampled 35 teeth and 19 bones with pathological lesions suggestive of active infection belonging to 41 individuals from five archaeological sites representing various time periods and subsistence strategies in the semi- arid region of Chile (Supplementary Information section 1). Both teeth and pathological bone were selected to permit identification of pathogens that contribute to either acute or chronic infection, and when available both tissue types were selected from an individual. Approximately 50mg of each tissue was extracted and converted into a single- stranded DNA library for sequencing on an Illumina HiSeq 4000 to a depth of ca. 5 million reads. Data were computationally screened for a variety of pathogenic bacteria and viruses following a hypothesis- free method using the MALT and HOPS platforms implemented through the nf- core EAGER 2 analysis pipeline \(^{30 - 32}\) . This process revealed several thousand DNA fragments with homology to M. lepromatosis in each of two archaeological tissues, representing the neighbouring sites of La Herradura (a tibia from an individual referred to here as "ECR001") and El Cerrito (a tooth from an individual referred to here as "ECR003") (Figure 1, Tables S1 and S2, Figures S1- S6). Radiocarbon dating of both skeletal elements indicate them to be roughly contemporaneous, from approximately 4,200 - 4,300 years ago (Figure 1).  
+
+Currently there is little information on the osteological manifestations of M. lepromatosis infection, but most reported examples are associated with the DLL and LP forms of Hansen's Disease \(^{1}\) . DLL primarily affects the skin and peripheral nerves but it can also cause ocular damage, rhinitis, destruction of the nasal septum causing saddle or crooked nose (usually without affecting the nasal bones), damage to the larynx, organ damage or failure, and sepsis. Generalized hypoesthesia or anesthesia resulting from neuritis can contribute to secondary injury of the extremities, which may result in bony changes. LP is a rare reaction most commonly associated with DLL that manifests as acute, necrotizing cutaneous vasculitis, generally affecting the legs, arms, torso, and face \(^{33}\) . Although LP does not necessarily affect the bones, the resulting inflammation and possible secondary infections could potentially cause osteological changes. Genetically- confirmed M. lepromatosis infections have also been associated with borderline lepromatous leprosy and lepromatous leprosy \(^{25}\) , the latter being the most common form of Hansen's Disease to cause osteological changes \(^{34}\) . While its modern presentation may differ from the spectrum of pathology observed in the past, both individuals display pathological lesions that are consistent with, though not diagnostic of Hansen's Disease, as well as additional changes that are associated with unrelated afflictions (see SI for complete descriptions of the remains). For example, skeleton ECR001 (male 35- 40 years, Figures S2 - S4) exhibits a slight widening of the nasal aperture compared to other individuals in the population, with rounding of the margins and possible osteolytic processes in the area. This individual also has slight recession of the alveolar bone of the anterior teeth (though this may be in part due to taphonomic breakage or in response to other pathological processes), as well as pitting on the palatine process and on the ribs. The right fibula and tibia are affected by mostly- healed lamellar periostosis and slight thickening and
+
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+bowing of the right tibial diaphysis. The small tubular bones of the hands display pitting, abnormal foramina, and periosteal new bone on the palmar surfaces, but no concentric resorption or evidence of hyperflexion, and there are pronounced osteolytic lesions on the right calcaneus. Skeleton ECR003 (male, 40- 44 years) has fewer preserved skeletal elements but also displays rounding of the inferior margins of the nasal aperture and slight thickening and bowing of the tibial diaphysis (Figures 1, S5). Although the aforementioned osteological changes in both individuals could be associated with Hansen's Disease (though not necessarily with the DLL or LP forms), they could equally be caused by other diseases, both infectious and non- infectious. For this reason we do not attempt a differential diagnosis based on osteological criteria, nor do we propose any new diagnostic criteria from these limited examples.  
+
+To explore the suitability of genomic reconstruction, DNA libraries were enriched via in- solution capture through use of a probe set designed from a modern M. leprae reference panel<sup>35</sup>, and sequenced to a read depth of 20 million fragments, as above. Distinction between several mycobacterial species was accomplished via a competitive mapping approach, which demonstrated much higher homology and hence high confidence in their assignment to M. lepromatosis (Table S3). Both genomes are of exceptional quality, yielding average genomic coverages of 45- and 74- fold for ECR001 and ECR003, respectively, when mapped against the modern FJ924 M. lepromatosis genomic reference (CP083405) (Table S4), isolated from a patient in Mexico<sup>29</sup>. The distribution of heterozygous positions is consistent with a single source of M. lepromatosis DNA for each individual, though with a detectable level of chemical damage and possibly sporadic reads of non- target origin in the mapped datasets (Figure S7), as expected of metagenomically- sourced ancient bacterial DNA. The spectrum of DNA damage from both pathogen and host (Figures S6, S8) is consistent with their contemporaneous antiquity as determined from radiocarbon data (Figure 1). An analysis of human DNA also indicates an exclusively American Indigenous host source (Table S5). Negative controls were free of M. lepromatosis DNA (Table S6).
+
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+## M. Iepromatosis pangenome and comparisons against M. leprae  
+
+Despite our use of an M. leprae capture panel, we observed a 278- and 23- fold increase in M. lepromatosis DNA content between the shotgun and enriched datasets, with \(83\%\) and \(88\%\) of the genome covered at four- fold read support for genomes ECR001 and ECR003, respectively (Tables S3 and S4, Figure 2). To investigate possible enrichment biases over individual regions, probes were mapped with high sensitivity against the M. lepromatosis reference and probe coverage was compared to that observed in the two ancient genomes over annotated coding regions (Figures 2, S9, and S10). Both ancient genomes include coverage over regions of the M. lepromatosis reference that were not included in probe design, and hence were not enriched. Coverage across these regions is higher for genome ECR003, which may be due to a higher abundance of M. lepromatosis DNA in the non- enriched fraction (Table S3). Importantly, we identify several regions with limited mapping reads in both ancient genomes where probe coverage is abundant. Further investigation revealed these regions to have asymmetric representation across host- associated modern genomes, which could indicate lineage- specific losses unrelated to host adaptation. This also reveals no pattern of gene loss/acquisition that distinguishes ancient from modern forms (Figure S10).  
+
+This analysis was complemented by evaluation of the two reconstructed ancient genomes alongside 16 modern M. lepromatosis (Table S7) based on a common mapping to the FJ924 reference (Table S8, Figure S11 and S12). No consistent pattern of gene acquisition or loss across the full annotated coding region distinguishes the human- associated strains from those associated with red squirrel populations in the north of the United Kingdom or Ireland (Figure S12). This implies that any long- term changes related to host- specificity are influenced by either nucleotide substitution, disruptions in synteny, or changes outside of the mapped coding regions that are undetected via the methods employed here. This analysis also revealed a surprisingly low coverage for genome FJ924_S_4 reported in Singh et al 202336 as a first example of M. lepromatosis in India (Table S9, Figures S11 and S12). A competitive mapping approach revealed this genome to show far greater homology to M. leprae, thus questioning the accuracy of its assignment to M. lepromatosis (Table S9).  
+
+Given the established observation of genome decay and reduction in M. leprae over evolutionary timescales37, divergence between M. lepromatosis and M. leprae were investigated on a gene level. There are currently four chromosomally resolved modern M. leprae genomes available, representative of branches 1 \((n = 2)\) , 3 \((n = 1)\) , and 4 \((n = 1)\) . A pangenomic analysis carried out in Roary38 indicated a strong level of divergence between the two pathogens, with 2000 (approximately half) of the 4097 protein coding regions identified in Prokka showing a minimum of \(50\%\) sequence homology between the two pathogens (Figure S13). This demonstrates a high sequence divergence despite M. leprae having been identified as the most closely related organism to M. lepromatosis29. This is further demonstrated via a mapping- based approach, which reveals the two to share only \(\sim 25\%\) nucleotide identity (Table S10). An alignment of the genomes using LASTZ39 and MAUVE40 shows several large rearrangements and approximately 0.5 Mbp ( \(\sim 12\%\) of the genome) present in M. lepromatosis FJ924 that is absent in M. leprae MRHRU- 235- G, either through acquisition in the former, decay in the latter, or a nucleotide homology that is too low for alignment. Less similarity is observed with the more distantly related Mycobacterium haemophilum (Figures S13
+
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+- S15). This would leave only disparate regions of similarity upon which to perform downstream genome-level analyses where M. leprae or another Mycobacterium representative are included.  
+
+## Phylogenetic analysis  
+
+The relationship of M. lepromatosis to other pathogenic mycobacteria was first determined through investigation of the 16S rRNA locus (Figure 3B), which confirmed M. leprae to be its closest relative despite extensive genomic divergence described above. This was complemented by a conservative approach to genome- level phylogenetic reconstruction, where focus was restricted to diversity within M. lepromatosis. These data are limited to the two ancient genomes presented here, four modern human genomes from Mexico, and six modern genomes isolated from red squirrels in Ireland and the United Kingdom. SNPs were called at 4- fold read support, and regions of low complexity, along with additional regions identified as potentially drawing background signal from co- enriched metagenomic DNA, were removed (Table S11). While M. leprae has not been observed to undergo recombination, Gubbins<sup>41</sup> was applied to investigate this phenomenon in this sparsely studied organism (Table S11). These various filters resulted in 650 variant positions upon which to base the phylogeny (Figure 3A, Tables S12 and S13). A maximum parsimony tree was generated in MEGA 11<sup>42</sup> with 100 bootstraps, mid- point rooting, and branch- length estimation (Figure 3C). The phylogeny supports a robust separation between the human and rodent- associated lineages, where the two ancient genomes form a sister clade to the cluster of all human M. lepromatosis thus far sequenced at the genomic level. For all polymorphic positions, 104 occur uniquely in the ancient genomes of which 43 correspond to non- synonymous changes with potential functional significance (Table S12).  
+
+## Emergence scenarios for M. lepromatosis  
+
+Reconstruction of the first ancient M. lepromatosis genomes with such deep chronology offers an unprecedented opportunity to explore the species' evolutionary history. Using the radiocarbon ages of skeletal elements from ECR001 and ECR003 and the collection year for all modern genomes (Table S14), time- calibrated phylogenetic trees were constructed to estimate divergence times and evolutionary rates using the BEAST v2.7.7 software package<sup>43</sup>. Topology of the Bayesian phylogeny agrees with that inferred from parsimony (Figure 3D). For thorough comparison we considered both strict and optimized uncorrelated relaxed lognormal clock models<sup>44</sup> along with both the Bayesian skyline plot (BSP)<sup>45</sup> and the coalescent constant population size model for demographic inference (Supplementary section 7.1). Model selection strongly supported a relaxed clock with BSP indicating rate heterogeneity among branches (Table S15a), which may reflect host- specific adaptations within human- and rodent- associated lineages.  
+
+Strength of temporal signal in the data was investigated via date randomization test (DRT)<sup>46</sup> (Figures S16 and S17). Simulations here showed a small proportion of overlap in the clock rate parameter (Figure S18), which indicated that a Bayesian framework may not estimate evolutionary rates and timescales with high confidence. This limitation likely arises from the small number of available genomes. We, therefore, chose to apply a prior distribution for the rate parameter based on previous estimates inferred for M. leprae (Supplementary text 8.3). The best- supported model estimates
+
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+an evolutionary rate of \(6.91\mathrm{e}^{- 09}\) subst./site/year (95% HDPI: \(0.34\mathrm{e}^{- 09} - 15.64\mathrm{e}^{- 09}\) subst./site/year) for M. lepromatosis, which agrees closely with estimates obtained via other models (Table S15b), as well as previous estimates for M. leprae genomic substitution rates (Table S16). From this, we estimate the median time for the most recent common ancestor (tMRCA) of M. lepromatosis to be approximately 26,800 years ago (95% HPDI range of 4,206 ... 115,340 yBP) (Table S15b). Genomes obtained from human hosts yield a divergence estimate of ca. 12,600 years (95% HPDI: 5,304 ... 49,659 yBP), while the tMRCA for the red squirrel clade is ca. 440 years (95% HPDI: 73 ... 2,063 yBP) (Table S15b). The estimates proposed here are highly consistent with results obtained from all iterations tested, supporting robustness across different demographic and molecular clock models (Table S15b, Figures S18- S21). Our tMRCA for M. lepromatosis closely aligns with results presented elsewhere based on modern data<sup>17</sup>, though with broader temporal intervals resulting from either our inclusion of ancient genomes or our selection of more permissive models. Further refinement of the origin, evolution, and relationship between the ancient strains and those from the regions where the disease is found today is expected to come with additional genomic examples made available through increased awareness for its detection in both clinical and archaeological contexts.  
+
+Recent investigations of M. leprae, as well as several other bacterial pathogens where ancient genomes are available, place their extrapolated coalescence date in the last 6000 years, which correlates with cultural adaptations such as the adoption of agriculture and animal husbandry in the Neolithic that are regarded as conducive to the emergence and maintenance of novel pathogens in human groups<sup>15,47- 50</sup>. The current analysis reveals a very different evolutionary history for M. lepromatosis: although based on only a small number of genomes, multiple simulations suggest a common ancestor for the human- associated lineages that temporally aligns with the Pleistocene- Holocene transition. This encompasses a warming period wherein human movements were less impeded by large ice sheets that covered 25% of the earth's land surface during the Last Glacial Maximum. Further exploration of the vast territories of the American continent soon followed, as demonstrated by the sudden increase in archaeological sites that indicate human activity<sup>51</sup>. Our finding of two M. lepromatosis infections in South America, prior to the periods of known contact with either Oceanian or European populations, implies either movement of the pathogen within human groups during an early peopling event, or its previously established endemicity in the continent in a separate reservoir species eventually acquired by humans. The latter would imply that its current distribution arises from a post- colonial dissemination, and would make it one of the few global diseases known to have emerged in the Americas<sup>52</sup>. Its presence in the continent has thus far remained undetected based on morphological analyses of human archaeological tissues, where skeletal lesions ascribed to Hansen's disease are limited to examples from the post- colonial period<sup>53</sup>, with the exception of two potential infections from the northern Pacific Coast that await molecular characterization and confirmation of their possible pre- AD1492 status<sup>54</sup>. Additional ancient genomes from either human or faunal remains may eventually disentangle the current mystery of its origin, and possible means of acquisition among the hunting- gathering- fishing groups studied here. It may also assist in the establishment of morphological diagnostic criteria for disease identification in the archaeological record.
+
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+While we observe a deep divergence between the human- and rodent- associated lineages, current data from non- human sources are limited to modern rodent lineages within a restrictive geographic spread in Ireland and the United Kingdom<sup>55</sup>, from a single introductory event of unknown origin within the last 500 years. While surveillance has as yet failed to identify M. lepromatosis or M. leprae in multiple squirrel species in mainland Europe<sup>56</sup>, analogous efforts in other parts of the world are needed to explore its ecological distribution in broader scale. Greater awareness of this pathogen and its potential for zoonotic transmission from armadillos is also being explored given that they are known reservoirs of M. leprae in the Americas. Previous contact with these animals (handling or consumption) has been reported in two individuals with confirmed M. lepromatosis infection in Mexico<sup>57</sup>. Screening efforts of multiple species of armadillos has also begun in Brazil, where human infections with M. lepromatosis represent greater than 10% of reported instances of Hansen's Disease<sup>58</sup>. Of note, both individuals studied here come from archaeological contexts in Chile that are outside the current range of armadillos.  
+
+## Modern M. lepromatosis in perspective  
+
+Since its discovery in 2008, M. lepromatosis has been regarded as a second causal pathogen for Hansen's disease. While associated with the more severe forms of DLL and LP, these presentations are equally considered within the clinical spectrum of M. leprae infection<sup>25</sup>. Distinction between the two pathogens through use of the recently validated species- specific PCR assay<sup>59</sup> has the potential to elucidate the true global prevalence of M. lepromatosis. Here we aim to raise awareness of M. lepromatosis infection through demonstration of its previously unknown health impact along the Pacific Coast of South America several millennia in the past. This region currently has a low incidence of Hansen's Disease where occasional reported cases, thus far attributed to M. leprae, are thought to result from travel to regions within Latin America where disease incidence is high<sup>60,61</sup>. Its restricted modern geographic distribution may in part be due to its decreased transmissibility in comparison to other globally dispersed pathogens. Management of human infections in living populations remains a principal concern, and adoption of a One Health perspective could provide the means to elucidate the zoonotic potential of this disease both in the present as well as the past<sup>18</sup>. Available data suggest that squirrel populations in Britain and Ireland may be the sole non- human reservoir for these pathogens in West Eurasia<sup>55,56</sup>. The results of such screenings from rodent populations in East Eurasia have yet to be reported, and recent evidence suggests wild rodents may be a natural source of M. leprae in Brazil<sup>62</sup>. This highlights the need for broader- scale investigations into potential wild reservoirs for both M. leprae and M. lepromatosis. The capacity of armadillos to harbour M. lepromatosis infection in Latin American countries, especially those where DLL representation is high such as Mexico and the Caribbean<sup>25</sup>, should also be considered. Given the narrow known host range for M. leprae, susceptibility in rodents, armadillos, or other animals may be related to their possible maintenance of M. lepromatosis in the past. Further contributions are also expected to come from paleogenomic analyses that continue to explore past disease landscapes represented in both human and animal remains.
+
+<--- Page Split --->
+
+## Acknowledgements  
+
+AcknowledgementsSkeletal elements for this work were obtained under permits \(N^{\circ} 43.341\) dated August 31 2022 of the Consejo de Monumentos Nacionales issued by the Ministerio de las Culturas, las Artes y el Patrimonio of Chile. We thank the Museo Arqueológico de La Serena, Chile and the laboratory processing teams of the Max Planck Institute of Evolutionary Anthropology at both the Jena satellite laboratory and the Leipzig Core Unit for their assistance in data generation. We also thank Alexander Herbig for helpful comments on an earlier draft of this manuscript, and support from the ancient pathogen research team at the Max Planck Institute for Evolutionary Anthropology.  
+
+## Author contributions  
+
+Author contributionsKIB, RN, and DAR conceived of the investigation. MJH- S, OEFS, JCD, and CLK performed archaeological and osteological analyses. TLS, SÖ, NP, DAR, RN, and KIB performed analyses. KIB, DAR, and RN wrote the manuscript with contributions from all coauthors.  
+
+## Funding  
+
+FundingThe Max Planck Society, European Research Council Starting Grant CoDisEASe (805268) to KIB, the German Academic Exchange Service (DAAD) to DAR under Short Term Grant number 57588366, the Social Sciences and Humanities Research Council of Canada postdoctoral fellowship no. 756- 2023- 0246 to CLK, Agencia Nacional de Investigación y Desarrollo de Chile (ANID) Doctorado Becas Chile Scholarship no. 2018- 72190531 to MJH- S, and the Secretaría de Ciencia y Tecnología (UNC) to RN.  
+
+## Data availability  
+
+Data are accessible via the ENA project ID ERR13916540 and ERR13916541.
+
+<--- Page Split --->
+
+## Figure captions  
+
+Figure 1. A) Map of the Semi-arid region of Chile showing the location of the two archaeological sites under study. B) Skeletal elements that yielded the two ancient genomes of M. lepromatosis. Left: tibia from ECR001 (bar = 5 cm). Right: tooth from ECR003 (bar = 0.5 cm). C) Modeled radiocarbon dates of the individuals ECR001 and ECR003 from La Herradura and El Cerrito sites, respectively.  
+
+Figure 2 - Overview of the recovery status of the newly identified ancient M. lepromatosis genomes. A) Indication of the genomic regions with a depth range between 0 and 5- fold depth averaged over bins of 1000 bp. B) Genome coverage of the M. leprae probes mapped to the M. lepromatosis FJ924 reference genome averaged over bins of 1000 bp (top based on permitted 3bp mismatch and bottom based on permitted 7bp mismatch). C) Visual representation of the location of the non- reference loci recovered for ECR001 and ECR003.  
+
+Figure 3 - Phylogenetic representation of ancient and modern M. lepromatosis. A) Network showing the number of SNPs that distinguish individual groupings. B) and C) Maximum parsimony trees (with branch length estimation) constructed in Mega X v11.0.11 with 1000 bootstrap iterations based on a 16S rRNA alignment of several mycobacterial representatives with ambiguous sites masked in the lower coverage genome ECR001 (B), and 650 full genomic alleles called at four- fold read support (C); D) Maximum clade credibility (MCC) tree with median heights, reconstructed using the Bayesian skyline plot and relaxed clock. Branches in (D) are color- coded based on the median rate estimates from the optimised relaxed clock model, with blue indicating lower rates and red indicating higher rates. Node labels show posterior support values, while the X- axis represents years before present.
+
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+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- RamirezSupplementaryTablesR1.xlsx- RamirezSitterSupplementaryMaterialR1.docx
+
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+<|ref|>title<|/ref|><|det|>[[44, 106, 904, 206]]<|/det|>
+# 4000-year-old Mycobacterium lepromatosis genomes from Chile reveal long-establishment of Hansen's Disease in the Americas  
+
+<|ref|>text<|/ref|><|det|>[[44, 229, 860, 272]]<|/det|>
+Dario Ramirez Universidad Nacional de Cordoba https://orcid.org/0000- 0001- 8982- 2550  
+
+<|ref|>text<|/ref|><|det|>[[44, 277, 860, 319]]<|/det|>
+T. Sitter Max Planck Institute for Evolutionary Anthropology https://orcid.org/0000- 0002- 7160- 6240  
+
+<|ref|>text<|/ref|><|det|>[[44, 323, 421, 365]]<|/det|>
+Sanni Oversti Max Planck Institute for Geoanthropology  
+
+<|ref|>text<|/ref|><|det|>[[44, 370, 308, 410]]<|/det|>
+Maria Herrera-Soto Universidad de Buenos Aires  
+
+<|ref|>text<|/ref|><|det|>[[44, 416, 905, 480]]<|/det|>
+Nicolás Pastor Instituto de Antropología de Córdoba, Consejo Nacional de Investigaciones Científicas y Técnicas, Córdoba, Argentina https://orcid.org/0000- 0001- 8971- 7910  
+
+<|ref|>text<|/ref|><|det|>[[44, 484, 357, 525]]<|/det|>
+Oscar Fontana Silva Museo Arqueológico de La Serena  
+
+<|ref|>text<|/ref|><|det|>[[44, 531, 622, 572]]<|/det|>
+Casey Kirkpatrick Simon Fraser University https://orcid.org/0000- 0001- 9755- 6459  
+
+<|ref|>text<|/ref|><|det|>[[44, 576, 270, 617]]<|/det|>
+José Castelleti Dellepiane Independent researcher  
+
+<|ref|>text<|/ref|><|det|>[[44, 623, 750, 665]]<|/det|>
+Rodrigo Nores Instituto de Antropología de Córdoba https://orcid.org/0000- 0002- 9153- 0626  
+
+<|ref|>text<|/ref|><|det|>[[44, 670, 146, 688]]<|/det|>
+Kirsten Bos  
+
+<|ref|>text<|/ref|><|det|>[[55, 697, 300, 714]]<|/det|>
+kirsten_bos@eva.mpg.de  
+
+<|ref|>text<|/ref|><|det|>[[52, 742, 857, 762]]<|/det|>
+Max Planck Institute for Evolutionary Anthropology https://orcid.org/0000- 0003- 2937- 3006  
+
+<|ref|>text<|/ref|><|det|>[[44, 803, 103, 821]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 841, 135, 859]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 879, 297, 898]]<|/det|>
+Posted Date: May 28th, 2025  
+
+<|ref|>text<|/ref|><|det|>[[44, 916, 474, 935]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 5776739/v1
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 44, 916, 87]]<|/det|>
+License: © ① This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 105, 535, 125]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 161, 938, 205]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Ecology & Evolution on June 30th, 2025. See the published version at https://doi.org/10.1038/s41559-025-02771- y.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[130, 100, 864, 133]]<|/det|>
+# 4000-year-old Mycobacterium lepromatosis genomes from Chile reveal long- establishment of Hansen's Disease in the Americas 
+
+<|ref|>text<|/ref|><|det|>[[116, 150, 835, 198]]<|/det|>
+Darío A. Ramirez*1, T. Lesley Sitter*2, Sanni Översti3, María José Herrera-Soto4, Nicolás Pastor5, Oscar Eduardo Fontana Silva6, Casey L. Kirkpatrick2,7,8, José Castelletti Dellepiane9, Rodrigo Nores1, and Kirsten Bos2 
+
+<|ref|>text<|/ref|><|det|>[[116, 216, 877, 264]]<|/det|>
+1 Instituto de Antropología de Córdoba CONICET-UNC, Museo de Antropologías, Departamento de Antropología, Facultad de Filosofía y Humanidades, Universidad Nacional de Córdoba. Av. Hipólito Yrigoyen 174, Córdoba, Argentina. 
+
+<|ref|>text<|/ref|><|det|>[[116, 281, 877, 313]]<|/det|>
+2 Max Planck Institute for Evolutionary Anthropology. Deutscher Platz 6, Leipzig, Germany. 
+
+<|ref|>text<|/ref|><|det|>[[116, 330, 864, 345]]<|/det|>
+3 Max Planck Institute of Geoanthropology. Kahlaische Strasse 10, Jena, Germany. 
+
+<|ref|>text<|/ref|><|det|>[[116, 363, 775, 377]]<|/det|>
+4 Facultad de Filosofía y Letras, Universidad de Buenos Aires, Argentina. 
+
+<|ref|>text<|/ref|><|det|>[[116, 395, 877, 459]]<|/det|>
+5 Instituto de Antropología de Córdoba CONICET-UNC, Museo de Antropologías, Facultad de Filosofía y Humanidades y Departamento de Diversidad Biológica y Ecología, Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba. Av. Hipólito Yrigoyen 174, Córdoba, Argentina. 
+
+<|ref|>text<|/ref|><|det|>[[116, 477, 876, 508]]<|/det|>
+6 Museo Arqueológico de La Serena. Gregorio Cordovez esquina Cienfuegos, S/N, La Serena, Chile. 
+
+<|ref|>text<|/ref|><|det|>[[116, 526, 876, 557]]<|/det|>
+7 Simon Fraser University, Dept. of Archaeology, 8888 University Drive, Burnaby, B.C., Canada 
+
+<|ref|>text<|/ref|><|det|>[[116, 576, 876, 606]]<|/det|>
+8 Western University, Dept. of Anthropology, 1151 Richmond St., London, Ontario, Canada. 
+
+<|ref|>text<|/ref|><|det|>[[116, 625, 412, 639]]<|/det|>
+9 Independent researcher, Chile. 
+
+<|ref|>text<|/ref|><|det|>[[117, 674, 539, 688]]<|/det|>
+*These authors contributed equally to this work 
+
+<|ref|>text<|/ref|><|det|>[[116, 706, 636, 737]]<|/det|>
+Address correspondence to: kirsten_bos@eva.mpg.de, or rodrigonores@ffyh.unc.edu.ar
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[70, 85, 880, 355]]<|/det|>
+1 Abstract2 Mycobacterium lepromatosis is a recently identified cause of Hansen's Disease, and3 is associated with the more severe and potentially lethal presentations of diffuse4 lepromatous leprosy (DLL) and Lucio's phenomenon (LP). Detection of this infection5 has been limited to a small number of individuals, leaving much to be learned about6 its global distribution and transmissibility. Its discovery in wild rodent populations in the7 United Kingdom and Ireland also raises questions about its zoonotic potential. Here8 we raise further awareness of this disease via analyses of two exceptionally well9 preserved M. lepromatosis genomes obtained from 4000- year- old human remains of10 two adult males from the archaeological sites of El Cerrito and La Herradura in11 Northern Chile. This formed the basis of genomic comparisons between ancient and12 modern forms of the pathogen. We demonstrate an unexpected long history of M.13 lepromatosis in the Americas, which contrasts with the more recent Eurasian history14 of the closely related Mycobacterium leprae. We offer relevant perspectives on its15 evolution while providing an incentive for further disease monitoring in both humans16 and other potential reservoir species in the Americas and elsewhere.17
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 240, 100]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[118, 101, 880, 266]]<|/det|>
+Hansen's disease, more commonly known as leprosy, is caused by the unculturable bacteria Mycobacterium leprae and the recently described Mycobacterium lepromatosis<sup>1</sup>. Transmission occurs via prolonged exposure to respiratory droplets from of an infected person<sup>2</sup>. Untreated individuals can develop a chronic peripheral neuropathy with associated physical impairment<sup>3</sup>. Many infected remain asymptomatic, which can obscure diagnoses and control measures<sup>4</sup>. The availability of curative multidrug treatments has decreased worldwide prevalence<sup>5</sup>; regardless, the disease persists in more than 100 countries, with up to 174,000 new cases reported globally in 2022 alone<sup>6</sup>. Risk of infection is closely correlated with conditions of overcrowding, poverty, malnutrition and an immunocompromised state<sup>7</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 280, 880, 641]]<|/det|>
+Written accounts describe the impact of disfiguring diseases presumed to be Hansen's Disease on Eurasian populations throughout the historic period<sup>8</sup>. As skeletal involvement occurs in advanced stages, past infections have been identified in archaeological tissues as early as 5,000 years ago in Europe, Asia, and Oceania<sup>9- 14</sup>. For M. leprae, analyses of ancient genomic data provide further support for its infectious potential having spanned several millennia<sup>16</sup>. While humans are regarded as the principal host of Hansen's Disease, maintenance of the causative bacteria in other animal species have raised concerns over their potential as zoonotic reservoirs from a One Health perspective. Nine- banded armadillos are known sources of M. leprae, where transmission may occur through human consumption<sup>16</sup>. Red squirrels in Britain and Ireland can harbour both M. leprae and M. lepromatosis<sup>17</sup>, and recent identification of M. leprae in archaeological rodent bone demonstrates cross- species infectivity in historical periods<sup>18</sup>. Detection of M. leprae in several species of non- human primates further demonstrates the broad host range of this pathogen<sup>19- 21</sup>. Viability of M. leprae in ticks and amoebae for several months opens the possibility of environmental reservoirs as well<sup>22,23</sup>. Unlike many bacterial diseases, presentation of symptoms and the development of its more severe multibacillary or lepromatous forms seem highly dependent on host immunological status<sup>2,24</sup>. While the few available reports tend to associate M. lepromatosis with severe disease presentation such as Diffuse Lepromatous Leprosy (DLL) and the potentially fatal Lucio's phenomenon (LP), a set of clinically defined criteria that distinguish it from M. leprae infection has yet to be established<sup>25</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 657, 880, 853]]<|/det|>
+Understanding of M. lepromatosis distribution and evolutionary history is limited as few examples of the infection have been molecularly confirmed. PCR- based detections demonstrate its presence in the Americas (Mexico, the Caribbean)<sup>1,26</sup>, as well as Southeast Asia (Myanmar, Singapore)<sup>27</sup>, consistent with the global occurrence of DLL<sup>25,28</sup>. Genome- level analyses are limited in scope: the available modern genomes suggest a deep divergence of M. lepromatosis and M. leprae, though with retention of genomic features that contribute to some similarities in disease presentation<sup>29</sup>. While investigations that draw upon both modern and ancient genomic data consistently support an origin for M. leprae outside the Americas<sup>15</sup>, the identification of M. lepromatosis in archaeological contexts has not been reported, though its modern association with Latin American contexts could suggest its endemicity in the continent in the pre- colonial period<sup>28,29</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 870, 880, 904]]<|/det|>
+Paleogenomic investigations of this disease are currently restricted to the recovery of M. leprae genomes, and are dominated by investigations that are limited to a Eurasian
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[117, 85, 880, 152]]<|/det|>
+context. Here we present two high- coverage M. lepromatosis genomes reconstructed from skeletal remains of individuals from distinct archaeological contexts from Chile, both dated to ca. 4,000 years ago. These data indicate a long and previously undocumented history of this infectious disease in the Americas.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 167, 710, 185]]<|/det|>
+## Archaeological context, morphology, and molecular recovery  
+
+<|ref|>text<|/ref|><|det|>[[115, 185, 880, 479]]<|/det|>
+To investigate infectious disease in the American pre- colonial period from a molecular perspective, we sampled 35 teeth and 19 bones with pathological lesions suggestive of active infection belonging to 41 individuals from five archaeological sites representing various time periods and subsistence strategies in the semi- arid region of Chile (Supplementary Information section 1). Both teeth and pathological bone were selected to permit identification of pathogens that contribute to either acute or chronic infection, and when available both tissue types were selected from an individual. Approximately 50mg of each tissue was extracted and converted into a single- stranded DNA library for sequencing on an Illumina HiSeq 4000 to a depth of ca. 5 million reads. Data were computationally screened for a variety of pathogenic bacteria and viruses following a hypothesis- free method using the MALT and HOPS platforms implemented through the nf- core EAGER 2 analysis pipeline \(^{30 - 32}\) . This process revealed several thousand DNA fragments with homology to M. lepromatosis in each of two archaeological tissues, representing the neighbouring sites of La Herradura (a tibia from an individual referred to here as "ECR001") and El Cerrito (a tooth from an individual referred to here as "ECR003") (Figure 1, Tables S1 and S2, Figures S1- S6). Radiocarbon dating of both skeletal elements indicate them to be roughly contemporaneous, from approximately 4,200 - 4,300 years ago (Figure 1).  
+
+<|ref|>text<|/ref|><|det|>[[115, 494, 880, 905]]<|/det|>
+Currently there is little information on the osteological manifestations of M. lepromatosis infection, but most reported examples are associated with the DLL and LP forms of Hansen's Disease \(^{1}\) . DLL primarily affects the skin and peripheral nerves but it can also cause ocular damage, rhinitis, destruction of the nasal septum causing saddle or crooked nose (usually without affecting the nasal bones), damage to the larynx, organ damage or failure, and sepsis. Generalized hypoesthesia or anesthesia resulting from neuritis can contribute to secondary injury of the extremities, which may result in bony changes. LP is a rare reaction most commonly associated with DLL that manifests as acute, necrotizing cutaneous vasculitis, generally affecting the legs, arms, torso, and face \(^{33}\) . Although LP does not necessarily affect the bones, the resulting inflammation and possible secondary infections could potentially cause osteological changes. Genetically- confirmed M. lepromatosis infections have also been associated with borderline lepromatous leprosy and lepromatous leprosy \(^{25}\) , the latter being the most common form of Hansen's Disease to cause osteological changes \(^{34}\) . While its modern presentation may differ from the spectrum of pathology observed in the past, both individuals display pathological lesions that are consistent with, though not diagnostic of Hansen's Disease, as well as additional changes that are associated with unrelated afflictions (see SI for complete descriptions of the remains). For example, skeleton ECR001 (male 35- 40 years, Figures S2 - S4) exhibits a slight widening of the nasal aperture compared to other individuals in the population, with rounding of the margins and possible osteolytic processes in the area. This individual also has slight recession of the alveolar bone of the anterior teeth (though this may be in part due to taphonomic breakage or in response to other pathological processes), as well as pitting on the palatine process and on the ribs. The right fibula and tibia are affected by mostly- healed lamellar periostosis and slight thickening and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 84, 880, 266]]<|/det|>
+bowing of the right tibial diaphysis. The small tubular bones of the hands display pitting, abnormal foramina, and periosteal new bone on the palmar surfaces, but no concentric resorption or evidence of hyperflexion, and there are pronounced osteolytic lesions on the right calcaneus. Skeleton ECR003 (male, 40- 44 years) has fewer preserved skeletal elements but also displays rounding of the inferior margins of the nasal aperture and slight thickening and bowing of the tibial diaphysis (Figures 1, S5). Although the aforementioned osteological changes in both individuals could be associated with Hansen's Disease (though not necessarily with the DLL or LP forms), they could equally be caused by other diseases, both infectious and non- infectious. For this reason we do not attempt a differential diagnosis based on osteological criteria, nor do we propose any new diagnostic criteria from these limited examples.  
+
+<|ref|>text<|/ref|><|det|>[[115, 281, 880, 578]]<|/det|>
+To explore the suitability of genomic reconstruction, DNA libraries were enriched via in- solution capture through use of a probe set designed from a modern M. leprae reference panel<sup>35</sup>, and sequenced to a read depth of 20 million fragments, as above. Distinction between several mycobacterial species was accomplished via a competitive mapping approach, which demonstrated much higher homology and hence high confidence in their assignment to M. lepromatosis (Table S3). Both genomes are of exceptional quality, yielding average genomic coverages of 45- and 74- fold for ECR001 and ECR003, respectively, when mapped against the modern FJ924 M. lepromatosis genomic reference (CP083405) (Table S4), isolated from a patient in Mexico<sup>29</sup>. The distribution of heterozygous positions is consistent with a single source of M. lepromatosis DNA for each individual, though with a detectable level of chemical damage and possibly sporadic reads of non- target origin in the mapped datasets (Figure S7), as expected of metagenomically- sourced ancient bacterial DNA. The spectrum of DNA damage from both pathogen and host (Figures S6, S8) is consistent with their contemporaneous antiquity as determined from radiocarbon data (Figure 1). An analysis of human DNA also indicates an exclusively American Indigenous host source (Table S5). Negative controls were free of M. lepromatosis DNA (Table S6).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 733, 101]]<|/det|>
+## M. Iepromatosis pangenome and comparisons against M. leprae  
+
+<|ref|>text<|/ref|><|det|>[[115, 101, 880, 381]]<|/det|>
+Despite our use of an M. leprae capture panel, we observed a 278- and 23- fold increase in M. lepromatosis DNA content between the shotgun and enriched datasets, with \(83\%\) and \(88\%\) of the genome covered at four- fold read support for genomes ECR001 and ECR003, respectively (Tables S3 and S4, Figure 2). To investigate possible enrichment biases over individual regions, probes were mapped with high sensitivity against the M. lepromatosis reference and probe coverage was compared to that observed in the two ancient genomes over annotated coding regions (Figures 2, S9, and S10). Both ancient genomes include coverage over regions of the M. lepromatosis reference that were not included in probe design, and hence were not enriched. Coverage across these regions is higher for genome ECR003, which may be due to a higher abundance of M. lepromatosis DNA in the non- enriched fraction (Table S3). Importantly, we identify several regions with limited mapping reads in both ancient genomes where probe coverage is abundant. Further investigation revealed these regions to have asymmetric representation across host- associated modern genomes, which could indicate lineage- specific losses unrelated to host adaptation. This also reveals no pattern of gene loss/acquisition that distinguishes ancient from modern forms (Figure S10).  
+
+<|ref|>text<|/ref|><|det|>[[115, 395, 880, 625]]<|/det|>
+This analysis was complemented by evaluation of the two reconstructed ancient genomes alongside 16 modern M. lepromatosis (Table S7) based on a common mapping to the FJ924 reference (Table S8, Figure S11 and S12). No consistent pattern of gene acquisition or loss across the full annotated coding region distinguishes the human- associated strains from those associated with red squirrel populations in the north of the United Kingdom or Ireland (Figure S12). This implies that any long- term changes related to host- specificity are influenced by either nucleotide substitution, disruptions in synteny, or changes outside of the mapped coding regions that are undetected via the methods employed here. This analysis also revealed a surprisingly low coverage for genome FJ924_S_4 reported in Singh et al 202336 as a first example of M. lepromatosis in India (Table S9, Figures S11 and S12). A competitive mapping approach revealed this genome to show far greater homology to M. leprae, thus questioning the accuracy of its assignment to M. lepromatosis (Table S9).  
+
+<|ref|>text<|/ref|><|det|>[[115, 640, 880, 904]]<|/det|>
+Given the established observation of genome decay and reduction in M. leprae over evolutionary timescales37, divergence between M. lepromatosis and M. leprae were investigated on a gene level. There are currently four chromosomally resolved modern M. leprae genomes available, representative of branches 1 \((n = 2)\) , 3 \((n = 1)\) , and 4 \((n = 1)\) . A pangenomic analysis carried out in Roary38 indicated a strong level of divergence between the two pathogens, with 2000 (approximately half) of the 4097 protein coding regions identified in Prokka showing a minimum of \(50\%\) sequence homology between the two pathogens (Figure S13). This demonstrates a high sequence divergence despite M. leprae having been identified as the most closely related organism to M. lepromatosis29. This is further demonstrated via a mapping- based approach, which reveals the two to share only \(\sim 25\%\) nucleotide identity (Table S10). An alignment of the genomes using LASTZ39 and MAUVE40 shows several large rearrangements and approximately 0.5 Mbp ( \(\sim 12\%\) of the genome) present in M. lepromatosis FJ924 that is absent in M. leprae MRHRU- 235- G, either through acquisition in the former, decay in the latter, or a nucleotide homology that is too low for alignment. Less similarity is observed with the more distantly related Mycobacterium haemophilum (Figures S13
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[118, 84, 879, 134]]<|/det|>
+- S15). This would leave only disparate regions of similarity upon which to perform downstream genome-level analyses where M. leprae or another Mycobacterium representative are included.  
+
+<|ref|>sub_title<|/ref|><|det|>[[119, 150, 331, 166]]<|/det|>
+## Phylogenetic analysis  
+
+<|ref|>text<|/ref|><|det|>[[115, 166, 880, 511]]<|/det|>
+The relationship of M. lepromatosis to other pathogenic mycobacteria was first determined through investigation of the 16S rRNA locus (Figure 3B), which confirmed M. leprae to be its closest relative despite extensive genomic divergence described above. This was complemented by a conservative approach to genome- level phylogenetic reconstruction, where focus was restricted to diversity within M. lepromatosis. These data are limited to the two ancient genomes presented here, four modern human genomes from Mexico, and six modern genomes isolated from red squirrels in Ireland and the United Kingdom. SNPs were called at 4- fold read support, and regions of low complexity, along with additional regions identified as potentially drawing background signal from co- enriched metagenomic DNA, were removed (Table S11). While M. leprae has not been observed to undergo recombination, Gubbins<sup>41</sup> was applied to investigate this phenomenon in this sparsely studied organism (Table S11). These various filters resulted in 650 variant positions upon which to base the phylogeny (Figure 3A, Tables S12 and S13). A maximum parsimony tree was generated in MEGA 11<sup>42</sup> with 100 bootstraps, mid- point rooting, and branch- length estimation (Figure 3C). The phylogeny supports a robust separation between the human and rodent- associated lineages, where the two ancient genomes form a sister clade to the cluster of all human M. lepromatosis thus far sequenced at the genomic level. For all polymorphic positions, 104 occur uniquely in the ancient genomes of which 43 correspond to non- synonymous changes with potential functional significance (Table S12).  
+
+<|ref|>sub_title<|/ref|><|det|>[[119, 546, 519, 562]]<|/det|>
+## Emergence scenarios for M. lepromatosis  
+
+<|ref|>text<|/ref|><|det|>[[118, 571, 880, 785]]<|/det|>
+Reconstruction of the first ancient M. lepromatosis genomes with such deep chronology offers an unprecedented opportunity to explore the species' evolutionary history. Using the radiocarbon ages of skeletal elements from ECR001 and ECR003 and the collection year for all modern genomes (Table S14), time- calibrated phylogenetic trees were constructed to estimate divergence times and evolutionary rates using the BEAST v2.7.7 software package<sup>43</sup>. Topology of the Bayesian phylogeny agrees with that inferred from parsimony (Figure 3D). For thorough comparison we considered both strict and optimized uncorrelated relaxed lognormal clock models<sup>44</sup> along with both the Bayesian skyline plot (BSP)<sup>45</sup> and the coalescent constant population size model for demographic inference (Supplementary section 7.1). Model selection strongly supported a relaxed clock with BSP indicating rate heterogeneity among branches (Table S15a), which may reflect host- specific adaptations within human- and rodent- associated lineages.  
+
+<|ref|>text<|/ref|><|det|>[[118, 794, 880, 910]]<|/det|>
+Strength of temporal signal in the data was investigated via date randomization test (DRT)<sup>46</sup> (Figures S16 and S17). Simulations here showed a small proportion of overlap in the clock rate parameter (Figure S18), which indicated that a Bayesian framework may not estimate evolutionary rates and timescales with high confidence. This limitation likely arises from the small number of available genomes. We, therefore, chose to apply a prior distribution for the rate parameter based on previous estimates inferred for M. leprae (Supplementary text 8.3). The best- supported model estimates
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[66, 82, 880, 382]]<|/det|>
+an evolutionary rate of \(6.91\mathrm{e}^{- 09}\) subst./site/year (95% HDPI: \(0.34\mathrm{e}^{- 09} - 15.64\mathrm{e}^{- 09}\) subst./site/year) for M. lepromatosis, which agrees closely with estimates obtained via other models (Table S15b), as well as previous estimates for M. leprae genomic substitution rates (Table S16). From this, we estimate the median time for the most recent common ancestor (tMRCA) of M. lepromatosis to be approximately 26,800 years ago (95% HPDI range of 4,206 ... 115,340 yBP) (Table S15b). Genomes obtained from human hosts yield a divergence estimate of ca. 12,600 years (95% HPDI: 5,304 ... 49,659 yBP), while the tMRCA for the red squirrel clade is ca. 440 years (95% HPDI: 73 ... 2,063 yBP) (Table S15b). The estimates proposed here are highly consistent with results obtained from all iterations tested, supporting robustness across different demographic and molecular clock models (Table S15b, Figures S18- S21). Our tMRCA for M. lepromatosis closely aligns with results presented elsewhere based on modern data<sup>17</sup>, though with broader temporal intervals resulting from either our inclusion of ancient genomes or our selection of more permissive models. Further refinement of the origin, evolution, and relationship between the ancient strains and those from the regions where the disease is found today is expected to come with additional genomic examples made available through increased awareness for its detection in both clinical and archaeological contexts.  
+
+<|ref|>text<|/ref|><|det|>[[66, 400, 880, 884]]<|/det|>
+Recent investigations of M. leprae, as well as several other bacterial pathogens where ancient genomes are available, place their extrapolated coalescence date in the last 6000 years, which correlates with cultural adaptations such as the adoption of agriculture and animal husbandry in the Neolithic that are regarded as conducive to the emergence and maintenance of novel pathogens in human groups<sup>15,47- 50</sup>. The current analysis reveals a very different evolutionary history for M. lepromatosis: although based on only a small number of genomes, multiple simulations suggest a common ancestor for the human- associated lineages that temporally aligns with the Pleistocene- Holocene transition. This encompasses a warming period wherein human movements were less impeded by large ice sheets that covered 25% of the earth's land surface during the Last Glacial Maximum. Further exploration of the vast territories of the American continent soon followed, as demonstrated by the sudden increase in archaeological sites that indicate human activity<sup>51</sup>. Our finding of two M. lepromatosis infections in South America, prior to the periods of known contact with either Oceanian or European populations, implies either movement of the pathogen within human groups during an early peopling event, or its previously established endemicity in the continent in a separate reservoir species eventually acquired by humans. The latter would imply that its current distribution arises from a post- colonial dissemination, and would make it one of the few global diseases known to have emerged in the Americas<sup>52</sup>. Its presence in the continent has thus far remained undetected based on morphological analyses of human archaeological tissues, where skeletal lesions ascribed to Hansen's disease are limited to examples from the post- colonial period<sup>53</sup>, with the exception of two potential infections from the northern Pacific Coast that await molecular characterization and confirmation of their possible pre- AD1492 status<sup>54</sup>. Additional ancient genomes from either human or faunal remains may eventually disentangle the current mystery of its origin, and possible means of acquisition among the hunting- gathering- fishing groups studied here. It may also assist in the establishment of morphological diagnostic criteria for disease identification in the archaeological record.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 84, 880, 331]]<|/det|>
+While we observe a deep divergence between the human- and rodent- associated lineages, current data from non- human sources are limited to modern rodent lineages within a restrictive geographic spread in Ireland and the United Kingdom<sup>55</sup>, from a single introductory event of unknown origin within the last 500 years. While surveillance has as yet failed to identify M. lepromatosis or M. leprae in multiple squirrel species in mainland Europe<sup>56</sup>, analogous efforts in other parts of the world are needed to explore its ecological distribution in broader scale. Greater awareness of this pathogen and its potential for zoonotic transmission from armadillos is also being explored given that they are known reservoirs of M. leprae in the Americas. Previous contact with these animals (handling or consumption) has been reported in two individuals with confirmed M. lepromatosis infection in Mexico<sup>57</sup>. Screening efforts of multiple species of armadillos has also begun in Brazil, where human infections with M. lepromatosis represent greater than 10% of reported instances of Hansen's Disease<sup>58</sup>. Of note, both individuals studied here come from archaeological contexts in Chile that are outside the current range of armadillos.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 346, 495, 363]]<|/det|>
+## Modern M. lepromatosis in perspective  
+
+<|ref|>text<|/ref|><|det|>[[115, 362, 880, 821]]<|/det|>
+Since its discovery in 2008, M. lepromatosis has been regarded as a second causal pathogen for Hansen's disease. While associated with the more severe forms of DLL and LP, these presentations are equally considered within the clinical spectrum of M. leprae infection<sup>25</sup>. Distinction between the two pathogens through use of the recently validated species- specific PCR assay<sup>59</sup> has the potential to elucidate the true global prevalence of M. lepromatosis. Here we aim to raise awareness of M. lepromatosis infection through demonstration of its previously unknown health impact along the Pacific Coast of South America several millennia in the past. This region currently has a low incidence of Hansen's Disease where occasional reported cases, thus far attributed to M. leprae, are thought to result from travel to regions within Latin America where disease incidence is high<sup>60,61</sup>. Its restricted modern geographic distribution may in part be due to its decreased transmissibility in comparison to other globally dispersed pathogens. Management of human infections in living populations remains a principal concern, and adoption of a One Health perspective could provide the means to elucidate the zoonotic potential of this disease both in the present as well as the past<sup>18</sup>. Available data suggest that squirrel populations in Britain and Ireland may be the sole non- human reservoir for these pathogens in West Eurasia<sup>55,56</sup>. The results of such screenings from rodent populations in East Eurasia have yet to be reported, and recent evidence suggests wild rodents may be a natural source of M. leprae in Brazil<sup>62</sup>. This highlights the need for broader- scale investigations into potential wild reservoirs for both M. leprae and M. lepromatosis. The capacity of armadillos to harbour M. lepromatosis infection in Latin American countries, especially those where DLL representation is high such as Mexico and the Caribbean<sup>25</sup>, should also be considered. Given the narrow known host range for M. leprae, susceptibility in rodents, armadillos, or other animals may be related to their possible maintenance of M. lepromatosis in the past. Further contributions are also expected to come from paleogenomic analyses that continue to explore past disease landscapes represented in both human and animal remains.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 310, 101]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[116, 101, 881, 234]]<|/det|>
+AcknowledgementsSkeletal elements for this work were obtained under permits \(N^{\circ} 43.341\) dated August 31 2022 of the Consejo de Monumentos Nacionales issued by the Ministerio de las Culturas, las Artes y el Patrimonio of Chile. We thank the Museo Arqueológico de La Serena, Chile and the laboratory processing teams of the Max Planck Institute of Evolutionary Anthropology at both the Jena satellite laboratory and the Leipzig Core Unit for their assistance in data generation. We also thank Alexander Herbig for helpful comments on an earlier draft of this manuscript, and support from the ancient pathogen research team at the Max Planck Institute for Evolutionary Anthropology.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 250, 320, 265]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[118, 265, 880, 330]]<|/det|>
+Author contributionsKIB, RN, and DAR conceived of the investigation. MJH- S, OEFS, JCD, and CLK performed archaeological and osteological analyses. TLS, SÖ, NP, DAR, RN, and KIB performed analyses. KIB, DAR, and RN wrote the manuscript with contributions from all coauthors.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 347, 200, 362]]<|/det|>
+## Funding  
+
+<|ref|>text<|/ref|><|det|>[[118, 363, 880, 478]]<|/det|>
+FundingThe Max Planck Society, European Research Council Starting Grant CoDisEASe (805268) to KIB, the German Academic Exchange Service (DAAD) to DAR under Short Term Grant number 57588366, the Social Sciences and Humanities Research Council of Canada postdoctoral fellowship no. 756- 2023- 0246 to CLK, Agencia Nacional de Investigación y Desarrollo de Chile (ANID) Doctorado Becas Chile Scholarship no. 2018- 72190531 to MJH- S, and the Secretaría de Ciencia y Tecnología (UNC) to RN.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 510, 272, 525]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[118, 526, 820, 543]]<|/det|>
+Data are accessible via the ENA project ID ERR13916540 and ERR13916541.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 85, 270, 102]]<|/det|>
+## Figure captions  
+
+<|ref|>text<|/ref|><|det|>[[118, 120, 870, 215]]<|/det|>
+Figure 1. A) Map of the Semi-arid region of Chile showing the location of the two archaeological sites under study. B) Skeletal elements that yielded the two ancient genomes of M. lepromatosis. Left: tibia from ECR001 (bar = 5 cm). Right: tooth from ECR003 (bar = 0.5 cm). C) Modeled radiocarbon dates of the individuals ECR001 and ECR003 from La Herradura and El Cerrito sites, respectively.  
+
+<|ref|>text<|/ref|><|det|>[[118, 253, 880, 370]]<|/det|>
+Figure 2 - Overview of the recovery status of the newly identified ancient M. lepromatosis genomes. A) Indication of the genomic regions with a depth range between 0 and 5- fold depth averaged over bins of 1000 bp. B) Genome coverage of the M. leprae probes mapped to the M. lepromatosis FJ924 reference genome averaged over bins of 1000 bp (top based on permitted 3bp mismatch and bottom based on permitted 7bp mismatch). C) Visual representation of the location of the non- reference loci recovered for ECR001 and ECR003.  
+
+<|ref|>text<|/ref|><|det|>[[118, 400, 880, 582]]<|/det|>
+Figure 3 - Phylogenetic representation of ancient and modern M. lepromatosis. A) Network showing the number of SNPs that distinguish individual groupings. B) and C) Maximum parsimony trees (with branch length estimation) constructed in Mega X v11.0.11 with 1000 bootstrap iterations based on a 16S rRNA alignment of several mycobacterial representatives with ambiguous sites masked in the lower coverage genome ECR001 (B), and 650 full genomic alleles called at four- fold read support (C); D) Maximum clade credibility (MCC) tree with median heights, reconstructed using the Bayesian skyline plot and relaxed clock. Branches in (D) are color- coded based on the median rate estimates from the optimised relaxed clock model, with blue indicating lower rates and red indicating higher rates. Node labels show posterior support values, while the X- axis represents years before present.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[205, 132, 872, 165]]<|/det|>
+1. Han, X.Y., Seo, Y.H., Schoberle, T. et al. A new Mycobacterium species causing diffuse lepromatous leprosy. Am J Clin Pathol. 130, 856–864 (2008). 
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+2. Ploemacher, T., Faber, W.R., Menke, H., Rutten, V. & Pieters, T. Reservoirs and transmission routes of leprosy; A systematic review. PLoS Negl Trop Dis. 14, e0008276 (2020). https://doi.org/10.1371/journal.pntd.0008276 
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+
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+<|ref|>image<|/ref|><|det|>[[0, 0, 999, 999]]<|/det|>
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+<--- Page Split --->
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+<|ref|>sub_title<|/ref|><|det|>[[42, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[42, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[59, 131, 476, 178]]<|/det|>
+- RamirezSupplementaryTablesR1.xlsx- RamirezSitterSupplementaryMaterialR1.docx
+
+<--- Page Split --->

preprint/preprint__06bb8347202433bb91b22abd4d31eeb57d2b64b25f7eb3fe4e53e20191446658/images_list.json

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+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig.1 | Comparison of UDD-AL and MD-AL approaches for a glycine test case. a Schematic",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 | 2D representation of glycine conformational space processed by UMAP dimensionality reduction technique. a 50ns test set. Heat-map represents the relative DFT energy. Glycine insets denote the corresponding conformational region. In panels b-d, data sets and scans are placed over the 50ns test set (gray). b Conformational paths through -COOH (cyan and purple) and -NH2 (red and green) rotations. c N-H (red) and C=O (cyan) bond length scans. d Comparison of training sets sampled by 350K MD-AL (blue) and 350K UDD-AL (orange). Green circle denotes the inner high-energy region. Red triangles denote the scan of -OH rotation around the C-O bond. e Comparison of training sets sampled by 350K MD-AL (blue) and 600K MD-AL (green). f Comparison of training sets sampled by 350K MD-AL (blue) and 1000K MD-AL (cyan).",
+    "footnote": [],
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+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 | Glycine interatomic distance distributions in MD-AL and UDD-AL data sets. Each subplot shows a comparison of bond length distributions in 350K MD-AL (blue), 350K UDD-AL (orange), 600K MD-AL (green), and 1000K MD-AL (cyan) data sets. Each subplot also lists the bond length standard deviation, in the legend. a O-H. b N-H. c C-H. d C=O, e C-N. f C-C.",
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+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 | Ensemble uncertainty and UDD in acetylacetone. a Acetylacetone molecule. Red circle denotes a hydrogen atom involved in a proton transfer. b Log-normalized map of disagreement \\(\\rho\\) of ANI-1x model ensemble with respect to a position of a circled hydrogen. c Log-normalized map of physical energy. d Log-normalized map of summed physical and bias energy. e and f show a comparison of C-H bond length distributions in the methyl and central groups, respectively, for 350K MD (blue), 350K UDD (orange), and 620K MD simulations. Red ellipse denotes a bond under consideration. Each subplot also lists the bond length standard deviation from the equilibrium distance per legend.",
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preprint/preprint__06bb8347202433bb91b22abd4d31eeb57d2b64b25f7eb3fe4e53e20191446658/preprint__06bb8347202433bb91b22abd4d31eeb57d2b64b25f7eb3fe4e53e20191446658.mmd

@@ -0,0 +1,402 @@
+
+# Uncertainty Driven Dynamics for Active Learning of Interatomic Potentials  
+
+Maksim Kulichenko ( mbulichenko@gmail.com) Los Alamos National Laboratory https://orcid.org/0000- 0002- 6194- 3008  
+
+Kipton Barros Los Alamos National Laboratory  
+
+Nicholas Lubbers Los Alamos National Laboratory  
+
+Ying Wai Li Los Alamos National Laboratory  
+
+Richard Messerly Los Alamos National Laboratory  
+
+Sergei Tretiak Los Alamos National Laboratory https://orcid.org/0000- 0001- 5547- 3647  
+
+Justin Smith Los Alamos National Laboratory  
+
+Benjamin Nebgen Los Alamos National Laboratory  
+
+Article  
+
+Keywords:  
+
+Posted Date: October 3rd, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 2109927/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+
+## Uncertainty Driven Dynamics for Active Learning of Interatomic Potentials.  
+
+Maksim Kulichenko<sup>1\*</sup>, Kipton Barros<sup>1,2</sup>, Nicholas Lubbers<sup>3</sup>, Ying Wai Li<sup>3</sup>, Richard Messerly<sup>1</sup>, Sergei Tretiak<sup>1,2,4</sup>, Justin S. Smith<sup>1,5,\*</sup>, Benjamin Nebgen<sup>1,\*</sup>  
+
+<sup>1</sup> Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States  <sup>2</sup> Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States   <sup>3</sup> Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States   <sup>4</sup> Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States   <sup>5</sup> Nvidia Corporation, Santa Clara, CA 9505, United States  
+
+\* Corresponding authors: maxim@lanl.gov, jusmith@nvidia.com, bnebgen@lanl.gov  
+
+## Abstract  
+
+Machine learning (ML) models, if trained to datasets of high- fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse datasets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the dataset. A key challenge in this process is locating structures for which the model lacks underlying training data. Here, we develop a strategy to more rapidly discover configurations that meaningfully augment the training dataset. The approach, uncertainty driven dynamics for active learning (UDD- AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. Performance of UDD- AL is demonstrated for two challenging AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore chemically relevant configuration
+
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+space, which may be inaccessible using regular dynamical sampling at target temperature conditions.  
+
+## Main  
+
+Machine learning (ML) is a firmly established approach in chemical science that demonstrates great promise for the acceleration of physical simulations. A particular strength of ML models is a robust representation of potential energy surfaces of molecular and materials systems, when trained to large and diverse datasets of high- fidelity quantum chemistry simulations. For example, ML based potentials \(^{1 - 11}\) approach ab initio \(^{12,13}\) or density functional theory (DFT) \(^{14}\) levels of accuracy at a computational cost near that of classical force fields. \(^{15 - 17}\) Over the recent years, various ML- models — such as neural networks (NNs), \(^{18 - 24}\) Gaussian approximation potentials, \(^{25}\) spectral neighbor analysis potentials, \(^{26}\) moment tensor potentials, \(^{27}\) symmetric gradient domain machine learning \(^{28,29}\) — have demonstrated remarkable success in the field atomic- scale discovery.  
+
+No matter how sophisticated the ML model architecture, however, the quality and diversity of the training data remains crucial to ultimate model accuracy since ML models are known to extrapolate poorly to unseen data. Therefore, training sets for ML potentials need to span as much phase (structural) space as possible to perform meaningful simulations. Additionally, the training set needs to be as diverse as possible to avoid overfitting towards excessively represented training data (e.g., near- equilibrium configurations in MD trajectories).  
+
+Entropy- maximization techniques \(^{30,31}\) help to partially overcome these problems by maximizing the structural diversity of a data set. When acquiring new data, these methods are focused on the structural dissimilarity compared to the existing data. However, these methods usually require training of a separate Gaussian process model and significantly rely on the structural representation in latent space. There are other opportunities for improvement as well. Active learning (AL) \(^{32,33}\) attempts to expand the dataset in areas where the ML model is most
+
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+uncertain, which leads to more rapid model improvement. Another feature of AL is that it can employ physically meaningful dynamical trajectories for the sampling of configurations. In the present work, we illustrate how to keep these benefits of AL, while accelerating the rate of new data collection.  
+
+AL<sup>32,33,34</sup> aims to iteratively collect diverse training datasets addressing any weaknesses identified in an ML model prediction. For this, it is necessary to estimate uncertainty for a model's predictions.<sup>35- 45</sup> A well- established practical strategy for AL with NN potentials is Query by Committee<sup>46</sup> (QBC); here, the estimate of uncertainty is the disagreement between a collection of models within an ensemble. Typically, there are 5 to 10 NNs in an ensemble, and these share the same architecture and hyperparameters but, crucially, use a different initial randomization of the model parameters prior to training, and different splits of the training/validation data. It is empirically observed that the variance of the ensemble predictions correlates strongly with actual prediction error,<sup>36</sup> suggesting that the prediction task requires extrapolation beyond the range of the training data. In the QBC strategy, if this ensemble variance is observed to be large, then the training set will be augmented with new quantum simulation data.  
+
+AL estimates uncertainty in properties predicted for structures generated by an underlying sampler at each iteration. Molecular dynamics (MD) is the most popular method for sampling chemically meaningful potential energy surfaces. However, MD is susceptible to trapping in near- minimum conformations and only rarely enters chemically important regions such as transition states, which are key data for reactive simulations of chemical processes. In general, capturing thermodynamically rare events is a challenging task for any sampler. For example, metadynamics<sup>47- 50</sup> is an effective method of potential energy surface exploration, which operates on the concept of collective variables (CVs). However, CVs require manual selection, and their number is limited in practice. The user needs to "look" at each specific molecule to determine the desired structural parameters to be scanned. Therefore, this approach is not suitable for automatic sampling.
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+Here, following the idea of QBC and ensemble uncertainty, we propose a new AL sampling algorithm biased towards regions of high uncertainty - Uncertainty Driven Dynamics (UDD). Due to model random initializations and the stochastic nature of training, regions of chemical space with low ensemble uncertainty will typically arise when similar regions are prevalent in the current training dataset, such that every member of the ensemble is making an accurate inference. Thus, biasing molecular dynamics in the direction of high ensemble uncertainty encourages the dynamics to visit new configurations, which are relevant for improving the diversity of the training set.  
+
+One can regard the uncertainty- based bias potential as similar to metadynamics in the sense that the sampling trajectories are pushed towards less- visited configurational regions. Here, however, CVs need not be defined. We show that within MD- based AL data acquisition, UDD helps substantially reduce the MD simulation time required to enter the high uncertainty region. Most importantly, the proposed approach enables efficient conformational and configurational sampling at low- temperature (low- T) conditions, making this approach essential for temperature sensitive molecules. UDD assists in sampling the chemically relevant subspace of high- energy space which contains important data such as transition states.  
+
+The value of the proposed approach is demonstrated in two test cases. First, UDD- AL is used for conformational sampling of a glycine molecule. We find that the bias potential technique generates a diverse dataset covering both low and high energy regions. This contrasts with high- temperature (high- T) MD- AL, which tends to skip over low energy regions. Second, in tests with acetylacetone at low- T conditions, the bias potential is observed to encourage the sampling of the phase space relevant to a proton transfer. Here we find that, in contrast with regular high- T MD, the bias potential technique encourages the reactive transition with very little distortion to the distribution of other degrees of freedom in the system.
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+## Results  
+
+## Uncertainty driven dynamics for active learning (UDD-AL)  
+
+Before introducing UDD- AL, let us first set the context by reviewing the related method of metadynamics. Here the CVs \(s(q)\) are user- defined structural parameters being scanned by external Gaussian bias potentials. Usually, \(3N - 6\) dimensional atomic coordinates \(q\) of the simulated system are mapped to CVs \(s(q)\) . The corresponding energy function is defined as  
+
+\[E_{\mathrm{metadynamics}}(s,t) = \sum_{k\tau < t}W(k\tau)\mathrm{exp}\big[-\sum_{i = 1}^{N_{CV}}\frac{1}{2b_{i}^{2}} (s_{i} - s_{i}(q(k\tau)))^{2}\big], \quad (1)\]  
+
+where \(b_{i}\) is the width of the Gaussian function for the \(i^{\mathrm{th}}\) collective variable, \(W(k\tau)\) is the height of the Gaussian at the simulation time \(t = k\tau\) , which is constant in the case of standard metadynamics, \(\tau\) is the deposition rate of the Gaussian functions, and \(N_{\mathrm{CV}}\) is the number of CVs. During simulations, more Gaussians are added, thus discouraging the system to go back to its previous steps.  
+
+Like metadynamics, UDD- AL method modifies the physical energy by adding a bias potential \(E_{\mathrm{bias}}\) . Here, however, \(E_{\mathrm{bias}}\) will be defined in terms of the model uncertainty rather than CVs. Such uncertainty estimates can be used to assist in the sampling of atomistic data. \(^{44}\) In the QBC approach, an ensemble of NN- potentials is trained, and the level of agreement between the NN predictions serves as the estimate of overall model uncertainty. The QBC uncertainty estimate is proportional to the variance in the energy \((\sigma_{E}^{2})\)  
+
+\[\sigma_{E}^{2} = \frac{1}{2}\Sigma_{i}^{N_{M}}(\hat{E}_{i} - \hat{E})^{2}, \quad (2)\]  
+
+where \(\hat{E}_{i}\) is the energy predicted by an ensemble member, \(\hat{E}\) is its ensemble average, and \(N_{\mathrm{M}}\) is the number of ensemble members, i.e., NN- potentials. Here, ensembles of ANI potentials are prepared using an 8- fold cross validation split of the data set which yields \(N_{\mathrm{M}} = 8\) ensemble members (see Methods). In previous applications of QBC- based AL, new data is collected when the uncertainty estimator  
+
+\[\rho = \sqrt{2 / N_{M}N_{A}}\sigma_{E} \quad (3)\]
+
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+exceeds a threshold, where \(N_{A}\) is the number of atoms in a configuration.  
+
+We seek to construct a bias energy \(E_{\mathrm{bias}}(\sigma_{E}^{2})\) that favors configurations with larger uncertainties \(\rho \propto \sigma_{E}\) ; such configurations are expected to correlate with regions that are underrepresented in the training data. A reasonable choice is the Gaussian function,  
+
+\[E_{\mathrm{bias}}(\sigma_{E}^{2}) = A\left[\exp \left(-\frac{\sigma_{E}^{2}}{N_{M}N_{A}B^{2}}\right) - 1\right]. \quad (4)\]  
+
+The magnitude \(A\) and width \(B\) of the biasing should be selected empirically. The bias potential goes to zero in the absence of uncertainty, \(E_{\mathrm{bias}}(0) = 0\) . Configurations with large uncertainty, \(\rho \gg B\) , are favored by a bias energy of magnitude \(E_{\mathrm{bias}} \approx - A\) . Forces derived from the bias potential are strongest when the uncertainty \(\rho\) is of the same order as the parameter \(B\) .  
+
+The combined potential \(\hat{E} + E_{\mathrm{bias}}\) is used to define an uncertainty driven dynamics (UDD). In applications to AL the overall strategy will be denoted UDD- AL. The schematic workflow of UDD- AL is depicted in Fig. 1a. It should be compared to the usual MD based approach (MD- AL), which does not incorporate the \(E_{\mathrm{bias}}\) term.  
+
+The optimal parameters \(A\) and \(B\) will be context dependent. For example, our applications to glycine and acetylacetone tests discussed below suggest that the bias magnitude \(A\) should be at least of the order of the energy barriers of interest. The bias width, \(B\) , should also be carefully selected. If \(B\) is either too small or too large, the bias forces could become negligibly small for the typical uncertainties \(\rho\) that are observed in the AL sampling.  
+
+Effective bias forces on an atom at position \(r\) can be calculated using the chain rule, \[ -\frac{\partial}{\partial r} E_{\mathrm{bias}}(\sigma_{E}^{2}) = -E_{\mathrm{bias}}(\sigma_{E}^{2})'\frac{\partial}{\partial r}\sigma_{E}^{2} \] and \[ -\frac{\partial}{\partial r}\sigma_{E}^{2} = -\sum_{i}^{M}(\hat{E}_{i} - \hat{E})\frac{\partial}{\partial r}(\hat{E}_{i} - \hat{E}) = \sum_{i}^{M}(\hat{E}_{i} - \hat{E})(\hat{f}_{i} - \hat{f}) \]  
+
+\[-\frac{\partial}{\partial r}\sigma_{E}^{2} = -\sum_{i}^{M}(\hat{E}_{i} - \hat{E})\frac{\partial}{\partial r} (\hat{E}_{i} - \hat{E}) = \sum_{i}^{M}(\hat{E}_{i} - \hat{E})(\hat{f}_{i} - \hat{f}) \quad (6)\]
+
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+
+where \(\hat{f}_{t}\) denotes the force vector predicted by an ensemble member and \(\hat{f}\) is the ensemble- averaged prediction. Since \(\sigma_{E}^{2}\) , \(\hat{E}_{t}\) , and \(\hat{f}_{t}\) are calculated at each MD step in any AL approach, including the bias potential has a negligible effect on the computational time.  
+
+## Glycine conformational space sampling  
+
+The glycine molecule is shown in Fig. 1a. We are interested in sampling the conformational space without bond- breaking events using various AL protocols. Dihedral rotations of \(- \mathrm{NH}_{2}\) and \(- \mathrm{COOH}\) groups correspond to 2.5- 3.5 kcal/mol barriers. Our numerical tests have shown that the bias magnitude \(A\) approximately five times higher than the average barrier of interest provides the best results for the glycine test. It helps keep the bias essentially high at higher uncertainty values. It also helps overcome possible barrier bottlenecks caused by possible overestimation of barrier heights by ML model. The geometries near global energy minimum (GM) of a glycine are already present in the initial training set, and each sampling MD simulation starts with this kind of structure. Depending on the AL iteration, near- GM structures have \(\rho\) of \(0.024 \pm 0.005 [\mathrm{kcal} \times \mathrm{mol}^{- 1} \times (\sqrt{\mathrm{N}_{\mathrm{A}}})^{- 1}]\) \((\sigma_{E} = 0.15 \pm 0.03 \mathrm{kcal / mol})\) . Thus, we selected \(A\) equal to 15.4 kcal/mol which corresponds to the bias potential value of \(- 15.0 \mathrm{kcal / mol}\) at near- GM values of \(\rho\) (with \(B = 0.12 \mathrm{kcal / mol}\) ). We further increase \(A\) by \(15\%\) at 140ps time step if the uncertainty criterion is not met at this simulation stage. Our tests also show that best results are achieved for \(B\) being close to near- GM uncertainty \(\sigma_{E}\) . Here we use \(B = 0.12 \mathrm{kcal / mol}\) for glycine.  
+
+We next compare the two active learning approaches – UDD- AL and MD- AL – for the task of collecting a dataset of the glycine conformational space. Each AL iteration performs 16 MD simulations with 200ps time limit and 1fs step (see Methods). An ensemble of NN- potentials for the first AL iteration is trained on the initial data set of 125 conformers that span near- equilibrium structures of the glycine global minimum. At each subsequent AL iteration, the MD simulation employs an ensemble of ANI- type NN- potentials (see Methods and Ref. 51), trained on the initial
+
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+data and data accumulated on all previous AL iterations. The starting geometries for MD simulations and the initial training set contain only near- equilibrium geometries of a glycine global minimum (Extended Data Fig. 1). Stated differently, NNs have no initial information about higher energy conformers, and MD simulations have to reach them from the bottom of the potential energy surface. Each MD simulation is terminated when the system meets the uncertainty selection criteria \(\rho\) of \(0.35 [\mathrm{kcal} \times \mathrm{mol}^{- 1} \times (\sqrt{N_{\mathrm{a}}})^{- 1}]\) (see Methods). If the MD simulation reaches the time limit, then the structure from the trajectory with the highest uncertainty is selected. Density Functional Theory (DFT) reference data (see Methods) is then computed for final conformations and added to the training set for the next iteration of the AL process.  
+
+Figure 1b shows the average MD simulation time required to meet the uncertainty criterion in different AL approaches with respect to AL iteration. The MD- AL at low- T conditions (350K) reaches the MD time limit at \(\sim 20^{\mathrm{th}}\) iteration which is continued until the final AL iteration (Fig. 1b, blue line). This means that the specified uncertainty criterion is almost never met, and the sampler returns the geometry of maximum available uncertainty from the MD trajectory. The uncertainty bias potential is introduced in low- T (350K) MD simulations (orange line). We do not activate the bias potential at earlier AL iterations for two reasons. First, the low- T MD- AL (Fig. 1b, blue line) does not reach the MD simulation time limit up to \(15 - 20^{\mathrm{th}}\) iteration. Thus, at this stage, the regular MD- AL manages to acquire new data satisfying the uncertainty criteria. Second, the NN potential might be unstable or not smooth at earlier iterations due to the lack of data. Therefore, the bias is activated at the \(15^{\mathrm{th}}\) iteration to avoid moving systems toward unphysical configurations. When the uncertainty bias potential is on (UDD- AL regime), it reduces the number of MD steps needed to meet the desired uncertainty. Moreover, the MD time limit plateau is still not reached till the final iteration.  
+
+Perhaps the most common way to accelerate sampling of high- energy states is to run high- T MD. Thus, to illustrate the difference between the bias potential and a simple temperature
+
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+increase, we also compare the low- T 350K UDD- AL with the high- T MD- ALs at 600K and 1000K simulation conditions (Fig. 1b). Like in case of UDD- AL sampling, the temperature is increased at the 15th iteration. 600K MD- AL approaches the MD time limit at \(\sim 40\) th iteration while UDD- AL reaches the time limit plateau by the end of AL procedure. Thus, 600K MD- AL does not perform as well as UDD- AL in terms of simulation time. On the other hand, the 1000K MD- AL (cyan line) exhibits a faster sampling, and the average MD time does not exceed 35ps even at the last AL iteration.  
+
+Energy ranges sampled by each AL approach are depicted in Fig.1c. Expectedly, high- T MD- AL data (green and cyan histograms) span wider energy ranges compared to low- T 350K MD- AL (blue histogram). What is more interesting is that the energy distribution of data from the 350K UDD- AL (orange histogram) is very similar to the shape of 600K MD- AL data; an advantage of UDD- AL is that many fewer MD steps are required to collect these samples.  
+
+After completing the entire AL procedure, the final models are trained on 1280 glycine conformers collected during the entire AL procedure (+125 conformers in the initial training set). In order to access the accuracy of the four models, we use a test set comprising 50,000 glycine structures from a 50ns MD simulation via the ANI- 1ccx potential run at 400K with a 0.5fs time step (see Methods).<sup>19</sup> As depicted in Fig. 1d, all models perform reasonably well with root- mean- square deviations (RMSEs) less than 0.3 kcal/mol. However, the RMSE of the model trained on low- T 350K MD- AL data is slightly yet systematically lower than RMSEs of the rest of the models with \(\sim 0.11\) kcal/mol difference. This is likely because MD simulations tend to oscillate in near- equilibrium positions, which is why this test set is dominated by low- energy geometries. Low- T 350K MD- AL, in turn, densely spans a narrow low- energy range, which might explain a slightly better performance of this model on a test set derived from a 50ns MD. Indeed, normalized histograms in Fig.1e point out that this seemingly large 50ns test set spans the energy region closest (but even lower) to the one covered by low- T 350K MD- AL data.
+
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+Note that the 50ns test set is a MD trajectory with no AL involved while MD- AL data comprises structures with high uncertainties. High uncertainty usually corresponds to a higher energy due to poor sampling in normal low- T MD. In other words, the 50ns MD test set is biased towards near- equilibrium oscillations, but MD- AL data are selectively augmented with higher energy isomers. Similar RMSE shift is observed for low energy rotations of \(- \text{COOH}\) and \(- \text{NH}_2\) functional groups (Extended Data Fig.2). Therefore, the various models should also be tested on higher energy pathways.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig.1 | Comparison of UDD-AL and MD-AL approaches for a glycine test case. a Schematic </center>  
+
+representation of UDD- AL workflow. b Average MD time required to meet the uncertainty criterion vs. AL iteration for four different MD simulation types: 350K MD- AL (blue), 600K MD- AL (green), 1000K MD- AL (cyan), and 350K UDD- AL (orange). c Energy distribution histograms of four datasets sampled by 350K MD- AL (blue), 600K AL MD- AL (green), 1000K MD- AL (cyan), and 350K UDD- AL (orange). Data from iterations 0- 14 is omitted because the bias is off, or the temperature is not increased at this stage. d
+
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+Comparison of potential energy RMSE obtained on the 50ns test set vs. AL iteration (i.e., training set size, 16 new glycine conformations per iteration). The legend shows RMSEs for models trained on data from the entire AL procedure. e Normalized energy distribution histograms of 50ns test set (red) and training set sampled by 350K MD- AL (blue). Lines in b and d, are averaged over three ensembles, each trained on data from an independent AL procedure.  
+
+To illustrate what types of chemical processes appear in the system, and how each sampling method covers them, we next visualize the glycine conformational space using dimensionality reduction. We project samples to a 2D plane using the Uniform Manifold Approximation and Projection (UMAP) \(^{52}\) technique, where each conformation is characterized by the 672- D vector of activations (concatenated atomic environment vectors) in the first layer of an independent pre- trained ANI- 1x model. \(^{19}\) Figure 2a shows the 50ns MD dataset spanning four low- lying glycine conformers represented by four regions in the 2D space. Torsional conformations, N- H bond scan, and C=O bond scan are depicted in Fig.2b- c to illustrate structural profiles in 2D space.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 | 2D representation of glycine conformational space processed by UMAP dimensionality reduction technique. a 50ns test set. Heat-map represents the relative DFT energy. Glycine insets denote the corresponding conformational region. In panels b-d, data sets and scans are placed over the 50ns test set (gray). b Conformational paths through -COOH (cyan and purple) and -NH2 (red and green) rotations. c N-H (red) and C=O (cyan) bond length scans. d Comparison of training sets sampled by 350K MD-AL (blue) and 350K UDD-AL (orange). Green circle denotes the inner high-energy region. Red triangles denote the scan of -OH rotation around the C-O bond. e Comparison of training sets sampled by 350K MD-AL (blue) and 600K MD-AL (green). f Comparison of training sets sampled by 350K MD-AL (blue) and 1000K MD-AL (cyan). </center>  
+
+Figure 2d- f depicts the four datasets visualized over the 50ns test set. Figure 2d provides a visual comparison of data sampled by MD- AL and UDD- AL at 350K. Both datasets cover the 50ns MD data reasonably well. However, there are three key differences. First, a high- energy configurational space (points inside the green circle) is more densely sampled in the UDD- AL dataset: there are 289 points in this non- equilibrium region in the UDD- AL sampling, compared to
+
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+
+105 points in 350K MD- AL. Second, UDD- AL encountered a new conformational path in the top right corner of the Fig.2d which was not accessed by 350K MD- AL. This region corresponds to the rotation of the - OH group around the C- O bond which is a distinct conformational transition and a high- energy profile with a 15 kcal/mol barrier.  
+
+Figure 2e presents a visual comparison of the sampling performance of MD- ALs at 350K and 600K. The 2D representation of 600K data is quite similar with the one of 350 UDD- AL data: there are 290 data points inside the inner circled region and a good coverage of - OH rotation region. As expected, MD- AL at the extreme temperature of 1000K (Fig.2f) samples the inner high- energy region even more densely (394 data points) as well as the - OH rotation region. This, however, comes at a cost. The low energy region in the lower left of Fig.2f clearly demonstrates lack of sampling. This is the primary deficiency of using high- T MD: as temperature increases, the system spends less time near low energy regions, since in these regions the kinetic energy is typically the greatest. Thus, it will be possible to 'skip over' regions of high stability thus resulting in a poor data coverage of near equilibrium region. On the other hand, UDD- AL sampling does not run this risk by sufficiently sampling any relevant region.  
+
+Thus, Figure 2 indicates that the UDD- AL is a good, balanced way of sampling chemical space, reaching most of the high energy points achieved with 1000K MD sampling without losing data density in low energy regions. However, alone, it is not clear that biased sampling presents advantages over unbiased high- T sampling; UDD- AL appears to sample similar configurations to 600K MD- AL. Therefore, we performed additional tests of high- energy pathways that illuminate the differences between 600K MD- AL and 350K UDD- AL. The discussion on high energy profiles - angle and bond scans - can be found in Supplementary Information. The overall trend is that the 350K UDD- AL model exhibits much better accuracy than the model trained on low- T 350K MD- AL data. When comparing the UDD- AL with 600K and 1000K MD- AL models, the former results in a better or, at least, comparable accuracy.
+
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+We also provide an overall assessment of the performance of the sampling strategy by cross- testing the associated models on the data from all sampling strategies in Supplementary information. Supplementary Table 2 summarizes RMSEs of the four models on the test sets accumulated by each AL sampler: 350K MD- AL, 350K UDD- AL, 600K MD- AL, and 1000K MD- AL. When testing models on data sets that are not generated by the same corresponding sampler, the UDD- AL model outperforms all other models. A detailed discussion on models' cross testing can be found in Supplementary Information.  
+
+Ultimately, when looking at a variety of bond rotations and stretches, the most accurate energy profile changes depending on the energy range of the specific scan. Low energy profiles tend to be modeled better by the low- T dataset while higher energy scans are accessed better by the high- T dataset. However, the UDD- AL sampling method yields a model that performs well on a wide range of energy profiles, while also maintaining a low error on each sampling method's held out test set (Table 2 in Supplementary Information). This difference suggests that UDD- AL is able to avoid the higher- energy and less chemically relevant structural distortions, which are typical at very high temperatures. Meanwhile, chemically relevant data present in the UDD- AL data set enables efficient extrapolation to higher- energy structures present in 1000K MD- AL data. As can be seen in Fig. 3, the shapes of interatomic distance distributions in UDD- AL closely mimic sharp distributions in low- T 350K MD- AL, although having a larger standard deviation. This deviation, however, is lower than in 600K and 1000K MD- AL data sets that span a wider distance range. This, in turn, further suggests that the UDD sampler tends to avoid random distortions found in high- T regimes.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 | Glycine interatomic distance distributions in MD-AL and UDD-AL data sets. Each subplot shows a comparison of bond length distributions in 350K MD-AL (blue), 350K UDD-AL (orange), 600K MD-AL (green), and 1000K MD-AL (cyan) data sets. Each subplot also lists the bond length standard deviation, in the legend. a O-H. b N-H. c C-H. d C=O, e C-N. f C-C. </center>  
+
+Since all models used the same hyperparameters, it is possible that each model could perform better if individual hyperparameter searches are carried out. Perhaps, data sets that cover a broader chemical space need more learnable parameters to be flexible enough to fit the effectively larger degrees of freedom they are being trained to. This will be a subject of future studies.  
+
+## Proton transfer in acetylacetone  
+
+We further examine the UDD performance for sampling of a reactive pathway in an acetylacetone enol tautomer depicted in Fig. 4a. Particularly, we are interested in the proton transfer between the two oxygen atoms, considering the proton position as a free variable. Instead of using AL techniques, here we use an ensemble of pre- trained ANI- 1x interatomic potentials,<sup>19</sup> which were not trained on bond- breaking reactions, and analyze trajectories from UDD and MD simulations. ANI- 1x was trained on wB97x DFT level of theory which yields a 4.7 kcal/mol barrier. However, ANI- 1x significantly overestimates the barrier giving the value of 6.3 kcal/mol. This value
+
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+is then selected as a bias magnitude \(A\) . Uncertainty values \(\rho\) of near-equilibrium acetylacetone structures within ANI- 1x model are higher by the order of magnitude than the ones produced by the newly trained model for glycine. Therefore, we set a higher value of bias width \(B = 0.45\) kcal/mol, being an empirically adjusted parameter.  
+
+Figure 4b shows log- normalized uncertainty \(\rho\) of the acetylacetone system with respect to the position of the proton. The dark region (near \(x = 0\) Å and \(y = - 1.5\) Å) demonstrates that there is a high- uncertainty region between oxygen atoms which corresponds to a proton transfer transition state. Figure 4c depicts the log- normalized relative potential energy (ANI- 1x) of the system with respect to the position of the free proton. The dark region (near \(x = - 0.5\) Å and \(y = - 1.5\) Å) indicates that the lowest energy corresponds to a proton position near the oxygen atom. This is an expected result since the hydrogen bound to the oxygen atom is the most stable geometry. However, as shown in Fig. 4d, the energy minimum can be shifted to the central position between the oxygen atoms (dark region near \(x = 0\) Å) when the bias potential is applied. For illustrative purposes, here we use a high value of bias magnitude \(A = 56.0\) kcal/mol. In practice, we use \(A = 6.3\) kcal/mol for the MD simulation discussed below. The effect of different \(A\) values on the total energy landscape is depicted in Extended Data Fig. 3.  
+
+We further analyze results from 0.5ns trajectories obtained using UDD and regular MD simulation techniques. No proton transfer occurs during the regular 350K MD simulation. Meanwhile, the uncertainty bias can direct the proton toward a high- uncertainty region between two oxygen atoms - 90 proton transitions observed in 350K UDD simulation. Finally, unbiased high- T 620K MD results in 48 proton transitions. Although at a lower rate compared to UDD, increased temperature also facilitates the proton transfer. Time traces of the two O- H distances can be further found in Extended Data Fig. 4.  
+
+A key difference between low- T UDD and regular high- T MDs can be found when analyzing oscillations of interatomic distances. Certainly, high- T conditions will affect the entire molecule causing larger distance deviations compared to low- T conditions. Indeed, the overall
+
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+spread of O- H distances is comparable using 350K MD (Extended Data Fig. 4), but far wider at 620K MD, even in segments of the trajectory without proton transfer. Further analysis of C- H distances in the molecule, shown in Fig. 4e- f, confirms this phenomenon. Figure 4e shows C- H distance distributions in the methyl group in 350K MD, 350K UDD, and 620K MD simulations. 620K MD exhibits higher deviations from the equilibrium C- H bond length compared to low- T UDD. The standard deviation of the methyl C- H distance in 620K MD is 0.04 Å against 0.03 Å in 350K UDD. Notably, the low- T 350K MD trajectory has the standard deviation of 0.03 Å, same as in low- T UDD. The same picture holds for the central C- H bond shown in Fig. 4f.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 | Ensemble uncertainty and UDD in acetylacetone. a Acetylacetone molecule. Red circle denotes a hydrogen atom involved in a proton transfer. b Log-normalized map of disagreement \(\rho\) of ANI-1x model ensemble with respect to a position of a circled hydrogen. c Log-normalized map of physical energy. d Log-normalized map of summed physical and bias energy. e and f show a comparison of C-H bond length distributions in the methyl and central groups, respectively, for 350K MD (blue), 350K UDD (orange), and 620K MD simulations. Red ellipse denotes a bond under consideration. Each subplot also lists the bond length standard deviation from the equilibrium distance per legend. </center>  
+
+These observations confirm that although high- T sampling promotes the activation of reactive pathways, it has a global effect on all degrees of freedom in the system, whereas the
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+UDD technique allows to sample the reactive pathway without significant changes to equilibrium distributions of other degrees of freedom. This is likely due to the composition of ANI- 1x training data, which has information on non- equilibrium extended bonds. However, a hydrogen which is equidistant between two oxygen atoms is not a commonly encountered configurational data. Thus, the UDD potential promotes sampling of this specific region.  
+
+## Discussion  
+
+In this work, we present a MD- based active learning (AL) algorithm assisted by the uncertainty- based bias potential. The algorithm is abbreviated as UDD- AL (uncertainty driven dynamics for active learning) and is compared to MD- based AL (MD- AL) in common use. We show that an uncertainty metric provided by an ensemble of NN- potentials can be used to construct the bias potential. The resulting energy term encourages the system to move toward underrepresented chemical regions, accelerating and improving sampling of high- energy regions.  
+
+The ANI model, trained on glycine conformational data from low- T UDD- AL, is shown to properly reproduce conformational pathways not accessible by low- T MD- AL. The resulting ANI model exhibits high accuracy for important high- energy conformational profiles. Importantly, while this accuracy is better than or comparable to the results for models trained on high- T MD- AL data, a low- T UDD- AL training set spans an energy range narrower than that in high- T sets. However, a model trained on low- T UDD- AL data exhibits excellent accuracy on data sampled at unbiased high- T conditions which is not the case in the reverse test. This, in turn, suggests that the UDD- AL approach avoids oversampling the extreme structural distortions that are common at very high temperatures.  
+
+The test case of acetylacetone shows that bias potential applied to a pre- trained ANI- 1x model promotes proton transfer in the enol tautomer keeping oscillations in the rest of the bond distances identical to low- T conditions. Opposite situation is observed for the unbiased high- T MD where interatomic distances exhibit larger deviations from equilibrium positions with a lower rate
+
+<--- Page Split --->
+
+of a proton transfer. The analysis of interatomic distances clearly indicates an advantage of the bias potential over the high- T approach: bias potential facilitates sampling of important underrepresented chemical data without random structural distortions caused by high- T conditions. This feature can be used for efficient sampling of conformational and/or configurational space of temperature sensitive systems.  
+
+Our tests indicate that the bias potential can facilitate sampling of high energy chemical space without sacrificing the sampling of low energy configurations. This means that UDD will produce robust datasets that are applicable to both lower energy, near global minimum data and high energy chemical space which usually corresponds to important reactive structural data such as transition states and intermediates.  
+
+As the results show, uncertainty- based bias potential is a promising technique for sampling rare events while being relatively faithful to the physical equilibrium distribution. The uncertainty driven dynamics is similar to metadynamics<sup>47- 50</sup> in its use a bias potential but avoids the need to manually select collective variables or to identify basins of attraction. In a way, it defines the best CV for the purpose of AL: training a more general and robust ML potential. The approach requires selection of two parameters: the bias magnitude and width; developing a method which can tune these algorithmically would be a productive future activity. Additionally, the algorithm for automatic selection of uncertainty criteria could improve the sampling efficiency.  
+
+## Methods  
+
+## Active learning  
+
+For glycine simulations, we use ANI deep learning model<sup>51</sup> to generate ensembles of NN potentials prepared using an 8- fold cross validation split of the data set. The empirical value 0.23 \([kcal \times mol^{- 1} \times (\sqrt{N_A})^{- 1}]\) for the uncertainty selection criteria \(\rho\) , equation (3), provided in the original work on active learning for organic molecules<sup>36</sup> turned out to be too low for the purposes
+
+<--- Page Split --->
+
+of training on one chemical system. It causes unnecessarily dense sampling of glycine conformational space which, in turn, hinders the MD simulation to reach higher energy regions. Therefore, we use a higher value of \(0.35 [kcal \times mol^{- 1} \times (\sqrt{N_A})^{- 1}]\) for this test case. Overall, automatic selection of uncertainty criteria is a nontrivial question which deserves a separate discussion and goes beyond the scope of this work. Each MD simulation is terminated when the system meets the uncertainty selection criteria \(\rho\) .  
+
+The initial training set consists of 125 glycine geometries that span near- equilibrium structures of the glycine global minimum. This data is acquired from a separate 5ps MD trajectory at 350K with a 0.5 fs timestep, initialized from the glycine global minimum. Every \(80^{\text{th}}\) MD step is included in the initial data training set. The MD simulation for the initial training set is carried out using the pre- trained ANI- 1x potential. \(^{51}\)  
+
+## MD Simulations  
+
+In all discussed cases, the Atomic Simulation Environment (ASE) Langevin thermostat was used to maintain temperature with a friction coefficient of 0.01 a.u. Each AL iteration performs 16 MD simulations with 1fs time step and a 200 000 steps limit (200ps). At each AL iteration, the MD is driven by an ensemble of ANI- type ML potentials, trained on initial data and data accumulated on previous AL iterations. The NN- based MD is interfaced with ASE code. \(^{53}\) The final data set has 1280 data points sampled in AL procedure + 125 data points from the initial data set.  
+
+The set of seed geometries for MD simulations comprises 25 structures that correspond to near- equilibrium geometries of a glycine global minimum (GM). These are selected as the first 25 structures from the initial training set. AL sampler randomly selects one of them for each MD initialization. Energies and forces of new conformers are calculated using the WB97X- D/cc- pVTZ \(^{54,55}\) level of theory as implemented in PSI4 code. \(^{56}\)
+
+<--- Page Split --->
+
+## NN architecture  
+
+NN architectureParameters for the atomic environment vector \(^{51}\) (a numerical vector used to encode the atomic local environment in ANI) used during the AL process were constant. 32 evenly spaced shifting parameters are used for the radial part of the vector with 4.6 Å cutoff radius and a total of 8 radial and 8 angular shifting parameters are used for the angular part with 3.5 Å cutoff radius. With four atom types, this gives 768 elements in the descriptor. The first atom- centered function is shifted to 0.8 Å from the atomic center. The ANI potential used in this work contains three hidden layers and has the following architecture: 768:32:16:8:1, each number describing the number of neurons at each subsequent layer in the network.  
+
+The ANI potential used in this work contains three hidden layers and has the following architecture: 768:32:16:8:1. Gaussian activation functions are used in hidden layers and linear activation in the final layer.  
+
+## Acknowledgements  
+
+AcknowledgementsK. B., N. L., R. M., S. T., and B. N. acknowledge support from the US DOE, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under Triad National Security, LLC ("Triad") contract Grant 89233218CNA000001 (FWP: LANLE3F2). M. K. and Y. W. L. acknowledge support from the Los Alamos National Laboratory (LANL) Directed Research and Development funds. This work was performed in part at the Center for Nonlinear Studies and the Center for Integrated Nanotechnology, a US Department of Energy (DOE) and Office of Basic Energy Sciences user facility. This research used resources provided by the LANL Institutional Computing Program, which is supported by the US DOE National Nuclear Security Administration under Contract 89233218CNA000001. We also acknowledge the CCS- 7 Darwin cluster at LANL for additional computing resources.
+
+<--- Page Split --->
+
+## Data Availability  
+
+Source data are provided with this Paper.  
+
+## Code Availability  
+
+Two implementations of the ANI neural network architecture are available online:  
+
+TorchANI (https://github.com/aiqm/torchani) and NeuroChem (https://github.com/  
+
+atomistic- ml/neurochem).  
+
+## References  
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+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- Sl.docx- ExtendedDataFig1.jpg- ExtendedDataFig2.jpg- ExtendedDataFig3.jpg- ExtendedDataFig4.jpg
+
+<--- Page Split --->

preprint/preprint__06bb8347202433bb91b22abd4d31eeb57d2b64b25f7eb3fe4e53e20191446658/preprint__06bb8347202433bb91b22abd4d31eeb57d2b64b25f7eb3fe4e53e20191446658_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 938, 175]]<|/det|>
+# Uncertainty Driven Dynamics for Active Learning of Interatomic Potentials  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 697, 238]]<|/det|>
+Maksim Kulichenko ( mbulichenko@gmail.com) Los Alamos National Laboratory https://orcid.org/0000- 0002- 6194- 3008  
+
+<|ref|>text<|/ref|><|det|>[[44, 243, 340, 285]]<|/det|>
+Kipton Barros Los Alamos National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 291, 340, 332]]<|/det|>
+Nicholas Lubbers Los Alamos National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 338, 340, 379]]<|/det|>
+Ying Wai Li Los Alamos National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 384, 340, 425]]<|/det|>
+Richard Messerly Los Alamos National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 430, 697, 471]]<|/det|>
+Sergei Tretiak Los Alamos National Laboratory https://orcid.org/0000- 0001- 5547- 3647  
+
+<|ref|>text<|/ref|><|det|>[[44, 476, 340, 517]]<|/det|>
+Justin Smith Los Alamos National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 522, 340, 563]]<|/det|>
+Benjamin Nebgen Los Alamos National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 603, 102, 620]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 641, 137, 659]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 678, 315, 697]]<|/det|>
+Posted Date: October 3rd, 2022  
+
+<|ref|>text<|/ref|><|det|>[[44, 716, 475, 735]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 2109927/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 754, 910, 797]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 800, 144]]<|/det|>
+## Uncertainty Driven Dynamics for Active Learning of Interatomic Potentials.  
+
+<|ref|>text<|/ref|><|det|>[[115, 167, 840, 206]]<|/det|>
+Maksim Kulichenko<sup>1\*</sup>, Kipton Barros<sup>1,2</sup>, Nicholas Lubbers<sup>3</sup>, Ying Wai Li<sup>3</sup>, Richard Messerly<sup>1</sup>, Sergei Tretiak<sup>1,2,4</sup>, Justin S. Smith<sup>1,5,\*</sup>, Benjamin Nebgen<sup>1,\*</sup>  
+
+<|ref|>text<|/ref|><|det|>[[113, 223, 881, 391]]<|/det|>
+<sup>1</sup> Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States  <sup>2</sup> Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States   <sup>3</sup> Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States   <sup>4</sup> Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States   <sup>5</sup> Nvidia Corporation, Santa Clara, CA 9505, United States  
+
+<|ref|>text<|/ref|><|det|>[[115, 408, 785, 427]]<|/det|>
+\* Corresponding authors: maxim@lanl.gov, jusmith@nvidia.com, bnebgen@lanl.gov  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 453, 215, 474]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[112, 483, 886, 858]]<|/det|>
+Machine learning (ML) models, if trained to datasets of high- fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse datasets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the dataset. A key challenge in this process is locating structures for which the model lacks underlying training data. Here, we develop a strategy to more rapidly discover configurations that meaningfully augment the training dataset. The approach, uncertainty driven dynamics for active learning (UDD- AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. Performance of UDD- AL is demonstrated for two challenging AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore chemically relevant configuration
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 139]]<|/det|>
+space, which may be inaccessible using regular dynamical sampling at target temperature conditions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 180, 175, 201]]<|/det|>
+## Main  
+
+<|ref|>text<|/ref|><|det|>[[113, 210, 886, 520]]<|/det|>
+Machine learning (ML) is a firmly established approach in chemical science that demonstrates great promise for the acceleration of physical simulations. A particular strength of ML models is a robust representation of potential energy surfaces of molecular and materials systems, when trained to large and diverse datasets of high- fidelity quantum chemistry simulations. For example, ML based potentials \(^{1 - 11}\) approach ab initio \(^{12,13}\) or density functional theory (DFT) \(^{14}\) levels of accuracy at a computational cost near that of classical force fields. \(^{15 - 17}\) Over the recent years, various ML- models — such as neural networks (NNs), \(^{18 - 24}\) Gaussian approximation potentials, \(^{25}\) spectral neighbor analysis potentials, \(^{26}\) moment tensor potentials, \(^{27}\) symmetric gradient domain machine learning \(^{28,29}\) — have demonstrated remarkable success in the field atomic- scale discovery.  
+
+<|ref|>text<|/ref|><|det|>[[113, 530, 885, 710]]<|/det|>
+No matter how sophisticated the ML model architecture, however, the quality and diversity of the training data remains crucial to ultimate model accuracy since ML models are known to extrapolate poorly to unseen data. Therefore, training sets for ML potentials need to span as much phase (structural) space as possible to perform meaningful simulations. Additionally, the training set needs to be as diverse as possible to avoid overfitting towards excessively represented training data (e.g., near- equilibrium configurations in MD trajectories).  
+
+<|ref|>text<|/ref|><|det|>[[113, 722, 885, 902]]<|/det|>
+Entropy- maximization techniques \(^{30,31}\) help to partially overcome these problems by maximizing the structural diversity of a data set. When acquiring new data, these methods are focused on the structural dissimilarity compared to the existing data. However, these methods usually require training of a separate Gaussian process model and significantly rely on the structural representation in latent space. There are other opportunities for improvement as well. Active learning (AL) \(^{32,33}\) attempts to expand the dataset in areas where the ML model is most
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 202]]<|/det|>
+uncertain, which leads to more rapid model improvement. Another feature of AL is that it can employ physically meaningful dynamical trajectories for the sampling of configurations. In the present work, we illustrate how to keep these benefits of AL, while accelerating the rate of new data collection.  
+
+<|ref|>text<|/ref|><|det|>[[112, 214, 886, 556]]<|/det|>
+AL<sup>32,33,34</sup> aims to iteratively collect diverse training datasets addressing any weaknesses identified in an ML model prediction. For this, it is necessary to estimate uncertainty for a model's predictions.<sup>35- 45</sup> A well- established practical strategy for AL with NN potentials is Query by Committee<sup>46</sup> (QBC); here, the estimate of uncertainty is the disagreement between a collection of models within an ensemble. Typically, there are 5 to 10 NNs in an ensemble, and these share the same architecture and hyperparameters but, crucially, use a different initial randomization of the model parameters prior to training, and different splits of the training/validation data. It is empirically observed that the variance of the ensemble predictions correlates strongly with actual prediction error,<sup>36</sup> suggesting that the prediction task requires extrapolation beyond the range of the training data. In the QBC strategy, if this ensemble variance is observed to be large, then the training set will be augmented with new quantum simulation data.  
+
+<|ref|>text<|/ref|><|det|>[[112, 567, 886, 907]]<|/det|>
+AL estimates uncertainty in properties predicted for structures generated by an underlying sampler at each iteration. Molecular dynamics (MD) is the most popular method for sampling chemically meaningful potential energy surfaces. However, MD is susceptible to trapping in near- minimum conformations and only rarely enters chemically important regions such as transition states, which are key data for reactive simulations of chemical processes. In general, capturing thermodynamically rare events is a challenging task for any sampler. For example, metadynamics<sup>47- 50</sup> is an effective method of potential energy surface exploration, which operates on the concept of collective variables (CVs). However, CVs require manual selection, and their number is limited in practice. The user needs to "look" at each specific molecule to determine the desired structural parameters to be scanned. Therefore, this approach is not suitable for automatic sampling.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 885, 331]]<|/det|>
+Here, following the idea of QBC and ensemble uncertainty, we propose a new AL sampling algorithm biased towards regions of high uncertainty - Uncertainty Driven Dynamics (UDD). Due to model random initializations and the stochastic nature of training, regions of chemical space with low ensemble uncertainty will typically arise when similar regions are prevalent in the current training dataset, such that every member of the ensemble is making an accurate inference. Thus, biasing molecular dynamics in the direction of high ensemble uncertainty encourages the dynamics to visit new configurations, which are relevant for improving the diversity of the training set.  
+
+<|ref|>text<|/ref|><|det|>[[113, 343, 885, 587]]<|/det|>
+One can regard the uncertainty- based bias potential as similar to metadynamics in the sense that the sampling trajectories are pushed towards less- visited configurational regions. Here, however, CVs need not be defined. We show that within MD- based AL data acquisition, UDD helps substantially reduce the MD simulation time required to enter the high uncertainty region. Most importantly, the proposed approach enables efficient conformational and configurational sampling at low- temperature (low- T) conditions, making this approach essential for temperature sensitive molecules. UDD assists in sampling the chemically relevant subspace of high- energy space which contains important data such as transition states.  
+
+<|ref|>text<|/ref|><|det|>[[113, 599, 885, 842]]<|/det|>
+The value of the proposed approach is demonstrated in two test cases. First, UDD- AL is used for conformational sampling of a glycine molecule. We find that the bias potential technique generates a diverse dataset covering both low and high energy regions. This contrasts with high- temperature (high- T) MD- AL, which tends to skip over low energy regions. Second, in tests with acetylacetone at low- T conditions, the bias potential is observed to encourage the sampling of the phase space relevant to a proton transfer. Here we find that, in contrast with regular high- T MD, the bias potential technique encourages the reactive transition with very little distortion to the distribution of other degrees of freedom in the system.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 91, 206, 112]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 123, 700, 146]]<|/det|>
+## Uncertainty driven dynamics for active learning (UDD-AL)  
+
+<|ref|>text<|/ref|><|det|>[[113, 153, 886, 290]]<|/det|>
+Before introducing UDD- AL, let us first set the context by reviewing the related method of metadynamics. Here the CVs \(s(q)\) are user- defined structural parameters being scanned by external Gaussian bias potentials. Usually, \(3N - 6\) dimensional atomic coordinates \(q\) of the simulated system are mapped to CVs \(s(q)\) . The corresponding energy function is defined as  
+
+<|ref|>equation<|/ref|><|det|>[[113, 280, 845, 315]]<|/det|>
+\[E_{\mathrm{metadynamics}}(s,t) = \sum_{k\tau < t}W(k\tau)\mathrm{exp}\big[-\sum_{i = 1}^{N_{CV}}\frac{1}{2b_{i}^{2}} (s_{i} - s_{i}(q(k\tau)))^{2}\big], \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 325, 886, 476]]<|/det|>
+where \(b_{i}\) is the width of the Gaussian function for the \(i^{\mathrm{th}}\) collective variable, \(W(k\tau)\) is the height of the Gaussian at the simulation time \(t = k\tau\) , which is constant in the case of standard metadynamics, \(\tau\) is the deposition rate of the Gaussian functions, and \(N_{\mathrm{CV}}\) is the number of CVs. During simulations, more Gaussians are added, thus discouraging the system to go back to its previous steps.  
+
+<|ref|>text<|/ref|><|det|>[[112, 486, 886, 670]]<|/det|>
+Like metadynamics, UDD- AL method modifies the physical energy by adding a bias potential \(E_{\mathrm{bias}}\) . Here, however, \(E_{\mathrm{bias}}\) will be defined in terms of the model uncertainty rather than CVs. Such uncertainty estimates can be used to assist in the sampling of atomistic data. \(^{44}\) In the QBC approach, an ensemble of NN- potentials is trained, and the level of agreement between the NN predictions serves as the estimate of overall model uncertainty. The QBC uncertainty estimate is proportional to the variance in the energy \((\sigma_{E}^{2})\)  
+
+<|ref|>equation<|/ref|><|det|>[[113, 678, 845, 708]]<|/det|>
+\[\sigma_{E}^{2} = \frac{1}{2}\Sigma_{i}^{N_{M}}(\hat{E}_{i} - \hat{E})^{2}, \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[112, 720, 886, 870]]<|/det|>
+where \(\hat{E}_{i}\) is the energy predicted by an ensemble member, \(\hat{E}\) is its ensemble average, and \(N_{\mathrm{M}}\) is the number of ensemble members, i.e., NN- potentials. Here, ensembles of ANI potentials are prepared using an 8- fold cross validation split of the data set which yields \(N_{\mathrm{M}} = 8\) ensemble members (see Methods). In previous applications of QBC- based AL, new data is collected when the uncertainty estimator  
+
+<|ref|>equation<|/ref|><|det|>[[112, 881, 845, 907]]<|/det|>
+\[\rho = \sqrt{2 / N_{M}N_{A}}\sigma_{E} \quad (3)\]
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 698, 108]]<|/det|>
+exceeds a threshold, where \(N_{A}\) is the number of atoms in a configuration.  
+
+<|ref|>text<|/ref|><|det|>[[113, 120, 884, 202]]<|/det|>
+We seek to construct a bias energy \(E_{\mathrm{bias}}(\sigma_{E}^{2})\) that favors configurations with larger uncertainties \(\rho \propto \sigma_{E}\) ; such configurations are expected to correlate with regions that are underrepresented in the training data. A reasonable choice is the Gaussian function,  
+
+<|ref|>equation<|/ref|><|det|>[[113, 214, 845, 250]]<|/det|>
+\[E_{\mathrm{bias}}(\sigma_{E}^{2}) = A\left[\exp \left(-\frac{\sigma_{E}^{2}}{N_{M}N_{A}B^{2}}\right) - 1\right]. \quad (4)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 262, 884, 380]]<|/det|>
+The magnitude \(A\) and width \(B\) of the biasing should be selected empirically. The bias potential goes to zero in the absence of uncertainty, \(E_{\mathrm{bias}}(0) = 0\) . Configurations with large uncertainty, \(\rho \gg B\) , are favored by a bias energy of magnitude \(E_{\mathrm{bias}} \approx - A\) . Forces derived from the bias potential are strongest when the uncertainty \(\rho\) is of the same order as the parameter \(B\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 393, 884, 510]]<|/det|>
+The combined potential \(\hat{E} + E_{\mathrm{bias}}\) is used to define an uncertainty driven dynamics (UDD). In applications to AL the overall strategy will be denoted UDD- AL. The schematic workflow of UDD- AL is depicted in Fig. 1a. It should be compared to the usual MD based approach (MD- AL), which does not incorporate the \(E_{\mathrm{bias}}\) term.  
+
+<|ref|>text<|/ref|><|det|>[[113, 522, 884, 670]]<|/det|>
+The optimal parameters \(A\) and \(B\) will be context dependent. For example, our applications to glycine and acetylacetone tests discussed below suggest that the bias magnitude \(A\) should be at least of the order of the energy barriers of interest. The bias width, \(B\) , should also be carefully selected. If \(B\) is either too small or too large, the bias forces could become negligibly small for the typical uncertainties \(\rho\) that are observed in the AL sampling.  
+
+<|ref|>text<|/ref|><|det|>[[113, 683, 844, 802]]<|/det|>
+Effective bias forces on an atom at position \(r\) can be calculated using the chain rule, \[ -\frac{\partial}{\partial r} E_{\mathrm{bias}}(\sigma_{E}^{2}) = -E_{\mathrm{bias}}(\sigma_{E}^{2})'\frac{\partial}{\partial r}\sigma_{E}^{2} \] and \[ -\frac{\partial}{\partial r}\sigma_{E}^{2} = -\sum_{i}^{M}(\hat{E}_{i} - \hat{E})\frac{\partial}{\partial r}(\hat{E}_{i} - \hat{E}) = \sum_{i}^{M}(\hat{E}_{i} - \hat{E})(\hat{f}_{i} - \hat{f}) \]  
+
+<|ref|>equation<|/ref|><|det|>[[113, 789, 845, 820]]<|/det|>
+\[-\frac{\partial}{\partial r}\sigma_{E}^{2} = -\sum_{i}^{M}(\hat{E}_{i} - \hat{E})\frac{\partial}{\partial r} (\hat{E}_{i} - \hat{E}) = \sum_{i}^{M}(\hat{E}_{i} - \hat{E})(\hat{f}_{i} - \hat{f}) \quad (6)\]
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 175]]<|/det|>
+where \(\hat{f}_{t}\) denotes the force vector predicted by an ensemble member and \(\hat{f}\) is the ensemble- averaged prediction. Since \(\sigma_{E}^{2}\) , \(\hat{E}_{t}\) , and \(\hat{f}_{t}\) are calculated at each MD step in any AL approach, including the bias potential has a negligible effect on the computational time.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 211, 517, 233]]<|/det|>
+## Glycine conformational space sampling  
+
+<|ref|>text<|/ref|><|det|>[[112, 240, 886, 708]]<|/det|>
+The glycine molecule is shown in Fig. 1a. We are interested in sampling the conformational space without bond- breaking events using various AL protocols. Dihedral rotations of \(- \mathrm{NH}_{2}\) and \(- \mathrm{COOH}\) groups correspond to 2.5- 3.5 kcal/mol barriers. Our numerical tests have shown that the bias magnitude \(A\) approximately five times higher than the average barrier of interest provides the best results for the glycine test. It helps keep the bias essentially high at higher uncertainty values. It also helps overcome possible barrier bottlenecks caused by possible overestimation of barrier heights by ML model. The geometries near global energy minimum (GM) of a glycine are already present in the initial training set, and each sampling MD simulation starts with this kind of structure. Depending on the AL iteration, near- GM structures have \(\rho\) of \(0.024 \pm 0.005 [\mathrm{kcal} \times \mathrm{mol}^{- 1} \times (\sqrt{\mathrm{N}_{\mathrm{A}}})^{- 1}]\) \((\sigma_{E} = 0.15 \pm 0.03 \mathrm{kcal / mol})\) . Thus, we selected \(A\) equal to 15.4 kcal/mol which corresponds to the bias potential value of \(- 15.0 \mathrm{kcal / mol}\) at near- GM values of \(\rho\) (with \(B = 0.12 \mathrm{kcal / mol}\) ). We further increase \(A\) by \(15\%\) at 140ps time step if the uncertainty criterion is not met at this simulation stage. Our tests also show that best results are achieved for \(B\) being close to near- GM uncertainty \(\sigma_{E}\) . Here we use \(B = 0.12 \mathrm{kcal / mol}\) for glycine.  
+
+<|ref|>text<|/ref|><|det|>[[113, 718, 886, 899]]<|/det|>
+We next compare the two active learning approaches – UDD- AL and MD- AL – for the task of collecting a dataset of the glycine conformational space. Each AL iteration performs 16 MD simulations with 200ps time limit and 1fs step (see Methods). An ensemble of NN- potentials for the first AL iteration is trained on the initial data set of 125 conformers that span near- equilibrium structures of the glycine global minimum. At each subsequent AL iteration, the MD simulation employs an ensemble of ANI- type NN- potentials (see Methods and Ref. 51), trained on the initial
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 885, 377]]<|/det|>
+data and data accumulated on all previous AL iterations. The starting geometries for MD simulations and the initial training set contain only near- equilibrium geometries of a glycine global minimum (Extended Data Fig. 1). Stated differently, NNs have no initial information about higher energy conformers, and MD simulations have to reach them from the bottom of the potential energy surface. Each MD simulation is terminated when the system meets the uncertainty selection criteria \(\rho\) of \(0.35 [\mathrm{kcal} \times \mathrm{mol}^{- 1} \times (\sqrt{N_{\mathrm{a}}})^{- 1}]\) (see Methods). If the MD simulation reaches the time limit, then the structure from the trajectory with the highest uncertainty is selected. Density Functional Theory (DFT) reference data (see Methods) is then computed for final conformations and added to the training set for the next iteration of the AL process.  
+
+<|ref|>text<|/ref|><|det|>[[112, 389, 886, 824]]<|/det|>
+Figure 1b shows the average MD simulation time required to meet the uncertainty criterion in different AL approaches with respect to AL iteration. The MD- AL at low- T conditions (350K) reaches the MD time limit at \(\sim 20^{\mathrm{th}}\) iteration which is continued until the final AL iteration (Fig. 1b, blue line). This means that the specified uncertainty criterion is almost never met, and the sampler returns the geometry of maximum available uncertainty from the MD trajectory. The uncertainty bias potential is introduced in low- T (350K) MD simulations (orange line). We do not activate the bias potential at earlier AL iterations for two reasons. First, the low- T MD- AL (Fig. 1b, blue line) does not reach the MD simulation time limit up to \(15 - 20^{\mathrm{th}}\) iteration. Thus, at this stage, the regular MD- AL manages to acquire new data satisfying the uncertainty criteria. Second, the NN potential might be unstable or not smooth at earlier iterations due to the lack of data. Therefore, the bias is activated at the \(15^{\mathrm{th}}\) iteration to avoid moving systems toward unphysical configurations. When the uncertainty bias potential is on (UDD- AL regime), it reduces the number of MD steps needed to meet the desired uncertainty. Moreover, the MD time limit plateau is still not reached till the final iteration.  
+
+<|ref|>text<|/ref|><|det|>[[114, 836, 883, 888]]<|/det|>
+Perhaps the most common way to accelerate sampling of high- energy states is to run high- T MD. Thus, to illustrate the difference between the bias potential and a simple temperature
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 885, 299]]<|/det|>
+increase, we also compare the low- T 350K UDD- AL with the high- T MD- ALs at 600K and 1000K simulation conditions (Fig. 1b). Like in case of UDD- AL sampling, the temperature is increased at the 15th iteration. 600K MD- AL approaches the MD time limit at \(\sim 40\) th iteration while UDD- AL reaches the time limit plateau by the end of AL procedure. Thus, 600K MD- AL does not perform as well as UDD- AL in terms of simulation time. On the other hand, the 1000K MD- AL (cyan line) exhibits a faster sampling, and the average MD time does not exceed 35ps even at the last AL iteration.  
+
+<|ref|>text<|/ref|><|det|>[[113, 311, 885, 458]]<|/det|>
+Energy ranges sampled by each AL approach are depicted in Fig.1c. Expectedly, high- T MD- AL data (green and cyan histograms) span wider energy ranges compared to low- T 350K MD- AL (blue histogram). What is more interesting is that the energy distribution of data from the 350K UDD- AL (orange histogram) is very similar to the shape of 600K MD- AL data; an advantage of UDD- AL is that many fewer MD steps are required to collect these samples.  
+
+<|ref|>text<|/ref|><|det|>[[112, 471, 886, 876]]<|/det|>
+After completing the entire AL procedure, the final models are trained on 1280 glycine conformers collected during the entire AL procedure (+125 conformers in the initial training set). In order to access the accuracy of the four models, we use a test set comprising 50,000 glycine structures from a 50ns MD simulation via the ANI- 1ccx potential run at 400K with a 0.5fs time step (see Methods).<sup>19</sup> As depicted in Fig. 1d, all models perform reasonably well with root- mean- square deviations (RMSEs) less than 0.3 kcal/mol. However, the RMSE of the model trained on low- T 350K MD- AL data is slightly yet systematically lower than RMSEs of the rest of the models with \(\sim 0.11\) kcal/mol difference. This is likely because MD simulations tend to oscillate in near- equilibrium positions, which is why this test set is dominated by low- energy geometries. Low- T 350K MD- AL, in turn, densely spans a narrow low- energy range, which might explain a slightly better performance of this model on a test set derived from a 50ns MD. Indeed, normalized histograms in Fig.1e point out that this seemingly large 50ns test set spans the energy region closest (but even lower) to the one covered by low- T 350K MD- AL data.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 886, 300]]<|/det|>
+Note that the 50ns test set is a MD trajectory with no AL involved while MD- AL data comprises structures with high uncertainties. High uncertainty usually corresponds to a higher energy due to poor sampling in normal low- T MD. In other words, the 50ns MD test set is biased towards near- equilibrium oscillations, but MD- AL data are selectively augmented with higher energy isomers. Similar RMSE shift is observed for low energy rotations of \(- \text{COOH}\) and \(- \text{NH}_2\) functional groups (Extended Data Fig.2). Therefore, the various models should also be tested on higher energy pathways.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 80, 860, 720]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 719, 816, 737]]<|/det|>
+<center>Fig.1 | Comparison of UDD-AL and MD-AL approaches for a glycine test case. a Schematic </center>  
+
+<|ref|>text<|/ref|><|det|>[[112, 746, 872, 882]]<|/det|>
+representation of UDD- AL workflow. b Average MD time required to meet the uncertainty criterion vs. AL iteration for four different MD simulation types: 350K MD- AL (blue), 600K MD- AL (green), 1000K MD- AL (cyan), and 350K UDD- AL (orange). c Energy distribution histograms of four datasets sampled by 350K MD- AL (blue), 600K AL MD- AL (green), 1000K MD- AL (cyan), and 350K UDD- AL (orange). Data from iterations 0- 14 is omitted because the bias is off, or the temperature is not increased at this stage. d
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 870, 222]]<|/det|>
+Comparison of potential energy RMSE obtained on the 50ns test set vs. AL iteration (i.e., training set size, 16 new glycine conformations per iteration). The legend shows RMSEs for models trained on data from the entire AL procedure. e Normalized energy distribution histograms of 50ns test set (red) and training set sampled by 350K MD- AL (blue). Lines in b and d, are averaged over three ensembles, each trained on data from an independent AL procedure.  
+
+<|ref|>text<|/ref|><|det|>[[112, 258, 886, 535]]<|/det|>
+To illustrate what types of chemical processes appear in the system, and how each sampling method covers them, we next visualize the glycine conformational space using dimensionality reduction. We project samples to a 2D plane using the Uniform Manifold Approximation and Projection (UMAP) \(^{52}\) technique, where each conformation is characterized by the 672- D vector of activations (concatenated atomic environment vectors) in the first layer of an independent pre- trained ANI- 1x model. \(^{19}\) Figure 2a shows the 50ns MD dataset spanning four low- lying glycine conformers represented by four regions in the 2D space. Torsional conformations, N- H bond scan, and C=O bond scan are depicted in Fig.2b- c to illustrate structural profiles in 2D space.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 120, 880, 459]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[112, 462, 884, 715]]<|/det|>
+<center>Fig. 2 | 2D representation of glycine conformational space processed by UMAP dimensionality reduction technique. a 50ns test set. Heat-map represents the relative DFT energy. Glycine insets denote the corresponding conformational region. In panels b-d, data sets and scans are placed over the 50ns test set (gray). b Conformational paths through -COOH (cyan and purple) and -NH2 (red and green) rotations. c N-H (red) and C=O (cyan) bond length scans. d Comparison of training sets sampled by 350K MD-AL (blue) and 350K UDD-AL (orange). Green circle denotes the inner high-energy region. Red triangles denote the scan of -OH rotation around the C-O bond. e Comparison of training sets sampled by 350K MD-AL (blue) and 600K MD-AL (green). f Comparison of training sets sampled by 350K MD-AL (blue) and 1000K MD-AL (cyan). </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 742, 885, 891]]<|/det|>
+Figure 2d- f depicts the four datasets visualized over the 50ns test set. Figure 2d provides a visual comparison of data sampled by MD- AL and UDD- AL at 350K. Both datasets cover the 50ns MD data reasonably well. However, there are three key differences. First, a high- energy configurational space (points inside the green circle) is more densely sampled in the UDD- AL dataset: there are 289 points in this non- equilibrium region in the UDD- AL sampling, compared to
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 202]]<|/det|>
+105 points in 350K MD- AL. Second, UDD- AL encountered a new conformational path in the top right corner of the Fig.2d which was not accessed by 350K MD- AL. This region corresponds to the rotation of the - OH group around the C- O bond which is a distinct conformational transition and a high- energy profile with a 15 kcal/mol barrier.  
+
+<|ref|>text<|/ref|><|det|>[[112, 216, 885, 555]]<|/det|>
+Figure 2e presents a visual comparison of the sampling performance of MD- ALs at 350K and 600K. The 2D representation of 600K data is quite similar with the one of 350 UDD- AL data: there are 290 data points inside the inner circled region and a good coverage of - OH rotation region. As expected, MD- AL at the extreme temperature of 1000K (Fig.2f) samples the inner high- energy region even more densely (394 data points) as well as the - OH rotation region. This, however, comes at a cost. The low energy region in the lower left of Fig.2f clearly demonstrates lack of sampling. This is the primary deficiency of using high- T MD: as temperature increases, the system spends less time near low energy regions, since in these regions the kinetic energy is typically the greatest. Thus, it will be possible to 'skip over' regions of high stability thus resulting in a poor data coverage of near equilibrium region. On the other hand, UDD- AL sampling does not run this risk by sufficiently sampling any relevant region.  
+
+<|ref|>text<|/ref|><|det|>[[112, 567, 885, 875]]<|/det|>
+Thus, Figure 2 indicates that the UDD- AL is a good, balanced way of sampling chemical space, reaching most of the high energy points achieved with 1000K MD sampling without losing data density in low energy regions. However, alone, it is not clear that biased sampling presents advantages over unbiased high- T sampling; UDD- AL appears to sample similar configurations to 600K MD- AL. Therefore, we performed additional tests of high- energy pathways that illuminate the differences between 600K MD- AL and 350K UDD- AL. The discussion on high energy profiles - angle and bond scans - can be found in Supplementary Information. The overall trend is that the 350K UDD- AL model exhibits much better accuracy than the model trained on low- T 350K MD- AL data. When comparing the UDD- AL with 600K and 1000K MD- AL models, the former results in a better or, at least, comparable accuracy.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 885, 299]]<|/det|>
+We also provide an overall assessment of the performance of the sampling strategy by cross- testing the associated models on the data from all sampling strategies in Supplementary information. Supplementary Table 2 summarizes RMSEs of the four models on the test sets accumulated by each AL sampler: 350K MD- AL, 350K UDD- AL, 600K MD- AL, and 1000K MD- AL. When testing models on data sets that are not generated by the same corresponding sampler, the UDD- AL model outperforms all other models. A detailed discussion on models' cross testing can be found in Supplementary Information.  
+
+<|ref|>text<|/ref|><|det|>[[112, 310, 886, 748]]<|/det|>
+Ultimately, when looking at a variety of bond rotations and stretches, the most accurate energy profile changes depending on the energy range of the specific scan. Low energy profiles tend to be modeled better by the low- T dataset while higher energy scans are accessed better by the high- T dataset. However, the UDD- AL sampling method yields a model that performs well on a wide range of energy profiles, while also maintaining a low error on each sampling method's held out test set (Table 2 in Supplementary Information). This difference suggests that UDD- AL is able to avoid the higher- energy and less chemically relevant structural distortions, which are typical at very high temperatures. Meanwhile, chemically relevant data present in the UDD- AL data set enables efficient extrapolation to higher- energy structures present in 1000K MD- AL data. As can be seen in Fig. 3, the shapes of interatomic distance distributions in UDD- AL closely mimic sharp distributions in low- T 350K MD- AL, although having a larger standard deviation. This deviation, however, is lower than in 600K and 1000K MD- AL data sets that span a wider distance range. This, in turn, further suggests that the UDD sampler tends to avoid random distortions found in high- T regimes.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 87, 881, 348]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 351, 860, 457]]<|/det|>
+<center>Fig. 3 | Glycine interatomic distance distributions in MD-AL and UDD-AL data sets. Each subplot shows a comparison of bond length distributions in 350K MD-AL (blue), 350K UDD-AL (orange), 600K MD-AL (green), and 1000K MD-AL (cyan) data sets. Each subplot also lists the bond length standard deviation, in the legend. a O-H. b N-H. c C-H. d C=O, e C-N. f C-C. </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 485, 885, 630]]<|/det|>
+Since all models used the same hyperparameters, it is possible that each model could perform better if individual hyperparameter searches are carried out. Perhaps, data sets that cover a broader chemical space need more learnable parameters to be flexible enough to fit the effectively larger degrees of freedom they are being trained to. This will be a subject of future studies.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 669, 441, 689]]<|/det|>
+## Proton transfer in acetylacetone  
+
+<|ref|>text<|/ref|><|det|>[[113, 698, 886, 910]]<|/det|>
+We further examine the UDD performance for sampling of a reactive pathway in an acetylacetone enol tautomer depicted in Fig. 4a. Particularly, we are interested in the proton transfer between the two oxygen atoms, considering the proton position as a free variable. Instead of using AL techniques, here we use an ensemble of pre- trained ANI- 1x interatomic potentials,<sup>19</sup> which were not trained on bond- breaking reactions, and analyze trajectories from UDD and MD simulations. ANI- 1x was trained on wB97x DFT level of theory which yields a 4.7 kcal/mol barrier. However, ANI- 1x significantly overestimates the barrier giving the value of 6.3 kcal/mol. This value
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 203]]<|/det|>
+is then selected as a bias magnitude \(A\) . Uncertainty values \(\rho\) of near-equilibrium acetylacetone structures within ANI- 1x model are higher by the order of magnitude than the ones produced by the newly trained model for glycine. Therefore, we set a higher value of bias width \(B = 0.45\) kcal/mol, being an empirically adjusted parameter.  
+
+<|ref|>text<|/ref|><|det|>[[112, 216, 886, 589]]<|/det|>
+Figure 4b shows log- normalized uncertainty \(\rho\) of the acetylacetone system with respect to the position of the proton. The dark region (near \(x = 0\) Å and \(y = - 1.5\) Å) demonstrates that there is a high- uncertainty region between oxygen atoms which corresponds to a proton transfer transition state. Figure 4c depicts the log- normalized relative potential energy (ANI- 1x) of the system with respect to the position of the free proton. The dark region (near \(x = - 0.5\) Å and \(y = - 1.5\) Å) indicates that the lowest energy corresponds to a proton position near the oxygen atom. This is an expected result since the hydrogen bound to the oxygen atom is the most stable geometry. However, as shown in Fig. 4d, the energy minimum can be shifted to the central position between the oxygen atoms (dark region near \(x = 0\) Å) when the bias potential is applied. For illustrative purposes, here we use a high value of bias magnitude \(A = 56.0\) kcal/mol. In practice, we use \(A = 6.3\) kcal/mol for the MD simulation discussed below. The effect of different \(A\) values on the total energy landscape is depicted in Extended Data Fig. 3.  
+
+<|ref|>text<|/ref|><|det|>[[113, 600, 885, 810]]<|/det|>
+We further analyze results from 0.5ns trajectories obtained using UDD and regular MD simulation techniques. No proton transfer occurs during the regular 350K MD simulation. Meanwhile, the uncertainty bias can direct the proton toward a high- uncertainty region between two oxygen atoms - 90 proton transitions observed in 350K UDD simulation. Finally, unbiased high- T 620K MD results in 48 proton transitions. Although at a lower rate compared to UDD, increased temperature also facilitates the proton transfer. Time traces of the two O- H distances can be further found in Extended Data Fig. 4.  
+
+<|ref|>text<|/ref|><|det|>[[113, 823, 884, 906]]<|/det|>
+A key difference between low- T UDD and regular high- T MDs can be found when analyzing oscillations of interatomic distances. Certainly, high- T conditions will affect the entire molecule causing larger distance deviations compared to low- T conditions. Indeed, the overall
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 333]]<|/det|>
+spread of O- H distances is comparable using 350K MD (Extended Data Fig. 4), but far wider at 620K MD, even in segments of the trajectory without proton transfer. Further analysis of C- H distances in the molecule, shown in Fig. 4e- f, confirms this phenomenon. Figure 4e shows C- H distance distributions in the methyl group in 350K MD, 350K UDD, and 620K MD simulations. 620K MD exhibits higher deviations from the equilibrium C- H bond length compared to low- T UDD. The standard deviation of the methyl C- H distance in 620K MD is 0.04 Å against 0.03 Å in 350K UDD. Notably, the low- T 350K MD trajectory has the standard deviation of 0.03 Å, same as in low- T UDD. The same picture holds for the central C- H bond shown in Fig. 4f.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[112, 123, 875, 624]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 628, 884, 821]]<|/det|>
+<center>Fig. 4 | Ensemble uncertainty and UDD in acetylacetone. a Acetylacetone molecule. Red circle denotes a hydrogen atom involved in a proton transfer. b Log-normalized map of disagreement \(\rho\) of ANI-1x model ensemble with respect to a position of a circled hydrogen. c Log-normalized map of physical energy. d Log-normalized map of summed physical and bias energy. e and f show a comparison of C-H bond length distributions in the methyl and central groups, respectively, for 350K MD (blue), 350K UDD (orange), and 620K MD simulations. Red ellipse denotes a bond under consideration. Each subplot also lists the bond length standard deviation from the equilibrium distance per legend. </center>  
+
+<|ref|>text<|/ref|><|det|>[[114, 850, 884, 902]]<|/det|>
+These observations confirm that although high- T sampling promotes the activation of reactive pathways, it has a global effect on all degrees of freedom in the system, whereas the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 236]]<|/det|>
+UDD technique allows to sample the reactive pathway without significant changes to equilibrium distributions of other degrees of freedom. This is likely due to the composition of ANI- 1x training data, which has information on non- equilibrium extended bonds. However, a hydrogen which is equidistant between two oxygen atoms is not a commonly encountered configurational data. Thus, the UDD potential promotes sampling of this specific region.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 275, 244, 297]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[113, 307, 885, 487]]<|/det|>
+In this work, we present a MD- based active learning (AL) algorithm assisted by the uncertainty- based bias potential. The algorithm is abbreviated as UDD- AL (uncertainty driven dynamics for active learning) and is compared to MD- based AL (MD- AL) in common use. We show that an uncertainty metric provided by an ensemble of NN- potentials can be used to construct the bias potential. The resulting energy term encourages the system to move toward underrepresented chemical regions, accelerating and improving sampling of high- energy regions.  
+
+<|ref|>text<|/ref|><|det|>[[112, 498, 885, 774]]<|/det|>
+The ANI model, trained on glycine conformational data from low- T UDD- AL, is shown to properly reproduce conformational pathways not accessible by low- T MD- AL. The resulting ANI model exhibits high accuracy for important high- energy conformational profiles. Importantly, while this accuracy is better than or comparable to the results for models trained on high- T MD- AL data, a low- T UDD- AL training set spans an energy range narrower than that in high- T sets. However, a model trained on low- T UDD- AL data exhibits excellent accuracy on data sampled at unbiased high- T conditions which is not the case in the reverse test. This, in turn, suggests that the UDD- AL approach avoids oversampling the extreme structural distortions that are common at very high temperatures.  
+
+<|ref|>text<|/ref|><|det|>[[113, 786, 884, 902]]<|/det|>
+The test case of acetylacetone shows that bias potential applied to a pre- trained ANI- 1x model promotes proton transfer in the enol tautomer keeping oscillations in the rest of the bond distances identical to low- T conditions. Opposite situation is observed for the unbiased high- T MD where interatomic distances exhibit larger deviations from equilibrium positions with a lower rate
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 235]]<|/det|>
+of a proton transfer. The analysis of interatomic distances clearly indicates an advantage of the bias potential over the high- T approach: bias potential facilitates sampling of important underrepresented chemical data without random structural distortions caused by high- T conditions. This feature can be used for efficient sampling of conformational and/or configurational space of temperature sensitive systems.  
+
+<|ref|>text<|/ref|><|det|>[[113, 248, 884, 395]]<|/det|>
+Our tests indicate that the bias potential can facilitate sampling of high energy chemical space without sacrificing the sampling of low energy configurations. This means that UDD will produce robust datasets that are applicable to both lower energy, near global minimum data and high energy chemical space which usually corresponds to important reactive structural data such as transition states and intermediates.  
+
+<|ref|>text<|/ref|><|det|>[[113, 408, 885, 650]]<|/det|>
+As the results show, uncertainty- based bias potential is a promising technique for sampling rare events while being relatively faithful to the physical equilibrium distribution. The uncertainty driven dynamics is similar to metadynamics<sup>47- 50</sup> in its use a bias potential but avoids the need to manually select collective variables or to identify basins of attraction. In a way, it defines the best CV for the purpose of AL: training a more general and robust ML potential. The approach requires selection of two parameters: the bias magnitude and width; developing a method which can tune these algorithmically would be a productive future activity. Additionally, the algorithm for automatic selection of uncertainty criteria could improve the sampling efficiency.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 690, 218, 711]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 723, 268, 744]]<|/det|>
+## Active learning  
+
+<|ref|>text<|/ref|><|det|>[[113, 753, 884, 883]]<|/det|>
+For glycine simulations, we use ANI deep learning model<sup>51</sup> to generate ensembles of NN potentials prepared using an 8- fold cross validation split of the data set. The empirical value 0.23 \([kcal \times mol^{- 1} \times (\sqrt{N_A})^{- 1}]\) for the uncertainty selection criteria \(\rho\) , equation (3), provided in the original work on active learning for organic molecules<sup>36</sup> turned out to be too low for the purposes
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 283]]<|/det|>
+of training on one chemical system. It causes unnecessarily dense sampling of glycine conformational space which, in turn, hinders the MD simulation to reach higher energy regions. Therefore, we use a higher value of \(0.35 [kcal \times mol^{- 1} \times (\sqrt{N_A})^{- 1}]\) for this test case. Overall, automatic selection of uncertainty criteria is a nontrivial question which deserves a separate discussion and goes beyond the scope of this work. Each MD simulation is terminated when the system meets the uncertainty selection criteria \(\rho\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 293, 885, 442]]<|/det|>
+The initial training set consists of 125 glycine geometries that span near- equilibrium structures of the glycine global minimum. This data is acquired from a separate 5ps MD trajectory at 350K with a 0.5 fs timestep, initialized from the glycine global minimum. Every \(80^{\text{th}}\) MD step is included in the initial data training set. The MD simulation for the initial training set is carried out using the pre- trained ANI- 1x potential. \(^{51}\)  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 478, 279, 499]]<|/det|>
+## MD Simulations  
+
+<|ref|>text<|/ref|><|det|>[[113, 507, 885, 719]]<|/det|>
+In all discussed cases, the Atomic Simulation Environment (ASE) Langevin thermostat was used to maintain temperature with a friction coefficient of 0.01 a.u. Each AL iteration performs 16 MD simulations with 1fs time step and a 200 000 steps limit (200ps). At each AL iteration, the MD is driven by an ensemble of ANI- type ML potentials, trained on initial data and data accumulated on previous AL iterations. The NN- based MD is interfaced with ASE code. \(^{53}\) The final data set has 1280 data points sampled in AL procedure + 125 data points from the initial data set.  
+
+<|ref|>text<|/ref|><|det|>[[113, 730, 885, 879]]<|/det|>
+The set of seed geometries for MD simulations comprises 25 structures that correspond to near- equilibrium geometries of a glycine global minimum (GM). These are selected as the first 25 structures from the initial training set. AL sampler randomly selects one of them for each MD initialization. Energies and forces of new conformers are calculated using the WB97X- D/cc- pVTZ \(^{54,55}\) level of theory as implemented in PSI4 code. \(^{56}\)
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 277, 110]]<|/det|>
+## NN architecture  
+
+<|ref|>text<|/ref|><|det|>[[113, 119, 886, 363]]<|/det|>
+NN architectureParameters for the atomic environment vector \(^{51}\) (a numerical vector used to encode the atomic local environment in ANI) used during the AL process were constant. 32 evenly spaced shifting parameters are used for the radial part of the vector with 4.6 Å cutoff radius and a total of 8 radial and 8 angular shifting parameters are used for the angular part with 3.5 Å cutoff radius. With four atom types, this gives 768 elements in the descriptor. The first atom- centered function is shifted to 0.8 Å from the atomic center. The ANI potential used in this work contains three hidden layers and has the following architecture: 768:32:16:8:1, each number describing the number of neurons at each subsequent layer in the network.  
+
+<|ref|>text<|/ref|><|det|>[[114, 374, 884, 459]]<|/det|>
+The ANI potential used in this work contains three hidden layers and has the following architecture: 768:32:16:8:1. Gaussian activation functions are used in hidden layers and linear activation in the final layer.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 497, 345, 520]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[112, 528, 886, 885]]<|/det|>
+AcknowledgementsK. B., N. L., R. M., S. T., and B. N. acknowledge support from the US DOE, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under Triad National Security, LLC ("Triad") contract Grant 89233218CNA000001 (FWP: LANLE3F2). M. K. and Y. W. L. acknowledge support from the Los Alamos National Laboratory (LANL) Directed Research and Development funds. This work was performed in part at the Center for Nonlinear Studies and the Center for Integrated Nanotechnology, a US Department of Energy (DOE) and Office of Basic Energy Sciences user facility. This research used resources provided by the LANL Institutional Computing Program, which is supported by the US DOE National Nuclear Security Administration under Contract 89233218CNA000001. We also acknowledge the CCS- 7 Darwin cluster at LANL for additional computing resources.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 304, 113]]<|/det|>
+## Data Availability  
+
+<|ref|>text<|/ref|><|det|>[[115, 123, 461, 141]]<|/det|>
+Source data are provided with this Paper.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 168, 311, 192]]<|/det|>
+## Code Availability  
+
+<|ref|>text<|/ref|><|det|>[[115, 201, 790, 220]]<|/det|>
+Two implementations of the ANI neural network architecture are available online:  
+
+<|ref|>text<|/ref|><|det|>[[115, 235, 790, 254]]<|/det|>
+TorchANI (https://github.com/aiqm/torchani) and NeuroChem (https://github.com/  
+
+<|ref|>text<|/ref|><|det|>[[115, 269, 328, 287]]<|/det|>
+atomistic- ml/neurochem).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 328, 252, 351]]<|/det|>
+## References  
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+53. Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys.: Condens. Matter 29, 273002 (2017).  
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+54. Chai, J.-D. & Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections. Phys. Chem. Chem. Phys. 10, 6615–6620 (2008).  
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+55. Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007–1023 (1989).  
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+
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+<|ref|>sub_title<|/ref|><|det|>[[44, 43, 311, 71]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 131, 280, 258]]<|/det|>
+- Sl.docx- ExtendedDataFig1.jpg- ExtendedDataFig2.jpg- ExtendedDataFig3.jpg- ExtendedDataFig4.jpg
+
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preprint/preprint__06ef6f0a131181318c342eb6f78c7a4f17407366557c7de9dbe200f81c0614f5/preprint__06ef6f0a131181318c342eb6f78c7a4f17407366557c7de9dbe200f81c0614f5.mmd

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+
+# dcHiC: differential compartment analysis of Hi-C datasets  
+
+Abhijit Chakraborty  La Jolla Institute for Allergy and Immunology  
+
+Jeffrey Wang  Harvard College https://orcid.org/0000- 0002- 5707- 5113  
+
+Ferhat Ay (☑ ferhatay@lji.org)  La Jolla Institute for Allergy and Immunology https://orcid.org/0000- 0002- 0708- 6914  
+
+## Article  
+
+# Keywords:  
+
+Posted Date: April 1st, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1483135/v1  
+
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on November 11th, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 34626- 6.
+
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+
+# dcHiC: differential compartment analysis of Hi-C datasets  
+
+Abhijit Chakraborty \(^{1,\# *}\) , Jeffrey Wang \(^{1,2,\# ,S}\) , Ferhat Ay \(^{1,3*}\)  
+
+\(^{1}\) La Jolla Institute for Immunology, La Jolla, California, USA. \(^{2}\) The Bishop's School, La Jolla, California, USA. \(^{3}\) School of Medicine, University of California San Diego, La Jolla, California, USA. \(^{\#}\) Equal contribution \(^{\S}\) Current address: Harvard College, Cambridge, Massachusetts, USA. \(^{*}\) Co- corresponding authors: abhijit@lji.org, ferhatay@lji.org  
+
+## Abstract  
+
+Compartmental organization of chromatin and its changes play important roles in distinct biological processes carried out by mammalian genomes. However, differential compartment analyses have been mostly limited to pairwise comparisons and with main focus on only the compartment flips (e.g., A- to- B). Here, we introduce dcHiC, which utilizes quantile normalized compartment scores and a multivariate distance measure to identify significant changes in compartmentalization among multiple contact maps. Evaluating dcHiC on three collections of Hi- C contact maps from mouse neural differentiation \((n = 3)\) , mouse hematopoiesis \((n = 10)\) and human LCL cell lines \((n = 20)\) , we show its effectiveness and sensitivity in detecting biologically relevant differences, including those validated by orthogonal experiments. Across these experiments, dcHiC reported regions with dynamically regulated genes associated with cell identity, along with correlated changes in chromatin states, replication timing and lamin B1 association. With its efficient implementation, dcHiC not only enables high- resolution compartment analysis but also includes a suite of additional features, including standalone browser visualization, differential interaction identification, and time- series clustering. As such, it is an essential addition to the Hi- C analysis toolbox for the ever- growing number of contact maps being generated. dcHiC is freely available at https://github.com/ay- lab/dcHiC and examples from this paper can be seen at https://ay- lab.github.io/dcHiC.
+
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+## BACKGROUND  
+
+The three- dimensional organization of chromatin in the nucleus has been of interest to scientist for more than a century now. The observation that different chromosomes occupy a defined space in the nucleus dates back to Carl Rabl's work in animal cells in 1885 [1]. Since then, many experimental techniques have been developed to image and map chromatin allowing us to look at chromatin organization at an ever- increasing resolution. The greatest strides in this area have been made in the past decade following the advent of genome- wide conformation capture techniques. We now know that interphase chromosomes are folded into multiple layers of hierarchical structures. Each layer contributes to the establishment and maintenance of the epigenetic landscape that controls cellular state and function.  
+
+Among these, the megabase- scale compartmental organization of eukaryotic genomes has been shown to play a critical role in transcription, DNA replication, accumulation of mutations, and DNA methylation [2- 12]. In broad terms, two types of compartments divide the genome into regions of open and active chromatin (compartment A) versus inactive and closed chromatin (compartment B) [13]. Further analysis of each compartment revealed subsets of regions with markedly different properties within each class called sub- compartments [14, 15] as well as to a putative third class (intermediate or I) that is at the interface between A and B and is reorganized in tumors [9].  
+
+The main method to extract compartment information has been to analyze high- throughput chromosome conformation capture (Hi- C) contact maps using Principal Components Analysis (PCA) [13, 16, 17]. Briefly, this process involves distance normalization (Observed/Expected for each genomic distance) of the Hi- C contact map for each chromosome at a particular resolution (generally between 100Kb to 1Mb) followed by transformation into a correlation matrix, where each entry \((i,j)\) denotes the correlation of row \(i\) and row \(j\) (or column \(i\) and \(j\) since symmetric) of the distance- normalized Hi- C map. The eigenvalue decomposition of the correlation matrix provides the eigenvectors, and the first eigenvector or principal component (PC1) typically represents the genomic compartments A and B. If PC1 corresponds to chromosome arms or other broad patterns in the Hi- C map (e.g., copy number differences), the second principal component (PC2) is likely to represent A and B compartments. The A/B compartment labels are assigned to the positive/negative stretches of the selected PC; however, depending on the implementation of eigenvalue decomposition, it may be necessary to re- orient these assignments correctly using GC content or gene density.  
+
+Whether one is interested in the two major compartments or their more nuanced subsets, the magnitude and sign of eigenvalues derived from PCA have been the major determinants of compartment type. However, standard PCA is limited in analyzing each Hi- C contact map individually, and to date, there is no method to compare compartmentalization across multiple (>2) Hi- C datasets systematically. This is becoming
+
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+an obstacle in analyzing the ever- increasing chromatin conformation data, either from Hi- C or its variants [18- 25], generated across many cell types and conditions [26]. Technical challenges such as selecting the correct PC and sign that represents A/B compartments, and their scaling across different datasets become larger problems while comparing many Hi- C contact maps. Thus far, comparative compartment analysis has been mainly limited to examining compartment flips between two Hi- C maps at a time [27, 28].  
+
+Here, we introduce dcHiC (differential compartment analysis of Hi- C), a method that identifies statistically significant differences in compartmentalization among two or more contact maps, including changes that are not accompanied by a compartment flip. Our method implements a memory- efficient and parallelized singular value decomposition (SVD) to derive principal components (i.e., eigenvectors) followed by quantile normalization to get the comparable compartment scores across two or more than two Hi- C maps at a time (Figure 1, Step1). dcHiC then utilizes the normalized component scores to derive a multivariate distance measure [29] (Figure 1, Step2) to estimate the statistical significance of compartment differences. If available, dcHiC utilizes variance among Hi- C replicates as covariates for Independent Hypothesis Weighting (IHW) [30] to correct for multiple testing. With our methodology, compartment analysis can be conducted on Hi- C maps with or without replicates at resolutions up to 10Kb for human and mouse genomes. Further downstream, dcHiC provides a raft of analysis features, including standalone IGV browser [31] visualization of results, detection of differential interactions involving significant differential compartments, time- series clustering of compartment scores, as well as a module for determining enriched Gene Ontology terms from differential compartments.  
+
+To assess the biological relevance of the identified differences, we applied dcHiC to several different collections of Hi- C datasets across various biological conditions, including mouse neuronal development \((n = 3)\) , mouse hematopoiesis \((n = 10)\) , and a set of lymphoblastoid cell lines (LCLs) from different human populations \((n = 20)\) . Analyzing each Hi- C dataset at 100Kb and 40Kb resolution, we identified relevant compartmentalization differences reflecting the underlying biology in the respective scenarios. In the mouse neuronal differentiation model, dcHiC identified compartmental changes for loci involving critical genes associated with cellular identities in mouse embryonic stem cells (mESC) and neuronal differentiation such as Dppa2/4, Zfp42, Ephb1, and Ptn as well as GO term enrichments consistent with these cellular identities. In a ten- way comparison \((n = 10)\) of key cell types from mouse hematopoiesis; across stem cells, progenitor cells, and terminally differentiated cells, dcHiC revealed significant compartmental changes involving key genes like Sox6, Meis1, Runx2, Klf5, and many others. Across both neural and hematopoietic differentiation models, our results also highlight the importance of generally ignored compartmentalization changes within the same compartment type (within A or within B - Figure 1). We also demonstrate the biological significance of our differential calls through strong correlations with cell- type specific differences in lamin B1 association, histone modifications and gene expression. For human LCLs, comparing twenty Hi- C maps from a diverse set of donors, dcHiC confirmed the previous findings,
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+with significant enrichment of various biological signals within the differential compartments across the population.  
+
+Overall, dcHiC provides an integrative framework and an easy- to- use tool for comparative analysis of Hi- C maps and identifies biologically relevant differences in compartmentalization across multiple cell types. With immediate application to hundreds of publicly available Hi- C datasets, dcHiC will play an essential role in providing deeper insights into dynamic genome organization and its downstream effects.  
+
+## RESULTS  
+
+## dcHiC identifies compartments consistent with the PCA-based approach  
+
+As more complex experimental designs emerge that compare different Hi- C profiles, a comprehensive method to compare the spatial organization of the genome is necessary. To do this, dcHiC first employs a time- and memory- efficient R implementation of singular value decomposition (SVD) to achieve the eigenvalue decomposition of each Hi- C contact map [32]. This is followed by the automated selection to find the principal component and its sign (reoriented if needed) that best correlates with gene density and GC content per sample (Methods). The resulting compartment scores are quantile normalized and a multivariate score (Mahalanobis distance) is computed based on an initial covariance estimation. We then refine the null distribution by removing outliers before calculating new covariance estimates that will be used for computing the final statistical significance (Chi- square test) of differences in compartmentalization (Methods). dcHiC provides standalone browser visualization as well as several other features facilitating the interpretation of its results. Figure 1 summarizes the overall workflow of dcHiC.  
+
+In order to establish the validity of dcHiC results, we first compared our implementation of the eigenvalue decomposition to commonly used PCA- based approaches, a representative of which is implemented in HOMER[33]. Beyond a few differences in pre- filtering of low coverage regions, the resulting compartment scores were highly similar between dcHiC and HOMER for the 100Kb resolution (replicates combined) mouse ESC (Pearson's \(r = 0.98\) , Figure 2A) and for mouse neuronal progenitor cell (NPC) Hi- C map (Pearson's \(r = 0.96\) , Figure 2D). Similar to A/B compartment decomposition from Hi- C data, association with the nuclear lamina (or radial position) is another strong indicator of a broad- level chromatin state with heterochromatin localizing at the periphery and euchromatin at the nucleus center. Such organization is a conserved feature of eukaryotic genomes across most cell types except special cases [34, 35]. Here we used lamin B1 association profiles of ESC and NPC cell types as an independent measure of compartmentalization and compared the lamin B1 signal distribution with dcHiC and HOMER scores. As expected, both our compartment scores and HOMER results showed a strong negative correlation with lamin B1 association, confirming the previous findings [27, 36] (Figure 2B- C, 2E- F). We further plotted the chromosome 16 compartment score
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+of ESC and NPC from dcHiC, HOMER, and lamin B1 association signal. Figure 2G- H shows the lamin B1 signal and compartment features captured by dcHiC and HOMER at a genome- wide scale in ESC and NPC cell types. These results establish that dcHiC, like the existing PCA- based (HOMER) approach, accurately captures compartment patterns.  
+
+## Pairwise differential compartment analysis of mouse neuronal differentiation model  
+
+Previous studies have reported substantial compartment flips during mouse embryonic cells (ESC) to neuronal progenitor cell (NPC) transition, a well- studied in vitro differentiation system [37, 38]. These differences have been studied further using replication timing profiling, lamin B1 association mapping, and fluorescence in situ hybridization (DNA FISH) [8, 27, 36]. Therefore, we chose these two cell types to demonstrate dcHiC's utility in a pairwise comparison to replicate known compartment flips and identify significant changes that do not involve flips from one compartment type to another. We also compared differential compartment calls from dcHiC and HOMER in this pairwise setting since HOMER does not readily allow multi- way comparisons.  
+
+Overall, dcHiC identified 1981 100Kb bins with statistically significant differential compartmentalization (FDR < 0.1), covering up to 7.5% of the genome. For ESC and NPC, these differences constituted around \(\sim 37\%\) (72.8 Mb) and \(\sim 51\%\) (101.6 Mb) of A (active) compartments, respectively. The differential compartments are further subdivided into flipping (A \(\rightarrow\) B or B \(\rightarrow\) A) or matching (A \(\rightarrow\) A or B \(\rightarrow\) B) compartment transitions. We observed that \(\sim 74\%\) of all the differential compartments were flips from A to B ( \(\sim 30\%\) ) or B to A ( \(\sim 44\%\) ) compartments during ESC to NPC transition whereas the remaining \(\sim 26\%\) were within matching compartments (Figure 3A). We further classified significant changes within the same compartments (A to A or B to B) based on whether the compartment scores were higher in ESC or NPC (Figure 3B- E). For the resulting set of six different types of differential compartments, we plotted the distributions of compartment scores (Figure 3B), lamin B1 association (Figure 3C), replication timing (Figure 3D) and gene expression (Figure 3E). As expected, more euchromatic compartments were associated with lower lamin B1 attachment, early replication timing and higher gene expression. These trends were consistent for compartment flips as well as changes within matched compartments (e.g., strong A in ESC to weak A in NPC).  
+
+Next, we compared the differential ESC vs NPC compartments from dcHiC to those from HOMER. HOMER reported a total of 3,042 100Kb bins with significant differential compartmentalization (FDR < 0.05). Only 1,355 of these 100Kb bins were found to be overlapping with dcHiC differential calls (+/- 1 bin slack; Figure 3F). To compare the calls made by the two different methods, we plotted the absolute differences of laminB1 signal, replication timing and log2 gene expression values of the reported differential compartments. Figure 3G shows the absolute difference distribution of all the respective signals from all the differential compartments between ESC and NPC, while Figure 3H shows the same but only for differential compartments exclusively identified by one method. These results show that dcHiC differential compartments are significantly
+
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+(unpaired t- test p- values \(< 0.05\) ) enriched for regions with higher ESC, NPC differentials for lamin association and replication timing signals. We also performed differential expression analysis between ESC and NPC to map the differentially expressed (DE) genes (DEseq2[39], FDR \(< 0.05\) , fold change \(>4\) ) on the differential compartments. We observed that dcHiC differential compartment bins were enriched in DE genes compared to HOMER (Figure 3l). The trend was similar for bins reported exclusively by each method (Figure 3l). These observations imply that the differential calls made by dcHiC are accompanied by larger changes between ESC and NPC in other biological signals relevant to compartmentalization.  
+
+To also show utility of our tool in detecting differences at higher resolution, we ran dcHiC at 10Kb resolution to call differential compartments between ESC and NPC. We found a total of 16,581 10Kb- bins i.e., 165.81Mb differential compartments between the conditions. Among the 1,981 100Kb dcHiC differential bins, \(72\%\) exactly overlapped at least one 10Kb differential bin (over \(86\%\) within \(+ / - 200\mathrm{kb}\) ). This suggest a significant overlap across resolutions but also highlights the prevalence of regions that are detectable only at higher or lower resolution compartment analysis (Supplementary Figure 1). We also evaluated the potential of false positive discoveries from dcHiC by running it to compare replicates of the same conditions/sample. We used all four biological Hi- C replicates available for ESC in different combinations (all 1 vs 3 and 2 vs 2 combinations of splitting the replicates). When we ran dcHiC on these combinations, the number of significant compartment changes (i.e., false positives) ranged from 1 to 32 with a median value of 2 bins (compared to 1,981 100Kb bins when ESC is compared to NPC), suggesting a low false positive rate for identifying differential compartments. When we ran the same analysis using 10kb bins we identified a median value of 751 differential bins ( \(\sim 0.2\%\) of the genome) suggesting higher resolution differential analysis may be more prone to false positives.  
+
+Example genes from ESC vs NPC differential compartments: Within dcHiC's calls, we also analyzed a set of key genes known for their critical role in ESC or NPC state that have been studied extensively for changes in their nuclear organization during the transition. For instance, we analyzed a set of genes for which Fluorescence in situ Hybridization (FISH) experiments were performed to study changes in radial positioning during the ESC to NPC transition. These included pluripotency markers specifically expressed in ESCs (e.g., Zfp42 or REX1 and Dppa2/4) as well as EPH Receptor B1 (Ephb1) and other marker genes specific to neuronal differentiation. Figure 3J shows the Dppa2/4 region in mouse chromosome 16 that is shown to change radial positioning, chromatin state, lamin B1 association and replication timing during differentiation [36, 40]. Consistent with these data, both dcHiC and HOMER reports a significant shift from A (active) to B (inactive) compartment during mouse ESC to NPC differentiation (Figure 3J). In addition, dcHiC reported significant compartment changes for several other important genes that HOMER missed. Figure 3K- L displays two genes, namely Dach1 and Nedd9, which are known to play a critical role in organogenesis and signal- transduction pathways for mouse neuronal development [41, 42]. We also detected these
+
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+genes in our differential gene expression analysis of ESC vs NPC as significantly upregulated in NPC (FDR<0.05; \(>160x\) for Dac1 and \(>30x\) for Nedd9). Dac1 lies in a compartment reported as flipped from ESC- B to NPC- A by dcHiC (Figure 3K). Nedd9 gene overlaps A- compartment in both cell types but with stronger compartmentalization in NPC that is detected as a significant change by dcHiC (Figure 3L).  
+
+To see whether the compartmental changes are accompanied by specific differences in local chromatin interactions, we implemented an extension of our comparative approach to identify differences in contact counts involving the differential compartments (Methods). This feature allows users to input a set of significant chromatin interactions (e.g., from Fit- Hi- C[43]) or chromatin loops (e.g., from HiCCUPS or Mustache), which will then be filtered for their overlap with differential compartments and tested for their difference across the compared conditions. The black square boxes in Figure 4A represent the dcHiC identified differential interactions (ESC vs NPC) that are anchored in the DppA2/4 region. These interactions are identified among FitHiC2 calls [44] (FDR < 0.05) that are reported as significant in at least one replicate of ESC and/or NPC datasets. The results show that the DppA2/4 domain in NPC has specifically gained interactions with its upstream region compared to ESC while the interactions with adjacent downstream region remained unchanged, a change that can be visualized on the Hi- C map (Figure 4A). Previous studies on Ephb1 have demonstrated a significant subnuclear repositioning of the gene from the periphery to the nuclear center during ESC to NPC differentiation [36] accompanied by a higher gene expression later. A similar analysis of the Ephb1 region shows that it has enriched interactions with a pair of upstream B compartments in ESCs which are weakened in NPC where Ephb1 is transitioned to the A compartment (Figure 4B). In addition, the same region gained interactions with a downstream A compartment in NPC. These results highlight the value of differential interaction analysis coupled with differential compartmentalization to better delineate important changes in the local chromatin environment. Finally, even though the above examples highlight cases where gene expression is tightly correlated with compartment changes and radial positioning, this is not necessarily the case for all genes. Figure 4C shows the pluripotency marker gene Pou5f1/Oct4 region with ESC- specific gene expression. The radial positioning of this gene locus was shown to remain unchanged during ESC to NPC transition[36] consistent with our results (Figure 4C). Overall, dcHiC identified both known compartment flips (A to B or B to A) as well as novel compartmentalization differences within the same compartment for important genes.  
+
+## Multi-cell-type differential compartment analysis of mouse neuronal system  
+
+The same in vitro system used to differentiate from ESC to NPC also allows further differentiation of NPCs to cortical neurons or CNs [38]. This developmental lineage provides an approach to demonstrate how dcHiC uses a multivariate distance measure to compare the compartmentalization of more than two cell types simultaneously. For such multiway comparisons, dcHiC provides a quick and straightforward approach to detect outliers in compartment scores and associated differential interactions, an
+
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+approach far easier with many experiments than the traditional paradigm of taking pairwise comparisons. In this section, we first illustrate the biological significance of \(dcHiC\) 's differential compartments using multiple lines of biological data. We then demonstrate functional term enrichments, and then show specific differential genes that illustrate the application's breadth of analysis.  
+
+Applying \(dcHiC\) at 100Kb resolution on intra- chromosomal Hi- C data from ESC, NPC, and CN samples, we identified a total of 5,055 significant differential bins covering about \(19.2\%\) of the genome. Compartment A and B were evenly split for NPC and CN, whereas ESC has \(\sim 63\%\) B compartments. Overall, regions in the B compartment for each cell type were more likely to exhibit statistically significant compartment changes compared to A compartment ( \(21 - 23\%\) vs \(16 - 18\%\) ). Figure 5A summarizes the number of differential compartment bins that involve flips (A \(\rightarrow\) B or B \(\rightarrow\) A) or remained within the same compartment throughput the lineage transition. Consistent with the literature [2, 5, 45], we showed that compartmental dynamics are strongly associated with variability of gene expression and histone modifications (Figure 5B, Methods).  
+
+To further analyze these changes simultaneously, rather than one transition (or pair) at a time, we utilized time- series analysis to cluster the compartmentalization score patterns of these differential bins across (Figure 5C) and plotted the expression pattern of the overlapping genes in each cluster across three different time- points. In order to focus on relative changes in compartmentalization, we further z- transformed the quantile normalized PCA scores for each 100Kb bin across the three cell types and applied TC- seq[46] to identify 6 major clusters (Methods). Two major clusters corresponded to regions that progressively became more euchromatic (cluster 1 and 6) and one corresponded to more heterochromatic (cluster 4). We observed other clusters that corresponded to one cell type showing highly different compartmentalization with respect to the other two (e.g., clusters 3 and 5 with NPC- specific patterns). To link these compartmentalization patterns to gene function, we identified genes overlapping with each differential compartment bin for each cluster. Performing functional enrichment analysis on these gene sets[47], we identified signatures that are consistent with cellular identity of the cell type with the highest compartment z- scores (i.e., more euchromatic). For instance, for the genes overlapping with clusters 1 and 6 with compartment scores increasing from ESC to NPC to CN, the enriched terms include neurogenesis and neuronal development (Figure 5D). For cluster 3, where CN compartment scores were highest, the enriched terms (cell- cell adhesion, biological adhesion, and others) were consistent with a general pattern for genes involved in regulating cell- type specific migration and development. We also observed that cluster 3 overlapped with an important class of gene family known as protocadherins [48]. Protocadherins are highly conserved genes across species and most of them are clustered in a single genomic locus in vertebrates [49]. They are shown to be differentially expressed in individual neurons and involved in diverse neurodevelopmental processes [50]. When we repeated the functional enrichment analysis per cell type using genes overlapping A compartments with the highest compartmentalization score for that cell type compared to the other two, we also
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+observed cellular identity- related annotation terms (Supplementary Data 1). While annotations related to cell adhesion were enriched in ESC as well as CN, CN specifically showed enrichment for neurogenesis, neuron differentiation and development (Supplementary Data 1). CN, but not NPC, also showed enrichment for synaptic signaling, synapse organization and neuron projection development, potentially related to its further differentiated state with respect to NPC.  
+
+Example genes from ESC- NPC- CN differential compartments: The differential compartments captured by dcHiC encompass a variety of traditionally studied as well as more nuanced scenarios. For instance, similar to Dppa2/4, Zfp42/Rex1 is a well- studied pluripotency marker primarily expressed in undifferentiated stem cells (Figure 5E). As is the case for Dppa2/4, Zfp42 is also in a small A compartment region surrounded by large stretches of B compartments in ESC. As expected, this region flipped into B compartment in NPC and stayed that way in CN consistent with lack of gene expression in these two cell types (Figure 5F). Ptn or Pleiotrophin, on the other hand, exhibits mitogenic and trophic effects on dopaminergic neurons, and is instead a marker gene for neuronal lineage. dcHiC reported this gene in a differential compartment that is B in ESC but A in NPC and CN, in concordance with gene expression (Figure 5G- H), which fits the compartmentalization pattern of cluster 1 (Figure 5C). These two examples represent strong compartment flips from A to B or B to A. An example of a more gradual compartmental change is the CN- specific Ctnna2 gene, which functions as a linker between cadherin adhesion receptors and the cytoskeleton to regulate cell- cell adhesion and differentiation in the nervous system. The B compartment encompassing Ctnna2 in ESC gradually weakens during the ESC- NPC- CN transition leading to transcription- permissive A compartment that starts in NPC and expands further in CN (Figure 5I- J).  
+
+Compartment shifts within the same compartment are also captured by dcHiC (Figure 5K- L). Etv5 encodes for a transcription factor that plays an important role in the segregation between epiblast and primitive endoderm specification during ESC differentiation [51]. Etv5 is highly expressed in ESC but gradually loses its expression (Figure 5L) as well as strong compartmentalization during ESC- NPC- CN transition while remaining in the A compartment all the time. This locus belongs to cluster 2 with enrichment for more euchromatic association specifically in ESC consistent with the highest expression for Etv5 for this cell type. Beyond Etv5, we also found a list of 199 other genes within A compartment throughout ESC- NPC- CN transition, for which the variation in expression profile strongly correlated with changes in compartmentalization (Pearson correlation \(> 0.7\) ; Supplementary Data 2). A similar analysis within differential B compartments revealed 245 genes with strong positive correlation between expression and compartmentalization change (Supplementary Data 2). Overall, our results demonstrate that dcHiC can comprehensively analyze multiple different Hi- C maps simultaneously and identify compartmental changes involving abrupt (e.g., compartment flips) as well as gradual changes.  
+
+Differential compartment analysis of mouse hematopoietic system
+
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+The hematopoietic system is a developmentally regulated and well- characterized cell differentiation model [52, 53]. This system provides an opportunity to understand the dynamic changes in the chromatin structure together with transcriptional and other epigenetic changes during differentiation in detail. The study of the genome organization changes during this complex process—involving many different progenitors and differentiated cell types—requires a systematic approach. A recent study by Zhang et al. [28] profiled the chromatin organization in the classic hematopoietic model with ten primary stem, progenitor, and terminally differentiated cell populations from mouse bone marrow (Figure 6A). In this model, long- term hematopoietic stem cells (LT- HSC) represent the starting point of the hematopoietic hierarchy with self- renewal and multilineage differentiation capability. LT- HSC first differentiates into short- term hematopoietic stem cells (ST- HSC) and then multipotent progenitor cells (MPP). MPP cells differentiate into either common lymphoid progenitor (CLP) or common myeloid progenitor (CMP) cells. CMP then further branches out into granulocyte- macrophage progenitors (GMP) and megakaryocyte- erythrocyte progenitors (MEP). The GMP cells are then terminally differentiated into granulocytes (GR), while MEP cells are further differentiated into megakaryocyte progenitors (MKP) and then terminally differentiated into megakaryocytes (MK).  
+
+Using the Hi- C data from this system, we carried out multivariate differential analysis using dcHiC at 100Kb resolution. We detected a total of 6,061 (60.61 Mb of the genome) differential compartment bins across the ten cell types encompassing many of the genomic regions previously shown to undergo hematopoiesis- related dynamic changes [28]. Figure 6A shows an overall summary of the significant compartment changes identified by dcHiC across these cell types. We observed that the number of A to B transitions keeps increasing from the LT- HSC stage to the MEP and GMP progenitor stages. The differentiation of CMP into MEP and GMP cells represent two of the most frequent A to B transitions ( \(\sim 27.4\%\) and \(\sim 15.7\%\) A \(\rightarrow\) B transition, respectively) within the hematopoietic hierarchy, likely reflecting the need for suppression of certain transcriptional profiles for commitment into each branch. This is consistent with the largest proportion of differential B compartments in MEP ( \(\sim 46.5\%\) ) and GMP ( \(\sim 42\%\) ) compared to all other cell types. With respect to the top of the hematopoietic tree (i.e., LT- HSC), early progenitors such as MPP has 571 100Kb bins with a significant compartment flip (either A to B or B to A), whereas the differentiated cells such as MK and GR had 949, and 1,212 such bins, respectively. This confirms the gradual divergence of chromatin compartmentalization from hematopoietic stem cells as cell progress further into differentiation.  
+
+Next, similar to ESC- NPC- CN transition, we also carried out functional enrichment analysis of differential regions with the highest A compartment score in each group and specific cell type. Figure 6B- E show these enrichments for four different stages of hematopoiesis (pre- bifurcation stage: LT- HSC, ST- HSC, progenitor stage: MPP, CMP, granulocyte branch: GMP, GR and the terminally differentiated Granulocytes or GR) with respect to the rest and for a specific cell type within each of these stages highlighting
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+biologically relevant processes in each case. For example, morphogenesis and development- related biological processes were enriched in the overall pre- bifurcation stage (set of genes with the highest A compartment score in either LT- HSC, ST- HSC) (Figure 6B) and the progenitor stage cells were enriched in morphogenesis, adhesion and migration related terms (Figure 6C). The granulocyte branch (GMP and GR) as well as the terminally differentiated granulocytes (GR) showed significant enrichments related to activation and regulation of neutrophils and granulocytes (Figure 6D- E). For the megakaryocyte branch (MEP, MKP, MK), however, we did not observe any statistically significant GO term biological process enrichments.  
+
+Example genes from mouse hematopoiesis differential compartments: After investigating the significance of the differential compartments from a high level, we examined the genes overlapping with the differential compartments involved in hematopoietic lineage differentiation and chromatin dynamics [54]. Figure 6F shows a set of important genes overlapping with differential compartments from our multivariate analysis. Zhang et al. showed that increased gene- body associating domain (GAD) scores are linked to active transcription and indicate cell- type specific features. We identified 12 out of 16 such differential GAD genes between ST- HSC and GR as part of dcHiC differential compartments identified across the system (FDR < 0.1; Figure 6F, marked by cyan stars). In addition, previous analysis by Lara- Astiaso et al. [54] also reported a set of critical genes for hematopoietic lineage differentiation. We identified 12 of these 26 genes within differential compartments (FDR < 0.1; Figure 6F, marked by red stars) supporting dcHiC's ability to pick up changes in regions harboring genes that are dynamically regulated during hematopoiesis. Among these genes, one example is the transmembrane transporter gene Abca13, which was the exclusive differential A compartment within GR but in the B compartment for all other cell types (Figure 6G). Other notable examples include Meis1, a transcription factor required to maintain hematopoiesis under stress and over the long term [55]. Notably, this particular example was a significant change solely within the A compartment (Figure 6H). Apart from Meis1, dcHiC also detected differences for other transcription factors like Runx2 and Sox6 that are essential for progenitor cell differentiation (Figure 6F) [56, 57]. We also identified Myc, known for its role in balancing hematopoietic stem cell self- renewal and differentiation [58] adjacent to a significant change within the A compartment that encompasses the Pvt1 gene. The long non- coding RNA Pvt1 harbors intronic enhancers that interact with Myc and promote Myc expression during tumorigenesis [59]. Overall, this complex system demonstrates the utility of dcHiC's multivariate compartment analysis, which discovers important changes in compartmentalization without requiring a large number of pairwise comparisons.  
+
+## Multiway differential compartment analysis across human-derived cell lines  
+
+Measuring the extent to which genetic variation across individuals influences chromatin features including 3D organization has significant implications in our understanding of human disease. Previous studies have revealed that the presence of variations such as
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+quantitative trait loci (QTLs) can affect histone modifications, transcription factor binding, and enhancer activity across populations [60, 61]. More recent work by Gorkin et al. [62] studied variation in chromatin conformation across individuals from different human populations. Using dilution Hi- C, they profiled lymphoblastoid cell lines (LCLs) derived from 13 Yoruban individuals, one Puerto Rican trio, one Han Chinese trio, and one European LCL (GM12878). They measured significant differences in 3D genome organization across individuals using different metrics, including Directionality Index (DI), Insulation Score (INS), Frequently Interacting REgions (FIREs), and compartment scores [62]. The study also carried out differential analysis of compartments across individuals and provided both compartment scores and "variable regions" at 40kb resolution (except for chromosomes 1, 9, 14, 19 and X). In order to minimize technical variation and ensure a fair comparison, we started directly from the 40Kb compartment scores reported by Gorkin et al. and ran \(dcHiC\) on these values (starting from quantile normalization). \(dcHiC\) allows direct utilization of pre- computed compartment scores, such as in this case, when available.  
+
+The Venn diagram (Figure 7A) of differential compartments from \(dcHiC\) and Gorkin et al. using the same set of 40Kb genomic bins shows a large overlap between the methods. A large fraction of \(dcHiC\) calls (7524 out of 7,876 or \(\sim 96\%\) ) were also reported by the original paper. However, Gorkin et al. reported an additional 765Mb of the human genome as variable compartment regions (Additional_file_4.xlsx from the original publication filtered for phenotype \(= PC1\) and discover_set \(= 20\) LCLs), which amounts to \(\sim 11K\) more bins at 40Kb resolution. To further study the overlap and differences between the two approaches, we plotted two statistical significance score distributions (- log10 of the adjusted p- value calculated by Gorkin et al.) for regions that the Gorkin study reported as differential, one with regions overlapping with \(dcHiC\) calls and the other of non- overlapping regions (Figure 7B). Variable compartments from the previous study that were not deemed significant by \(dcHiC\) have substantially lower statistical significance, as computed by the original paper suggesting \(dcHiC\) calls are enriched for stronger differences. Next, we compared the full- set of differential compartments called by both methods and their fraction covering each individual chromosome (Figure 7C). The figure shows that Gorkin et al. calls cover a larger fraction of smaller chromosomes, with more than half the entire length reported as a significant variable compartment for some chromosomes (e.g., chr18). \(dcHiC\) , on the other hand, has a more uniform representation of differential compartments across chromosomes with differential fractions ranging between \(10\%\) to \(20\%\) for most chromosomes. Lastly, we compared the top 5000 differential compartment bins ranked by their significance scores from each approach. Figure 7D shows that about \(\sim 61\%\) of these top 5000 differential bins are identical, suggesting substantial differences in each approach's ranking with respect to statistical significance (Spearman rank correlation of 0.55). Although the ranking is substantially different between the methods, the overlapping fraction of the top 5000 differential compartments for \(dcHiC\) had more significant differences (Figure 7E). Using other variable chromatin organization metrics from the Gorkin paper, we observed that \(dcHiC\) calls are more enriched in FIRE- QTLs (Figure 7F) as well as DI- QTLs (Figure 7G).
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+Preferential enrichment of such signals suggests a better concordance of \(dChIC\) identified compartmental differences and chromatin organization variability at other levels across individuals.  
+
+Example genes from differential compartments among human- derived LCLs: Figures 7H- I show two examples of a variable region (overlapping with NR2F2, and THEMIS/PTPRK genes) identified by \(dChIC\) . The NR2F2 region was investigated using FISH by Gorkin et al., which confirmed individual- specific changes in 3D chromatin conformation. Two of the individuals from the cohort (YRI- 4 and YRI- 8) showed enriched interaction between the NR2F2 FISH and another placed upstream as compared to YRI- 3 and YRI- 5. The variability of 3D genome organization among individuals is also apparent from compartment scores for this region. The NR2F2 locus across the cohort is found to be a part of strong B- compartment for all Yoruban individuals except for YRI- 4, YRI- 8 and YRI- 9 (Figure 7H). Figure 7I shows another example of such variable region with coordinated changes in epigenetic marks across individuals with support from differential compartments documented in the previous paper. Gorkin et al. have identified variations in different epigenetic marks like H3K4me1 and H3K27ac, binding of CTCF and most importantly gene expression pattern within this region across different individuals (YRI- 2 and 13 vs 11 and 12). The PC score track in Figure 7I also supports the previous findings as some of the individuals from YRI population, especially YRI- 3, YRI- 5, YRI- 11, YRI- 12 showed a clear flip from B to A compartment and both our approach and Gorkin et al. labeled this region as a differential compartment. Taken together, \(dChIC\) identified fewer differential compartment bins with enrichment towards capturing regions with higher variability in different levels of chromatin organization and those with additional evidence for difference among individuals.  
+
+## DISCUSSION  
+
+This paper presents a new application, \(dChIC\) , to compare compartmentalization across Hi- C datasets. \(dChIC\) employs principal component analysis followed by quantile normalization of the compartment scores and a multivariate distance measure to systematically identify significant compartmentalization changes among multiple contact maps. By facilitating comparative analysis across multiple integrated datasets, it helps identify biologically relevant differential compartments with statistical confidence scores. Along with conventional pairwise differential analysis, \(dChIC\) allows a single multivariate differential comparison of Hi- C datasets, utilizing replicates when available, and provides an efficient approach to analyze multiple Hi- C maps without the need for generating many different combinations.  
+
+We applied \(dChIC\) to various biological scenarios, ranging from neuronal and hematopoietic stem cell differentiation in mice to Hi- C data from different human populations. Our results confirmed that \(dChIC\) detects known compartmental changes among cell types, including those previously validated to play a role in neuronal and hematopoietic differentiation. When comparing \(dChIC\) to existing approaches, we showed that it identifies regions with higher differences in replication timing, Lamin B1 signals,
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+and differentially expressed genes, suggesting better prioritization of relevant biological regions. Even though differences of compartmentalization between ESC and NPC generally aligned with changes in Lamin B1 association, a recent work highlighted the importance of nucleolus association in revealing layers of compartmentalization with distinct repressive chromatin states [63]. Our initial analysis showed that over \(10\%\) of all significant compartment differences we found between ESC and NPC belongs to nucleolus associated domains (NADs) that were deemed exclusive to either ESC or NPC [63] providing an explanation for a subset of differences in compartmentalization during differentiation. Expanding to a three- way \((n = 3)\) mouse neuronal differentiation model, we showed that dcHiC continues to systematically identify critical biological marker genes and can recover cell- specific functions from differential compartment analysis alone. Across dcHiC's differential compartments, we observed significant and relevant enrichment of biological processes such as neuron differentiation in NPC and CN cells. More broadly, dcHiC's differential compartments also compellingly aligned with changes in Lamin B1, gene expression, and histone modification data. Taken together, these results demonstrate dcHiC's ability to find regions with the most biologically variable compartmentalization across the genome.  
+
+The hierarchical mouse hematopoietic stem cell differentiation model, consisting of ten different cell types with Hi- C data, provided a unique opportunity to demonstrate the utility of dcHiC. A ten- way multivariate differential comparison of the hematopoietic system revealed previously known lineage- specific critical genes encompassing the differential compartments. Notably, we identified vital transcription factors like Sox6, Runx2, Meis1, Foxo1, and many other critical genes like Abca13, by solely analyzing the differential calls. Our functional enrichment analysis of gene sets overlapping with the lineage- specific differential compartments reported from the apex to the bottom of the hematopoietic model- tree reconfirmed that genome compartments play a contributory role in determining the accessibility of genes in specific cell types. Measuring the extent of compartment variability across twenty- cell human types also highlighted our method's novel utility and strength. Most dcHiC calls overlapped with a subset of variable compartments reported by the previous study, but dcHiC calls were enriched for higher variability. Similarly, the regions encompassing Frequently Interacting Region (FIRE)- QTLS and Directionality Index (DI)- QTLS defined by the previous study were more enriched in the top differential compartment calls of dcHiC compared to the top calls defined in the previous study. The analysis also demonstrated an important feature of dcHiC: the ability to directly utilize previously computed compartment scores to run differential compartmentalization analysis.  
+
+The framework we developed here provides a systematic way to identify differential compartments and visualize these differences in different scenarios, including multi- way, hierarchical and time- series setting. Although we focused on human and mouse Hi- C data in this work, our method is readily applicable to Hi- C data or its variants (e.g., Micro- C [64]) derived from any organism with compartmental genome organization. With hundreds of publicly available Hi- C datasets in the 4D Nucleome Data Portal and others published every day, dcHiC will play an essential role in comparative analysis of high- level genome
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+organization. As single- cell Hi- C data starts providing better resolution, dcHiC and methods derive from it will be critical to enable compartment comparison across thousands of cells.  
+
+## METHODS  
+
+## Data processing, result generation, and visualization  
+
+Hi- C data: All the Hi- C data, except for the Gorkin et. al. 2019 were mapped on mm10 reference genome and processed using HiCpro (v2.7.9) pipeline [65]. The raw Hi- C interaction maps retrieved after HiC- Pro processing are used for downstream compartment score calculation by dcHiC. In the section analyzing data from the Gorkin et. al. study, we used the provided compartment scores (40Kb resolution) across all samples mapped on hg19 reference genome [62]. Statistically significant interactions were called using FitHiC2 [44] with default parameters and an FDR threshold of 0.05 for each replicate and/or each sample.  
+
+RNA- seq data: The RNA- seq data from Bonev et. al. 2017 [38] study concerning mouse neural development were processed using our in- house and open- source RNA- seq processing pipeline (https://github.com/ay- lab/LJI RNA_SEQ_PIPELINE_V2.git), which utilizes STAR [66]. The differential gene expression analysis between mouse ESC and NPC cell lines (two- replicates each) was performed using DESeq2 method [39] with all the default parameter settings.  
+
+ChIP- seq data: For ChIP- seq peak calling (H3K27ac, H3K4me3 and H3K4me1 histone marks), we first mapped the respective fastq files on the mm10 genome using the bowtie2 [67] and generated the corresponding bam files (MAPQ \(>20\) ). The aligned files were then used as input to the MACS2 program [68] to call peaks (p- value \(< 1e - 5\) ) against their respective input controls. The continuous ChIP- seq peaks were then merged and the unique set was mapped to the 100Kb differential compartments to calculate the average number of peaks. The enrichment of signal difference is calculated by first quantifying the absolute difference in signal (number of ChIP- seq peaks and gene expression TPM values) within ESC to NPC differential and non- differential compartments. The enrichment of absolute signal difference between the differential and non- differential compartments between ESC and NPC was then compared by un- paired T- test.  
+
+Time- series analysis: The time- series clustering was generated using the TCseq package [46]. For gene- term enrichment analysis, the differential compartments are scanned against the gene coordinates of the respected genome defined by the user using 'bedtools map' function [69]. The unique overlapping set of genes are then extracted and are used for GO biological function enrichment analysis using the ToppGene suite API function or directly from their webserver [47].
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+IGV Browser visualization: dcHiC generates a Javascript based stand-alone dynamic IGV-HTML page to visualize the compartments and differential compartment calls, with an option to add additional tracks.  
+
+## Computation and quantile normalization of compartment scores for comparison  
+
+To perform principal component analysis (PCA) on Hi- C maps dcHiC utilizes the singular value decomposition (SVD) implementation of the bigstatsr R package [32]. The input to SVD is \(K\) different distance- normalized chromosome- wise correlation matrices \((X_{1},X_{2},X_{3}\ldots X_{K})\) for each Hi- C data. For each such matrix, dcHiC finds the decomposition:  
+
+\[X_{K} = U_{K}\cdot \Gamma_{K}\cdot V_{K}^{T}\quad with U_{K}^{T}\cdot U_{K} = V_{K}^{T}\cdot V_{K} = I \quad (1)\]  
+
+The matrices \(U_{K}\) and \(V_{K}\) store the left and right singular vectors of the matrix \(X_{K}\) . The singular values of \(X_{K}\) are stored in the diagonal matrix \(\Gamma_{K}\) . The principal components for each matrix are then obtained as:  
+
+\[P C_{K} = X_{K}\cdot \mathrm{V}_{K} \quad (2)\]  
+
+The eigen- decomposition of the \(K^{th}\) correlation matrix provides the eigenvectors, and the sign of the first eigenvector or principal component \((PC1_{K})\) typically represents the genomic compartments A and B for the \(K^{th}\) chromosome. If \(PC1_{K}\) corresponds to chromosome arms or other broad patterns in the Hi- C matrix, the second principal component \((PC2_{K})\) may represent A and B compartments. The A/B compartment labels are assigned to the positive/negative stretches of the selected \(PC_{K}\) depending on the implementation of eigen- decomposition. It may be necessary to re- orient these assignments and select the correct \(PC_{K}\) using GC content or gene density. Thus, before the quantile normalization step, dcHiC performs an intermediate correlation analysis of the first two principal component scores (user- defined) of each chromosome per sample against the GC content and gene density of that chromosome. The principal component which obtains the highest sum of GC content and gene density correlation is considered the compartment score, and the A/B compartments of the selected principal components are assigned based on the GC content correlation (A compartment and positive values representing higher GC content). These generate a set of compartment score vectors representing each sample (M samples) for a given chromosome \((C_{1},C_{2},C_{3}\ldots C_{M})\) . Once the properly labeled compartment scores are obtained, dcHiC performs quantile normalization (QN) using the limma package [70] on the set \((C_{1},C_{2},C_{3}\ldots C_{M})\) per chromosome to even out the scaling across the group for downstream analysis.  
+
+\[(q_{1},q_{2},q_{3}\ldots q_{M}) = QN(C_{1},C_{2},C_{3}\ldots C_{M}) \quad (3)\]  
+
+In the case of samples with replicates, dcHiC performs the above steps by including each replicate from each sample (i.e., quantile normalize all replicates together). dcHiC then
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+calculates the average of quantile normalized values of each genomic bin across all the replicates of a given sample to represent sample- wise compartment scores.  
+
+## Differential compartment identification  
+
+Mahalanobis distance (MD) is a multivariate statistical measure of the extent to which the multivariate data points are marked as outliers, based on a Chi- square distribution [71]. The Mahalanobis distance of a point \(i\) from a multi- dimensional distribution defined by set \(s\) (sample) and its center \(\mu\) is defined as:  
+
+\[M D_{s a m p l e}^{i} = (s_{i} - \mu_{i})^{T}\cdot \Sigma^{-1}\cdot (s_{i} - \mu_{i}) \quad (4)\]  
+
+Where \(s_{i} = (q_{1}^{i}, q_{2}^{i}, q_{3}^{i} \ldots q_{M}^{i})\) is the set of quantile normalized compartment score distributions and \(\mu_{i} = (\mu_{1}^{i}, \mu_{2}^{i}, \mu_{3}^{i} \ldots \mu_{M}^{i})\) is the set of weighted centers for each point \(i\) from set \(s\) . The inverse of the covariance matrix of set \(s\) is represented as \(\Sigma^{- 1}\) . The weighted centers \(\mu_{i}\) is calculated as:  
+
+\[\mu_{i} = s_{i} * w_{i} \quad (5)\]  
+
+Where \(0 \leq w_{i} \leq 1\) is the cumulative Normal distribution probability associated with the maximum z- score among the z- scores of all samples for \(i\) :  
+
+\[w_{i} = \max \{Pr(Z_{M}^{i})\} \quad (6)\]  
+
+Where \(Z_{N}^{i}\) , the z- score for point \(i\) for sample \(N\) is computed as:  
+
+\[Z_{N}^{i} = \frac{(d_{N}^{i} - \overline{d_{N}})}{\sigma(d_{N})} \quad (7)\]  
+
+Here \(\overline{d_{N}}\) and \(\sigma (d_{N})\) represent the average distance and standard deviation within sample \(N\) among all \(d_{N}^{i}\) values that are computed as:  
+
+\[d_{N}^{i} = \frac{\sqrt{\Sigma_{t = 1}^{M}(q_{t}^{i} - q_{N}^{i})^{2}}}{(M - 1)} \quad (8)\]  
+
+Essentially, the approach provides more weight to the points that are distant from others among the samples (further from the diagonal) than to points that are closer together in the multi- dimensional space (close to the diagonal). Equation (4) is the standard MD formulation, which we modify using the weighted centers as computed through Equations (6) to (8).  
+
+In order to increase the sensitivity of our difference detection, we implemented an outlier removal step that eliminates genomic bins (or points) with high MD (as computed above) at the initial pass (1st pass). We use a pre- defined upper- tail critical value of the chi- square distribution with \(df\) degrees of freedom as our threshold for outlier removal (default value we used is: \(MD threshold \sim \chi_{0.90,df}^{2}\) ). We then recompute the covariance matrix \(\Sigma^{- 1}\) after
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+removal of these outliers and calculate the MD (through Equation (4)) one more time for each point \((2^{\mathrm{nd}}\) pass). The significance of the corresponding \(MD_{sample}^{i}\) \((2^{\mathrm{nd}}\) pass) is calculated from the critical chi- square distribution table as \(\chi^{2}(MD_{sample}^{i},df)\) using \(pchisq\) function of R programming language followed by multiple testing correction to retrieve adjusted p- values.  
+
+In case of samples \((s)\) with replicates \((r)\) \(dchIC\) calculates an additional covariate \(MD_{replicate}\) and applies Independent Hypothesis Weighting (IHW) to adjust the \(p\) - values.  
+
+The covariate is calculated as:  
+
+\[MD_{repl}^{i} = \{(s_{i}^{T} - s_{i}^{T}\mu_{i})^{T}\cdot (diag(\Sigma^{-1}))\cdot (s_{i}^{T} - s_{i}^{T}\mu_{i})|s\in (1,2\dots M),r\in (1,2\dots R)\} (9)\]  
+
+Where \(R\) is the total number of all replicates combined across all samples, \(s_{i}^{T} =\) \((r_{1}^{i},r_{2}^{i},r_{3}^{i},\dots r_{R}^{i})\) is the set of quantile normalized compartment score distributions of all replicates from samples \(s\in (1,2\dots M)\) and \(\bar{s}_{i}^{T}\mu_{i} = (\frac{1}{s}\mu_{i},\frac{2}{s}\mu_{i},\frac{3}{s}\mu_{i},\dots \frac{5}{s}\mu_{i})\) is the is the set of weighted centers for each point \(i\) from \(R\) replicates. \(diag\) is an operation that masks all non- diagonal entries (sets to zero) of the covariance matrix.  
+
+The weighted centers \(\bar{s}_{i}^{T}\mu_{i}\) are calculated as:  
+
+\[\bar{s}_{i}^{T}\mu_{i} = s_{i}^{T}*(1 - \bar{s}_{i}^{T}w_{i}) \quad (10)\]  
+
+Where \(0\leq \bar{s}_{i}^{T}w_{i}\leq 1\) is calculated as:  
+
+\[\bar{s}_{i}^{T}w_{i} = max\{Pr(\bar{s}_{i}^{T}Z_{R})\} \quad (11)\]  
+
+And \(\bar{s}_{i}^{T}Z_{i}\) for replicate \(r\) of sample \(s\) is computed as:  
+
+\[\begin{array}{l}{{\bar{s}_{i}^{T}d_{i}=\frac{\sqrt{\Sigma_{t=1}^{R}(r_{i}^{t}-r_{R}^{t})^{2}}}{(R-1)}}}\\ {{\bar{s}_{i}^{T}Z_{i}=\frac{(\bar{s}_{i}^{T}d_{i}-\overline{\bar{s}_{i}^{d}})}{\sigma(\bar{s}_{i}^{d})}}}\end{array} \quad (13)\]  
+
+Here the variables are defined as similar to Equations (7) and (8) and \(R\) is used to represent the number of replicates of the same sample (i.e., distances across replicates of different samples are not taken into account).  
+
+This approach provides more weight to the features that are closer to each other within replicates of a sample (close to the diagonal) and as opposed to the calculation across different samples (Equation (5)) where higher weights were given to the points with samples distant from each other (far from the diagonal). The significance of the corresponding \(MD\) for each point are calculated using chi- square distribution as mentioned above. \(dchIC\) applies the IHW approach to adjust the p- values using FDR
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+correction obtain from \(MD_{sample}\) using \(MD_{replicate}\) replicate variation measure as a covariate.  
+
+## Differential interaction identification  
+
+Using the same Mahalanobis distance (MD) measure, \(dcHiC\) enables the user to find differential interactions across samples that are either linking two differential compartments together or a differential compartment with other parts of the same chromosome. The goal of this feature is to provide more information on the chromatin organization changes related to or correlated with compartmental differences. For this analysis, we have used FitHiC2 to call significant interactions (FDR \(5\%\) ) for each sample or replicate (when available), but users are free to provide their own set of interaction or loop calls from any other tool. Using these calls, \(dcHiC\) first finds the interaction subset that overlaps with differential compartments (on either end or both) using the bedtools 'paitobed' function. \(dcHiC\) utilizes the \(log2(Observed / Expected)\) values of a chromatin interaction \(i\) from to perform differential interaction calling as:  
+
+\[MD_{interaction}^{i} = (oe_{i}^{s} - \mu^{s})^{T}\cdot \Sigma^{-1}\cdot (oe_{i}^{s} - \mu^{s})\mid s\in (1,2,3\dots M) \quad (14)\]  
+
+where \(oe_{i}^{s}\) represents \(log2(Observed / Expected)\) values for chromatin interactions of locus pair \(i\) for sample \(s\) and \(\mu^{s}\) represents the vector of centers of distance normalized interactions from sample \(s\) . Here \(\Sigma^{- 1}\) represents the inverse of covariance matrix of interactions among the samples. The approach provides more weight to the interactions that are distant from the expected interaction strength among the samples than to the interactions that are closer to the expected range in the multi- dimensional space. The significance of the corresponding \(MD_{interaction}^{i}\) is calculated from the critical chi- square distribution table as \(\chi^{2}(MD_{interaction}^{i},df)\) using \(pchisq\) function embedded within R programming environment followed by the FDR correction to retrieve adjusted p- values.  
+
+## Availability of data and materials  
+
+A Python/R implementation of \(dcHiC\) is freely available at https://github.com/ay- lab/dcHiC. This application is compatible with Hi- C data in HiC- Pro, .hic, and .cool formats. The data used in this study are available at the following GEO accession numbers: GSE96107 (mESC- NPC- CN), GSE152918 (mouse hematopoiesis), GSE128678 (human LCLs). These are also available in Supplemental Table 1 (see Supplementary Information). All reported compartments for all cell lines, multivariate differential scores, RNA- seq, and ChIP- seq data used in this manuscript can be viewed interactively at: ay- lab.github.io/dcHiC. These standalone HTML files employ \(dcHiC\) 's visualization utility through IGV browser.
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+## FIGURE LEGENDS  
+
+Figure 1: Outline of the method. The figure panel shows the dcHiC workflow in two steps. In step 1, dcHiC calculates the principal components followed by the quantile normalization of the compartment scores across all input Hi- C data. In the step 2, for each genomic bin, dcHiC calculates a Mahalanobis distance, which is a statistical measure of the extent to which each bin is a multivariate outlier with respect to the overall multivariate compartment score distribution across all input Hi- C maps (Methods). dcHiC then utilizes the Mahalanobis distance to assign a statistical significance using Chi- square test (p- value) for each compartment bin and employs independent hypothesis weighting (IHW - when there are replicate samples) or FDR (when no replicates are available) correction on these p- values. dcHiC outputs a standalone dynamic IGV web browser view and enables the user to integrate other datasets into the same view for an integrated visualization.  
+
+Figure 2: Comparison of dcHiC compartment scores with HOMER compartment scores and Lamin B1 association data. (A- B) Genome- wide comparison of dcHiC compartment scores against HOMER compartment scores and Lamin B1 profiles for mouse ESC. (C) Comparison between HOMER compartment scores and Lamin B1 association. (D- F) Plots similar to (A- C) but for NPC Hi- C data. Pearson correlation value between two axes are reported for each plot. (G- H) Browser views of the compartment scores and Lamin B1 signal for a chromosome 16 region with arrows pointing to some small differences among the compartment scores of dcHiC and HOMER.  
+
+Figure 3: Pairwise differential compartment analysis between ESC and NPC. (A) The breakdown of the numbers of differential compartment calls (100Kb resolution) belonging to different types. (B- E) The distributions of compartment scores, Lamin B1, replication timing, association and gene expression across different subtypes of differential compartment calls made by dcHiC. Strong (s) and Weak (w) were used to indicate the relative compartment strength (or absolute value) between the two cell types. (F) The Venn- diagram shows the overlap between dcHiC and HOMER differential compartment calls. (G- H) The absolute difference of Lamin B1, replication timing signal and gene expression values (TPM) overlapping with all and exclusive differential compartments identified by dcHiC and HOMER, respectively (statistical significance was calculated by unpaired T- test). (I) The average number of differential (DE) genes overlapping with differential compartment bins (100Kb) identified by dcHiC and HOMER. (J- L) dcHiC differential compartments involving three DE genes: Dppa2/4, Dach1 and Nedd9.  
+
+Figure 4: Differences in local chromatin interactions of differential compartments. Detailed browser views (top), Hi- C contact maps (mid) and differential chromatin interactions (bottom) of three gene loci – (A) Dppa2/4, (B) Ephb1 and (C) Oct4. Visible changes in interactions involving Dppa2/4 locus and Ephb1 locus are highlighted through each plot. Although Oct4 shows a dramatic change in gene expression, the region does
+
+<--- Page Split --->
+
+not alter its radial position within nucleus (FISH experiments) which is also consistent with the lack of change in compartmentalization as reported by \(dcHiC\) .  
+
+Figure 5: Three- way differential compartment analysis of ESC, NPC, and CN. (A) The breakdown of the numbers of differential compartment calls belonging to different types. (B) The enrichment of signal difference in different histone marks and gene expression in \(dcHiC\) differential bins with compartment flips (A \(\rightarrow\) B or B \(\rightarrow\) A) compared to bins with non- significant compartment flips. (C) Time- series clustering of normalized compartment scores into six different clusters from the three cell types along with their overlapping gene expression profile. For the clustering analysis, the quantile normalized PCA scores for each 100Kb bin across ESC- NPC- CN were further z- transformed to focus on relative changes in compartmentalization. (D) Gene term enrichment results of GO biological functions from genes overlapping with cluster 1, 3 and 6 compartments. (E- L) Differential compartments overlapping with representative genes in each of the cell types shown along with the differential chromatin interactions involving the respective compartments and gene expression values (TPM) across the ESC- NPC- CN transition for four example genes each representing one cluster pattern.  
+
+Figure 6: Ten- way multivariate differential compartment analysis of mouse hematopoiesis. (A) Summary of overall compartment decomposition and significant compartment changes observed across the 10 cell types. The orange and blue arrows represent A to B and B to A compartment flips, respectively. The numbers next to the arrows represent the total number of flipping compartments and the numbers within the parentheses next to it shows the significantly differential flipping compartments. The bottom- right plot shows the proportion of A and B bins among \(dcHiC\) differential compartments for each cell type. Figure adopted from Zhang et. al. [28]. (B- E) The functional enrichment of genes overlapping with differential compartments from 10- way comparison that have the strongest A compartment scores in either (B) LT- HSC or ST- HSC, (C) MPP or CMP, (D) GMP or GR, or (E) GR alone. (F) Differential compartments identified by \(dcHiC\) overlap a set of critical genes previously known to play role in mouse hematopoiesis. (G) An IGV browser snapshot of Abca13 gene and its overlapping differential compartment across the ten cell types. The Abca13 gene is exclusively found to be a part of A- compartment in GR while in the B- compartment in all other cell types. (H) An IGV browser view surrounding Meis1 genic region. This region is overlapping with the A compartment for all the cell types but with varying magnitude of strength. \(dcHiC\) captured this region as a differential compartment.  
+
+Figure 7: Twenty- way multivariate differential compartment analysis of human lymphoblastoid cell lines (LCLs). (A) A Venn diagram of the overlap of differential compartments called by \(dcHiC\) and the variable compartment regions by a previous study (Gorkin et. al, 2019). (B) The distribution of - log10(p- adj) values of \(dcHiC\) - overlapping and non- overlapping variable regions calculated by the previous study. (C) The total number of chromosome- wise differential compartments and the fraction of each chromosome (except those filtered by Gorkin et. al. 2019) covered by such calls for \(dcHiC\) and the
+
+<--- Page Split --->
+
+previous study. (D- E) Venn diagrams of overlapping compartments of the top 5000 differential region from both the approaches and the \(- \log 10(p - adj)\) value distribution of the overlapping and non- overlapping set from \(dcHiC\) . (F- G) The cumulative number of FIRE- QTLs and DI- QTLs overlapping the top 5000 differential compartment calls by \(dcHiC\) and Gorkin et al. (H- I) Two differential compartments overlapping genic regions of \(NR2F2\) and THEMIS/PTPRK. Both of the genes and especially \(NR2F2\) region was shown to be a variable region across the population through FISH experiments in the previous study (Gorkin et. al, 2019).  
+
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+56. de Bruijn M, Dzierzak E: Runx transcription factors in the development and function of the definitive hematopoietic system. Blood 2017, 129:2061-2069.57. Dumitriu B, Patrick MR, Petschek JP, Cherukuri S, Klingmuller U, Fox PL, Lefebvre V: Sox6 cell-autonomously stimulates erythroid cell survival, proliferation, and terminal maturation and is thereby an important enhancer of definitive erythropoiesis during mouse development. Blood 2006, 108:1198-1207.58. Wilson A, Murphy MJ, Oskarsson T, Kaloulis K, Bettess MD, Oser GM, Pasche AC, Knabenhans C, Macdonald HR, Trumpp A: c-Myc controls the balance between hematopoietic stem cell self-renewal and differentiation. Genes Dev 2004, 18:2747-2763.59. Jin K, Wang S, Zhang Y, Xia M, Mo Y, Li X, Li G, Zeng Z, Xiong W, He Y: Long non-coding RNA PVT1 interacts with MYC and its downstream molecules to synergistically promote tumorigenesis. Cell Mol Life Sci 2019, 76:4275-4289.60. McVicker G, van de Geijn B, Degner JF, Cain CE, Banovich NE, Raj A, Lewellen N, Myrthil M, Gilad Y, Pritchard JK: Identification of genetic variants that affect histone modifications in human cells. Science 2013, 342:747-749.61. Kasowski M, Kyriazopoulou-Panagiotopoulou S, Grubert F, Zaugg JB, Kundaje A, Liu Y, Boyle AP, Zhang QC, Zakharia F, Spacek DV, et al: Extensive variation in chromatin states across humans. Science 2013, 342:750-752.62. Gorkin DU, Qiu Y, Hu M, Fletez-Brant K, Liu T, Schmitt AD, Noor A, Chiou J, Gaulton KJ, Sebat J, et al: Common DNA sequence variation influences 3-dimensional conformation of the human genome. Genome Biol 2019, 20:255.63. Bersaglieri C, Kresoja-Rakic J, Gupta S, Bar D, Kuzyakiv R, Panatta M, Santoro R: Genome-wide maps of nucleolus interactions reveal distinct layers of repressive chromatin domains. Nat Commun 2022, 13:1483.64. Hsieh TH, Weiner A, Lajoie B, Dekker J, Friedman N, Rando OJ: Mapping Nucleosome Resolution Chromosome Folding in Yeast by Micro-C. Cell 2015, 162:108-119.65. Servant N, Varoquaux N, Lajoie BR, Viara E, Chen CJ, Vert JP, Heard E, Dekker J, Barillot E: HiC-Pro: an optimized and flexible pipeline for Hi-C data processing. Genome Biol 2015, 16:259.66. Dobin A, Gingeras TR: Mapping RNA-seq Reads with STAR. Curr Protoc Bioinformatics 2015, 51:11-14 11-11 14 19.67. Langmead B, Salzberg SL: Fast gapped-read alignment with Bowtie 2. Nat Methods 2012, 9:357-359.68. Feng J, Liu T, Qin B, Zhang Y, Liu XS: Identifying ChIP-seq enrichment using MACS. Nat Protoc 2012, 7:1728-1740.69. Quinlan AR, Hall IM: BEDTools: a flexible suite of utilities for comparing genomic features. Bioinformatics 2010, 26:841-842.70. Ritchie ME, Phipson B, Wu D, Hu Y, Law CW, Shi W, Smyth GK: limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Res 2015, 43:e47.71. Brereton RG: The Mahalanobis distance and its relationship to principal component scores. Journal of Chemometrics 2015.
+
+<--- Page Split --->
+
+## Figures  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+Outline of the method. The figure panel shows the dcHiC workflow in two steps. In step 1, dcHiC calculates the principal components followed by the quantile normalization of the compartment scores across all input Hi- C data. In the step 2, for each genomic bin, dcHiC calculates a Mahalanobis distance, which is a statistical measure of the extent to which each bin is a multivariate outlier with respect to the overall multivariate compartment score distribution across all input Hi- C maps (Methods). dcHiC then utilizes the Mahalanobis distance to assign a statistical significance using Chi- square test (p- value) for each compartment bin and employs independent hypothesis weighting (IHW – when there are replicate samples) or FDR (when no replicates are available) correction on these p- values. dcHiC outputs a standalone dynamic IGV web browser view and enables the user to integrate other datasets into the same view for an integrated visualization.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+Comparison of dChIC compartment scores with HOMER compartment scores and Lamin B1 association data. (A- B) Genome- wide comparison of dChIC compartment scores against HOMER compartment scores and Lamin B1 profiles for mouse ESC. (C) Comparison between HOMER compartment scores and Lamin B1 association. (D- F) Plots similar to (A- C) but for NPC Hi- C data. Pearson correlation value between two axes are reported for each plot. (G- H) Browser views of the compartment scores and Lamin B1 signal for a chromosome 16 region with arrows pointing to some small differences among the compartment scores of dChIC and HOMER.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>  
+
+Pairwise differential compartment analysis between ESC and NPC. (A) The breakdown of the numbers of differential compartment calls (100Kb resolution) belonging to different types. (B- E) The distributions of compartment scores, Lamin B1, replication timing, association and gene expression across different subtypes of differential compartment calls made by \(dcHiC\) . Strong (s) and Weak (w) were used to indicate the relative compartment strength (or absolute value) between the two cell types. (F) The Venn-
+
+<--- Page Split --->
+
+diagram shows the overlap between dcHiC and HOMER differential compartment calls. (G-H) The absolute difference of Lamin B1, replication timing signal and gene expression values (TPM) overlapping with all and exclusive differential compartments identified by dcHiC and HOMER, respectively (statistical significance was calculated by unpaired T-test). (I) The average number of differential (DE) genes overlapping with differential compartment bins (100Kb) identified by dcHiC and HOMER. (J-L) dcHiC differential compartments involving three DE genes: DppA2/4, Dach1 and Nedd9.  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4 </center>  
+
+Differences in local chromatin interactions of differential compartments. Detailed browser views (top), HiC contact maps (mid) and differential chromatin interactions (bottom) of three gene loci – (A) DppA2/4, (B) Ephb1 and (C) Oct4. Visible changes in interactions involving DppA2/4 locus and Ephb1 locus are highlighted through each plot. Although Oct4 shows a dramatic change in gene expression, the region
+
+<--- Page Split --->
+
+does not alter its radial position within nucleus (FISH experiments) which is also consistent with the lack of change in compartmentalization as reported by \(dcHiC\) .  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5 </center>  
+
+Three- way differential compartment analysis of ESC, NPC, and CN. (A) The breakdown of the numbers of differential compartment calls belonging to different types. (B) The enrichment of signal difference in
+
+<--- Page Split --->
+
+different histone marks and gene expression in dcHiC differential bins with compartment flips (A à B or B à A) compared to bins with non- significant compartment flips. (C) Time- series clustering of normalized compartment scores into six different clusters from the three cell types along with their overlapping gene expression profile. For the clustering analysis, the quantile normalized PCA scores for each 100Kb bin across ESC- NPC- CN were further z- transformed to focus on relative changes in compartmentalization. (D) Gene term enrichment results of GO biological functions from genes overlapping with cluster 1, 3 and 6 compartments. (E- L) Differential compartments overlapping with representative genes in each of the cell types shown along with the differential chromatin interactions involving the respective compartments and gene expression values (TPM) across the ESC- NPC- CN transition for four example genes each representing one cluster pattern.
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Figure 6 </center>  
+
+Ten- way multivariate differential compartment analysis of mouse hematopoiesis. (A) Summary of overall compartment decomposition and significant compartment changes observed across the 10 cell types. The orange and blue arrows represent A to B and B to A compartment flips, respectively. The numbers next to the arrows represent the total number of flipping compartments and the numbers within the parentheses next to it shows the significantly differential flipping compartments. The bottom- right
+
+<--- Page Split --->
+
+plot shows the proportion of A and B bins among dcHiC differential compartments for each cell type. Figure adopted from Zhang et. al. [28]. (B- E) The functional enrichment of genes overlapping with differential compartments from 10- way comparison that have the strongest A compartment scores in either (B) LTHSC or ST- HSC, (C) MPP or CMP, (D) GMP or GR, or (E) GR alone. (F) Differential compartments identified by dcHiC overlap a set of critical genes previously known to play role in mouse hematopoiesis. (G) An IGV browser snapshot of Abca13 gene and its overlapping differential compartment across the ten cell types. The Abca13 gene is exclusively found to be a part of A- compartment in GR while in the B- compartment in all other cell types. (H) An IGV browser view surrounding Meis1 genic region. This region is overlapping with the A compartment for all the cell types but with varying magnitude of strength. dcHiC captured this region as a differential compartment.
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Figure 7 </center>  
+
+Twenty- way multivariate differential compartment analysis of human lymphoblastoid cell lines (LCLs). (A) A Venn diagram of the overlap of differential compartments called by \(dcHiC\) and the variable compartment regions by a previous study (Gorkin et. al, 2019). (B) The distribution of - log10(p- adj) values of \(dcHiC\) overlapping and non- overlapping variable regions calculated by the previous study. (C) The total number of chromosome- wise differential compartments and the fraction of each chromosome (except
+
+<--- Page Split --->
+
+those filtered by Gorkin et. al. 2019) covered by such calls for \(dcHiC\) and the previous study. (D- E) Venn diagrams of overlapping compartments of the top 5000 differential region from both the approaches and the \(- \log 10(p\) - adj) value distribution of the overlapping and non- overlapping set from \(dcHiC\) (F- G) The cumulative number of FIRE- QTLs and DI- QTLs overlapping the top 5000 differential compartment calls by \(dcHiC\) and Gorkin et al. (H- I) Two differential compartments overlapping genic regions of \(NR2F2\) and THEMIS/PTPRK. Both of the genes and especially \(NR2F2\) region was shown to be a variable region across the population through FISH experiments in the previous study (Gorkin et. al, 2019).  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryData1. xlsx SupplementaryData2. xlsx Reportingsummary002. pdf dcHiCdemo.zip SupplementaryInformation.docx
+
+<--- Page Split --->

preprint/preprint__070706503cff2b0c5895a72491f41d6927ffe121f452603fa7f93aef50b5eb1a/images_list.json

@@ -0,0 +1,168 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1. Construction of PuuE tube via NIPAD. | a, AF2 prediction of the heterodimeric peptide pair, M3L2 (yellow) and p66α (blue). b, Crystal structure of PuuE (PDB ID: 3CL6). C-terminus positions are circled. Detailed structure, face, side, and back are shown for clarity. c, Schematic diagram of the protein sequence (top) and the AF2-predicted structures of PuuE-M and PuuE-p (bottom). PuuE-M and PuuE-p are coloured yellow and blue to match the respective peptides and overall structure to clear the tube structure (d). The peptide parts, M3L2 and p66α, are highlighted in darker colours. d, Left, predicted model of the tubular assembly consisting of PuuE-M and PuuE-p. Right, brief schematic diagram of how many proteins (n) form a system of tube structures. e, nsTEM images of tubular assemblies constructed from PuuE-M and PuuE-p; 12.5 μM PuuE-M and 12.5 μM PuuE-p in NaCl (+) buffer was incubated at 40 °C for 24 h and imaged via nsTEM. Scale bars, 1 μm (white), 50 nm (black).",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
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+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2. Condition optimisation for PuuE tube assembly. | a, b, The kinetics of tubular assembly. nsTEM images of tubular assembly (a) and length analysis (b). c, nsTEM images of tubular assemblies with varying NaCl concentration. d, nsTEM images showing the reversibility of tube structures with changing NaCl concentration. e, Tube length analysis of nsTEM images. For tube length analysis, tubes were picked up and calculated from 5k images at each step; 150 tubes from the longest tube length were used at each data point. \\*\\*\\* p<0.001 (Welch's t-test). Scale bar, 1 μm.",
+    "footnote": [],
+    "bbox": [
+      [
+        293,
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+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_1b.jpg",
+    "caption": "Fig. 3. Structural characterisation of PuuE tube. | a, 2D class-averaged images of tube structures. The population of each structure was determined from the total pickings of 206,658 tube segments. Scale bar, 500 Å. b 3D reconstructed models of tube structures with \\(C_4\\) , \\(C_5\\) , and \\(C_6\\) symmetries. The fitting results suggest that PuuE-p is less likely to fit into units located inside the tube structure and more likely to fit into units located on the outside. Based on the predictions, the units were colour-coded as shown in Fig. 1c. For visibility, only the molecular model of the PuuE (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. c, Time-lapse images of random bending of the tube structures monitored by TIRFM. Top: snapshots at the starting point (0 sec) and after 4 sec (top). Bottom: enlarged images of tubes in green or orange rectangles in the top images, showing the dynamic flexibility of tube structures between 0 to 4 sec (0.4 sec per image). Scale bar, 5 μm. d, Left, a relationship between contour length (L) and mean square of end-to-end distance (<R²>) of the tube structures for estimation of the persistence length (Lp). The continued lines represent fitting curves (black for PuuE tube, red for actin filament) to experimental data (black open circle for PuuE tube, red cross mark for actin filament). Right, comparison of persistence length with cytoskeletal elements. PuuE tube (PT, black) and actin filaments (AF, red) were determined in this study (A wider range of plots is shown in Supplementary Fig. 1b). Intermediate filaments (IF, blue) and microtubules (MT, green) are taken from ref. 41 and 38, respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
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+        881,
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+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Extended_Data_Figure_9.jpg",
+    "caption": "Fig. 4. Emulation of actin filament by D-loop grafting. | a, Schematic representations of PuuE(D-loop)-M. The position of D-loop graft (red) is indicated by protein sequence (top) and the AF2-predicted structure (bottom). b, nsTEM images of tubes with a helical conformation composed of PuuE(D-loop)-M and PuuE-p. The helical pattern of two (centre) or three (right) intertwined tubes is shown in the high-magnification image. c, nsTEM images showing the reversibility of tube structure with helical conformations by temperature change. d, Representative cryo-EM images (top) and 2D class-averaged images (bottom) of helical tube structures. e, Representative cryo-EM image (top) and 2D class-averaged image of tube structure with \\(C_3\\) symmetry. Tube structures with other symmetries found in this study are shown in Extended Data Fig. 9. f, 3D reconstructed model of tube structure with \\(C_3\\) symmetry. For visibility, only the PuuE structure (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. g, Fitting of AF2-predicted model of PuuE-p into the 3D reconstructed model. The fitting results suggest that PuuE-p is unlikely to fit in the units located inside the tube structure; it is better accommodated by the units on the outside. Based on this prediction, the units in f are colour-coded as described in Fig. 1c. 6xHis-TEVcs region of the PuuE-p model is not shown to improve visibility. Scale bars, 1 \\(\\mu \\mathrm{m}\\) (white), 100 nm (black), 10 nm (grey).",
+    "footnote": [],
+    "bbox": [
+      [
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Extended_Data_Figure_2.jpg",
+    "caption": "Extended Data Fig. 2. | nsTEM characterisation of PuuE-M, PuuE-p, and the mixture for PuuE-M and PuuE-p. a, 12.5 \\(\\mu \\mathrm{M}\\) PuuE-M or b, 12.5 \\(\\mu \\mathrm{M}\\) PuuE-p in NaCl (+) buffer was incubated at \\(40^{\\circ}\\mathrm{C}\\) for 24 h. Scale bars, 200 nm (white), 50 nm (black). c, Dependency of PuuE tube assemblies on protein concentration. 250 nM (top), 2.5 \\(\\mu \\mathrm{M}\\) (middle), and 12.5 \\(\\mu \\mathrm{M}\\) (bottom) of PuuE-M and PuuE-p each in NaCl (+) buffer was incubated at \\(40^{\\circ}\\mathrm{C}\\) for 24 h and imaged by nsTEM. The tube structure observed in the nsTEM images was flexible as it was curved and collapsed. Scale bars, 1 \\(\\mu \\mathrm{m}\\) (white), 50 nm (black).",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Extended_Data_Figure_3.jpg",
+    "caption": "Extended Data Fig. 3. | Time dependence of PuuE tube assemblies and their stability over time. a, 12.5 \\(\\mu \\mathrm{M}\\) of PuuE-M and PuuE-p each in \\(\\mathrm{NaCl}(+)\\) buffer was incubated at \\(40^{\\circ}\\mathrm{C}\\) for indicated time points and imaged via nsTEM. b, After \\(24\\mathrm{h}\\) of tube formation, the sample was kept at \\(25\\pm 1^{\\circ}\\mathrm{C}\\) for the indicated time and imaged using nsTEM. Tube structures remained unchanged after 2 weeks and even after 1 month, suggesting stability. Scale bars, \\(1\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
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+      ]
+    ],
+    "page_idx": 24
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "C4 tube: 2D classifications (2 rounds): 51,590 segments",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 25
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "C5 tube: 2D classifications (2 rounds): 44,868 segments",
+    "footnote": [],
+    "bbox": [
+      [
+        210,
+        268,
+        520,
+        415
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "3D Refinement \\((C_4)\\) : 12,052 segments Post-processing",
+    "footnote": [],
+    "bbox": [
+      [
+        536,
+        310,
+        808,
+        416
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "C6 tube: 2D classification (1 round): 117,636 segments",
+    "footnote": [],
+    "bbox": [
+      [
+        210,
+        434,
+        500,
+        592
+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "3D Refinement \\((C_5)\\) : 12,572 segments Post-processing",
+    "footnote": [],
+    "bbox": [
+      [
+        536,
+        434,
+        808,
+        592
+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "3D classification \\((C_1)\\) : 39,841 segments",
+    "footnote": [],
+    "bbox": [
+      [
+        177,
+        633,
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+      ]
+    ],
+    "page_idx": 28
+  }
+]

preprint/preprint__070706503cff2b0c5895a72491f41d6927ffe121f452603fa7f93aef50b5eb1a/preprint__070706503cff2b0c5895a72491f41d6927ffe121f452603fa7f93aef50b5eb1a.mmd

@@ -0,0 +1,371 @@
+
+# Protein design of two-component tubular assemblies like cytoskeletons  
+
+Yuta Suzuki suzuki.yuta.2m@kyoto- u.ac.jp  
+
+Kyoto University https://orcid.org/0000- 0002- 4863- 4585  Masahiro Noji  Kyoto University  Yukihiko Sugita  Institute for Life and Medical Sciences, Kyoto University https://orcid.org/0000- 0001- 6861- 4840  Yosuke Yamazaki  RIKEN  Makito Miyazaki  RIKEN https://orcid.org/0000- 0002- 4603- 851X  
+
+## Article  
+
+# Keywords:  
+
+Posted Date: October 21st, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4976952/v1  
+
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.  
+
+Version of Record: A version of this preprint was published at Nature Communications on July 22nd, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 62076- 3.
+
+<--- Page Split --->
+
+# Protein design of two-component tubular assemblies like cytoskeletons  
+
+2  
+
+3 Masahiro Noji \(^{1,2,3}\) , Yukihiko Sugita \(^{4,5,6}\) , Yosuke Yamazaki \(^{7,8}\) , Makito Miyazaki \(^{6,7,8,9}\) , and Yuta Suzuki \(^{3,6,9}\) .\*  
+
+4 \(^{1}\) Research Fellow of Japan Society for the Promotion of Science, Japan; \(^{2}\) Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan; \(^{3}\) Institute for Integrated Cell- Material Sciences, Kyoto University, Kyoto, Japan; \(^{4}\) Institute for Life and Medical Sciences, Kyoto University, Kyoto, Japan; \(^{5}\) Graduate School of Biostudies, Kyoto University, Kyoto, Japan; \(^{6}\) Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan; \(^{7}\) Graduate School of Science, Kyoto University, Kyoto, Japan; \(^{8}\) RIKEN Center for Biosystems Dynamics Research, Yokohama, Japan; \(^{9}\) PRESTO, JST, Saitama, Japan  
+
+Recent advances in protein design have ushered in an era of constructing intricate higher- order structures \(^{1}\) . Nonetheless, orchestrating the assembly of diverse protein units into cohesive artificial structures akin to biological assembly systems, especially in tubular forms, remains elusive. To this end, here, we introduce the Nature- Inspired Protein Assembly Design (NIPAD), a novel methodology that utilises two distinct protein units to create unique tubular structures under carefully designed conditions. These structures demonstrate dynamic flexibility similar to that of actin filaments, with cryo- electron microscopy revealing diverse morphologies, like microtubules. By mimicking actin filaments, helical conformations were incorporated into tubular assemblies, thereby enriching their structural diversity. Notably, these assemblies can be reversibly disassembled and reassembled in response to environmental stimuli, including changes in salt concentration and temperature, mirroring the dynamic behaviour of natural systems. NIPAD combines rational protein design with biophysical insights, leading to the creation of biomimetic, adaptable, and reversible higher- order assemblies. This approach deepens our understanding of protein assembly design and complex biological structures. Concurrently, it broadens the horizons of synthetic biology and material science, holding significant implications for unravelling life's fundamental processes and pioneering new applications.  
+
+Life phenomena rely on the dynamic and reversible assembly and disassembly of various higher- order protein assemblies. Actin filaments \(^{2,3}\) and microtubules \(^{4,5}\) in the cytoskeleton and the capsid proteins of viruses \(^{6,7}\) are examples of such naturally occurring structures. These are tightly regulated in function and complexity. Synthesising higher- order structures of heterogeneous protein units poses a significant challenge, particularly regarding replicating the diversity and flexibility inherent to natural assemblies. Although recent advances in computational design have enabled the creation of artificial higher- order
+
+<--- Page Split --->
+
+protein structures from two protein components<sup>8- 10</sup>, the design of heterogeneous higher- order protein assemblies with the flexibility and reversible assembly/disassembly characteristics of natural structures, especially tube structures reminiscent of the cytoskeleton, remains a formidable challenge.  
+
+Herein, we introduced Nature- Inspired Protein Assembly Design (NIPAD), a novel methodology that draws inspiration from the principles underlying natural protein complexes. By integrating rational protein design with biophysical insights to optimise assembly conditions, NIPAD recapitulates flexibility and reversible assembly principles. We employed NIPAD to create a novel assembly of two distinct protein units, successfully forming unique two- component tube structures. This development represents a significant step toward replicating the properties of complex natural structures at the molecular level.  
+
+## Results and discussion  
+
+## The concept of NIPAD  
+
+In developing the protein components for NIPAD, we employed rational design principles with hints from natural biological systems, integrating naturally occurring ‘heterolinkers’ with ‘scaffold proteins’ to streamline design. For the heterolinker, we chose the heterodimeric peptide pair ‘MBD3L2 (M3L2)/p66α’ (Fig. 1a). Our choice of M3L2/p66α was influenced by its role in the MBD2- NuRD complex, where the ‘MBD2/p66α’ anti- parallel coiled- coil domain is essential for complex assembly<sup>11</sup>. Given the moderate denaturation midpoint temperature \((T_{\mathrm{m}})\) of M3L2/p66α \((T_{\mathrm{m}} = 35^{\circ}\mathrm{C})\) compared to MBD2/p66α \((T_{\mathrm{m}} = 65^{\circ}\mathrm{C})^{12}\) , we anticipated that M3L2/p66α would provide a balance between stability and reversible assembly control through temperature modulation. We then sought to identify a scaffold protein that could connect the heterolinker in the simplest manner possible. The positions of connecting sites at the corners of such scaffold proteins facilitate the desired assembly formation<sup>13</sup>. Therefore, we chose the ‘Pseudomonas fluorescens PuuE allantoinase (PuuE)’, a homotetramer with \(C_4\) symmetry where each C- terminus is located at each vertex of the quaternary structure (Fig. 1b)<sup>14</sup>. This arrangement enabled straightforward genetic fusion of heterolinkers to the scaffold’s C- termini, leveraging specificity and reversibility of heterolinker interactions to drive assembly formation. This approach simplifies the assembly process and enhances expression and purification efficiency for each protein unit, preventing spontaneous assembly and ensuring the controlled formation of higher- order structures.  
+
+We constructed protein units ‘PuuE- M’ and ‘PuuE- p’ through genetic engineering, fusing M3L2 and p66α to the C- terminus of PuuE, respectively (Fig. 1c). AlphaFold2 (AF2)<sup>15,16</sup> modelling suggested a configuration with a relatively flexible orientation of M3L2 in PuuE- M, whereas a highly constrained orientation of p66α in PuuE- p (Extended Data Fig. 1). Owing to the constrained orientation of PuuE- p, an
+
+<--- Page Split --->
+
+angular interface was formed between PuuE- M and PuuE- p, and we predicted that assembly of these two units would form a tubular structure (Fig. 1d). Additionally, depending on the number of PuuE- M and PuuE- p units, different tubular structures were expected. Protein expression in Escherichia coli provided both constructs in a soluble form, facilitating their purification. In isolation, neither protein unit exhibits self- assembly (Extended Data Fig. 2a, b). However, when combined under optimised conditions (discussed in the following section), we successfully observed the expected chessboard- patterned tube (PuuE tube) using negative- stain transmission electron microscopy (nsTEM) (Fig. 1e, Extended Data Fig. 2c). Although previous studies have assembled cages \(^{8,9}\) , sheets \(^{10}\) , and three- dimensional (3D) crystals \(^{17}\) using two- component protein systems, this study is unique in that tube structures were successfully created.  
+
+## The condition design of tubular assemblies  
+
+Based on established principles observed in biological systems, including actin filaments \(^{18,19}\) , microtubules \(^{20,21}\) , and amyloid fibrils \(^{22,23}\) , protein concentration, temperature, time, and salinity have a significant influence on assembly formation. Thus, we carefully tailored assembly conditions to exploit the complex interactions between these factors. This approach allowed us to optimise experimental conditions for constructing the desired tubular structures.  
+
+First, we focused on the dependency of PuuE tube assembly on protein concentration (Extended Data Fig. 2c). Mixing PuuE- M and PuuE- p at a concentration of \(250~\mathrm{nM}\) each (considering tetramer equivalence) led to the formation of tubular structures after an incubation period of \(24\mathrm{~h}\) at \(40^{\circ}\mathrm{C}\) , consistent with the dissociation constant \((K_{\mathrm{d}})\) for M3L2/p66α dimer formation, which is approximately \(268~\mathrm{nM}^{12}\) . Increasing protein concentration to \(2.5~\mu \mathrm{M}\) markedly enhanced the quantity and length of formed tubular structures. Elevating the concentration to \(12.5~\mu \mathrm{M}\) for each component significantly increased tube formation efficiency, underscoring the concentration- dependent nature of PuuE- M- and PuuE- p- facilitated tubular assembly.  
+
+Next, PuuE tube formation kinetics were investigated. The incubation of mixtures containing \(12.5~\mu \mathrm{M}\) of each protein at \(40^{\circ}\mathrm{C}\) resulted in the formation of nascent tube structures within \(30~\mathrm{min}\) , evolving into distinguishable tubes spanning several hundred nanometres to \(1\mu \mathrm{m}\) in length within \(1 - 2\mathrm{~h}\) (Fig. 2a, b, Extended Data Fig. 3a). Over time, these tubes elongated, reaching several micrometres in length after \(24\mathrm{~h}\) and extending up to approximately \(5\mu \mathrm{m}\) after \(48\mathrm{~h}\) . Once formed, the tubes remained structurally stable for at least 1 month at \(25\pm 1^{\circ}\mathrm{C}\) (Extended Data Fig. 3b).
+
+<--- Page Split --->
+
+We then explored the influence of temperature on PnuE tube formation (Extended Data Fig. 4a). While the melting temperature of the M3L2/p66α dimer is around \(35^{\circ}\mathrm{C}\) , tube assembly was hardly observed at sufficiently lower temperatures of \(20 - 25^{\circ}\mathrm{C}\) , even after \(24\mathrm{h}\) of incubation. Conversely, temperatures near \(T_{\mathrm{m}}\) , specifically between 30 and \(40^{\circ}\mathrm{C}\) , markedly promoted tube formation. Therefore, temperatures below \(T_{\mathrm{m}}\) may excessively enhance the binding force between M3L2 and p66α, causing kinetic entrapment of assemblies. However, temperatures close to \(T_{\mathrm{m}}\) modulate this binding force, allowing the dynamic rearrangement of M3L2/p66α interactions under thermal fluctuations, thus facilitating the assembly of thermodynamically stable, ordered structures. This principle is consistent with general crystallisation theories \(^{24,25}\) and reports on the formation of ordered structures in natural protein assemblies \(^{22,23,26}\) . Importantly, temperatures above \(45^{\circ}\mathrm{C}\) led to thermal denaturation and aggregation of PnuE- M ( \(T_{\mathrm{m}} = 46.2^{\circ}\mathrm{C}\) ) and PnuE- p ( \(T_{\mathrm{m}} = 48.1^{\circ}\mathrm{C}\) ), significantly diminishing tube formation capabilities (Extended Data Fig. 4b, c). This finding implies that the original concept of tube formation with reversible temperature control was not realised.  
+
+## Reversibility of tubular assemblies  
+
+Finally, we examined the effects of salt concentration on PnuE tube assembly. We prepared mixtures with different NaCl concentrations ranging from 0 to \(400\mathrm{mM}\) and incubated them at \(40^{\circ}\mathrm{C}\) for \(24\mathrm{h}\) . Tube formation was clearly observed within the NaCl concentration window of \(50 - 200\mathrm{mM}\) , with no tube formation detected outside this range (Fig. 2c, Extended Data Fig. 5a). Since both PnuE- M ( \(\mathrm{pI} = 6.44\) ) and PnuE- p ( \(\mathrm{pI} = 6.02\) ) were similarly charged under \(\mathrm{pH}8.0\) , tube formation at low salt concentrations was likely inhibited by electrostatic repulsion. Conversely, moderate electrostatic shielding facilitated by \(50 - 200\mathrm{mM}\) NaCl likely provided conducive conditions for tube assembly, whereas higher NaCl concentrations may have induced excessive shielding or aggregation due to salting out, inhibiting tube formation. This observation aligns with known phenomena in protein crystallisation, where electrostatic shielding above a certain threshold can prevent crystal growth \(^{17,27 - 29}\) , although crystals formed by a combination of electrostatic and hydrophobic interactions can remain stable up to approximately \(200\mathrm{mM}\) NaCl \(^{30}\) . The association of M3L2/p66α involves both electrostatic and hydrophobic interactions \(^{12}\) , consistent with the latter scenario.  
+
+The salt- dependent PnuE tube formation and the dynamic nature of PnuE- M/PnuE- p interactions near their \(T_{\mathrm{m}}(35^{\circ}\mathrm{C})\) led us to hypothesise that tubes could undergo reversible disassembly and reassembly in response to changes in NaCl concentration. Confirming our hypothesis, tubes initially formed in \(100\mathrm{mM}\) NaCl solution were significantly shortened when subjected to solvent exchange with \(0\mathrm{mM}\) NaCl buffer (NaCl (- ) buffer) and subsequent incubation at \(40^{\circ}\mathrm{C}\) for \(24\mathrm{h}\) (Fig. 2d, e, Extended Data Fig. 5b). Subsequent
+
+<--- Page Split --->
+
+solvent exchange with \(100\mathrm{mMNaCl}\) buffer \((\mathrm{NaCl} + )\) buffer) resulted in notable tube reassembly. This salt- concentration- driven reversibility, although divergent from the initial temperature- controlled reversibility hypothesis, marks a significant advance in artificial protein assembly design, allowing for the biomimetic replication of dynamic structural changes under relatively mild conditions, akin to the behaviour of actin filaments in cellular structures \(^{18,19}\) . Unlike the irreversible aggregation observed in amyloid structures, our assemblies exhibit a reversible and dynamic assembly process akin to the cytoskeleton behaviour, successfully demonstrating the potential for the biomimetic replication of natural cellular dynamics under controlled conditions.  
+
+## Diversity and flexibility of tubes  
+
+Based on these findings, we determined the ideal conditions for PuuE tube formation in \(100\mathrm{mMNaCl}\) at \(40^{\circ}\mathrm{C}\) for \(24\mathrm{h}\) . To further characterise the structural features of tubes formed under these conditions, cryo- electron microscopy (cryo- EM) was employed (Extended Data Fig. 6, Extended Data Table 1). Analysis of 2D class- averaged images revealed a spectrum of tube diameters and symmetries similar to the diversity observed in microtubules \(^{31 - 34}\) (Fig. 3a). From these images, we successfully reconstructed the 3D structures with \(C_4\) , \(C_5\) , and \(C_6\) symmetries within tube structures (Fig. 3b). Insights from the PuuE crystal structure \(^{14}\) , notably its unique central indentation on the back surface (Fig 1b), allowed us to deduce that PuuE units are alternately oriented face- to- back across all 3D models. Additionally, cryo- EM analysis suggested that connection flexibility allowed the contraction of the entire tube structure (Extended Data Fig. 6, Supplementary Movie 1). Although definitive conclusions are difficult owing to its inherent flexibility, the comparison of the cryo- EM 3D reconstruction with the AF2- predicted model of PuuE- p suggests that PuuE- p is less likely to fit inside the tube structure and instead fits better on the outside (Supplementary Movie 2). Furthermore, tubes with larger diameters, presumably having \(C_7\) to \(C_{10}\) symmetries, were identified at low resolution, likely owing to the flexibility of connection sites influencing tube structure. In fact, nsTEM and cryo- EM images frequently showed tubes appearing bent or compressed (Extended Data Fig. 2–6). In contrast to prior strategies by engineering on scaffold proteins itself to create higher- order protein assemblies \(^{8 - 10,13,35}\) , NIPAD integrates a flexible linker with the scaffold protein, resulting in varied structures and arrangements among higher- order assemblies. This variation in tube diameter, akin to that observed in microtubules \(^{31 - 34}\) , is presumably a hallmark of NIPAD.  
+
+To further explore PuuE tube structure flexibility, we labelled tubes with Alexa Fluor 488 succinimidyl ester and observed them in real- time using total internal reflection fluorescence microscopy (TIRFM). Tube structures were constrained in the evanescent field by the depletion effect of methylcellulose contained in the observation buffer and underwent thermally driven two- dimensional random bending (Fig. 3c,
+
+<--- Page Split --->
+
+Supplementary Fig. 1a, Supplementary Movie 3). Analysis of the fluctuation in shape yielded the persistence length \((L_{\mathrm{p}})\) of \(19.7 \mu \mathrm{m}\) (Fig. 3d, Supplementary Fig. 1b). \(L_{\mathrm{p}}\) is the mean length over which a semiflexible polymer remains straight, characterising polymer stiffness<sup>36</sup>. The \(L_{\mathrm{p}}\) value of the tube structures is nearly equal to that of actin filaments measured in this study, \(12.5 \mu \mathrm{m}\) (Fig. 3d), and previously reported values of \(9 - 20 \mu \mathrm{m}^{37}\) . Microtubules have much longer persistence lengths \((0.1 - 10 \mathrm{mm})^{38 - 40}\) . Conversely, intermediate filaments, another cytoskeletal fibre structure, typically have shorter persistence lengths \((< 1 \mu \mathrm{m})^{41}\) . Therefore, the tube structure is as flexible as actin filaments, more flexible than microtubules, and stiffer than intermediate filaments.  
+
+## Emulation of actin filaments  
+
+Finally, we sought to modify the morphology of PuuE tube assemblies. Specifically, we hypothesised that grafting the D- loop of actin onto PuuE- M would produce tubes with a helical conformation reminiscent of actin filaments. The D- loop plays an important role in helical actin filament formation via hydrophobic pockets<sup>42- 45</sup>. The hydrophobic nature of a prominent indentation on the 'back' side of PuuE (Extended Data Fig. 7a) guided our hypothesis. The loop structure on the back side of PuuE- M was chosen as the grafting site for the D- loop, and the 'PuuE(D- loop)- M' fusion construct was constructed (Fig. 4a). When PuuE(D- loop)- M was expressed in \(E\) . coli, it was found in the soluble fraction and was purified as PuuE- M. Since PuuE(D- loop)- M has a lower thermal stability \((T_{\mathrm{m}} = 35.6^{\circ}\mathrm{C})\) than PuuE- M \((T_{\mathrm{m}} = 46.2^{\circ}\mathrm{C}\) , Extended Data Fig. 4b, 7b), we performed sample incubation at a lower temperature \((30^{\circ}\mathrm{C})\) . Although PuuE(D- loop)- M alone did not assemble, its combination with PuuE- p replicated the PuuE tube and introduced novel helical patterns, with two or three tubes intertwined (PuuE D- loop tube), as verified via nsTEM (Fig. 4b, Extended Data Fig. 7c). The emergence of helical formations, absent in the PuuE- M and PuuE- p mixtures, clearly stems from D- loop integration. While the D- loop likely plays a crucial role in the helical formation of actin filaments<sup>42- 45</sup>, its complete mechanism remains unclear. Our study, by successfully grafting the D- loop to replicate actin- like helical structures, offers a novel perspective on its significance. This approach confirms the critical role of the D- loop in helical conformations and opens new avenues for understanding the intricate design principles of actin filaments.  
+
+As mentioned above, the helical conformation of tube structures is thought to arise from hydrophobic interactions, which are inherently sensitive to temperature and weaken at lower temperatures<sup>46- 48</sup>. This led us to posit that alterations in temperature can serve as reversible switches for disassembly and reassembly. Notably, exposing the samples to \(0^{\circ}\mathrm{C}\) for 1 h suggested a dissociation of the helical conformations and hinted at a possible breakdown of the tubular structures (Fig. 4c, Extended Data Fig. 7d). Remarkably, when these disassembled samples were reintroduced to \(30^{\circ}\mathrm{C}\) for \(24 \mathrm{h}\) , the elongated tubular formations
+
+<--- Page Split --->
+
+with helical conformations were restored. By grafting D- loop, the tube structure could form helical conformations and acquired a new temperature- dependent reversibility. This thermal responsiveness parallels the behaviour of microtubules<sup>20,21,49</sup>, underscoring the ability of the NIPAD approach to mimic the dynamic properties of biomolecular assemblies in artificial protein design to create complex higher- order protein structures. This dual responsiveness (salt and temperature dependence) enhances the biomimetic potential of our design, which is a promising avenue for advanced applications in synthetic biology and materials science.  
+
+To determine the intricate helical configurations, structural analyses were performed using cryo- EM (Fig. 4d, Extended Data Fig. 8, Extended Data Table 1). In addition to the inherent flexibility of the tube structure, the ability of tubes to form helical bundles introduces an additional layer of complexity to the structural analysis. This complexity is underscored by cryo- EM results, which render a detailed analysis of these higher- order structures particularly challenging. However, analysis of 2D class- averaged images of the helical structures revealed double and triple helical tubes, which was consistent with the nsTEM observation (Fig. 4b, d, Extended Data Fig. 7c, 8). Moreover, the tube structures forming these helices seem to show a thinner diameter of approximately \(24~\mathrm{nm}\) , which does not align with any of the original PuuE tubes with diameters starting at \(28.6~\mathrm{nm}\) (Fig. 3b, Extended Data Fig. 6). Therefore, an attempt was made to elucidate the characteristics of the tube structures forming the helical conformations by employing temperature- induced structural disassembly (Fig. 4c). The cryo- EM sample was initially prepared at \(25 \pm 1^{\circ}\mathrm{C}\) to prevent disassembly; however, to unwind the helical structures, the sample was briefly chilled on ice for approximately \(1\mathrm{~h}\) . By observing these chilled samples with cryo- EM, we successfully identified a new tube structure with \(C_3\) symmetry (Fig. 4e, f, Extended Data Table 1) in addition to the previously observed structures (Extended Data Fig. 9). A comparison of this tube structure with \(C_3\) symmetry with the structures forming the helical conformations indicated a match, suggesting that the tubes forming the helical conformation have indeed \(C_3\) symmetry (Fig. 4d bottom). Additionally, the diameter of approximately \(23.6\mathrm{~nm}\) , as determined by cryo- EM 3D reconstruction, corresponds to the tubes forming helical structures, further supporting these findings. Considering its inherent flexibility, it is challenging to reach a definitive conclusion, but further examination of the tube structure with \(C_3\) symmetry suggests that PuuE- p is likely positioned on the outside (Fig. 4g, Supplementary Movie 4), consistent with the original PuuE tube structures (Fig. 3b, Supplementary Movie 2). This arrangement indicates that the D- loop of PuuE(D- loop)- M appears on the exterior of the tubes, which is crucial for forming helical structures not observed in PuuE tubes lacking the D- loop. The \(C_3\) symmetry enhances the exposure of internal PuuE(D- loop)- M on the outer surface compared to structures with \(C_4\) or higher symmetry, enabling hydrophobic interactions between tubes. Therefore, the formation of the \(C_3\) symmetric tube structure likely facilitated
+
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+
+the creation of the helical conformations. Furthermore, the lack of \(C_3\) symmetry in PuuE tubes (Fig. 3a, b) suggests that they are unstable as single tubes without forming helical conformations. The formation of helical conformations may stabilise the structure with \(C_3\) symmetry, as evidenced by its successful identification in tube structures with helical conformations. Additionally, the temperature- induced degradation leading to the rapid collapse of tubes with \(C_3\) symmetry suggests that helical structure stabilisation is essential for maintaining structural integrity under physiological conditions.  
+
+## Conclusions  
+
+We introduce NIPAD, a pioneering approach that intricately weaves together protein unit design and assembly, drawing inspiration from the complexity and adaptability of natural protein assemblies. By employing NIPAD, we created a unique higher- order tubular assembly composed of two protein units, exhibiting the reversible, flexible, and diverse characteristics of natural structures. A noteworthy highlight of our study was the successful induction of helical conformations within these tube assemblies, akin to those observed in actin filaments, achieved through strategic integration of the D- loop into assembly design.  
+
+This advance in protein assembly highlights the complexity of emulating the dynamic behaviour observed in biological systems. The design and assembly of protein structures in vitro, although closely controlled, cannot fully replicate the complex cellular environment. In vivo, myriad factors, including macromolecular crowding, post- translational modifications, and interactions with other cellular components can significantly influence protein behaviour<sup>50</sup>. Our designed protein assemblies exhibit remarkable biomimicry regarding flexibility, reversibility, and structural diversity, but have yet to be demonstrated and validated in biological systems, where the true complexity of biological interactions is present. Furthermore, our approach, which focuses on the assembly of tubular structures inspired by cytoskeletal elements, including actin filaments and microtubules, does not address the full range of complex protein structures found within biological systems. Natural protein assemblies contain structural and functional diversity, and much remains to be explored. Computational methods have an important role to play in improving the accuracy and breadth of protein assembly design<sup>1,8- 10</sup>. By utilising computational predictions about protein interactions and assembly outcomes, our design would be refined into more complex and functional biomimetic structures, with applications ranging from novel biomaterials and nanodevices to therapeutic innovations.  
+
+Our research extends the boundaries of protein assembly design and provides new insights into its applications in synthetic biology and life sciences. This research encourages a comprehensive approach that bridges the divide between the biological and materials sciences and suggests that the exploration of
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+nature's complex systems has the potential to transform science and technology. As we continue to explore this intersection of life and materials sciences, we anticipate that future investigations will provide fundamental insights into the natural world, heralding a new era of scientific discoveries and technological breakthroughs.  
+
+# References  
+
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+370 45 Das, S. et al. D- loop Dynamics and Near- Atomic- Resolution Cryo- EM Structure of Phalloidin- 371 Bound F- Actin. Structure 28, 586- 593 e583 (2020). 372 46 Pratt, L. R., Chaudhari, M. I. & Rempe, S. B. Statistical Analyses of Hydrophobic Interactions: A 373 Mini- Review. J Phys Chem B 120, 6455- 6460 (2016). 374 47 Koga, K. & Yamamoto, N. Hydrophobicity Varying with Temperature, Pressure, and Salt 375 Concentration. J Phys Chem B 122, 3655- 3665 (2018). 376 48 Sun, Q., Fu, Y. F. & Wang, W. Q. Temperature effects on hydrophobic interactions: Implications 377 for protein unfolding. Chem Phys 559 (2022). 378 49 Echandia, E. L. & Piezzi, R. S. Microtubules in the nerve fibers of the toad Bufo arenarum 379 Hensel. Effect of low temperature on the sciatic nerve. J Cell Biol 39, 491- 497 (1968). 380 50 Nakajima, K. et al. Macromolecular crowding and supersaturation protect hemodialysis patients 381 from the onset of dialysis- related amyloidosis. Nat Commun 13, 5689 (2022). 382 51 Pace, C. N., Vajdos, F., Fee, L., Grimsley, G. & Gray, T. How to measure and predict the molar 383 absorption coefficient of a protein. Protein Sci 4, 2411- 2423 (1995). 384 52 Schindelin, J. et al. Fiji: an open- source platform for biological- image analysis. Nat Methods 9, 385 676- 682 (2012). 386 53 Scheres, S. H. A Bayesian view on cryo- EM structure determination. J Mol Biol 415, 406- 418 387 (2012). 388 54 He, S. & Scheres, S. H. W. Helical reconstruction in RELION. J Struct Biol 198, 163- 176 (2017). 389 55 Rohou, A. & Grigorieff, N. CTFFIND4: Fast and accurate defocus estimation from electron 390 micrographs. J Struct Biol 192, 216- 221 (2015). 391 56 Smith, M. B. et al. Segmentation and tracking of cytoskeletal filaments using open active 392 contours. Cytoskeleton (Hoboken) 67, 693- 705 (2010). 393 57 Schrodinger, LLC. The PyMOL Molecular Graphics System, Version 2.5. 394 58 Meng, E. C. et al. UCSF ChimeraX: Tools for structure building and analysis. Protein Sci 32, 395 e4792 (2023). 396 59 Bjellqvist, B. et al. The focusing positions of polypeptides in immobilized pH gradients can be 397 predicted from their amino acid sequences. Electrophoresis 14, 1023- 1031 (1993). 398 60 Eisenberg, D., Schwarz, E., Komaromy, M. & Wall, R. Analysis of membrane and surface protein 399 sequences with the hydrophobic moment plot. J Mol Biol 179, 125- 142 (1984).
+
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+![](images/Figure_1.jpg)
+
+<center>Fig. 1. Construction of PuuE tube via NIPAD. | a, AF2 prediction of the heterodimeric peptide pair, M3L2 (yellow) and p66α (blue). b, Crystal structure of PuuE (PDB ID: 3CL6). C-terminus positions are circled. Detailed structure, face, side, and back are shown for clarity. c, Schematic diagram of the protein sequence (top) and the AF2-predicted structures of PuuE-M and PuuE-p (bottom). PuuE-M and PuuE-p are coloured yellow and blue to match the respective peptides and overall structure to clear the tube structure (d). The peptide parts, M3L2 and p66α, are highlighted in darker colours. d, Left, predicted model of the tubular assembly consisting of PuuE-M and PuuE-p. Right, brief schematic diagram of how many proteins (n) form a system of tube structures. e, nsTEM images of tubular assemblies constructed from PuuE-M and PuuE-p; 12.5 μM PuuE-M and 12.5 μM PuuE-p in NaCl (+) buffer was incubated at 40 °C for 24 h and imaged via nsTEM. Scale bars, 1 μm (white), 50 nm (black). </center>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2. Condition optimisation for PuuE tube assembly. | a, b, The kinetics of tubular assembly. nsTEM images of tubular assembly (a) and length analysis (b). c, nsTEM images of tubular assemblies with varying NaCl concentration. d, nsTEM images showing the reversibility of tube structures with changing NaCl concentration. e, Tube length analysis of nsTEM images. For tube length analysis, tubes were picked up and calculated from 5k images at each step; 150 tubes from the longest tube length were used at each data point. \*\*\* p<0.001 (Welch's t-test). Scale bar, 1 μm. </center>
+
+<--- Page Split --->
+![](images/Supplementary_Figure_1b.jpg)
+
+<center>Fig. 3. Structural characterisation of PuuE tube. | a, 2D class-averaged images of tube structures. The population of each structure was determined from the total pickings of 206,658 tube segments. Scale bar, 500 Å. b 3D reconstructed models of tube structures with \(C_4\) , \(C_5\) , and \(C_6\) symmetries. The fitting results suggest that PuuE-p is less likely to fit into units located inside the tube structure and more likely to fit into units located on the outside. Based on the predictions, the units were colour-coded as shown in Fig. 1c. For visibility, only the molecular model of the PuuE (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. c, Time-lapse images of random bending of the tube structures monitored by TIRFM. Top: snapshots at the starting point (0 sec) and after 4 sec (top). Bottom: enlarged images of tubes in green or orange rectangles in the top images, showing the dynamic flexibility of tube structures between 0 to 4 sec (0.4 sec per image). Scale bar, 5 μm. d, Left, a relationship between contour length (L) and mean square of end-to-end distance (<R²>) of the tube structures for estimation of the persistence length (Lp). The continued lines represent fitting curves (black for PuuE tube, red for actin filament) to experimental data (black open circle for PuuE tube, red cross mark for actin filament). Right, comparison of persistence length with cytoskeletal elements. PuuE tube (PT, black) and actin filaments (AF, red) were determined in this study (A wider range of plots is shown in Supplementary Fig. 1b). Intermediate filaments (IF, blue) and microtubules (MT, green) are taken from ref. 41 and 38, respectively. </center>
+
+<--- Page Split --->
+![](images/Extended_Data_Figure_9.jpg)
+
+<center>Fig. 4. Emulation of actin filament by D-loop grafting. | a, Schematic representations of PuuE(D-loop)-M. The position of D-loop graft (red) is indicated by protein sequence (top) and the AF2-predicted structure (bottom). b, nsTEM images of tubes with a helical conformation composed of PuuE(D-loop)-M and PuuE-p. The helical pattern of two (centre) or three (right) intertwined tubes is shown in the high-magnification image. c, nsTEM images showing the reversibility of tube structure with helical conformations by temperature change. d, Representative cryo-EM images (top) and 2D class-averaged images (bottom) of helical tube structures. e, Representative cryo-EM image (top) and 2D class-averaged image of tube structure with \(C_3\) symmetry. Tube structures with other symmetries found in this study are shown in Extended Data Fig. 9. f, 3D reconstructed model of tube structure with \(C_3\) symmetry. For visibility, only the PuuE structure (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. g, Fitting of AF2-predicted model of PuuE-p into the 3D reconstructed model. The fitting results suggest that PuuE-p is unlikely to fit in the units located inside the tube structure; it is better accommodated by the units on the outside. Based on this prediction, the units in f are colour-coded as described in Fig. 1c. 6xHis-TEVcs region of the PuuE-p model is not shown to improve visibility. Scale bars, 1 \(\mu \mathrm{m}\) (white), 100 nm (black), 10 nm (grey). </center>
+
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+
+## Methods  
+
+## Plasmids and cloning  
+
+Primers for cloning and synthetic genes of N- terminal 6xHis- tagged PuuE- M and PuuE- p were purchased from Eurofins Genomics. PCRs were performed using the PrimeSTAR Max DNA Polymerase (Takara Bio) according to the manufacturer's protocol. Sizes of PCR products were verified using standard agarose gel electrophoresis. The In- Fusion Snap Assembly (Takara Bio) was used as the standard method for cloning according to the manufacturer's protocol, and each amplified gene fragment was ligated between the Ndel and BamHI multicoloring sites of the pET11a expression vector (Novagen). Primers for cloning and a synthetic DNA fragment of D- loop were purchased from Eurofins Genomics. The plasmid encoding N- terminal 6xHis- tagged PuuE- D- loop- M was generated from the PuuE- M plasmid following the same procedures as above. All plasmids were amplified in E. coli strain DH5α (NIPPON GENE) and extracted using the NucleoSpin Plasmid EasyPure (MACHEREY- NAGEL) according to the manufacturer's protocol. DNA sequences were confirmed by a sequencing service (Eurofins Genomics).  
+
+## Protein expression and purification  
+
+The recombinant proteins were expressed using E. coli strain BL21 (DE3) (NIPPON GENE) cotransformed with a pGro7 chaperone plasmid (Takara Bio) and purified as follows. After transformation with plasmid DNA, colonies grown overnight on LB agar plates supplemented with \(100~\mu \mathrm{g / mL}\) ampicillin (Amp) and \(20~\mu \mathrm{g / mL}\) chloramphenicol (Crm) at \(37^{\circ}\mathrm{C}\) were picked to inoculate \(5\mathrm{mL}\) of liquid LB- AmpCrm broth and grown overnight at \(37^{\circ}\mathrm{C}\) and \(200~\mathrm{rpm}\) . Overnight cultures were diluted in \(1\mathrm{L}\) of liquid LB- Amp- Crm broth supplemented with \(0.5\mathrm{mg / mL}\) L- arabinose and grown at \(37^{\circ}\mathrm{C}\) and \(200~\mathrm{rpm}\) until reaching an optical density at \(600\mathrm{nm}\) of 0.6- 0.8. Protein synthesis was induced by adding \(0.1\mathrm{mM}\) isopropyl- \(\beta\) - D- thiogalactopyranoside and the cultures were grown at \(16^{\circ}\mathrm{C}\) for \(16 - 20\mathrm{h}\) . Cells were harvested by centrifugation at \(15,317\mathrm{g}\) and \(4^{\circ}\mathrm{C}\) for \(5\mathrm{min}\) and then frozen at - 80 °C. Cell pellets were thawed at \(25\pm 1^{\circ}\mathrm{C}\) , resuspended in \(60~\mathrm{mL}\) of ice- cold purification buffer ( \(20\mathrm{mM}\) Tris- HCl, \(\mathrm{pH}8.0\) , containing \(300\mathrm{mM}\) NaCl), and lysed using sonication ( \(9\mathrm{min}\) with 1:2 on/off cycles and \(70\%\) amplitude; SFX250, Branson) on ice. Cell debris was cleared by centrifugation at \(15,317\mathrm{g}\) and \(4^{\circ}\mathrm{C}\) for \(30\mathrm{min}\) . The supernatant (i.e., crude protein) was filtered through a \(0.45 - \mu \mathrm{m}\) pore size membrane filter (Merck), applied onto HisTrap FF crude column (Cytiva) pre- equilibrated with the purification buffer and washed with \(5\mathrm{cm}\) volumes of \(2\%\) elution buffer ( \(20\mathrm{mM}\) Tris- HCl, \(\mathrm{pH}8.0\) , containing \(300\mathrm{mM}\) NaCl and \(1\mathrm{M}\) imidazole; \(2\%\) means \(20\mathrm{mM}\) imidazole). 6xHis- tagged proteins were eluted with \(10\mathrm{cm}\) volumes of elution buffer with a linear gradient of \(2 - 40\%\) (i.e., \(20 - 400\mathrm{mM}\) imidazole). The fractions containing the proteins confirmed by means of UV absorption and SDS- PAGE were again collected and dialysed against 50- fold volume of NaCl (+) or NaCl (- ) buffer ( \(50\mathrm{mM}\) Tris- HCl, \(\mathrm{pH}8.0\) , containing \(\pm 100\mathrm{mM}\) NaCl and \(0.5\mathrm{mM}\) EDTA) at \(4^{\circ}\mathrm{C}\) twice.
+
+<--- Page Split --->
+
+Each of the purified proteins was concentrated by an Amicon Ultra centrifugal filter unit (Merck) with an appropriate molecular weight cutoff followed by filtration through a \(0.45 \mu \mathrm{m}\) pore size membrane filter (Merck). Protein concentration was determined by absorbance measurements at \(280 \mathrm{nm}\) using a NanoDrop OneC spectrophotometer (Thermo Scientific). The molar extinction coefficients at \(280 \mathrm{nm}\) for the proteins were calculated from the basis of amino acid composition<sup>51</sup>. The concentrated proteins were frozen in liquid nitrogen and stored at \(- 80^{\circ} \mathrm{C}\) before experiments.  
+
+## Sample preparation  
+
+All proteins were thawed immediately before tube formation experiments on ice. Each sample was prepared in a \(1.5 \mathrm{mL}\) microtube using an appropriate buffer to adjust the concentration described in the manuscript and the volume to \(200 \mu \mathrm{L}\) at \(25 \pm 1^{\circ} \mathrm{C}\) . Except for the NaCl concentration- dependent experiments, NaCl (+) protein stock solution and buffer were used. For the NaCl concentration- dependent experiments, \(50 \mathrm{mM}\) Tris- HCl (pH 8.0), \(1 \mathrm{M} \mathrm{NaCl}\) , and \(0.5 \mathrm{mM}\) EDTA were used in addition to NaCl (- ) protein stock solution and buffer. Incubation of the samples was carried out using a ThermoMixer C (Eppendorf) or a MATRIX Orbital Delta Plus (IKA) with shaking of \(300 \mathrm{rpm}\) at the temperature described in the manuscript. For the disassembly and reassembly experiments, buffer substitution procedures were conducted using NaCl (- ) and NaCl (+) buffer, respectively, with Microcon 50 centrifugal filter units (Merck) according to the manufacturer's protocol four times at each step.  
+
+## Negative-stain transmission electron microscopy (nSTEM)  
+
+A naked G600TT copper grid (Nisshin EM) was carbon- coated using a VE- 2030 (VACUUM DEVICE). The grid was glow- discharged using a PIB- 10 (VACUUM DEVICE). Then, a \(5 - \mu \mathrm{L}\) aliquot of the sample solution was placed on the grid for \(1 \mathrm{min}\) , and the remaining solution was removed with filter paper (No. 2, ADVANTEC) followed by rinsing thrice with a \(5 - \mu \mathrm{L}\) aliquot of Milli- Q water. After blotting off the water with filter paper, the sample was stained briefly with a \(3 - \mu \mathrm{L}\) aliquot of \(2\%\) (w/v) uranyl acetate solution three times. The remaining solution was removed with filter paper and the grid was dried on the bench- top. TEM observation was performed using a transmission electron microscope HT- 7700 (Hitachi) with an acceleration voltage of \(80 \mathrm{kV}\) . The images were recorded using HT- 7700 control software (Hitachi).  
+
+## Tube length analysis  
+
+Hundreds of discriminable tubes were picked up manually on 5k- magnification TEM images. The tube lengths were calculated as half of the perimeter analysed with ImageJ (Fiji)<sup>52</sup>. The plots were drawn by selecting 150 tubes from the longer lengths using Igor Pro 9 (WaveMetrics). For the disassembly and reassembly analysis, Welch's t- test was carried out.
+
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+
+## Circular dichroism (CD) spectrum measurements  
+
+All proteins were thawed immediately before CD measurements on ice. Each sample was prepared in a 1.5- mL microtube using \(\mathrm{NaCl(+)}\) buffer to adjust the concentration to \(2.5\mu \mathrm{M}\) and the volume to \(200\mu \mathrm{L}\) at 25 \(\pm 1^{\circ}\mathrm{C}\) . Far- UV CD spectra were obtained at a wavelength of \(200–250\mathrm{nm}\) using a J- 1100 spectropolarimeter (JASCO) with a quartz cell with a light path of \(1\mathrm{mm}\) . Thermal denaturation was performed at a temperature change rate of \(1^{\circ}\mathrm{C / min}\) . The CD spectral data were collected using Spectra Manager (version 2.5, JASCO). All CD data were expressed as mean residue ellipticity. The \(T_{\mathrm{m}}\) of each protein was calculated from the thermal denaturation curve at a wavelength of \(222\mathrm{nm}\) by sigmoid fitting using Igor Pro 9 (WaveMetrics).  
+
+## Cryo-EM structural analysis  
+
+All proteins were thawed immediately before tube formation on ice. Each sample was prepared in a 1.5- mL microtube using \(\mathrm{NaCl(+)}\) buffer to adjust the concentration to \(12.5\mu \mathrm{M}\) and the volume to \(200\mu \mathrm{L}\) at 25 \(\pm 1^{\circ}\mathrm{C}\) . Incubation of the samples was carried out as described above for \(24\mathrm{h}\) at \(40^{\circ}\mathrm{C}\) for the PnuE tube and \(30^{\circ}\mathrm{C}\) for the PnuE D- loop tube, and then the samples were provided for grid preparation. For unwinding the helical structures of the PnuE D- loop tube, additional incubation was carried out for \(1\mathrm{h}\) on ice immediately before grid preparation.  
+
+The PnuE D- loop tube sample prepared at \(25\pm 1^{\circ}\mathrm{C}\) was used at the original concentration. In contrast, the PnuE tube and the PnuE D- loop tube preincubated on ice were diluted to one- third and one- sixth of their original concentrations, respectively. Quantifoil R1.2/1.3 Cu 300 grids coated with a holey carbon film (Quantifoil) were treated for hydrophilisation using a JEC- 3000FC Auto Fine Coater (JEOL) at \(20\mathrm{Pa}\) and \(10\mathrm{mA}\) for \(30\mathrm{s}\) . Subsequently, \(2.5\mathrm{- }\mu \mathrm{L}\) aliquots of the respective diluted samples were applied to the prepared grids. After blotting off excess solution, the grids were rapidly immersed in liquid ethane for vitrification using a Vitrobot Mark IV (Thermo Fisher Scientific). Vitrobot was set at \(4^{\circ}\mathrm{C}\) and \(100\%\) humidity for PnuE and PnuE D- loop samples preincubated on ice, and \(25^{\circ}\mathrm{C}\) and \(100\%\) humidity for PnuE D- loop sample prepared at \(25\pm 1^{\circ}\mathrm{C}\) .  
+
+Sample screening and data acquisition were performed using a Glacios cryo- transmission electron microscope (Thermo Fisher Scientific) operated at an accelerated voltage of \(200\mathrm{kV}\) , equipped with a Falcon4EC camera, at the Institute of Life and Medical Sciences, Kyoto University. Images were automatically acquired using the EPU software as movies with nominal magnifications and corresponding calibrated pixel sizes of \(120,000\mathrm{x}\) (1.22 A/pixel) for the PnuE sample, and \(150,000\mathrm{x}\) (0.925 A/pixel) for PnuE D- loop samples.  
+
+## Cryo-EM image processing
+
+<--- Page Split --->
+
+Image analysis was conducted using similar workflows for each dataset of the three samples with the software package RELION 5.0beta<sup>53,54</sup>.  
+
+For the PuuE tube sample, 4,346 movies were subjected to motion- correction using RELION's algorithm, and the contrast transfer function (CTF) was estimated using CTFFIND<sup>45</sup>. Tube coordinates were manually registered, and 709,722 segments were extracted with 3x binning into 260×260- pixel boxes (approximately 950x950 Å) with an inter- box spacing of 80 Å. The extracted segments were subjected to two rounds of 2D classification, and the resulting class averages were visually inspected to categorise the segments based on tube diameters. In parallel, an additional round of 2D classification with 10 classes was performed to assess the structural diversity of the tubes roughly. Each subset of segments, categorised by diameter, was then re- extracted and subjected to further 2D classifications to remove junk images. 3D classification with symmetry search was performed on each subset without imposing symmetry (C1). Finally, 3D refinement was carried out for the subsets with the three smallest diameters, applying \(C_4\) , \(C_5\) , and \(C_6\) symmetries, respectively. The subsets with larger diameters exhibited significant heterogeneity and did not yield reliable 3D reconstructions.  
+
+For the PuuE D- loop tube sample prepared at \(25 \pm 1^{\circ}\mathrm{C}\) , 4,871 movies were motion- corrected and CTF- estimated using RELION and CTFFIND4, respectively. A total of 126,987 segments were extracted with 5x binning into 320×320- pixel or 640×640- pixel segmented boxes (1480x1480 or 2960x2960 Å) with an inter- box spacing of 60 Å. The extracted segments were subjected to six rounds of 2D classification, yielding class averages displaying single, double, and triple helical tube architectures.  
+
+For the PuuE D- loop tube sample, preincubated on ice to unwind the helical structures, 4,346 movies were subjected to motion correction and CTF estimation. A total of 709,722 segments were extracted with 3x binning into 360×360- pixel boxes (approximately 1000x1000 Å) with an inter- box spacing of 80 Å. The extracted segments were subjected to two rounds of 2D classification, and the resulting class averages were visually inspected to categorise the segments based on tube diameters. In parallel, two rounds of 2D classification were performed to assess the structural diversity of the tubes. Each subset of segments, categorised by diameter, was re- extracted and subjected to further 2D classifications to remove junk images. 3D classification with symmetry search was performed on each subset without imposing symmetry (C1). During the 3D classification of the initially selected C5- tube subset, C6 tubes were found to be present and were subsequently combined with the C6- tube subset from the 2D classification. Finally, 3D refinement was carried out for the subsets with the four smallest diameters, applying \(C_3\) , \(C_4\) , \(C_5\) , and \(C_6\) symmetries, respectively. As observed in the PuuE dataset, the subsets with larger diameters displayed considerable heterogeneity and failed to yield reliable 3D reconstructions. Detailed image processing workflows are depicted in Extended Data Figures. 6, 8, and 9.
+
+<--- Page Split --->
+
+## Fluorescent labelling  
+
+Fluorescent labellingTube formation was conducted as described above under the optimised condition described in the manuscript. Labelling reaction was achieved by adding Alexa Fluor 488 succinimidyl ester dissolved in dimethyl sulfoxide (DMSO) to the tube solution at a final concentration of \(0.7 \mathrm{mM}\) . The reaction was then incubated at \(25 \pm 1^{\circ} \mathrm{C}\) for \(1 \mathrm{~h}\) with gentle shaking under shading. The excess dye was removed using NaCl (+) buffer with Microcon 300 centrifugal filter units (Merck) according to the manufacturer's protocol four times. The labelled tubes were then stored under shading at \(25 \pm 1^{\circ} \mathrm{C}\) until further experiments.  
+
+## Fluorescence microscopy  
+
+Fluorescence microscopyAn observation chamber was assembled by placing two double- sided tapes (thickness \(\sim 100 \mu \mathrm{m}\) ) onto a silicone- coated coverslip \((24 \times 36 \mathrm{~mm}^2\) , thickness No. 1; Matsunami) with another coverslip \((18 \times 18 \mathrm{~mm}^2\) , thickness No. 1; Matsunami) on top. To passivate the surface of the coverslips against nonspecific adhesion of protein, the chamber was filled with \(10 \mathrm{mg} \mathrm{mL}^{- 1}\) of Pluronic F- 127 (Sigma- Aldrich) dissolved in distilled water for more than 10 minutes at \(25^{\circ} \mathrm{C}\) . After washing out Pluronic F- 127 solution with 5 chamber volumes of \(\mathrm{NaCl}\) (+) buffer, the chamber was filled with TIRFM buffer ( \(50 \mathrm{mM}\) Tris- HCl pH 8.0, \(100 \mathrm{mM}\) NaCl, \(0.5 \mathrm{mM}\) EDTA, \(0.2\%\) (w/v) methylcellulose (1500 cP, Wako), \(1 \mathrm{mM}\) DTT, \(2 \mathrm{mM}\) Trolox). Next, the Alexa488- tube solution was diluted to \(1 / 10\) in \(\mathrm{NaCl}\) (+) solution, and further diluted to \(1 / 10\) (final \(1 / 100\) dilution) in TIRFM buffer. Then, the diluted tube solution was perfused into the observation chamber and sealed by Valap to prevent flow. The fluorescence images of tube structures were acquired at intervals of \(40 \mathrm{ms}\) with an inverted microscope (IX- 71, Olympus) equipped with a \(60 \times\) objective lens (PlanApo NA 1.45 oil, Olympus), an EMCCD camera (iXon3, Andor Technology) and an excitation laser with the wavelength at \(488 \mathrm{nm}\) (OBIS 488- 60- LS, COHERENT). All observations were performed at \(25 \pm 1^{\circ} \mathrm{C}\) .  
+
+## Mechanical property analysis  
+
+Mechanical property analysisThe persistence length of the tube structures was estimated as follows. First, the fluorescence images were converted to 8- bit images using the ImageJ function. Then, the skeletons of the tube structures were tracked using ImageJ plugin, JFilament<sup>6</sup>. Distances between adjacent nodes composing the skeletons were set as 1 pixel. Next, the contour length \((L)\) and end- to- end distance \((R)\) of the tube structures at each frame were calculated using the coordinates of the nodes with custom- written Python scripts. The mean square of \(R\) \((\langle R^2 \rangle)\) of each tube structure was calculated by averaging \(R^2\) along 100–200 frames. \(\langle R^2 \rangle\) and \(L\) follow the following equation when the shape fluctuation is driven thermally<sup>36</sup>. \(\langle R^2 \rangle = 4L_{\mathrm{p}}^2 [2\exp (- L / 2L_{\mathrm{p}}) - 2 + L / L_{\mathrm{p}}]\) , where \(L_{\mathrm{p}}\) is the persistence length of the tube structure. The \(L_{\mathrm{p}}\) values of the tube structures were estimated by fitting this equation to the experimental data using 'curve_fit' function of Python package  
+
+by fitting this equation to the experimental data using 'curve_fit' function of Python package
+
+<--- Page Split --->
+
+'scipy.optimize'. \(L_{\mathrm{p}}\) of actin filaments was estimated by the same analysis. Totally, 55 tube structures and 37 actin filaments were analysed.  
+
+## Molecular modelling  
+
+All predicted protein structures were generated by AlphaFold 2.2 or 2.3 multimer- mode (DeepMind) \(^{15,16}\) . Cartoon models of the proteins were drawn using PyMOL 2.5 (Schrödinger) \(^{57}\) and UCSF ChimeraX (UCSF RBVI and NIH) \(^{58}\) . Isoelectric points of PuuE- M and PuuE- p were calculated from the basis of amino acid composition \(^{59}\) . Surface hydrophobicity of PuuE was drawn using Color_h script (PyMOL Wiki) based on the hydrophobicity scale \(^{60}\) .  
+
+## Data availability  
+
+The cryo- EM structures have been deposited in the Electron Microscopy Data Bank (EMDB) with the following accession codes: EMD- 60617, EMD- 60618, and EMD- 60619 for the PuuE tubes with C4, C5, and C6 symmetry, respectively; and EMD- 60620, EMD- 60621, EMD- 60622, and EMD- 60623 for the PuuE D- loop tubes with C3, C4, C5, and C6 symmetry, respectively.  
+
+## Acknowledgements  
+
+This work was supported by JSPS KAKENHI (grant nos. 19H02832, 19K22253, and 21H05116 to Y. Suzuki; 21H05117 to Y. Suzuki and Y. Sugita; and 20K22628, 21J00530, and 22KJ1644 to M.N.), JST PRESTO (grant no. JPMJPR22A7 to Y. Suzuki and JPMJPR20ED to M.M.), Takeda Science Foundation to Y. Suzuki, Chubei Itoh Foundation to Y. Suzuki, and The Hakubi Center for Advanced Research to Y. Sugita, M.M., and Y. Suzuki.  
+
+## Author contributions  
+
+Y. Suzuki directed the project. Y. Suzuki and M.N. conceived and designed the overall study. M.N. conducted experiment works with contributions from Y. Suzuki, Y. Sugita, and Y.Y.. Y. Sugita and M.N. performed cryo- EM data collection and analysed data. Y.Y. conducted TIRFM experiments, and Y.Y. and M.M. analysed mechanical properties. M.N. and Y. Suzuki wrote the manuscript with contributions from Y. Sugita, Y.Y., and M.M.  
+
+## Competing interest declaration  
+
+Y. Suzuki and M.N. are inventors of a provisional patent submitted by Kyoto University for ‘Protein Assembly Structure’.
+
+<--- Page Split --->
+
+# Additional information  
+
+Supplementary Information is available for this paper.  
+
+Correspondence and requests for materials should be addressed to Yuta Suzuki.  
+
+Tel: +81- 75- 753- 9766  
+
+E- mail address: suzuki.yuta.2m@kyoto- u.ac.jp
+
+<--- Page Split --->
+![](images/Extended_Data_Figure_2.jpg)
+  
+
+Extended Data Fig. 1. | AF2 prediction of PuuE- M and PuuE- p. a, Fifty prediction models overlapped for PuuE- M (top) and PuuE- p (bottom). Peptide parts, M3L2 and p66α, are indicated with a red box. b, Predicted local distance difference test plots for the most reliable prediction models for PuuE- M (top) and PuuE- p (bottom). Arrows indicate the N- terminal region of M3L2 and p66α. For these regions, PuuE- M has a lower predictive reliability than does PuuE- p, suggesting that the structure may be more flexible. c, The most reliable prediction model for PuuE- p. The region from the C- terminus of PuuE to the N- terminus of p66α (i.e. \(^{313}\mathrm{HPYTPE}^{318}\) ) is depicted by a stick model. The two Pro residues highlighted in red are thought to be responsible for the rigidity of the PuuE- p structure. Because of the rigidity of PuuE- p, the final product of the mixture was predicted to be a tube, as shown in Fig. 1d.
+
+<--- Page Split --->
+![](images/Extended_Data_Figure_3.jpg)
+
+<center>Extended Data Fig. 2. | nsTEM characterisation of PuuE-M, PuuE-p, and the mixture for PuuE-M and PuuE-p. a, 12.5 \(\mu \mathrm{M}\) PuuE-M or b, 12.5 \(\mu \mathrm{M}\) PuuE-p in NaCl (+) buffer was incubated at \(40^{\circ}\mathrm{C}\) for 24 h. Scale bars, 200 nm (white), 50 nm (black). c, Dependency of PuuE tube assemblies on protein concentration. 250 nM (top), 2.5 \(\mu \mathrm{M}\) (middle), and 12.5 \(\mu \mathrm{M}\) (bottom) of PuuE-M and PuuE-p each in NaCl (+) buffer was incubated at \(40^{\circ}\mathrm{C}\) for 24 h and imaged by nsTEM. The tube structure observed in the nsTEM images was flexible as it was curved and collapsed. Scale bars, 1 \(\mu \mathrm{m}\) (white), 50 nm (black). </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+<center>Extended Data Fig. 3. | Time dependence of PuuE tube assemblies and their stability over time. a, 12.5 \(\mu \mathrm{M}\) of PuuE-M and PuuE-p each in \(\mathrm{NaCl}(+)\) buffer was incubated at \(40^{\circ}\mathrm{C}\) for indicated time points and imaged via nsTEM. b, After \(24\mathrm{h}\) of tube formation, the sample was kept at \(25\pm 1^{\circ}\mathrm{C}\) for the indicated time and imaged using nsTEM. Tube structures remained unchanged after 2 weeks and even after 1 month, suggesting stability. Scale bars, \(1\mu \mathrm{m}\) . </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_1.jpg)
+  
+
+Extended Data Fig. 4. | Temperature dependence of PuuE tube assemblies and determination of \(T_{\mathrm{m}}\) for PuuE- M and PuuE- p. a, 12.5 \(\mu \mathrm{M}\) of PuuE- M and PuuE- p each in NaCl (+), buffer was incubated at the indicated temperature for 24 h and imaged via nsTEM. Scale bars, 1 \(\mu \mathrm{m}\) . b, c, \(T_{\mathrm{m}}\) measurements using CD for PuuE- M (b) and PuuE- p (c). 2.5 \(\mu \mathrm{M}\) of PuuE- M or PuuE- p in NaCl (+), buffer was incubated from 25 to 55 °C with temperature change of 1 °C/min. Left panel, overall CD spectra; right panel, thermal denaturation profiles.
+
+<--- Page Split --->
+![](images/Figure_unknown_2.jpg)
+  
+
+Extended Data Fig. 5. | Salt concentration dependence and reversibility of PuuE tube assemblies. a, Left, \(12.5 \mu \mathrm{M}\) of PuuE- M and PuuE- p each in \(\mathrm{NaCl}(+)\) buffer was incubated at \(40^{\circ} \mathrm{C}\) for \(24 \mathrm{~h}\) with indicated \(\mathrm{NaCl}\) concentration and imaged via nsTEM. Right: diagram of salt concentration effects described in the main text. b, Additional images in Fig. 2d prove the reversibility of tubular assemblies. These images were used for statistical analysis of tube length, as shown in Fig. 2e. Scale bars, \(1 \mu \mathrm{m}\) (white).
+
+<--- Page Split --->
+![](images/Figure_unknown_3.jpg)
+  
+
+![](images/Figure_unknown_4.jpg)
+
+<center>C4 tube: 2D classifications (2 rounds): 51,590 segments </center>  
+
+![](images/Figure_unknown_5.jpg)
+
+<center>C5 tube: 2D classifications (2 rounds): 44,868 segments </center>  
+
+![PLACEHOLDER_28_3]
+
+<center>3D Refinement \((C_4)\) : 12,052 segments Post-processing </center>  
+
+![PLACEHOLDER_28_4]
+
+<center>C6 tube: 2D classification (1 round): 117,636 segments </center>  
+
+![PLACEHOLDER_28_5]
+
+<center>3D Refinement \((C_5)\) : 12,572 segments Post-processing </center>  
+
+![PLACEHOLDER_28_6]
+
+<center>3D classification \((C_1)\) : 39,841 segments </center>  
+
+Extended Data Fig. 6. | Cryo- EM image processing workflow of the PuuE tubes. Flowchart illustrating the image processing steps. Scale bars: \(100 \mathrm{nm}\) (white), \(250 \mathrm{\AA}\) (black). Gold- standard Fourier shell correlation (FSC) curve of the independently refined half maps indicating a global resolution at the 0.143 threshold.
+
+<--- Page Split --->
+![PLACEHOLDER_29_0]
+  
+
+Extended Data Fig. 7. D- loop grafting to emulate actin filaments. a, Surface hydrophobicity calculation for PuuE. D- loop was grafted into the 'back' side of PuuE owing to the hydrophobic nature of a prominent indentation. b, \(T_{\mathrm{m}}\) measurement of PuuE(D- loop)- M via CD. \(2.5 \mu \mathrm{M}\) of PuuE(D- loop)- M in NaCl (+) buffer was incubated from 25 to \(55^{\circ}\mathrm{C}\) with temperature change of \(1^{\circ}\mathrm{C / min}\) . Top: overall CD spectra; bottom: thermal denaturation profiles, respectively. c, \(12.5 \mu \mathrm{M}\) of PuuE(D- loop)- M and PuuE- p in NaCl (+) buffer were incubated at \(30^{\circ}\mathrm{C}\) for \(24 \mathrm{h}\) and imaged using nsTEM. A novel helical pattern of two or three intertwined tubes was clearly observed. Flexibility was also noted when curved structures were observed. Scale bars, \(1 \mu \mathrm{m}\) (white), \(100 \mathrm{nm}\) (black). d, Additional images for reversibility of tube formation depends on temperature changes in Fig. 4c. For this observation, we focused on the presence of tube structures with helical conformations. After \(1 \mathrm{h}\) at \(0^{\circ}\mathrm{C}\) , there were no such structures observed via nsTEM.
+
+<--- Page Split --->
+![PLACEHOLDER_30_0]
+  
+
+![PLACEHOLDER_30_1]
+  
+
+2D classifications (6 rounds) with 2960x2960- Å segments: 9,989 segments  
+
+![PLACEHOLDER_30_2]
+  
+
+718  
+
+719 Extended Data Fig. 8. | Cryo- EM image processing workflow of PuuE D- loop tubes prepared at \(25 \pm 720\) 1 °C. Flowchart illustrating the image processing steps. Scale bars: 100 nm (white), 500 Å (black).
+
+<--- Page Split --->
+![PLACEHOLDER_31_0]
+  
+
+![PLACEHOLDER_31_1]
+  
+
+Extended Data Fig. 9. | Cryo- EM image processing workflow of PuuE D- loop tubes preincubated on ice to unwind the helical structures. Flowchart illustrating the image processing steps. Scale bars: 100 nm (white), 250 Å (black). Gold- standard Fourier shell correlation (FSC) curve of the independently refined half maps indicating a global resolution at the 0.143 threshold.
+
+<--- Page Split --->
+
+<table><tr><td></td><td>#1 C4 tube (EMD-60617)</td><td>#2 C5 tube (EMD-60618)</td><td>#3 C6 tube (EMD-60619)</td></tr><tr><td>Data collection and processing</td><td></td><td></td><td></td></tr><tr><td>Magnification</td><td>120,000</td><td></td><td></td></tr><tr><td>Voltage (kV)</td><td>200</td><td></td><td></td></tr><tr><td>Electron exposure (e-/Ų)</td><td>40</td><td></td><td></td></tr><tr><td>Defocus range (μm)</td><td>-0.8 to -1.6</td><td></td><td></td></tr><tr><td>Pixel size (Å)</td><td>1.22</td><td></td><td></td></tr><tr><td>Symmetry imposed</td><td>C4 helical</td><td>C5 helical</td><td>C6 helical</td></tr><tr><td>Initial helical segments (no.)</td><td>709,722</td><td>709,722</td><td>709,722</td></tr><tr><td>Final helical segments (no.)</td><td>12,052</td><td>12,572</td><td>39,841</td></tr><tr><td>Map resolution (Å)</td><td>11.3</td><td>20.6</td><td>17.5</td></tr><tr><td>FSC threshold</td><td>0.143</td><td>0.143</td><td>0.143</td></tr></table>
+
+727 
+
+2D analysis of the PuuE D-loop tube prepared at 25 ± 1 °C 
+
+<table><tr><td></td><td>#1 Tubes</td></tr><tr><td>Data collection and processing</td><td></td></tr><tr><td>Magnification</td><td>150,000</td></tr><tr><td>Voltage (kV)</td><td>200</td></tr><tr><td>Electron exposure (e-/Ų)</td><td>40</td></tr><tr><td>Defocus range (μm)</td><td>-0.8 to -1.6</td></tr><tr><td>Pixel size (Å)</td><td>0.925</td></tr><tr><td>Symmetry imposed</td><td>No</td></tr><tr><td>Initial helical segments (no.)</td><td>126,987</td></tr><tr><td>Final helical segments (no.)</td><td>104,748</td></tr></table>
+
+729 
+
+730 
+
+PuuE D-loop tube preincubated on ice to unwind the helical structures 
+
+<table><tr><td><td>#1 C3 tube (EMD-60620)</td><td>#2 C4 tube (EMD-60621)</td><td>#3 C5 tube (EMD-60622)</td><td>#4 C6 tube (EMD-60623)</td></td></tr><tr><td>Data collection and processing</td><td></td><td></td><td></td><td></td></tr><tr><td>Magnification</td><td>150,000</td><td></td><td></td><td></td></tr><tr><td>Voltage (kV)</td><td>200</td><td></td><td></td><td></td></tr><tr><td>Electron exposure (e-/Ų)</td><td>40</td><td></td><td></td><td></td></tr><tr><td>Defocus range (μm)</td><td>-0.8 to -1.6</td><td></td><td></td><td></td></tr><tr><td>Pixel size (Å)</td><td>0.925</td><td></td><td></td><td></td></tr><tr><td>Symmetry imposed</td><td>C3 helical</td><td>C4 helical</td><td>C5 helical</td><td>C6 helical</td></tr><tr><td>Initial helical segments (no.)</td><td>397,778</td><td>397,778</td><td>397,778</td><td>397,778</td></tr><tr><td>Final helical segments (no.)</td><td>2,675</td><td>3,262</td><td>2,998</td><td>1,291</td></tr><tr><td>Map resolution (Å)</td><td>9.7</td><td>14.6</td><td>18.2</td><td>26.0</td></tr><tr><td>FSC threshold</td><td>0.143</td><td>0.143</td><td>0.143</td><td>0.143</td></tr></table>
+
+734 
+
+Extended Data Table 1. | Cryo-EM data collection, refinement, and validation statistics
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryInformation.pdf Supplementarymovie1. mov Supplementarymovie2. mov Supplementarymovie3. mov Supplementarymovie4. mov
+
+<--- Page Split --->

preprint/preprint__070706503cff2b0c5895a72491f41d6927ffe121f452603fa7f93aef50b5eb1a/preprint__070706503cff2b0c5895a72491f41d6927ffe121f452603fa7f93aef50b5eb1a_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 760, 175]]<|/det|>
+# Protein design of two-component tubular assemblies like cytoskeletons  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 368, 240]]<|/det|>
+Yuta Suzuki suzuki.yuta.2m@kyoto- u.ac.jp  
+
+<|ref|>text<|/ref|><|det|>[[44, 268, 907, 479]]<|/det|>
+Kyoto University https://orcid.org/0000- 0002- 4863- 4585  Masahiro Noji  Kyoto University  Yukihiko Sugita  Institute for Life and Medical Sciences, Kyoto University https://orcid.org/0000- 0001- 6861- 4840  Yosuke Yamazaki  RIKEN  Makito Miyazaki  RIKEN https://orcid.org/0000- 0002- 4603- 851X  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 515, 103, 532]]<|/det|>
+## Article  
+
+<|ref|>title<|/ref|><|det|>[[44, 553, 135, 570]]<|/det|>
+# Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 590, 328, 608]]<|/det|>
+Posted Date: October 21st, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 628, 473, 647]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4976952/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 666, 914, 708]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 727, 535, 747]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 783, 914, 825]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on July 22nd, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 62076- 3.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[67, 90, 660, 110]]<|/det|>
+# Protein design of two-component tubular assemblies like cytoskeletons  
+
+<|ref|>text<|/ref|><|det|>[[66, 115, 860, 137]]<|/det|>
+2  
+
+<|ref|>text<|/ref|><|det|>[[66, 140, 857, 161]]<|/det|>
+3 Masahiro Noji \(^{1,2,3}\) , Yukihiko Sugita \(^{4,5,6}\) , Yosuke Yamazaki \(^{7,8}\) , Makito Miyazaki \(^{6,7,8,9}\) , and Yuta Suzuki \(^{3,6,9}\) .\*  
+
+<|ref|>text<|/ref|><|det|>[[66, 185, 888, 325]]<|/det|>
+4 \(^{1}\) Research Fellow of Japan Society for the Promotion of Science, Japan; \(^{2}\) Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan; \(^{3}\) Institute for Integrated Cell- Material Sciences, Kyoto University, Kyoto, Japan; \(^{4}\) Institute for Life and Medical Sciences, Kyoto University, Kyoto, Japan; \(^{5}\) Graduate School of Biostudies, Kyoto University, Kyoto, Japan; \(^{6}\) Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan; \(^{7}\) Graduate School of Science, Kyoto University, Kyoto, Japan; \(^{8}\) RIKEN Center for Biosystems Dynamics Research, Yokohama, Japan; \(^{9}\) PRESTO, JST, Saitama, Japan  
+
+<|ref|>text<|/ref|><|det|>[[66, 352, 888, 732]]<|/det|>
+Recent advances in protein design have ushered in an era of constructing intricate higher- order structures \(^{1}\) . Nonetheless, orchestrating the assembly of diverse protein units into cohesive artificial structures akin to biological assembly systems, especially in tubular forms, remains elusive. To this end, here, we introduce the Nature- Inspired Protein Assembly Design (NIPAD), a novel methodology that utilises two distinct protein units to create unique tubular structures under carefully designed conditions. These structures demonstrate dynamic flexibility similar to that of actin filaments, with cryo- electron microscopy revealing diverse morphologies, like microtubules. By mimicking actin filaments, helical conformations were incorporated into tubular assemblies, thereby enriching their structural diversity. Notably, these assemblies can be reversibly disassembled and reassembled in response to environmental stimuli, including changes in salt concentration and temperature, mirroring the dynamic behaviour of natural systems. NIPAD combines rational protein design with biophysical insights, leading to the creation of biomimetic, adaptable, and reversible higher- order assemblies. This approach deepens our understanding of protein assembly design and complex biological structures. Concurrently, it broadens the horizons of synthetic biology and material science, holding significant implications for unravelling life's fundamental processes and pioneering new applications.  
+
+<|ref|>text<|/ref|><|det|>[[66, 760, 888, 900]]<|/det|>
+Life phenomena rely on the dynamic and reversible assembly and disassembly of various higher- order protein assemblies. Actin filaments \(^{2,3}\) and microtubules \(^{4,5}\) in the cytoskeleton and the capsid proteins of viruses \(^{6,7}\) are examples of such naturally occurring structures. These are tightly regulated in function and complexity. Synthesising higher- order structures of heterogeneous protein units poses a significant challenge, particularly regarding replicating the diversity and flexibility inherent to natural assemblies. Although recent advances in computational design have enabled the creation of artificial higher- order
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 886, 157]]<|/det|>
+protein structures from two protein components<sup>8- 10</sup>, the design of heterogeneous higher- order protein assemblies with the flexibility and reversible assembly/disassembly characteristics of natural structures, especially tube structures reminiscent of the cytoskeleton, remains a formidable challenge.  
+
+<|ref|>text<|/ref|><|det|>[[115, 185, 886, 325]]<|/det|>
+Herein, we introduced Nature- Inspired Protein Assembly Design (NIPAD), a novel methodology that draws inspiration from the principles underlying natural protein complexes. By integrating rational protein design with biophysical insights to optimise assembly conditions, NIPAD recapitulates flexibility and reversible assembly principles. We employed NIPAD to create a novel assembly of two distinct protein units, successfully forming unique two- component tube structures. This development represents a significant step toward replicating the properties of complex natural structures at the molecular level.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 355, 292, 371]]<|/det|>
+## Results and discussion  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 378, 293, 395]]<|/det|>
+## The concept of NIPAD  
+
+<|ref|>text<|/ref|><|det|>[[112, 400, 886, 781]]<|/det|>
+In developing the protein components for NIPAD, we employed rational design principles with hints from natural biological systems, integrating naturally occurring ‘heterolinkers’ with ‘scaffold proteins’ to streamline design. For the heterolinker, we chose the heterodimeric peptide pair ‘MBD3L2 (M3L2)/p66α’ (Fig. 1a). Our choice of M3L2/p66α was influenced by its role in the MBD2- NuRD complex, where the ‘MBD2/p66α’ anti- parallel coiled- coil domain is essential for complex assembly<sup>11</sup>. Given the moderate denaturation midpoint temperature \((T_{\mathrm{m}})\) of M3L2/p66α \((T_{\mathrm{m}} = 35^{\circ}\mathrm{C})\) compared to MBD2/p66α \((T_{\mathrm{m}} = 65^{\circ}\mathrm{C})^{12}\) , we anticipated that M3L2/p66α would provide a balance between stability and reversible assembly control through temperature modulation. We then sought to identify a scaffold protein that could connect the heterolinker in the simplest manner possible. The positions of connecting sites at the corners of such scaffold proteins facilitate the desired assembly formation<sup>13</sup>. Therefore, we chose the ‘Pseudomonas fluorescens PuuE allantoinase (PuuE)’, a homotetramer with \(C_4\) symmetry where each C- terminus is located at each vertex of the quaternary structure (Fig. 1b)<sup>14</sup>. This arrangement enabled straightforward genetic fusion of heterolinkers to the scaffold’s C- termini, leveraging specificity and reversibility of heterolinker interactions to drive assembly formation. This approach simplifies the assembly process and enhances expression and purification efficiency for each protein unit, preventing spontaneous assembly and ensuring the controlled formation of higher- order structures.  
+
+<|ref|>text<|/ref|><|det|>[[115, 809, 886, 900]]<|/det|>
+We constructed protein units ‘PuuE- M’ and ‘PuuE- p’ through genetic engineering, fusing M3L2 and p66α to the C- terminus of PuuE, respectively (Fig. 1c). AlphaFold2 (AF2)<sup>15,16</sup> modelling suggested a configuration with a relatively flexible orientation of M3L2 in PuuE- M, whereas a highly constrained orientation of p66α in PuuE- p (Extended Data Fig. 1). Owing to the constrained orientation of PuuE- p, an
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 886, 300]]<|/det|>
+angular interface was formed between PuuE- M and PuuE- p, and we predicted that assembly of these two units would form a tubular structure (Fig. 1d). Additionally, depending on the number of PuuE- M and PuuE- p units, different tubular structures were expected. Protein expression in Escherichia coli provided both constructs in a soluble form, facilitating their purification. In isolation, neither protein unit exhibits self- assembly (Extended Data Fig. 2a, b). However, when combined under optimised conditions (discussed in the following section), we successfully observed the expected chessboard- patterned tube (PuuE tube) using negative- stain transmission electron microscopy (nsTEM) (Fig. 1e, Extended Data Fig. 2c). Although previous studies have assembled cages \(^{8,9}\) , sheets \(^{10}\) , and three- dimensional (3D) crystals \(^{17}\) using two- component protein systems, this study is unique in that tube structures were successfully created.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 330, 447, 348]]<|/det|>
+## The condition design of tubular assemblies  
+
+<|ref|>text<|/ref|><|det|>[[113, 352, 886, 468]]<|/det|>
+Based on established principles observed in biological systems, including actin filaments \(^{18,19}\) , microtubules \(^{20,21}\) , and amyloid fibrils \(^{22,23}\) , protein concentration, temperature, time, and salinity have a significant influence on assembly formation. Thus, we carefully tailored assembly conditions to exploit the complex interactions between these factors. This approach allowed us to optimise experimental conditions for constructing the desired tubular structures.  
+
+<|ref|>text<|/ref|><|det|>[[112, 496, 886, 682]]<|/det|>
+First, we focused on the dependency of PuuE tube assembly on protein concentration (Extended Data Fig. 2c). Mixing PuuE- M and PuuE- p at a concentration of \(250~\mathrm{nM}\) each (considering tetramer equivalence) led to the formation of tubular structures after an incubation period of \(24\mathrm{~h}\) at \(40^{\circ}\mathrm{C}\) , consistent with the dissociation constant \((K_{\mathrm{d}})\) for M3L2/p66α dimer formation, which is approximately \(268~\mathrm{nM}^{12}\) . Increasing protein concentration to \(2.5~\mu \mathrm{M}\) markedly enhanced the quantity and length of formed tubular structures. Elevating the concentration to \(12.5~\mu \mathrm{M}\) for each component significantly increased tube formation efficiency, underscoring the concentration- dependent nature of PuuE- M- and PuuE- p- facilitated tubular assembly.  
+
+<|ref|>text<|/ref|><|det|>[[112, 712, 886, 852]]<|/det|>
+Next, PuuE tube formation kinetics were investigated. The incubation of mixtures containing \(12.5~\mu \mathrm{M}\) of each protein at \(40^{\circ}\mathrm{C}\) resulted in the formation of nascent tube structures within \(30~\mathrm{min}\) , evolving into distinguishable tubes spanning several hundred nanometres to \(1\mu \mathrm{m}\) in length within \(1 - 2\mathrm{~h}\) (Fig. 2a, b, Extended Data Fig. 3a). Over time, these tubes elongated, reaching several micrometres in length after \(24\mathrm{~h}\) and extending up to approximately \(5\mu \mathrm{m}\) after \(48\mathrm{~h}\) . Once formed, the tubes remained structurally stable for at least 1 month at \(25\pm 1^{\circ}\mathrm{C}\) (Extended Data Fig. 3b).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 888, 396]]<|/det|>
+We then explored the influence of temperature on PnuE tube formation (Extended Data Fig. 4a). While the melting temperature of the M3L2/p66α dimer is around \(35^{\circ}\mathrm{C}\) , tube assembly was hardly observed at sufficiently lower temperatures of \(20 - 25^{\circ}\mathrm{C}\) , even after \(24\mathrm{h}\) of incubation. Conversely, temperatures near \(T_{\mathrm{m}}\) , specifically between 30 and \(40^{\circ}\mathrm{C}\) , markedly promoted tube formation. Therefore, temperatures below \(T_{\mathrm{m}}\) may excessively enhance the binding force between M3L2 and p66α, causing kinetic entrapment of assemblies. However, temperatures close to \(T_{\mathrm{m}}\) modulate this binding force, allowing the dynamic rearrangement of M3L2/p66α interactions under thermal fluctuations, thus facilitating the assembly of thermodynamically stable, ordered structures. This principle is consistent with general crystallisation theories \(^{24,25}\) and reports on the formation of ordered structures in natural protein assemblies \(^{22,23,26}\) . Importantly, temperatures above \(45^{\circ}\mathrm{C}\) led to thermal denaturation and aggregation of PnuE- M ( \(T_{\mathrm{m}} = 46.2^{\circ}\mathrm{C}\) ) and PnuE- p ( \(T_{\mathrm{m}} = 48.1^{\circ}\mathrm{C}\) ), significantly diminishing tube formation capabilities (Extended Data Fig. 4b, c). This finding implies that the original concept of tube formation with reversible temperature control was not realised.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 425, 384, 443]]<|/det|>
+## Reversibility of tubular assemblies  
+
+<|ref|>text<|/ref|><|det|>[[112, 448, 886, 754]]<|/det|>
+Finally, we examined the effects of salt concentration on PnuE tube assembly. We prepared mixtures with different NaCl concentrations ranging from 0 to \(400\mathrm{mM}\) and incubated them at \(40^{\circ}\mathrm{C}\) for \(24\mathrm{h}\) . Tube formation was clearly observed within the NaCl concentration window of \(50 - 200\mathrm{mM}\) , with no tube formation detected outside this range (Fig. 2c, Extended Data Fig. 5a). Since both PnuE- M ( \(\mathrm{pI} = 6.44\) ) and PnuE- p ( \(\mathrm{pI} = 6.02\) ) were similarly charged under \(\mathrm{pH}8.0\) , tube formation at low salt concentrations was likely inhibited by electrostatic repulsion. Conversely, moderate electrostatic shielding facilitated by \(50 - 200\mathrm{mM}\) NaCl likely provided conducive conditions for tube assembly, whereas higher NaCl concentrations may have induced excessive shielding or aggregation due to salting out, inhibiting tube formation. This observation aligns with known phenomena in protein crystallisation, where electrostatic shielding above a certain threshold can prevent crystal growth \(^{17,27 - 29}\) , although crystals formed by a combination of electrostatic and hydrophobic interactions can remain stable up to approximately \(200\mathrm{mM}\) NaCl \(^{30}\) . The association of M3L2/p66α involves both electrostatic and hydrophobic interactions \(^{12}\) , consistent with the latter scenario.  
+
+<|ref|>text<|/ref|><|det|>[[113, 785, 886, 900]]<|/det|>
+The salt- dependent PnuE tube formation and the dynamic nature of PnuE- M/PnuE- p interactions near their \(T_{\mathrm{m}}(35^{\circ}\mathrm{C})\) led us to hypothesise that tubes could undergo reversible disassembly and reassembly in response to changes in NaCl concentration. Confirming our hypothesis, tubes initially formed in \(100\mathrm{mM}\) NaCl solution were significantly shortened when subjected to solvent exchange with \(0\mathrm{mM}\) NaCl buffer (NaCl (- ) buffer) and subsequent incubation at \(40^{\circ}\mathrm{C}\) for \(24\mathrm{h}\) (Fig. 2d, e, Extended Data Fig. 5b). Subsequent
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 886, 277]]<|/det|>
+solvent exchange with \(100\mathrm{mMNaCl}\) buffer \((\mathrm{NaCl} + )\) buffer) resulted in notable tube reassembly. This salt- concentration- driven reversibility, although divergent from the initial temperature- controlled reversibility hypothesis, marks a significant advance in artificial protein assembly design, allowing for the biomimetic replication of dynamic structural changes under relatively mild conditions, akin to the behaviour of actin filaments in cellular structures \(^{18,19}\) . Unlike the irreversible aggregation observed in amyloid structures, our assemblies exhibit a reversible and dynamic assembly process akin to the cytoskeleton behaviour, successfully demonstrating the potential for the biomimetic replication of natural cellular dynamics under controlled conditions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 306, 365, 323]]<|/det|>
+## Diversity and flexibility of tubes  
+
+<|ref|>text<|/ref|><|det|>[[112, 329, 886, 781]]<|/det|>
+Based on these findings, we determined the ideal conditions for PuuE tube formation in \(100\mathrm{mMNaCl}\) at \(40^{\circ}\mathrm{C}\) for \(24\mathrm{h}\) . To further characterise the structural features of tubes formed under these conditions, cryo- electron microscopy (cryo- EM) was employed (Extended Data Fig. 6, Extended Data Table 1). Analysis of 2D class- averaged images revealed a spectrum of tube diameters and symmetries similar to the diversity observed in microtubules \(^{31 - 34}\) (Fig. 3a). From these images, we successfully reconstructed the 3D structures with \(C_4\) , \(C_5\) , and \(C_6\) symmetries within tube structures (Fig. 3b). Insights from the PuuE crystal structure \(^{14}\) , notably its unique central indentation on the back surface (Fig 1b), allowed us to deduce that PuuE units are alternately oriented face- to- back across all 3D models. Additionally, cryo- EM analysis suggested that connection flexibility allowed the contraction of the entire tube structure (Extended Data Fig. 6, Supplementary Movie 1). Although definitive conclusions are difficult owing to its inherent flexibility, the comparison of the cryo- EM 3D reconstruction with the AF2- predicted model of PuuE- p suggests that PuuE- p is less likely to fit inside the tube structure and instead fits better on the outside (Supplementary Movie 2). Furthermore, tubes with larger diameters, presumably having \(C_7\) to \(C_{10}\) symmetries, were identified at low resolution, likely owing to the flexibility of connection sites influencing tube structure. In fact, nsTEM and cryo- EM images frequently showed tubes appearing bent or compressed (Extended Data Fig. 2–6). In contrast to prior strategies by engineering on scaffold proteins itself to create higher- order protein assemblies \(^{8 - 10,13,35}\) , NIPAD integrates a flexible linker with the scaffold protein, resulting in varied structures and arrangements among higher- order assemblies. This variation in tube diameter, akin to that observed in microtubules \(^{31 - 34}\) , is presumably a hallmark of NIPAD.  
+
+<|ref|>text<|/ref|><|det|>[[115, 808, 886, 899]]<|/det|>
+To further explore PuuE tube structure flexibility, we labelled tubes with Alexa Fluor 488 succinimidyl ester and observed them in real- time using total internal reflection fluorescence microscopy (TIRFM). Tube structures were constrained in the evanescent field by the depletion effect of methylcellulose contained in the observation buffer and underwent thermally driven two- dimensional random bending (Fig. 3c,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 277]]<|/det|>
+Supplementary Fig. 1a, Supplementary Movie 3). Analysis of the fluctuation in shape yielded the persistence length \((L_{\mathrm{p}})\) of \(19.7 \mu \mathrm{m}\) (Fig. 3d, Supplementary Fig. 1b). \(L_{\mathrm{p}}\) is the mean length over which a semiflexible polymer remains straight, characterising polymer stiffness<sup>36</sup>. The \(L_{\mathrm{p}}\) value of the tube structures is nearly equal to that of actin filaments measured in this study, \(12.5 \mu \mathrm{m}\) (Fig. 3d), and previously reported values of \(9 - 20 \mu \mathrm{m}^{37}\) . Microtubules have much longer persistence lengths \((0.1 - 10 \mathrm{mm})^{38 - 40}\) . Conversely, intermediate filaments, another cytoskeletal fibre structure, typically have shorter persistence lengths \((< 1 \mu \mathrm{m})^{41}\) . Therefore, the tube structure is as flexible as actin filaments, more flexible than microtubules, and stiffer than intermediate filaments.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 306, 338, 323]]<|/det|>
+## Emulation of actin filaments  
+
+<|ref|>text<|/ref|><|det|>[[111, 328, 888, 732]]<|/det|>
+Finally, we sought to modify the morphology of PuuE tube assemblies. Specifically, we hypothesised that grafting the D- loop of actin onto PuuE- M would produce tubes with a helical conformation reminiscent of actin filaments. The D- loop plays an important role in helical actin filament formation via hydrophobic pockets<sup>42- 45</sup>. The hydrophobic nature of a prominent indentation on the 'back' side of PuuE (Extended Data Fig. 7a) guided our hypothesis. The loop structure on the back side of PuuE- M was chosen as the grafting site for the D- loop, and the 'PuuE(D- loop)- M' fusion construct was constructed (Fig. 4a). When PuuE(D- loop)- M was expressed in \(E\) . coli, it was found in the soluble fraction and was purified as PuuE- M. Since PuuE(D- loop)- M has a lower thermal stability \((T_{\mathrm{m}} = 35.6^{\circ}\mathrm{C})\) than PuuE- M \((T_{\mathrm{m}} = 46.2^{\circ}\mathrm{C}\) , Extended Data Fig. 4b, 7b), we performed sample incubation at a lower temperature \((30^{\circ}\mathrm{C})\) . Although PuuE(D- loop)- M alone did not assemble, its combination with PuuE- p replicated the PuuE tube and introduced novel helical patterns, with two or three tubes intertwined (PuuE D- loop tube), as verified via nsTEM (Fig. 4b, Extended Data Fig. 7c). The emergence of helical formations, absent in the PuuE- M and PuuE- p mixtures, clearly stems from D- loop integration. While the D- loop likely plays a crucial role in the helical formation of actin filaments<sup>42- 45</sup>, its complete mechanism remains unclear. Our study, by successfully grafting the D- loop to replicate actin- like helical structures, offers a novel perspective on its significance. This approach confirms the critical role of the D- loop in helical conformations and opens new avenues for understanding the intricate design principles of actin filaments.  
+
+<|ref|>text<|/ref|><|det|>[[114, 760, 886, 899]]<|/det|>
+As mentioned above, the helical conformation of tube structures is thought to arise from hydrophobic interactions, which are inherently sensitive to temperature and weaken at lower temperatures<sup>46- 48</sup>. This led us to posit that alterations in temperature can serve as reversible switches for disassembly and reassembly. Notably, exposing the samples to \(0^{\circ}\mathrm{C}\) for 1 h suggested a dissociation of the helical conformations and hinted at a possible breakdown of the tubular structures (Fig. 4c, Extended Data Fig. 7d). Remarkably, when these disassembled samples were reintroduced to \(30^{\circ}\mathrm{C}\) for \(24 \mathrm{h}\) , the elongated tubular formations
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 886, 252]]<|/det|>
+with helical conformations were restored. By grafting D- loop, the tube structure could form helical conformations and acquired a new temperature- dependent reversibility. This thermal responsiveness parallels the behaviour of microtubules<sup>20,21,49</sup>, underscoring the ability of the NIPAD approach to mimic the dynamic properties of biomolecular assemblies in artificial protein design to create complex higher- order protein structures. This dual responsiveness (salt and temperature dependence) enhances the biomimetic potential of our design, which is a promising avenue for advanced applications in synthetic biology and materials science.  
+
+<|ref|>text<|/ref|><|det|>[[112, 280, 886, 903]]<|/det|>
+To determine the intricate helical configurations, structural analyses were performed using cryo- EM (Fig. 4d, Extended Data Fig. 8, Extended Data Table 1). In addition to the inherent flexibility of the tube structure, the ability of tubes to form helical bundles introduces an additional layer of complexity to the structural analysis. This complexity is underscored by cryo- EM results, which render a detailed analysis of these higher- order structures particularly challenging. However, analysis of 2D class- averaged images of the helical structures revealed double and triple helical tubes, which was consistent with the nsTEM observation (Fig. 4b, d, Extended Data Fig. 7c, 8). Moreover, the tube structures forming these helices seem to show a thinner diameter of approximately \(24~\mathrm{nm}\) , which does not align with any of the original PuuE tubes with diameters starting at \(28.6~\mathrm{nm}\) (Fig. 3b, Extended Data Fig. 6). Therefore, an attempt was made to elucidate the characteristics of the tube structures forming the helical conformations by employing temperature- induced structural disassembly (Fig. 4c). The cryo- EM sample was initially prepared at \(25 \pm 1^{\circ}\mathrm{C}\) to prevent disassembly; however, to unwind the helical structures, the sample was briefly chilled on ice for approximately \(1\mathrm{~h}\) . By observing these chilled samples with cryo- EM, we successfully identified a new tube structure with \(C_3\) symmetry (Fig. 4e, f, Extended Data Table 1) in addition to the previously observed structures (Extended Data Fig. 9). A comparison of this tube structure with \(C_3\) symmetry with the structures forming the helical conformations indicated a match, suggesting that the tubes forming the helical conformation have indeed \(C_3\) symmetry (Fig. 4d bottom). Additionally, the diameter of approximately \(23.6\mathrm{~nm}\) , as determined by cryo- EM 3D reconstruction, corresponds to the tubes forming helical structures, further supporting these findings. Considering its inherent flexibility, it is challenging to reach a definitive conclusion, but further examination of the tube structure with \(C_3\) symmetry suggests that PuuE- p is likely positioned on the outside (Fig. 4g, Supplementary Movie 4), consistent with the original PuuE tube structures (Fig. 3b, Supplementary Movie 2). This arrangement indicates that the D- loop of PuuE(D- loop)- M appears on the exterior of the tubes, which is crucial for forming helical structures not observed in PuuE tubes lacking the D- loop. The \(C_3\) symmetry enhances the exposure of internal PuuE(D- loop)- M on the outer surface compared to structures with \(C_4\) or higher symmetry, enabling hydrophobic interactions between tubes. Therefore, the formation of the \(C_3\) symmetric tube structure likely facilitated
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 886, 228]]<|/det|>
+the creation of the helical conformations. Furthermore, the lack of \(C_3\) symmetry in PuuE tubes (Fig. 3a, b) suggests that they are unstable as single tubes without forming helical conformations. The formation of helical conformations may stabilise the structure with \(C_3\) symmetry, as evidenced by its successful identification in tube structures with helical conformations. Additionally, the temperature- induced degradation leading to the rapid collapse of tubes with \(C_3\) symmetry suggests that helical structure stabilisation is essential for maintaining structural integrity under physiological conditions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 260, 213, 276]]<|/det|>
+## Conclusions  
+
+<|ref|>text<|/ref|><|det|>[[115, 281, 886, 420]]<|/det|>
+We introduce NIPAD, a pioneering approach that intricately weaves together protein unit design and assembly, drawing inspiration from the complexity and adaptability of natural protein assemblies. By employing NIPAD, we created a unique higher- order tubular assembly composed of two protein units, exhibiting the reversible, flexible, and diverse characteristics of natural structures. A noteworthy highlight of our study was the successful induction of helical conformations within these tube assemblies, akin to those observed in actin filaments, achieved through strategic integration of the D- loop into assembly design.  
+
+<|ref|>text<|/ref|><|det|>[[113, 448, 886, 803]]<|/det|>
+This advance in protein assembly highlights the complexity of emulating the dynamic behaviour observed in biological systems. The design and assembly of protein structures in vitro, although closely controlled, cannot fully replicate the complex cellular environment. In vivo, myriad factors, including macromolecular crowding, post- translational modifications, and interactions with other cellular components can significantly influence protein behaviour<sup>50</sup>. Our designed protein assemblies exhibit remarkable biomimicry regarding flexibility, reversibility, and structural diversity, but have yet to be demonstrated and validated in biological systems, where the true complexity of biological interactions is present. Furthermore, our approach, which focuses on the assembly of tubular structures inspired by cytoskeletal elements, including actin filaments and microtubules, does not address the full range of complex protein structures found within biological systems. Natural protein assemblies contain structural and functional diversity, and much remains to be explored. Computational methods have an important role to play in improving the accuracy and breadth of protein assembly design<sup>1,8- 10</sup>. By utilising computational predictions about protein interactions and assembly outcomes, our design would be refined into more complex and functional biomimetic structures, with applications ranging from novel biomaterials and nanodevices to therapeutic innovations.  
+
+<|ref|>text<|/ref|><|det|>[[115, 832, 886, 900]]<|/det|>
+Our research extends the boundaries of protein assembly design and provides new insights into its applications in synthetic biology and life sciences. This research encourages a comprehensive approach that bridges the divide between the biological and materials sciences and suggests that the exploration of
+
+<--- Page Split --->
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+nature's complex systems has the potential to transform science and technology. As we continue to explore this intersection of life and materials sciences, we anticipate that future investigations will provide fundamental insights into the natural world, heralding a new era of scientific discoveries and technological breakthroughs.  
+
+<|ref|>title<|/ref|><|det|>[[115, 211, 202, 226]]<|/det|>
+# References  
+
+<|ref|>text<|/ref|><|det|>[[111, 230, 884, 910]]<|/det|>
+Zhu, J. et al. Protein Assembly by Design. Chem Rev 121, 13701- 13796 (2021). Korn, E. D., Carlier, M. F. & Pantaloni, D. Actin polymerization and ATP hydrolysis. Science 238, 638- 644 (1987). Pollard, T. D. & Cooper, J. A. Actin, a central player in cell shape and movement. Science 326, 1208- 1212 (2009). Desai, A. & Mitchison, T. J. Microtubule polymerization dynamics. Annu Rev Cell Dev Biol 13, 83- 117 (1997). Gudimchuk, N. B. & McIntosh, J. R. Regulation of microtubule dynamics, mechanics and function through the growing tip. Nat Rev Mol Cell Biol 22, 777- 795 (2021). Perlmutter, J. D. & Hagan, M. F. Mechanisms of virus assembly. Annu Rev Phys Chem 66, 217- 239 (2015). Sevvana, M., Klose, T. & Rossmann, M. G. Principles of Virus Structure. Encyclopedia of Virology, 257- 277 (2021). King, N. P. et al. Accurate design of co- assembling multi- component protein nanomaterials. Nature 510, 103- 108 (2014). Bale, J. B. et al. Accurate design of megadalton- scale two- component icosahedral protein complexes. Science 353, 389- 394 (2016). Ben- Sasson, A. J. et al. Design of biologically active binary protein 2D materials. Nature 589, 468- 473 (2021). Gnanapragasam, M. N. et al. p66Alpha- MBD2 coiled- coil interaction and recruitment of Mi- 2 are critical for globin gene silencing by the MBD2- NuRD complex. Proc Natl Acad Sci U S A 108, 7487- 7492 (2011). Walavalkar, N. M., Gordon, N. & Williams, D. C., Jr. Unique features of the anti- parallel, heterodimeric coiled- coil interaction between methyl- cytosine binding domain 2 (MBD2) homologues and GATA zinc finger domain containing 2A (GATAD2A/p66alpha). J Biol Chem 288, 3419- 3427 (2013). Suzuki, Y. et al. Self- assembly of coherently dynamic, auxetic, two- dimensional protein crystals. Nature 533, 369- 373 (2016). Ramazzina, I. et al. Logical identification of an allantoinase analog (puuE) recruited from polysaccharide deacetylases. J Biol Chem 283, 23295- 23304 (2008). Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583- 589 (2021). Evans, R. et al. Protein complex prediction with AlphaFold- Multimer. Preprint at bioRxiv https://doi.org/10.1101/2021.10.04.463034 (2022). Patrian, M. et al. Supercharged Fluorescent Protein- Apoferritin Cocrystals for Lighting Applications. ACS Nano 17, 21206- 21215 (2023). Kang, H. et al. Identification of cation- binding sites on actin that drive polymerization and modulate bending stiffness. Proc Natl Acad Sci U S A 109, 16923- 16927 (2012). Kang, H., Bradley, M. J., Elam, W. A. & De La Cruz, E. M. Regulation of actin by ion- linked equilibria. Biophys J 105, 2621- 2628 (2013). Weisenberg, R. C. Microtubule formation in vitro in solutions containing low calcium concentrations. Science 177, 1104- 1105 (1972).
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+320 21 Li, G. & Moore, J. K. Microtubule dynamics at low temperature: evidence that tubulin recycling 321 limits assembly. Mol Biol Cell 31, 1154- 1166 (2020). 322 Noji, M. et al. Heating during agitation of beta(2)- microglobulin reveals that supersaturation 323 breakdown is required for amyloid fibril formation at neutral pH. J Biol Chem 294, 15826- 15835 324 (2019). 325 23 Goto, Y., Nakajima, K., Yamamoto, S. & Yamaguchi, K. Supersaturation, a Critical Factor 326 Underlying Proteostasis of Amyloid Fibril Formation. J Mol Biol, 168475 (2024). 327 24 De Yoreo, J. J. et al. CRYSTAL GROWTH. Crystallization by particle attachment in synthetic, 328 biogenic, and geologic environments. Science 349, aaa6760 (2015). 329 25 Chen, Y. et al. Morphology selection kinetics of crystallization in a sphere. Nature Physics 17, 121- 127 (2021). 330 26 Bruinsma, R. F., Wuite, G. J. L. & Roos, W. H. Physics of viral dynamics. Nat Rev Phys 3, 76- 91 331 27 Kostiainen, M. A. et al. Electrostatic assembly of binary nanoparticle superlattices using protein 332 cages. Nat Nanotechnol 8, 52- 56 (2013). 333 28 Liljestrom, V., Seitsonen, J. & Kostiainen, M. A. Electrostatic Self- Assembly of Soft Matter 334 Nanoparticle Cocrystals with Tunable Lattice Parameters. ACS Nano 9, 11278- 11285 (2015). 335 29 Anaya- Plaza, E. et al. Phthalocyanine- Virus Nanofibers as Heterogeneous Catalysts for 336 Continuous- Flow Photo- Oxidation Processes. Adv Mater 31, e1902582 (2019). 337 30 Liu, Q. et al. Optically Controlled Construction of Three- Dimensional Protein Arrays. Angew 338 Chem Int Ed Engl 62, e202303880 (2023). 339 31 Chalfie, M. & Thomson, J. N. Structural and functional diversity in the neuronal microtubules of 340 Caenorhabditis elegans. J Cell Biol 93, 15- 23 (1982). 341 32 Amos, L. A. Microtubule structure and its stabilisation. Org Biomol Chem 2, 2153- 2160 (2004). 342 Chaaban, S. & Brouhard, G. J. A microtubule bestiary: structural diversity in tubulin polymers. 343 Mol Biol Cell 28, 2924- 2931 (2017). 344 Ferreira, J. L. et al. Variable microtubule architecture in the malaria parasite. Nat Commun 14, 1216 (2023). 345 Golub, E. et al. Constructing protein polyhedra via orthogonal chemical interactions. Nature 578, 476- 176 (2020). 346 Landau, L. D., Lifshits, E. M. & Pitaevskii, L. P. Statistical Physics. 3rd ed., rev. and enl. / by 347 E.M. Lifshitz and L.P. Pitaevskii, Repr. with corrections edn, (Pergamon Press, 1993). 348 Isambert, H. et al. Flexibility of actin filaments derived from thermal fluctuations. Effect of 349 bound nucleotide, phalloidin, and muscle regulatory proteins. J Biol Chem 270, 11437- 11444 350 (1995). 351 Janson, M. E. & Dogterom, M. A bending mode analysis for growing microtubules: evidence for 352 a velocity- dependent rigidity. Biophys J 87, 2723- 2736 (2004). 353 Pampaloni, F. et al. Thermal fluctuations of grafted microtubules provide evidence of a length- 354 dependent persistence length. Proc Natl Acad Sci U S A 103, 10248- 10253 (2006). 355 Van den Heuvel, M. G., de Graaff, M. P. & Dekker, C. Microtubule curvatures under 356 perpendicular electric forces reveal a low persistence length. Proc Natl Acad Sci U S A 105, 7941- 357 364 (2008). 358 Block, J., Schroeder, V., Pawelzyk, P., Willenbacher, N. & Koster, S. Physical properties of 359 cytoplasmic intermediate filaments. Biochim Biophys Acta 1853, 3053- 3064 (2015). 360 Oda, T., Iwasa, M., Aihara, T., Maeda, Y. & Narita, A. The nature of the globular- to fibrous- actin 361 transition. Nature 457, 441- 445 (2009). 362 Murakami, K. et al. Structural basis for actin assembly, activation of ATP hydrolysis, and delayed 363 phosphate release. Cell 143, 275- 287 (2010). 364 Durer, Z. A. et al. Structural states and dynamics of the D- loop in actin. Biophys J 103, 930- 939 365 (2012).
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+370 45 Das, S. et al. D- loop Dynamics and Near- Atomic- Resolution Cryo- EM Structure of Phalloidin- 371 Bound F- Actin. Structure 28, 586- 593 e583 (2020). 372 46 Pratt, L. R., Chaudhari, M. I. & Rempe, S. B. Statistical Analyses of Hydrophobic Interactions: A 373 Mini- Review. J Phys Chem B 120, 6455- 6460 (2016). 374 47 Koga, K. & Yamamoto, N. Hydrophobicity Varying with Temperature, Pressure, and Salt 375 Concentration. J Phys Chem B 122, 3655- 3665 (2018). 376 48 Sun, Q., Fu, Y. F. & Wang, W. Q. Temperature effects on hydrophobic interactions: Implications 377 for protein unfolding. Chem Phys 559 (2022). 378 49 Echandia, E. L. & Piezzi, R. S. Microtubules in the nerve fibers of the toad Bufo arenarum 379 Hensel. Effect of low temperature on the sciatic nerve. J Cell Biol 39, 491- 497 (1968). 380 50 Nakajima, K. et al. Macromolecular crowding and supersaturation protect hemodialysis patients 381 from the onset of dialysis- related amyloidosis. Nat Commun 13, 5689 (2022). 382 51 Pace, C. N., Vajdos, F., Fee, L., Grimsley, G. & Gray, T. How to measure and predict the molar 383 absorption coefficient of a protein. Protein Sci 4, 2411- 2423 (1995). 384 52 Schindelin, J. et al. Fiji: an open- source platform for biological- image analysis. Nat Methods 9, 385 676- 682 (2012). 386 53 Scheres, S. H. A Bayesian view on cryo- EM structure determination. J Mol Biol 415, 406- 418 387 (2012). 388 54 He, S. & Scheres, S. H. W. Helical reconstruction in RELION. J Struct Biol 198, 163- 176 (2017). 389 55 Rohou, A. & Grigorieff, N. CTFFIND4: Fast and accurate defocus estimation from electron 390 micrographs. J Struct Biol 192, 216- 221 (2015). 391 56 Smith, M. B. et al. Segmentation and tracking of cytoskeletal filaments using open active 392 contours. Cytoskeleton (Hoboken) 67, 693- 705 (2010). 393 57 Schrodinger, LLC. The PyMOL Molecular Graphics System, Version 2.5. 394 58 Meng, E. C. et al. UCSF ChimeraX: Tools for structure building and analysis. Protein Sci 32, 395 e4792 (2023). 396 59 Bjellqvist, B. et al. The focusing positions of polypeptides in immobilized pH gradients can be 397 predicted from their amino acid sequences. Electrophoresis 14, 1023- 1031 (1993). 398 60 Eisenberg, D., Schwarz, E., Komaromy, M. & Wall, R. Analysis of membrane and surface protein 399 sequences with the hydrophobic moment plot. J Mol Biol 179, 125- 142 (1984).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 87, 880, 445]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 453, 886, 688]]<|/det|>
+<center>Fig. 1. Construction of PuuE tube via NIPAD. | a, AF2 prediction of the heterodimeric peptide pair, M3L2 (yellow) and p66α (blue). b, Crystal structure of PuuE (PDB ID: 3CL6). C-terminus positions are circled. Detailed structure, face, side, and back are shown for clarity. c, Schematic diagram of the protein sequence (top) and the AF2-predicted structures of PuuE-M and PuuE-p (bottom). PuuE-M and PuuE-p are coloured yellow and blue to match the respective peptides and overall structure to clear the tube structure (d). The peptide parts, M3L2 and p66α, are highlighted in darker colours. d, Left, predicted model of the tubular assembly consisting of PuuE-M and PuuE-p. Right, brief schematic diagram of how many proteins (n) form a system of tube structures. e, nsTEM images of tubular assemblies constructed from PuuE-M and PuuE-p; 12.5 μM PuuE-M and 12.5 μM PuuE-p in NaCl (+) buffer was incubated at 40 °C for 24 h and imaged via nsTEM. Scale bars, 1 μm (white), 50 nm (black). </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[293, 90, 705, 744]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 766, 886, 905]]<|/det|>
+<center>Fig. 2. Condition optimisation for PuuE tube assembly. | a, b, The kinetics of tubular assembly. nsTEM images of tubular assembly (a) and length analysis (b). c, nsTEM images of tubular assemblies with varying NaCl concentration. d, nsTEM images showing the reversibility of tube structures with changing NaCl concentration. e, Tube length analysis of nsTEM images. For tube length analysis, tubes were picked up and calculated from 5k images at each step; 150 tubes from the longest tube length were used at each data point. \*\*\* p<0.001 (Welch's t-test). Scale bar, 1 μm. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 881, 480]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 485, 886, 863]]<|/det|>
+<center>Fig. 3. Structural characterisation of PuuE tube. | a, 2D class-averaged images of tube structures. The population of each structure was determined from the total pickings of 206,658 tube segments. Scale bar, 500 Å. b 3D reconstructed models of tube structures with \(C_4\) , \(C_5\) , and \(C_6\) symmetries. The fitting results suggest that PuuE-p is less likely to fit into units located inside the tube structure and more likely to fit into units located on the outside. Based on the predictions, the units were colour-coded as shown in Fig. 1c. For visibility, only the molecular model of the PuuE (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. c, Time-lapse images of random bending of the tube structures monitored by TIRFM. Top: snapshots at the starting point (0 sec) and after 4 sec (top). Bottom: enlarged images of tubes in green or orange rectangles in the top images, showing the dynamic flexibility of tube structures between 0 to 4 sec (0.4 sec per image). Scale bar, 5 μm. d, Left, a relationship between contour length (L) and mean square of end-to-end distance (<R²>) of the tube structures for estimation of the persistence length (Lp). The continued lines represent fitting curves (black for PuuE tube, red for actin filament) to experimental data (black open circle for PuuE tube, red cross mark for actin filament). Right, comparison of persistence length with cytoskeletal elements. PuuE tube (PT, black) and actin filaments (AF, red) were determined in this study (A wider range of plots is shown in Supplementary Fig. 1b). Intermediate filaments (IF, blue) and microtubules (MT, green) are taken from ref. 41 and 38, respectively. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 95, 886, 520]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 528, 886, 585]]<|/det|>
+<center>Fig. 4. Emulation of actin filament by D-loop grafting. | a, Schematic representations of PuuE(D-loop)-M. The position of D-loop graft (red) is indicated by protein sequence (top) and the AF2-predicted structure (bottom). b, nsTEM images of tubes with a helical conformation composed of PuuE(D-loop)-M and PuuE-p. The helical pattern of two (centre) or three (right) intertwined tubes is shown in the high-magnification image. c, nsTEM images showing the reversibility of tube structure with helical conformations by temperature change. d, Representative cryo-EM images (top) and 2D class-averaged images (bottom) of helical tube structures. e, Representative cryo-EM image (top) and 2D class-averaged image of tube structure with \(C_3\) symmetry. Tube structures with other symmetries found in this study are shown in Extended Data Fig. 9. f, 3D reconstructed model of tube structure with \(C_3\) symmetry. For visibility, only the PuuE structure (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. g, Fitting of AF2-predicted model of PuuE-p into the 3D reconstructed model. The fitting results suggest that PuuE-p is unlikely to fit in the units located inside the tube structure; it is better accommodated by the units on the outside. Based on this prediction, the units in f are colour-coded as described in Fig. 1c. 6xHis-TEVcs region of the PuuE-p model is not shown to improve visibility. Scale bars, 1 \(\mu \mathrm{m}\) (white), 100 nm (black), 10 nm (grey). </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 92, 186, 107]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 115, 283, 131]]<|/det|>
+## Plasmids and cloning  
+
+<|ref|>text<|/ref|><|det|>[[112, 137, 886, 397]]<|/det|>
+Primers for cloning and synthetic genes of N- terminal 6xHis- tagged PuuE- M and PuuE- p were purchased from Eurofins Genomics. PCRs were performed using the PrimeSTAR Max DNA Polymerase (Takara Bio) according to the manufacturer's protocol. Sizes of PCR products were verified using standard agarose gel electrophoresis. The In- Fusion Snap Assembly (Takara Bio) was used as the standard method for cloning according to the manufacturer's protocol, and each amplified gene fragment was ligated between the Ndel and BamHI multicoloring sites of the pET11a expression vector (Novagen). Primers for cloning and a synthetic DNA fragment of D- loop were purchased from Eurofins Genomics. The plasmid encoding N- terminal 6xHis- tagged PuuE- D- loop- M was generated from the PuuE- M plasmid following the same procedures as above. All plasmids were amplified in E. coli strain DH5α (NIPPON GENE) and extracted using the NucleoSpin Plasmid EasyPure (MACHEREY- NAGEL) according to the manufacturer's protocol. DNA sequences were confirmed by a sequencing service (Eurofins Genomics).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 426, 390, 443]]<|/det|>
+## Protein expression and purification  
+
+<|ref|>text<|/ref|><|det|>[[111, 448, 886, 902]]<|/det|>
+The recombinant proteins were expressed using E. coli strain BL21 (DE3) (NIPPON GENE) cotransformed with a pGro7 chaperone plasmid (Takara Bio) and purified as follows. After transformation with plasmid DNA, colonies grown overnight on LB agar plates supplemented with \(100~\mu \mathrm{g / mL}\) ampicillin (Amp) and \(20~\mu \mathrm{g / mL}\) chloramphenicol (Crm) at \(37^{\circ}\mathrm{C}\) were picked to inoculate \(5\mathrm{mL}\) of liquid LB- AmpCrm broth and grown overnight at \(37^{\circ}\mathrm{C}\) and \(200~\mathrm{rpm}\) . Overnight cultures were diluted in \(1\mathrm{L}\) of liquid LB- Amp- Crm broth supplemented with \(0.5\mathrm{mg / mL}\) L- arabinose and grown at \(37^{\circ}\mathrm{C}\) and \(200~\mathrm{rpm}\) until reaching an optical density at \(600\mathrm{nm}\) of 0.6- 0.8. Protein synthesis was induced by adding \(0.1\mathrm{mM}\) isopropyl- \(\beta\) - D- thiogalactopyranoside and the cultures were grown at \(16^{\circ}\mathrm{C}\) for \(16 - 20\mathrm{h}\) . Cells were harvested by centrifugation at \(15,317\mathrm{g}\) and \(4^{\circ}\mathrm{C}\) for \(5\mathrm{min}\) and then frozen at - 80 °C. Cell pellets were thawed at \(25\pm 1^{\circ}\mathrm{C}\) , resuspended in \(60~\mathrm{mL}\) of ice- cold purification buffer ( \(20\mathrm{mM}\) Tris- HCl, \(\mathrm{pH}8.0\) , containing \(300\mathrm{mM}\) NaCl), and lysed using sonication ( \(9\mathrm{min}\) with 1:2 on/off cycles and \(70\%\) amplitude; SFX250, Branson) on ice. Cell debris was cleared by centrifugation at \(15,317\mathrm{g}\) and \(4^{\circ}\mathrm{C}\) for \(30\mathrm{min}\) . The supernatant (i.e., crude protein) was filtered through a \(0.45 - \mu \mathrm{m}\) pore size membrane filter (Merck), applied onto HisTrap FF crude column (Cytiva) pre- equilibrated with the purification buffer and washed with \(5\mathrm{cm}\) volumes of \(2\%\) elution buffer ( \(20\mathrm{mM}\) Tris- HCl, \(\mathrm{pH}8.0\) , containing \(300\mathrm{mM}\) NaCl and \(1\mathrm{M}\) imidazole; \(2\%\) means \(20\mathrm{mM}\) imidazole). 6xHis- tagged proteins were eluted with \(10\mathrm{cm}\) volumes of elution buffer with a linear gradient of \(2 - 40\%\) (i.e., \(20 - 400\mathrm{mM}\) imidazole). The fractions containing the proteins confirmed by means of UV absorption and SDS- PAGE were again collected and dialysed against 50- fold volume of NaCl (+) or NaCl (- ) buffer ( \(50\mathrm{mM}\) Tris- HCl, \(\mathrm{pH}8.0\) , containing \(\pm 100\mathrm{mM}\) NaCl and \(0.5\mathrm{mM}\) EDTA) at \(4^{\circ}\mathrm{C}\) twice.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 89, 886, 227]]<|/det|>
+Each of the purified proteins was concentrated by an Amicon Ultra centrifugal filter unit (Merck) with an appropriate molecular weight cutoff followed by filtration through a \(0.45 \mu \mathrm{m}\) pore size membrane filter (Merck). Protein concentration was determined by absorbance measurements at \(280 \mathrm{nm}\) using a NanoDrop OneC spectrophotometer (Thermo Scientific). The molar extinction coefficients at \(280 \mathrm{nm}\) for the proteins were calculated from the basis of amino acid composition<sup>51</sup>. The concentrated proteins were frozen in liquid nitrogen and stored at \(- 80^{\circ} \mathrm{C}\) before experiments.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 259, 272, 276]]<|/det|>
+## Sample preparation  
+
+<|ref|>text<|/ref|><|det|>[[113, 281, 886, 515]]<|/det|>
+All proteins were thawed immediately before tube formation experiments on ice. Each sample was prepared in a \(1.5 \mathrm{mL}\) microtube using an appropriate buffer to adjust the concentration described in the manuscript and the volume to \(200 \mu \mathrm{L}\) at \(25 \pm 1^{\circ} \mathrm{C}\) . Except for the NaCl concentration- dependent experiments, NaCl (+) protein stock solution and buffer were used. For the NaCl concentration- dependent experiments, \(50 \mathrm{mM}\) Tris- HCl (pH 8.0), \(1 \mathrm{M} \mathrm{NaCl}\) , and \(0.5 \mathrm{mM}\) EDTA were used in addition to NaCl (- ) protein stock solution and buffer. Incubation of the samples was carried out using a ThermoMixer C (Eppendorf) or a MATRIX Orbital Delta Plus (IKA) with shaking of \(300 \mathrm{rpm}\) at the temperature described in the manuscript. For the disassembly and reassembly experiments, buffer substitution procedures were conducted using NaCl (- ) and NaCl (+) buffer, respectively, with Microcon 50 centrifugal filter units (Merck) according to the manufacturer's protocol four times at each step.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 547, 564, 564]]<|/det|>
+## Negative-stain transmission electron microscopy (nSTEM)  
+
+<|ref|>text<|/ref|><|det|>[[113, 568, 886, 754]]<|/det|>
+A naked G600TT copper grid (Nisshin EM) was carbon- coated using a VE- 2030 (VACUUM DEVICE). The grid was glow- discharged using a PIB- 10 (VACUUM DEVICE). Then, a \(5 - \mu \mathrm{L}\) aliquot of the sample solution was placed on the grid for \(1 \mathrm{min}\) , and the remaining solution was removed with filter paper (No. 2, ADVANTEC) followed by rinsing thrice with a \(5 - \mu \mathrm{L}\) aliquot of Milli- Q water. After blotting off the water with filter paper, the sample was stained briefly with a \(3 - \mu \mathrm{L}\) aliquot of \(2\%\) (w/v) uranyl acetate solution three times. The remaining solution was removed with filter paper and the grid was dried on the bench- top. TEM observation was performed using a transmission electron microscope HT- 7700 (Hitachi) with an acceleration voltage of \(80 \mathrm{kV}\) . The images were recorded using HT- 7700 control software (Hitachi).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 787, 275, 803]]<|/det|>
+## Tube length analysis  
+
+<|ref|>text<|/ref|><|det|>[[115, 809, 886, 898]]<|/det|>
+Hundreds of discriminable tubes were picked up manually on 5k- magnification TEM images. The tube lengths were calculated as half of the perimeter analysed with ImageJ (Fiji)<sup>52</sup>. The plots were drawn by selecting 150 tubes from the longer lengths using Igor Pro 9 (WaveMetrics). For the disassembly and reassembly analysis, Welch's t- test was carried out.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 115, 500, 132]]<|/det|>
+## Circular dichroism (CD) spectrum measurements  
+
+<|ref|>text<|/ref|><|det|>[[115, 137, 886, 302]]<|/det|>
+All proteins were thawed immediately before CD measurements on ice. Each sample was prepared in a 1.5- mL microtube using \(\mathrm{NaCl(+)}\) buffer to adjust the concentration to \(2.5\mu \mathrm{M}\) and the volume to \(200\mu \mathrm{L}\) at 25 \(\pm 1^{\circ}\mathrm{C}\) . Far- UV CD spectra were obtained at a wavelength of \(200–250\mathrm{nm}\) using a J- 1100 spectropolarimeter (JASCO) with a quartz cell with a light path of \(1\mathrm{mm}\) . Thermal denaturation was performed at a temperature change rate of \(1^{\circ}\mathrm{C / min}\) . The CD spectral data were collected using Spectra Manager (version 2.5, JASCO). All CD data were expressed as mean residue ellipticity. The \(T_{\mathrm{m}}\) of each protein was calculated from the thermal denaturation curve at a wavelength of \(222\mathrm{nm}\) by sigmoid fitting using Igor Pro 9 (WaveMetrics).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 330, 341, 347]]<|/det|>
+## Cryo-EM structural analysis  
+
+<|ref|>text<|/ref|><|det|>[[115, 353, 886, 491]]<|/det|>
+All proteins were thawed immediately before tube formation on ice. Each sample was prepared in a 1.5- mL microtube using \(\mathrm{NaCl(+)}\) buffer to adjust the concentration to \(12.5\mu \mathrm{M}\) and the volume to \(200\mu \mathrm{L}\) at 25 \(\pm 1^{\circ}\mathrm{C}\) . Incubation of the samples was carried out as described above for \(24\mathrm{h}\) at \(40^{\circ}\mathrm{C}\) for the PnuE tube and \(30^{\circ}\mathrm{C}\) for the PnuE D- loop tube, and then the samples were provided for grid preparation. For unwinding the helical structures of the PnuE D- loop tube, additional incubation was carried out for \(1\mathrm{h}\) on ice immediately before grid preparation.  
+
+<|ref|>text<|/ref|><|det|>[[115, 495, 886, 707]]<|/det|>
+The PnuE D- loop tube sample prepared at \(25\pm 1^{\circ}\mathrm{C}\) was used at the original concentration. In contrast, the PnuE tube and the PnuE D- loop tube preincubated on ice were diluted to one- third and one- sixth of their original concentrations, respectively. Quantifoil R1.2/1.3 Cu 300 grids coated with a holey carbon film (Quantifoil) were treated for hydrophilisation using a JEC- 3000FC Auto Fine Coater (JEOL) at \(20\mathrm{Pa}\) and \(10\mathrm{mA}\) for \(30\mathrm{s}\) . Subsequently, \(2.5\mathrm{- }\mu \mathrm{L}\) aliquots of the respective diluted samples were applied to the prepared grids. After blotting off excess solution, the grids were rapidly immersed in liquid ethane for vitrification using a Vitrobot Mark IV (Thermo Fisher Scientific). Vitrobot was set at \(4^{\circ}\mathrm{C}\) and \(100\%\) humidity for PnuE and PnuE D- loop samples preincubated on ice, and \(25^{\circ}\mathrm{C}\) and \(100\%\) humidity for PnuE D- loop sample prepared at \(25\pm 1^{\circ}\mathrm{C}\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 712, 886, 850]]<|/det|>
+Sample screening and data acquisition were performed using a Glacios cryo- transmission electron microscope (Thermo Fisher Scientific) operated at an accelerated voltage of \(200\mathrm{kV}\) , equipped with a Falcon4EC camera, at the Institute of Life and Medical Sciences, Kyoto University. Images were automatically acquired using the EPU software as movies with nominal magnifications and corresponding calibrated pixel sizes of \(120,000\mathrm{x}\) (1.22 A/pixel) for the PnuE sample, and \(150,000\mathrm{x}\) (0.925 A/pixel) for PnuE D- loop samples.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 880, 330, 897]]<|/det|>
+## Cryo-EM image processing
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 90, 884, 132]]<|/det|>
+Image analysis was conducted using similar workflows for each dataset of the three samples with the software package RELION 5.0beta<sup>53,54</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[112, 137, 886, 417]]<|/det|>
+For the PuuE tube sample, 4,346 movies were subjected to motion- correction using RELION's algorithm, and the contrast transfer function (CTF) was estimated using CTFFIND<sup>45</sup>. Tube coordinates were manually registered, and 709,722 segments were extracted with 3x binning into 260×260- pixel boxes (approximately 950x950 Å) with an inter- box spacing of 80 Å. The extracted segments were subjected to two rounds of 2D classification, and the resulting class averages were visually inspected to categorise the segments based on tube diameters. In parallel, an additional round of 2D classification with 10 classes was performed to assess the structural diversity of the tubes roughly. Each subset of segments, categorised by diameter, was then re- extracted and subjected to further 2D classifications to remove junk images. 3D classification with symmetry search was performed on each subset without imposing symmetry (C1). Finally, 3D refinement was carried out for the subsets with the three smallest diameters, applying \(C_4\) , \(C_5\) , and \(C_6\) symmetries, respectively. The subsets with larger diameters exhibited significant heterogeneity and did not yield reliable 3D reconstructions.  
+
+<|ref|>text<|/ref|><|det|>[[112, 422, 886, 539]]<|/det|>
+For the PuuE D- loop tube sample prepared at \(25 \pm 1^{\circ}\mathrm{C}\) , 4,871 movies were motion- corrected and CTF- estimated using RELION and CTFFIND4, respectively. A total of 126,987 segments were extracted with 5x binning into 320×320- pixel or 640×640- pixel segmented boxes (1480x1480 or 2960x2960 Å) with an inter- box spacing of 60 Å. The extracted segments were subjected to six rounds of 2D classification, yielding class averages displaying single, double, and triple helical tube architectures.  
+
+<|ref|>text<|/ref|><|det|>[[112, 543, 886, 875]]<|/det|>
+For the PuuE D- loop tube sample, preincubated on ice to unwind the helical structures, 4,346 movies were subjected to motion correction and CTF estimation. A total of 709,722 segments were extracted with 3x binning into 360×360- pixel boxes (approximately 1000x1000 Å) with an inter- box spacing of 80 Å. The extracted segments were subjected to two rounds of 2D classification, and the resulting class averages were visually inspected to categorise the segments based on tube diameters. In parallel, two rounds of 2D classification were performed to assess the structural diversity of the tubes. Each subset of segments, categorised by diameter, was re- extracted and subjected to further 2D classifications to remove junk images. 3D classification with symmetry search was performed on each subset without imposing symmetry (C1). During the 3D classification of the initially selected C5- tube subset, C6 tubes were found to be present and were subsequently combined with the C6- tube subset from the 2D classification. Finally, 3D refinement was carried out for the subsets with the four smallest diameters, applying \(C_3\) , \(C_4\) , \(C_5\) , and \(C_6\) symmetries, respectively. As observed in the PuuE dataset, the subsets with larger diameters displayed considerable heterogeneity and failed to yield reliable 3D reconstructions. Detailed image processing workflows are depicted in Extended Data Figures. 6, 8, and 9.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 91, 280, 108]]<|/det|>
+## Fluorescent labelling  
+
+<|ref|>text<|/ref|><|det|>[[115, 113, 886, 252]]<|/det|>
+Fluorescent labellingTube formation was conducted as described above under the optimised condition described in the manuscript. Labelling reaction was achieved by adding Alexa Fluor 488 succinimidyl ester dissolved in dimethyl sulfoxide (DMSO) to the tube solution at a final concentration of \(0.7 \mathrm{mM}\) . The reaction was then incubated at \(25 \pm 1^{\circ} \mathrm{C}\) for \(1 \mathrm{~h}\) with gentle shaking under shading. The excess dye was removed using NaCl (+) buffer with Microcon 300 centrifugal filter units (Merck) according to the manufacturer's protocol four times. The labelled tubes were then stored under shading at \(25 \pm 1^{\circ} \mathrm{C}\) until further experiments.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 282, 311, 299]]<|/det|>
+## Fluorescence microscopy  
+
+<|ref|>text<|/ref|><|det|>[[112, 304, 886, 614]]<|/det|>
+Fluorescence microscopyAn observation chamber was assembled by placing two double- sided tapes (thickness \(\sim 100 \mu \mathrm{m}\) ) onto a silicone- coated coverslip \((24 \times 36 \mathrm{~mm}^2\) , thickness No. 1; Matsunami) with another coverslip \((18 \times 18 \mathrm{~mm}^2\) , thickness No. 1; Matsunami) on top. To passivate the surface of the coverslips against nonspecific adhesion of protein, the chamber was filled with \(10 \mathrm{mg} \mathrm{mL}^{- 1}\) of Pluronic F- 127 (Sigma- Aldrich) dissolved in distilled water for more than 10 minutes at \(25^{\circ} \mathrm{C}\) . After washing out Pluronic F- 127 solution with 5 chamber volumes of \(\mathrm{NaCl}\) (+) buffer, the chamber was filled with TIRFM buffer ( \(50 \mathrm{mM}\) Tris- HCl pH 8.0, \(100 \mathrm{mM}\) NaCl, \(0.5 \mathrm{mM}\) EDTA, \(0.2\%\) (w/v) methylcellulose (1500 cP, Wako), \(1 \mathrm{mM}\) DTT, \(2 \mathrm{mM}\) Trolox). Next, the Alexa488- tube solution was diluted to \(1 / 10\) in \(\mathrm{NaCl}\) (+) solution, and further diluted to \(1 / 10\) (final \(1 / 100\) dilution) in TIRFM buffer. Then, the diluted tube solution was perfused into the observation chamber and sealed by Valap to prevent flow. The fluorescence images of tube structures were acquired at intervals of \(40 \mathrm{ms}\) with an inverted microscope (IX- 71, Olympus) equipped with a \(60 \times\) objective lens (PlanApo NA 1.45 oil, Olympus), an EMCCD camera (iXon3, Andor Technology) and an excitation laser with the wavelength at \(488 \mathrm{nm}\) (OBIS 488- 60- LS, COHERENT). All observations were performed at \(25 \pm 1^{\circ} \mathrm{C}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 642, 346, 660]]<|/det|>
+## Mechanical property analysis  
+
+<|ref|>text<|/ref|><|det|>[[112, 664, 886, 880]]<|/det|>
+Mechanical property analysisThe persistence length of the tube structures was estimated as follows. First, the fluorescence images were converted to 8- bit images using the ImageJ function. Then, the skeletons of the tube structures were tracked using ImageJ plugin, JFilament<sup>6</sup>. Distances between adjacent nodes composing the skeletons were set as 1 pixel. Next, the contour length \((L)\) and end- to- end distance \((R)\) of the tube structures at each frame were calculated using the coordinates of the nodes with custom- written Python scripts. The mean square of \(R\) \((\langle R^2 \rangle)\) of each tube structure was calculated by averaging \(R^2\) along 100–200 frames. \(\langle R^2 \rangle\) and \(L\) follow the following equation when the shape fluctuation is driven thermally<sup>36</sup>. \(\langle R^2 \rangle = 4L_{\mathrm{p}}^2 [2\exp (- L / 2L_{\mathrm{p}}) - 2 + L / L_{\mathrm{p}}]\) , where \(L_{\mathrm{p}}\) is the persistence length of the tube structure. The \(L_{\mathrm{p}}\) values of the tube structures were estimated by fitting this equation to the experimental data using 'curve_fit' function of Python package  
+
+<|ref|>text<|/ref|><|det|>[[112, 861, 886, 902]]<|/det|>
+by fitting this equation to the experimental data using 'curve_fit' function of Python package
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 884, 132]]<|/det|>
+'scipy.optimize'. \(L_{\mathrm{p}}\) of actin filaments was estimated by the same analysis. Totally, 55 tube structures and 37 actin filaments were analysed.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 162, 280, 179]]<|/det|>
+## Molecular modelling  
+
+<|ref|>text<|/ref|><|det|>[[115, 185, 884, 300]]<|/det|>
+All predicted protein structures were generated by AlphaFold 2.2 or 2.3 multimer- mode (DeepMind) \(^{15,16}\) . Cartoon models of the proteins were drawn using PyMOL 2.5 (Schrödinger) \(^{57}\) and UCSF ChimeraX (UCSF RBVI and NIH) \(^{58}\) . Isoelectric points of PuuE- M and PuuE- p were calculated from the basis of amino acid composition \(^{59}\) . Surface hydrophobicity of PuuE was drawn using Color_h script (PyMOL Wiki) based on the hydrophobicity scale \(^{60}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 331, 247, 347]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[115, 353, 884, 444]]<|/det|>
+The cryo- EM structures have been deposited in the Electron Microscopy Data Bank (EMDB) with the following accession codes: EMD- 60617, EMD- 60618, and EMD- 60619 for the PuuE tubes with C4, C5, and C6 symmetry, respectively; and EMD- 60620, EMD- 60621, EMD- 60622, and EMD- 60623 for the PuuE D- loop tubes with C3, C4, C5, and C6 symmetry, respectively.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 475, 268, 491]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[115, 497, 884, 610]]<|/det|>
+This work was supported by JSPS KAKENHI (grant nos. 19H02832, 19K22253, and 21H05116 to Y. Suzuki; 21H05117 to Y. Suzuki and Y. Sugita; and 20K22628, 21J00530, and 22KJ1644 to M.N.), JST PRESTO (grant no. JPMJPR22A7 to Y. Suzuki and JPMJPR20ED to M.M.), Takeda Science Foundation to Y. Suzuki, Chubei Itoh Foundation to Y. Suzuki, and The Hakubi Center for Advanced Research to Y. Sugita, M.M., and Y. Suzuki.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 642, 282, 658]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[115, 664, 884, 778]]<|/det|>
+Y. Suzuki directed the project. Y. Suzuki and M.N. conceived and designed the overall study. M.N. conducted experiment works with contributions from Y. Suzuki, Y. Sugita, and Y.Y.. Y. Sugita and M.N. performed cryo- EM data collection and analysed data. Y.Y. conducted TIRFM experiments, and Y.Y. and M.M. analysed mechanical properties. M.N. and Y. Suzuki wrote the manuscript with contributions from Y. Sugita, Y.Y., and M.M.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 810, 357, 827]]<|/det|>
+## Competing interest declaration  
+
+<|ref|>text<|/ref|><|det|>[[115, 833, 884, 875]]<|/det|>
+Y. Suzuki and M.N. are inventors of a provisional patent submitted by Kyoto University for ‘Protein Assembly Structure’.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[115, 91, 297, 107]]<|/det|>
+# Additional information  
+
+<|ref|>text<|/ref|><|det|>[[115, 114, 510, 132]]<|/det|>
+Supplementary Information is available for this paper.  
+
+<|ref|>text<|/ref|><|det|>[[115, 138, 688, 156]]<|/det|>
+Correspondence and requests for materials should be addressed to Yuta Suzuki.  
+
+<|ref|>text<|/ref|><|det|>[[115, 163, 280, 179]]<|/det|>
+Tel: +81- 75- 753- 9766  
+
+<|ref|>text<|/ref|><|det|>[[115, 187, 457, 204]]<|/det|>
+E- mail address: suzuki.yuta.2m@kyoto- u.ac.jp
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[216, 123, 714, 690]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[112, 696, 886, 907]]<|/det|>
+Extended Data Fig. 1. | AF2 prediction of PuuE- M and PuuE- p. a, Fifty prediction models overlapped for PuuE- M (top) and PuuE- p (bottom). Peptide parts, M3L2 and p66α, are indicated with a red box. b, Predicted local distance difference test plots for the most reliable prediction models for PuuE- M (top) and PuuE- p (bottom). Arrows indicate the N- terminal region of M3L2 and p66α. For these regions, PuuE- M has a lower predictive reliability than does PuuE- p, suggesting that the structure may be more flexible. c, The most reliable prediction model for PuuE- p. The region from the C- terminus of PuuE to the N- terminus of p66α (i.e. \(^{313}\mathrm{HPYTPE}^{318}\) ) is depicted by a stick model. The two Pro residues highlighted in red are thought to be responsible for the rigidity of the PuuE- p structure. Because of the rigidity of PuuE- p, the final product of the mixture was predicted to be a tube, as shown in Fig. 1d.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[201, 95, 797, 765]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 772, 884, 910]]<|/det|>
+<center>Extended Data Fig. 2. | nsTEM characterisation of PuuE-M, PuuE-p, and the mixture for PuuE-M and PuuE-p. a, 12.5 \(\mu \mathrm{M}\) PuuE-M or b, 12.5 \(\mu \mathrm{M}\) PuuE-p in NaCl (+) buffer was incubated at \(40^{\circ}\mathrm{C}\) for 24 h. Scale bars, 200 nm (white), 50 nm (black). c, Dependency of PuuE tube assemblies on protein concentration. 250 nM (top), 2.5 \(\mu \mathrm{M}\) (middle), and 12.5 \(\mu \mathrm{M}\) (bottom) of PuuE-M and PuuE-p each in NaCl (+) buffer was incubated at \(40^{\circ}\mathrm{C}\) for 24 h and imaged by nsTEM. The tube structure observed in the nsTEM images was flexible as it was curved and collapsed. Scale bars, 1 \(\mu \mathrm{m}\) (white), 50 nm (black). </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[123, 115, 880, 744]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 744, 884, 862]]<|/det|>
+<center>Extended Data Fig. 3. | Time dependence of PuuE tube assemblies and their stability over time. a, 12.5 \(\mu \mathrm{M}\) of PuuE-M and PuuE-p each in \(\mathrm{NaCl}(+)\) buffer was incubated at \(40^{\circ}\mathrm{C}\) for indicated time points and imaged via nsTEM. b, After \(24\mathrm{h}\) of tube formation, the sample was kept at \(25\pm 1^{\circ}\mathrm{C}\) for the indicated time and imaged using nsTEM. Tube structures remained unchanged after 2 weeks and even after 1 month, suggesting stability. Scale bars, \(1\mu \mathrm{m}\) . </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 882, 650]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[111, 653, 886, 789]]<|/det|>
+Extended Data Fig. 4. | Temperature dependence of PuuE tube assemblies and determination of \(T_{\mathrm{m}}\) for PuuE- M and PuuE- p. a, 12.5 \(\mu \mathrm{M}\) of PuuE- M and PuuE- p each in NaCl (+), buffer was incubated at the indicated temperature for 24 h and imaged via nsTEM. Scale bars, 1 \(\mu \mathrm{m}\) . b, c, \(T_{\mathrm{m}}\) measurements using CD for PuuE- M (b) and PuuE- p (c). 2.5 \(\mu \mathrm{M}\) of PuuE- M or PuuE- p in NaCl (+), buffer was incubated from 25 to 55 °C with temperature change of 1 °C/min. Left panel, overall CD spectra; right panel, thermal denaturation profiles.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[112, 88, 880, 750]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[113, 765, 886, 880]]<|/det|>
+Extended Data Fig. 5. | Salt concentration dependence and reversibility of PuuE tube assemblies. a, Left, \(12.5 \mu \mathrm{M}\) of PuuE- M and PuuE- p each in \(\mathrm{NaCl}(+)\) buffer was incubated at \(40^{\circ} \mathrm{C}\) for \(24 \mathrm{~h}\) with indicated \(\mathrm{NaCl}\) concentration and imaged via nsTEM. Right: diagram of salt concentration effects described in the main text. b, Additional images in Fig. 2d prove the reversibility of tubular assemblies. These images were used for statistical analysis of tube length, as shown in Fig. 2e. Scale bars, \(1 \mu \mathrm{m}\) (white).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[175, 92, 828, 190]]<|/det|>  
+
+<|ref|>image<|/ref|><|det|>[[190, 210, 595, 250]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[192, 252, 512, 266]]<|/det|>
+<center>C4 tube: 2D classifications (2 rounds): 51,590 segments </center>  
+
+<|ref|>image<|/ref|><|det|>[[210, 268, 520, 415]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[192, 418, 500, 432]]<|/det|>
+<center>C5 tube: 2D classifications (2 rounds): 44,868 segments </center>  
+
+<|ref|>image<|/ref|><|det|>[[536, 310, 808, 416]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[536, 280, 756, 308]]<|/det|>
+<center>3D Refinement \((C_4)\) : 12,052 segments Post-processing </center>  
+
+<|ref|>image<|/ref|><|det|>[[210, 434, 500, 592]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[192, 595, 490, 610]]<|/det|>
+<center>C6 tube: 2D classification (1 round): 117,636 segments </center>  
+
+<|ref|>image<|/ref|><|det|>[[536, 434, 808, 592]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[536, 447, 756, 475]]<|/det|>
+<center>3D Refinement \((C_5)\) : 12,572 segments Post-processing </center>  
+
+<|ref|>image<|/ref|><|det|>[[177, 633, 808, 805]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[192, 612, 440, 626]]<|/det|>
+<center>3D classification \((C_1)\) : 39,841 segments </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 817, 886, 909]]<|/det|>
+Extended Data Fig. 6. | Cryo- EM image processing workflow of the PuuE tubes. Flowchart illustrating the image processing steps. Scale bars: \(100 \mathrm{nm}\) (white), \(250 \mathrm{\AA}\) (black). Gold- standard Fourier shell correlation (FSC) curve of the independently refined half maps indicating a global resolution at the 0.143 threshold.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[133, 88, 860, 660]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[112, 666, 886, 899]]<|/det|>
+Extended Data Fig. 7. D- loop grafting to emulate actin filaments. a, Surface hydrophobicity calculation for PuuE. D- loop was grafted into the 'back' side of PuuE owing to the hydrophobic nature of a prominent indentation. b, \(T_{\mathrm{m}}\) measurement of PuuE(D- loop)- M via CD. \(2.5 \mu \mathrm{M}\) of PuuE(D- loop)- M in NaCl (+) buffer was incubated from 25 to \(55^{\circ}\mathrm{C}\) with temperature change of \(1^{\circ}\mathrm{C / min}\) . Top: overall CD spectra; bottom: thermal denaturation profiles, respectively. c, \(12.5 \mu \mathrm{M}\) of PuuE(D- loop)- M and PuuE- p in NaCl (+) buffer were incubated at \(30^{\circ}\mathrm{C}\) for \(24 \mathrm{h}\) and imaged using nsTEM. A novel helical pattern of two or three intertwined tubes was clearly observed. Flexibility was also noted when curved structures were observed. Scale bars, \(1 \mu \mathrm{m}\) (white), \(100 \mathrm{nm}\) (black). d, Additional images for reversibility of tube formation depends on temperature changes in Fig. 4c. For this observation, we focused on the presence of tube structures with helical conformations. After \(1 \mathrm{h}\) at \(0^{\circ}\mathrm{C}\) , there were no such structures observed via nsTEM.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[137, 88, 844, 300]]<|/det|>  
+
+<|ref|>image<|/ref|><|det|>[[155, 306, 780, 411]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[155, 419, 644, 435]]<|/det|>
+2D classifications (6 rounds) with 2960x2960- Å segments: 9,989 segments  
+
+<|ref|>image<|/ref|><|det|>[[210, 444, 784, 808]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[60, 800, 90, 814]]<|/det|>
+718  
+
+<|ref|>text<|/ref|><|det|>[[60, 817, 884, 835]]<|/det|>
+719 Extended Data Fig. 8. | Cryo- EM image processing workflow of PuuE D- loop tubes prepared at \(25 \pm 720\) 1 °C. Flowchart illustrating the image processing steps. Scale bars: 100 nm (white), 500 Å (black).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[180, 92, 824, 190]]<|/det|>  
+
+<|ref|>image<|/ref|><|det|>[[180, 201, 789, 811]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[113, 816, 886, 909]]<|/det|>
+Extended Data Fig. 9. | Cryo- EM image processing workflow of PuuE D- loop tubes preincubated on ice to unwind the helical structures. Flowchart illustrating the image processing steps. Scale bars: 100 nm (white), 250 Å (black). Gold- standard Fourier shell correlation (FSC) curve of the independently refined half maps indicating a global resolution at the 0.143 threshold.
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[115, 106, 765, 305]]<|/det|>
+<table><tr><td></td><td>#1 C4 tube (EMD-60617)</td><td>#2 C5 tube (EMD-60618)</td><td>#3 C6 tube (EMD-60619)</td></tr><tr><td>Data collection and processing</td><td></td><td></td><td></td></tr><tr><td>Magnification</td><td>120,000</td><td></td><td></td></tr><tr><td>Voltage (kV)</td><td>200</td><td></td><td></td></tr><tr><td>Electron exposure (e-/Ų)</td><td>40</td><td></td><td></td></tr><tr><td>Defocus range (μm)</td><td>-0.8 to -1.6</td><td></td><td></td></tr><tr><td>Pixel size (Å)</td><td>1.22</td><td></td><td></td></tr><tr><td>Symmetry imposed</td><td>C4 helical</td><td>C5 helical</td><td>C6 helical</td></tr><tr><td>Initial helical segments (no.)</td><td>709,722</td><td>709,722</td><td>709,722</td></tr><tr><td>Final helical segments (no.)</td><td>12,052</td><td>12,572</td><td>39,841</td></tr><tr><td>Map resolution (Å)</td><td>11.3</td><td>20.6</td><td>17.5</td></tr><tr><td>FSC threshold</td><td>0.143</td><td>0.143</td><td>0.143</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[60, 310, 92, 323]]<|/det|>
+727 
+
+<|ref|>text<|/ref|><|det|>[[60, 328, 568, 344]]<|/det|>
+2D analysis of the PuuE D-loop tube prepared at 25 ± 1 °C 
+
+<|ref|>table<|/ref|><|det|>[[115, 344, 460, 492]]<|/det|>
+<table><tr><td></td><td>#1 Tubes</td></tr><tr><td>Data collection and processing</td><td></td></tr><tr><td>Magnification</td><td>150,000</td></tr><tr><td>Voltage (kV)</td><td>200</td></tr><tr><td>Electron exposure (e-/Ų)</td><td>40</td></tr><tr><td>Defocus range (μm)</td><td>-0.8 to -1.6</td></tr><tr><td>Pixel size (Å)</td><td>0.925</td></tr><tr><td>Symmetry imposed</td><td>No</td></tr><tr><td>Initial helical segments (no.)</td><td>126,987</td></tr><tr><td>Final helical segments (no.)</td><td>104,748</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[60, 495, 92, 508]]<|/det|>
+729 
+
+<|ref|>text<|/ref|><|det|>[[60, 513, 92, 526]]<|/det|>
+730 
+
+<|ref|>text<|/ref|><|det|>[[115, 512, 671, 528]]<|/det|>
+PuuE D-loop tube preincubated on ice to unwind the helical structures 
+
+<|ref|>table<|/ref|><|det|>[[115, 528, 857, 728]]<|/det|>
+<table><tr><td><td>#1 C3 tube (EMD-60620)</td><td>#2 C4 tube (EMD-60621)</td><td>#3 C5 tube (EMD-60622)</td><td>#4 C6 tube (EMD-60623)</td></td></tr><tr><td>Data collection and processing</td><td></td><td></td><td></td><td></td></tr><tr><td>Magnification</td><td>150,000</td><td></td><td></td><td></td></tr><tr><td>Voltage (kV)</td><td>200</td><td></td><td></td><td></td></tr><tr><td>Electron exposure (e-/Ų)</td><td>40</td><td></td><td></td><td></td></tr><tr><td>Defocus range (μm)</td><td>-0.8 to -1.6</td><td></td><td></td><td></td></tr><tr><td>Pixel size (Å)</td><td>0.925</td><td></td><td></td><td></td></tr><tr><td>Symmetry imposed</td><td>C3 helical</td><td>C4 helical</td><td>C5 helical</td><td>C6 helical</td></tr><tr><td>Initial helical segments (no.)</td><td>397,778</td><td>397,778</td><td>397,778</td><td>397,778</td></tr><tr><td>Final helical segments (no.)</td><td>2,675</td><td>3,262</td><td>2,998</td><td>1,291</td></tr><tr><td>Map resolution (Å)</td><td>9.7</td><td>14.6</td><td>18.2</td><td>26.0</td></tr><tr><td>FSC threshold</td><td>0.143</td><td>0.143</td><td>0.143</td><td>0.143</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[60, 730, 92, 743]]<|/det|>
+734 
+
+<|ref|>text<|/ref|><|det|>[[60, 750, 783, 766]]<|/det|>
+Extended Data Table 1. | Cryo-EM data collection, refinement, and validation statistics
+
+<--- 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|>[[59, 130, 353, 257]]<|/det|>
+SupplementaryInformation.pdf Supplementarymovie1. mov Supplementarymovie2. mov Supplementarymovie3. mov Supplementarymovie4. mov
+
+<--- Page Split --->

preprint/preprint__07090632be97150b9482692b3758503018ba474d5a059546c8cd240472d00789/images_list.json

@@ -0,0 +1,152 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 | Disulphide-locked BamA variants and Fab1 binding impair BAM-mediated OMP folding in vitro. (a) BAM-P5L (G393C/G584C) is expected to lock BamA in the lateral-open conformation (PDB code 5LJO<sup>8</sup>), while (b) BAM-LL (E435C/S665C) is expected to lock BamA in the lateral-closed conformation (PDB code 5DOO<sup>6</sup>). BamA POTRAs 1-4 and BamBCDE are rendered semi-transparent for emphasis on the BamA \\(\\beta\\) -barrel and POTRA-5. The position of the disulphide bond is shown as a yellow bar. Figure made in PyMOL v1.7.2.3. (c and d) Quantification of folded and unfolded bands from SDS-PAGE band-shift",
+    "footnote": [],
+    "bbox": [
+      [
+        112,
+        78,
+        870,
+        760
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 | CryoEM resolves two conformations of BAM-LL in detergent. (a) 4.1 A cryoEM map of the BAM-LL lateral-closed conformation at a contour of \\(10\\sigma\\) , coloured by subunit. The lateral-gate is closed and POTRA-5 does not block the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA-5 of BamA. \\(\\beta 1\\) and \\(\\beta 16\\) contact to close the gate. (c) The same density viewed from the periplasmic side, showing the open lumen of the BamA barrel in this conformation. (d) 4.8 Å cryoEM map of the BAM-LL lateral-open conformation at a contour of \\(10\\sigma\\) , coloured by subunit. The lateral-gate is open and POTRA-5 occludes the BamA barrel (schematic inset). (e) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on segmented density for the barrel and POTRA-5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel to contact eL6. (f) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA-5 in this conformation. Fig. made in UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
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+      ]
+    ],
+    "page_idx": 25
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 | Fab1-bound BAM is in a lateral-open conformation. (a) 5.1 Å cryoEM map of the BAM-Fab1 complex in a lateral-open conformation at a contour of \\(10\\sigma\\) , coloured by subunit. The lateral-gate is fully-open and POTRA-5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA-5 of BamA. \\(\\beta 1\\) is in a conformation that makes limited contact with \\(\\beta 16\\) . (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA-5 in this conformation. Panels made using UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d) Close up of the BamA-Fab1 interface region highlighting the Fab1 CDRs (red) interacting with eL4 of BamA (dark blue). Other regions of BamA are rendered semi-transparent to highlight eL4. Heavy and light chains of Fab1 are coloured cyan and pink, respectively. (e) The \\(\\mathrm{V_L}\\) and \\(\\mathrm{V_H}\\) domains of Fab1 variable form a complementary binding surface for eL4 of BamA involving residues Y550, E554 and H555.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        80,
+        875,
+        550
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 | Additive effect of BAM inhibition by disulphide-locking and binding of Fab1. (a) 7.1 Å cryoEM map of the Fab1-bound LL-BAM in a lateral-open conformation at a contour of 9.5 σ, coloured by subunit. The lateral-gate is open and POTRA-5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the β-barrel and",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        80,
+        870,
+        789
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 | BAM variants reduce the phase transition temperature of DMPC liposomes. Global lipid phase transition behaviour for each BAM variant and BamA in DMPC proteoliposomes, with an empty liposomes control measured using laurdan fluorescence. (a) The ratio of laurdan fluorescence at \\(440 \\text{nm}\\) and \\(490 \\text{nm}\\) was plotted as generalised polarisation (GP, see Methods) against temperature for \\(0.8 \\mu \\text{M BAM/BamA proteoliposome}\\) suspensions at a \\(1600:1\\) (mol/mol) lipid-to-protein ratio (LPR) with added laurdan (at a \\(305:1\\) lipid-to-laurdan ratio) in TBS pH 8.0. (b) The first derivative of data shown in (a) showing the transition temperature for each liposome suspension as the point of steepest (most negative) gradient. Whilst empty DMPC (grey) and BamA proteoliposomes (purple) have a transition temperature of \\(24 \\text{‰}\\) , the presence of WT BAM (black), BAM-Fab1 (red), BAM-P5L (green), BAM-LL (blue), BAM-P5L + Fab1 (orange) and BAM-LL + Fab1 (yellow)",
+    "footnote": [],
+    "bbox": [
+      [
+        122,
+        100,
+        820,
+        680
+      ]
+    ],
+    "page_idx": 29
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
+    "footnote": [],
+    "bbox": [
+      [
+        66,
+        108,
+        800,
+        830
+      ]
+    ],
+    "page_idx": 36
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2",
+    "footnote": [],
+    "bbox": [
+      [
+        72,
+        295,
+        884,
+        770
+      ]
+    ],
+    "page_idx": 37
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3",
+    "footnote": [],
+    "bbox": [
+      [
+        60,
+        260,
+        901,
+        817
+      ]
+    ],
+    "page_idx": 38
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
+    "bbox": [
+      [
+        71,
+        50,
+        820,
+        785
+      ]
+    ],
+    "page_idx": 40
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5",
+    "footnote": [],
+    "bbox": [
+      [
+        75,
+        68,
+        830,
+        300
+      ]
+    ],
+    "page_idx": 42
+  }
+]

preprint/preprint__07090632be97150b9482692b3758503018ba474d5a059546c8cd240472d00789/preprint__07090632be97150b9482692b3758503018ba474d5a059546c8cd240472d00789.mmd

@@ -0,0 +1,343 @@
+
+# The role of membrane destabilisation and protein dynamics in BAM catalysed OMP folding.  
+
+Paul White University of Leeds  Samuel Haysom University of Leeds https://orcid.org/0000- 0002- 8769- 090X  Matthew ladanza University of Leeds  Anna Higgins University of Leeds  Jonathan Machin University of Leeds  Jim Home University of Leeds https://orcid.org/0000- 0001- 5260- 2634  Bob Schiffrin University of Leeds  Charlotte Carpenter-Platt University of Leeds  James Whitehouse University of Leeds  Kelly Storek Genentech Inc  Steven Rutherford Genentech Inc https://orcid.org/0000- 0002- 4758- 4248  David Brockwell University of Leeds https://orcid.org/0000- 0002- 0802- 5937  Neil Ranson University of Leeds https://orcid.org/0000- 0002- 3640- 5275  Sheena Radford ( s.e.radford@leeds.ac.uk ) University of Leeds https://orcid.org/0000- 0002- 3079- 8039  
+
+## Article  
+
+Keywords: outer membrane proteins (OMPs), \(\beta\) - barrel assembly machinery (BAM), OMP folding.
+
+<--- Page Split --->
+
+**Posted Date:** February 2nd, 2021 
+
+**DOI:** https://doi.org/10.21203/rs.3.rs-155135/v1 
+
+**License:** © This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License 
+
+**Version of Record:** A version of this preprint was published at Nature Communications on July 7th, 2021.
+See the published version at https://doi.org/10.1038/s41467-021-24432-x.
+
+<--- Page Split --->
+
+1 The role of membrane destabilisation and protein dynamics in BAM catalysed OMP folding 3 4 Paul White1\\*, Samuel F. Haysom1\\*, Matthew G. Iadanza1\\*, Anna J. Higgins1, Jonathan M. Machin1, Jim E. Horne1#, Bob Schiffrin1, Charlotte Carpenter-Platt1, James M. Whitehouse1, Kelly M. Storek2, Steven T. Rutherford2, David J. Brockwell1, Neil A. Ranson1\\*, Sheena E. Radford1\* 8 9 1 Astbury Centre for Structural Molecular Biology, School of Molecular and Cellular Biology, 10 Faculty of Biological Sciences, University of Leeds, Leeds, LS2 9JT, UK 11 2 Department of Infectious Diseases, Genentech Inc., South San Francisco, CA 94080 12 4 Contributed equally 13 \* Current affiliation Scientific Computing Department, Science and Technology Facilities 14 Council, Research Complex at Harwell, Didcot, OX11 0FA, UK 15 # Current affiliation: Department of Biochemistry, University of Oxford, Oxford, OX1 3QU, UK 16 17 \*Correspondence: n.a.ranson@leeds.ac.uk; s.e.radford@leeds.ac.uk 18
+
+<--- Page Split --->
+
+## 19 Abstract  
+
+The folding of \(\beta\) - barrel outer membrane proteins (OMPs) in Gram- negative bacteria is catalysed by the \(\beta\) - barrel assembly machinery (BAM). How lateral opening in the \(\beta\) - barrel of the major subunit BamA assists in OMP folding, and the contribution of membrane disruption to BAM catalysis remain unresolved. Here, we use an anti- BamA monoclonal antibody fragment (Fab1) and two disulphide- crosslinked BAM variants (lid- locked (LL), and POTRA- 5- locked (P5L)) to dissect these roles. Despite being lethal in vivo, we show that all complexes catalyse folding in vitro, albeit less efficiently than wild- type BAM. CryoEM revealed that while Fab1 and BAM- P5L trap an open- barrel state, BAM- LL contains a mixture of closed and contorted, partially- open structures. Finally, all three complexes globally destabilise the lipid bilayer, while BamA does not, revealing that the BAM lipoproteins are required for this function. Together the results provide new insights into the role of BAM structure and lipid dynamics in OMP folding.
+
+<--- Page Split --->
+
+Outer membrane proteins (OMPs) in Gram negative bacteria are functionally diverse, but share a common \(\beta\) - barrel fold involving between 8 and 36 \(\beta\) - strands<sup>1</sup>. The folding and membrane insertion of OMPs is catalysed by the essential \(\beta\) - barrel assembly machinery (BAM)<sup>2- 4</sup> which in E. coli comprises five proteins (BamABCDE). The major conserved subunit, BamA, is a 16- stranded Omp85 family member that contains five N- terminal polypeptide transport associated (POTRA) domains that extend into the periplasm to scaffold four lipoprotein BamB- E<sup>5- 8</sup>, all of which are required for maximally- efficient OMP folding<sup>9,10</sup>. BAM is essential for bacterial survival, highly conserved, and surface accessible via the extracellular loops of BamA, making the complex an attractive target for small molecule<sup>11- 13</sup>, peptide<sup>14,15</sup> and antibody- based antibiotics<sup>16,17</sup>.  
+
+BAM exists in an ensemble of conformations, with one of the most notable differences between published structures occurring around the seam or 'lateral gate' involving \(\beta\) - strands 1 ( \(\beta 1\) ) and 16 ( \(\beta 16\) ) in the BamA barrel<sup>6- 18,20</sup>. In the 'lateral- open' conformation, as captured by cryoEM of the intact complex<sup>8</sup> and X- ray crystallography of the BamACDE subcomplex<sup>5,6</sup>, \(\beta 1\) and \(\beta 16\) are separated. In contrast, crystal structures of the intact BAM complex are in a 'lateral- closed' conformation in both in the absence<sup>6,7</sup> or presence of substrates<sup>21,22</sup>, wherein \(\beta 1\) and \(\beta 16\) are hydrogen bonded, albeit with fewer hydrogen bonds than exist between the other strands in the barrel<sup>1</sup>. The POTRA domains are also dynamically organised, with motions of POTRA- 5 being tightly correlated with gate conformation, with POTRA- 5 plugging entrance to the BamA \(\beta\) - barrel lumen only in the lateral- open state<sup>18</sup>. These conformational changes are essential for cell viability as disulphide bonds that purportedly lock BamA in either conformation have a lethal phenotype that is rescued by reducing agent<sup>6,19</sup>. Such variants include those that lock the lateral gate closed (e.g. G433C/N805C linking \(\beta 1\) to \(\beta 16^{8,19}\) , or E435C/S665C locking extracellular loop 1 (eL1) to eL6<sup>6,19</sup>), or those that lock the BamA lateral gate in an open conformation by introducing a disulphide bond between POTRA- 5 and \(\beta\) - turn between \(\beta 8\) and \(\beta 9\) at the base of the barrel (e.g. G393C/G584C<sup>6</sup>). Disulphide bonds which restrict flexibility between POTRA domains 2 and 3 also impair growth<sup>23</sup>; how, or if, these motions correlate with structural changes at the BamA \(\beta\) - barrel is unclear.  
+
+Models of BAM- catalysed OMP insertion and folding broadly invoke two distinct roles for BAM (reviewed in<sup>24</sup>). Firstly conformational changes in BAM, and protein- protein interactions between BAM and substrate OMPs are thought to be involved in catalysing folding<sup>25- 29</sup>. These models all involve a folding intermediate in which the C- terminal \(\beta\) - strand of the substrate is associated with BamA- \(\beta 1\) , as supported by crosslinking<sup>26,27</sup>, a recent cryoEM structure of a hybrid barrel formed between BAM and tBamA (the transmembrane domain of a BamA substrate)<sup>29</sup>, and crystal structures of BAM covalently tethered to the C- terminal \(\beta\) - strands of OMP substrates OmpA and OmpLA<sup>22</sup>. Variations of these models include the
+
+<--- Page Split --->
+
+'barrel elongation'<sup>25</sup> and 'swing'<sup>27</sup> models which suggest that folding begins in the periplasm, and also 'budding' models<sup>1,3,25</sup> wherein OMPs are thought to enter the lumen of the BamA barrel and fold via sequential addition of \(\beta\) - hairpin units<sup>26</sup>. This is akin to the role proposed for the mitochondrial homologue Sam50 of the sorting and assembly machinery (SAM) complex<sup>26</sup>. An alternative model proposes that BAM may disorder its lipid environment, lowering the kinetic barrier to OMP folding, potentially allowing OMPs to fold and insert into the outer membrane without direct interaction with the \(\beta 1 - \beta 16\) seam. This 'BamA- assisted' model<sup>18,30- 32</sup> is supported by molecular dynamics (MD) simulations which show lipid disordering and bilayer thinning by BamA<sup>20,25,30- 35</sup>, and by BAM- mediated distortion of a nanodisc<sup>18</sup>. Both protein dynamics and lipid disordering may act synergistically to maximise the efficiency of OMP folding, and different OMPs may depend on each effect to different degrees. However, little mechanistic insight is available, beyond that which has been inferred from the observation of a lethal phenotype.  
+
+Here, we investigate the roles of BAM structure/dynamics and membrane stability in OMP folding by exploiting two disulphide- locked variants termed lid- lock (LL) and POTRA- 5- lock (P5L) which are lethal in vivo<sup>6,19</sup>, and purportedly lock BamA's barrel closed and open, respectively. We also investigate a bactericidal Fab fragment (Fab1), that binds to eL4 of BamA<sup>16</sup>. We report cryoEM structures for the two disulphide locked BAM variants and the BAM- Fab1 complex, revealing that BAM- P5L and Fab1 stabilise a lateral- open conformation, whilst BAM- LL adopts both a lateral- closed state and a distorted, partially- open conformation. Despite being lethal in vivo, the two disulphide variants and the Fab1- BAM complex are all able to catalyse the folding of the 8- stranded OMPs OmpX and tOmpA (the transmembrane region of OmpA) in vitro, though less efficiently than wild- type BAM, and by combining Fab1 and disulphide- locking, BAM is further inactivated. We also demonstrate that all BAM variants studied lower the phase transition temperature of their lipid environment, but that BamA alone does not, providing direct experimental evidence that lipid disordering by BAM requires the presence of its lipoproteins. The results provide new insights into the structural features of BAM's catalytic mechanism and suggest that even subtle disruption of BAM activity may provide an effective route to the development of novel antibiotics.
+
+<--- Page Split --->
+
+## Results  
+
+## Disulphide-locked and Fab1-bound BAM can catalyse OMP folding in vitro  
+
+To assess the relationship between bacterial lethality and the catalytic ability of BAM we determined the in vitro folding activity of two paired cysteine mutations in BamA that are bactericidal<sup>6,19</sup>. In the BAM- P5L variant (BamA G393C/G584C)<sup>6</sup>, tethering of POTRA- 5 to the base of the BamA barrel is expected to stabilise a lateral- open conformation (Fig. 1a). By contrast, the BAM- LL variant, (BamA E435C/S665C)<sup>19</sup> is expected to lock eL1 to eL6, and stabilise a lateral- closed conformation (Fig. 1b). The BAM- LL and BAM- P5L variants were made in a BAM construct in which the two Cys of BamA that naturally form a disulphide bond (C690 and C700), are replaced with Ser (Cys- free BAM). This variant is able to complement WT BamA in E. coli<sup>19,36</sup> and has little effect on BAM- catalysed OMP folding rates in vitro<sup>9</sup>. We also investigated how a bactericidal anti- BamA binding antibody Fab fragment, known as Fab<sup>16,37</sup>, affects OMP folding in vitro. BAM- P5L, BAM- LL and the BAM- Fab1 complex were each reconstituted into liposomes comprised of E. coli polar lipids, and their ability to fold the 8- stranded OMPs, OmpX and tOmpA, in the presence of SurA was determined by SDS- PAGE band- shift assays<sup>38</sup>. In each case, BamA was folded (as judged by a band- shift relative to the boiled (denatured) BamA band) and all four BAM lipoproteins were present (Supplementary Fig. 1). Interestingly, Fab1 formed a stable, SDS- resistant complex with BamA (Supplementary Fig. 1b), consistent with its IC<sub>50</sub> of 0.095 nM determined for \(\Delta waaD E. coli^{16}\) . Disulphide bond formation in BAM- P5L and BAM- LL was confirmed by the lack of fluorescein- C5- maleimide labelling, and electrophoretic band- shifts in oxidising/reducing conditions (Supplementary Fig. 2). Both tOmpA or OmpX do not fold spontaneously into the liposomes formed from E. coli polar lipids, but fold rapidly and efficiently into liposomes formed from the same lipids containing WT BAM (Fig. 1c and d). Remarkably, considering their in vivo lethality<sup>6,16,19</sup>, the efficiency of folding and membrane insertion of tOmpA and OmpX is reduced, but not abolished, by BAM- P5L, BAM- LL and BAM- Fab1, with folding yields of \(\sim 50\%\) for tOmpA and \(\sim 15 - 30\%\) for OmpX after 3 hours at 25 °C (note that tOmpA folds more rapidly than OmpX with WT BAM) (Fig. 1c and d, and Supplementary Fig. 3 and 4). Relative to WT BAM, the initial rates of folding for BAM- Fab1, BAM- LL and BAM- P5L ranged from 16- 20% for tOmpA, and 8- 29% for OmpX (Fig. 1e and f, respectively, and Supplementary Table 1). When the disulphide bond in BAM- P5L and BAM- LL is reduced with DTT, folding activity surpassed that of WT BAM. This effect was not observed for WT BAM, or Cys- free BAM (Supplementary Fig. 5). Folding into proteoliposomes containing BamA alone was much slower than observed with BAM- P5L, BAM- LL, or BAM- Fab1, with initial folding rates for both substrates reaching \(\sim 3\%\) of that WT BAM, highlighting the importance of the accessory lipoproteins for efficient catalysis of folding of these OMPs<sup>39</sup>. Importantly, the inhibited BAM variants were able to fold their OMP substrates to 80- 100% completion after 24 hours, whilst incubation with BamA alone resulted in folding yields of only 50% and 16% for tOmpA and OmpX, respectively, after 24
+
+<--- Page Split --->
+
+hours (note that both substrates were unable to fold into empty liposomes even on these extended timescales) (Supplementary Table 2). Collectively, these results show that although both Fab1 binding and disulphide- locking of BamA are lethal in vivo<sup>6,16,19</sup>, the BAM- catalysed folding of OmpX and tOmpA is only partially inhibited in vitro.  
+
+## Lid-locked BAM exists in two conformations  
+
+To understand the molecular basis of inhibition, we determined the structure of BAM- LL in DDM detergent micelles using cryoEM. We predicted, based on the lethality of this mutation and the crystal/cryoEM structures of BAM in its different conformational states<sup>5- 8</sup>, that the formation of a disulphide bond between C435 and C665 would trap BAM in a lateral- closed state (Fig. 1b). However, 3D classification of cryoEM data of this construct revealed two distinct, approximately equally populated, structures (Fig. 2 and Supplementary Fig. 6). The first structure (at 4.1 Å resolution) is similar to the crystal structure of intact BAM in the lateral- closed conformation, with pairing of β1 and β16 (Fig. 2a,b) and displacement of POTRA- 5 from beneath the barrel (Fig. 2c). The second structure (at 4.8 Å) has β1 and β16 separated (Fig. 2d, e) and POTRA- 5 occludes the periplasmic face of the BamA barrel (Fig. 2f), and is thus consistent with a lateral- open conformation. In all previous lateral- open structures<sup>5,6,8</sup>, extracellular loop 1 (eL1) bends away from the BamA β- barrel, separating the lid- lock cysteine positions (C435 and C665) by \(\sim 20\) Å. Given the unequivocal in vitro biochemical evidence for formation of the lid- lock disulphide (Supplementary Fig. 2), eL1 must be distorted to allow disulphide bond formation with eL6. However, poor resolution in this region of the map, itself indicative of mobility, prevented modelling of this new eL1 conformation. We therefore used molecular dynamics- based flexible fitting (MDFF)<sup>40</sup> to morph the lateral- closed BAM- LL atomic model into the density observed in the second conformation, whilst maintaining the disulphide link. This generated a chemically plausible loop conformation (Fig. 2e), but this is not constrained by the EM density. The difference between eL1 conformations in the two BAM- LL structures is striking, and suggests that this region must be highly malleable to allow disulphide bond formation within the BamA β- barrel. Interestingly, the 'contorted open' BAM- LL structure closely resembles a recent structure of WT BAM in saponin nanodiscs<sup>22</sup> in which eL1 adopts this inward conformation in the absence of disulphide tethering. In accord with this idea, eL1 can adopt a wide range of conformations in lateral- open BAM structures (Supplementary Fig. 7). Overall, these data suggest that the lid- lock disulphide biases the conformational ensemble toward a lateral- closed conformation, but cannot completely pull the conformational equilibrium over to that state, consistent with BAM adopting only the lateral- open state in DDM detergent<sup>8</sup>.
+
+<--- Page Split --->
+
+## Fab1-bound BAM and BAM-P5L adopt a lateral-open state  
+
+Inspired by the findings that MAB1 (and Fab1) binding is lethal in vivo \(^{16}\) and also retards OMP folding rates in vitro (Figure 1), we next investigated the effect of Fab1 binding on the conformation of BAM using cryoEM. The structure of BAM in complex with a bactericidal molecule (Fab1) was solved in DDM micelles to 5.1 Å resolution. The cryoEM map contained unambiguous density for Fab1 bound to the extracellular region of BamA (Fig. 3a, Supplementary Fig. 8), and revealed that BAM is in a lateral-open conformation when bound to Fab1, as defined by the position of POTRA- 5, the shape of the BamA \(\beta\) - barrel, and the orientation of \(\beta 1\) and \(\beta 16\) (Fig. 3b and c). The structure of Fab1 alone was also solved by X- ray diffraction to \(\sim 3.0\) Å resolution and this structure was flexibly fitted into the EM density map (Supplementary Table 3). In agreement with mutagenesis data \(^{16}\) , Fab1 binds specifically to eL4 (Fig. 3d) (contributing 98% of the total interface area of 934 Å \(^{2}\) as determined by PISA interface analysis \(^{41}\) ), and the complementarity determining regions (CDRs) bind to residues Y550, E554 and H555 in BamA (Fig. 3e). Interestingly, a BamA- specific nanobody (nanoE6) has also been found to bind eL4 (involving E554) and also influences dynamics in the lateral gate \(^{17}\) . However, since binding of Fab1 to BAM (and nanoE6 to BamA \(^{17}\) ) does not drastically alter the conformation of eL4 from that seen in lateral- closed structures, how Fab1 binding stabilises a lateral- open conformation remains obscure. Finally, we determined the cryoEM structure of BAM- P5L at lower resolution (10.3 Å; Supplementary Figs. 9 and 10), and although the conformation of the lateral gate is not clearly observed at this resolution (Supplementary Fig. 10a), POTRA- 5 unambiguously occludes the BamA barrel suggesting that BAM- P5L is in a "lateral- open"- like state (Supplementary Fig. 10b). Cross- correlation of the BAM- P5L, WT BAM \(^{8}\) (open) and BAM- LL (closed) density maps, as well as comparison of the shapes of the BamA barrel in the different structures add further evidence that BAM- P5L is indeed in a lateral- open state, as expected from the design of the Cys mutants, (Supplementary Figure 10d,e).  
+
+## Fab1 binding to disulphide-locked BAM further inhibits OMP folding  
+
+As BAM can populate a lateral- open conformation in the presence or absence of Fab1, we determined the cryoEM structure of BAM- LL bound to Fab1 to ascertain whether Fab1 binding could further stabilise a lateral- open conformation, potentially further blocking the conformational changes required for BAM's catalytic action. In contrast with BAM- LL, the cryoEM structure of the BAM- LL: Fab1 complex (at 7.1 Å resolution) contains a single structure which is in a lateral- open conformation (Fig. 4a, Supplementary Fig. 11), consistent with Fab1 biasing BamA's conformational equilibrium towards a lateral- open state (Fig. 4b) in which POTRA- 5 occludes the barrel (Fig. 4c). Further evidence for the lateral
+
+<--- Page Split --->
+
+closed state being incompatible with Fab1 binding was observed by SDS- PAGE, where the SDS- resistant BamA- Fab1 band observed for WT BAM- Fab1 was weaker for BAM- LL- Fab1, with a compensating increase in the band corresponding to non- complexed BamA, suggestive of the BAM- LL- Fab1 complex being less stable under SDS- PAGE conditions (Supplementary Fig. 12a). Interestingly, since MAB1 binds to BAM in the E. coli OM<sup>16</sup>, this suggests that a lateral- open conformation is formed in situ in the OM, consistent with previous data<sup>36</sup>. Conversely, the Fab1- bound BAM- P5L complex produces an SDS- resistant band, consistent with stable binding to its lateral- open state (Supplementary Fig. 12b). tOmpA and OmpX folding assays revealed that the addition of Fab1 to BAM- P5L or BAM- LL each resulted in increased inhibition, with folding yields of \(\sim 10 - 20\%\) for tOmpA (Fig. 4d, Supplementary Fig. 13a) and \(5 - 10\%\) for OmpX (Fig. 4e, Supplementary Fig. 13b) after 3 hours at \(25^{\circ}C\) , and initial folding rates of only \(1 - 3\%\) and \(1 - 6\%\) of that of WT BAM for tOmpA and OmpX, respectively (Fig. 4f and g). This additive inhibition could arise from a synergistic reduction in conformational dynamics within the BAM complex, or from Fab1 binding and disulphide locking inhibiting distinct mechanisms of BAM- mediated folding catalysis.  
+
+## BAM lipoproteins mediate destabilisation of the lipid bilayer  
+
+In vitro studies have shown that spontaneous OMP folding rates and efficiencies are increased in membranes with decreased thickness, increased fluidity, or containing bilayer defects<sup>42- 45</sup>. As well as directly interacting with its substrate OMPs<sup>27,29</sup>, BAM is also thought to reduce the stability of the lipid bilayer to facilitate folding, due to asymmetry in the hydrophobic thickness of the BamA \(\beta\) - barrel (which is narrowest in the vicinity of the lateral gate)<sup>18,32</sup>. Evidence for membrane destabilisation has been provided by molecular dynamics (MD) simulations of BamA in lipid bilayers<sup>20,24,25,30- 35</sup> and by cryoEM and MD simulations of BAM in nanodiscs formed from E. coli polar lipids<sup>18</sup>. To determine how the different conformational states of BAM affect bilayer stability more directly, we measured the effect of the different BAM complexes studied above on the lipid phase transition of liposomes formed from 1,2- dimyristoyl- sn- glycero- 3- phosphocholine (DMPC, \(d / C_{14:0}PC\) ) using the fluorescent lipid probe laurdan (Supplementary Fig. 14), the fluorescence emission spectrum of which depends on lipid phase<sup>46</sup>. DMPC was chosen for these experiments as it undergoes a gel- liquid phase transition with a midpoint of \(\sim 24^{\circ}C\) , compared with \(\sim 3^{\circ}C\) for E. coli polar lipid<sup>47</sup> and BAM has been shown to be active in DMPC liposomes<sup>48</sup>. As expected, a phase transition for empty DMPC liposomes was observed at \(24^{\circ}C\) (Fig. 5a, see also Supplementary Fig. 15). Interestingly, the transition phase temperature (T<sub>m</sub>) was not affected by the presence of BamA alone (Fig. 5a), demonstrating that the asymmetric BamA \(\beta\) - barrel does not itself cause this global perturbation of the lipid bilayer, at least as judged by this assay. By contrast, in all proteoliposomes containing the full BAM complex,
+
+<--- Page Split --->
+
+regardless of whether that complex is inhibited, the gel- liquid phase transition occurred at a lower temperature ( \(\sim 22 - 23^{\circ}C\) ) and over a broader temperature range (Fig. 5b). These results thus demonstrate that BAM disrupts bilayer stability independently of the structure of the \(\beta 1 - \beta 16\) seam and shows that the BamB- E lipoproteins are essential for this perturbation of the membrane.  
+
+## Discussion  
+
+Protein- protein interactions between BAM and substrate OMPs, and lipid disordering have both been implicated as important features in BAM function<sup>3,24</sup>, but how these different facets of BAM are balanced to enable OMP folding remained unclear. Here, we have used structural, biochemical and kinetic refolding analyses to dissect these two roles, at least for the 8- stranded OMPs, tOmpA and OmpX. BAM is well- known to be conformationally dynamic, with cryo- EM and X- ray structures capturing the complex in lateral- open<sup>5,6,8</sup> and lateral- closed<sup>6,7,21,22</sup> conformations, and a recent cryoEM, MD and single molecule FRET study demonstrating dynamics of the complex in nanodiscs<sup>18</sup>. Furthermore, recent X- ray structures have demonstrated that the C- terminal strand of the OMP substrates tOMPa and OMPLA forms an antiparallel \(\beta\) - strand pairing with lateral- closed BamA \(\beta 1\) , possibly capturing an early stage intermediate in OMP assembly<sup>22</sup>. A recent cryoEM structure of a BAM:tBamA complex revealed that the tBamA substrate forms a \(\beta\) - strand pairing with lateral- open BamA \(\beta 1\) of BAM, whilst making a side- chain mediated interface involving BamA \(\beta 16\) , to form a hybrid barrel<sup>29</sup> that presumably mimics a late- stage assembly intermediate. This observation is consistent with crosslinking studies of EspP<sup>27</sup> and LptD<sup>28</sup> to BAM, and Por1 to SAM<sup>26</sup>. Given these insights, it is perhaps unsurprising that trapping BamA in the BAM complex in an open or closed conformation by disulphide bonding has a profound effect on bacterial viability, akin to the observations found using nanobodies<sup>17</sup>, small molecules and peptidomimetic antibiotics, which also have a lethal outcome<sup>11,12</sup>. Remarkably, we show here that this in vivo lethality masks a more subtle effect on BAM activity that is revealed by in vitro activity assays. Both disulphide- locking and Fab1 binding inhibit, but do not abolish, BAM- catalysed folding of tOmpA and OmpX in vitro (Fig. 1, and Supplementary Tables 1 and 2). The finding that these inhibitory effects are distinct and additive (Fig. 4) highlights the importance of different, presumably parallel, facets of BAM action for OMP folding catalysis. Our cryoEM structures confirm that in solution, both BAM- P5L and Fab1 lock BamA in a lateral- open conformation (Figs. 3, 4, and Supplementary Fig. 10). Presumably this prevents substrate access and pairing to BamA \(\beta 1\) which recent structures suggest initially occurs to a lateral- closed conformation<sup>22</sup>. It may also inhibit substrate binding by occlusion of entry to the BamA barrel by POTRA- 5. Consistent with this, it has recently been shown that the BAM substrate, RcsF, binds in the lumen of the BamA \(\beta\) - barrel only in the lateral- closed conformation<sup>21</sup>, and that the essential mediator of
+
+<--- Page Split --->
+
+LPS assembly, LptD, contacts the internal lumen of BamA during folding<sup>28</sup>. An inability to assemble larger and essential BAM-dependent substrates, such as LptD, could explain why disulphide locking/Fab1 binding are lethal in vivo<sup>6,16,19</sup>, despite smaller OMPs potentially remaining able to fold and insert into the OM, albeit more slowly than with WT BAM. For the latter OMPs, lethality may result from a reduced flux through the OMP biogenesis pathway when BAM is impaired, inducing cell envelope stress caused by accumulation of unfolded OMPs in the periplasmid. Indeed, increased envelope stress was observed upon addition of MAB1 to \(\Delta \text{waaD} E\) . coli<sup>16</sup>. Moreover, a small molecule inhibitor of the regulator of sigma E protease (RseP)<sup>49</sup>, that is a key component of this pathway, has a lethal outcome by blocking the \(\sigma^{\mathrm{F}}\) stress response that normally responds to envelope stress by increasing BAM expression<sup>50</sup>, decreasing OMP expression<sup>51</sup>, and increasing protein degradation<sup>52</sup>. The extent to which the folding of larger OMPs is inhibited by the BAM variants examined here remains unclear, but we speculate that for these proteins there could be a greater dependence on a direct interaction with BAM for successful insertion and folding, with BAM being unable to destabilise membranes sufficiently to allow larger OMPs to fold solely via this route.  
+
+Despite the apparent incompatibility of BAM- LL's disulphide bond and a lateral- open conformation<sup>6,8</sup>, both open- like and closed structures are present in approximately equal populations in solution. The BAM- LL structures presented here thus provide direct evidence that at least \(\beta 1\) and \(\beta 2\) of BamA are malleable in the lateral- open state, being able to bend inwards towards the barrel lumen (Supplementary Fig. 7). Such plasticity appears to be functionally relevant, especially considering the more severe outward motion observed when BAM is engaged with tBamA as a substrate<sup>29</sup> (Supplementary Fig. 7). Such an extended conformation would presumably be impossible in BAM- LL, perhaps explaining the partial inhibitory effects observed here for OmpX and tOmpA. Superposition of all the lateral- open BAM structures reported to date thus support a model in which the N- terminal half of the BamA barrel is conformationally dynamic, whilst the C- terminal half provides a stable scaffold that supports these functionally important conformational changes.  
+
+Lipid destabilisation by BAM has been proposed previously as a potentially important facet of the catalysis of OMP folding and insertion into the OM<sup>3,25,53</sup>. This has been supported by MD simulations that reveal destabilisation of the membrane surrounding BamA<sup>20,24,25,30- 35</sup>, and a recent cryoEM structure of BAM in a nanodiscs containing \(E\) . coli polar lipids that shows distortion of the bilayer adjacent to the lateral gate<sup>18</sup>. Whilst these effects are localised to the BamA barrel, the laurdan fluorescence data provide direct biochemical evidence that BAM causes global destabilisation of a bilayer, as revealed by a reduction in the lipid phase transition temperature of DMPC liposomes (Fig. 5). They also reveal that this is mediated by lipoproteins BamB- E, since BamA alone had no discernible effect. This is consistent with cryoEM structures which have identified interactions between BamB, BamD and BamE and detergent micelles<sup>8</sup> as well as with lipid in nanodiscs<sup>18</sup>, whilst BamC is
+
+<--- Page Split --->
+
+thought to span the membrane necessary for surface exposure of the two C- terminal helix- grip domains54. In addition to the roles of BamB- E in substrate recognition15,55, in mediating BAM oligomerisation into 'precincts'56, and coordinating conformational changes in BamA36,57, the results presented here highlight the importance of these lipoproteins in mediating changes in membrane stability.  
+
+In summary, the results presented allow different facets of BAM- mediated catalysis of OMP folding and membrane insertion to be discerned. By structural analysis of Fab1- bound and two different disulphide locked BAM complexes we reveal a remarkable structural malleability of the BamA barrel, and show that interconversion between these different structures is not essential for folding and membrane insertion of the 8- stranded tOmpA and OmpX substrates in vitro. In addition, we provide direct biochemical evidence that BAM causes global destabilisation of a lipid bilayer and reveal that this is not endowed by asymmetry in the depth of the BamA barrel, but instead requires the presence of BamB- E, demonstrating a new role for its lipoproteins. Finally, by demonstrating a significant, but reduced folding capacity of the Fab1- bound and disulphide- locked BAM variants in vitro, we provide evidence in support of models that suggest that bacterial viability depends on a delicate balance between the rates of OMP synthesis and their chaperone- dependent delivery to BAM, with the catalytic power of BAM to insert OMPs into the OM. Perturbing this balance thus offers exciting opportunities to create new antibacterial agents by targeting the different protein complexes required for OMP biogenesis.
+
+<--- Page Split --->
+
+## Methods  
+
+## Expression and purification of WT and disulphide-locked BAM complexes  
+
+BAM- LL (BamA(E435C/S665C/C690S/C700S)BCDE- His) and BAM- P5L (BamA(G393C/G584C/C690S/C700S)BCDE- His) in a pTrc99a vector were generated using Q5 site- directed mutagenesis (New England BioLabs) using plasmid pJH114 (kindly provided by Harris Bernstein58) as a template. WT BAM, BAM- LL and BAM- P5L were expressed in E. coli BL21(DE3) cells and were purified from the membrane fraction using a combination of Ni- affinity and size exclusion chromatography, as described previously8.  
+
+## Expression and purification of BamA, OmpX and tOmpA  
+
+BamA, OmpX and tOmpA were expressed as inclusion bodies in E. coli BL21(DE3) cells, using a procedure modified from McMorran et al.50. Briefly, inclusion bodies were solubilised in \(25~\mathrm{mM}\) Tris- HCl pH 8.0, \(6M\) guanidine- HCl and were centrifuged (20,000 g, \(20\mathrm{min}\) , \(4^{\circ}\mathrm{C}\) ) to remove remaining insoluble material. The solubilised inclusion bodies were purified by SEC using a Superdex 75 HiLoad 26/60 column (GE Healthcare) for tOmpA and OmpX, and Sephacryl 200 26/60 column for BamA, equilibrated in \(25~\mathrm{mM}\) Tris- HCl pH 8.0, \(6M\) guanidine- HCl. For folding experiments, OmpX and tOmpA were buffer exchanged into Tris- buffered saline (TBS, \(20~\mathrm{mM}\) Tris- HCl, \(150~\mathrm{mM}\) NaCl) pH 8.0, \(8M\) urea using ZebaTM Spin Desalting Columns, \(7k\) MWCO, \(0.5~\mathrm{mL}\) (Thermo Scientific). BamA was refolded in LDAO detergent prior to reconstitution into proteoliposomes, as described previously59.  
+
+## Refolding of BamA  
+
+BamA was refolded as described by Hartmann et al.59. Briefly, BamA added dropwise into ice- cold \(50~\mathrm{mM}\) Tris- HCl pH 8.0, \(300~\mathrm{mM}\) NaCl, \(500~\mathrm{mM}\) arginine, \(0.5\%\) (w/v) LDAO, \(10~\mathrm{mM}\) DTT whilst rapidly stirring. Following 24 hours incubation, BamA was dialysed against 50 mM Tris- HCl pH 8.0, \(0.1\%\) (w/v) LDAO overnight before loading on a \(5~\mathrm{mL}\) HiTrap Q (GE Healthcare) anion exchange column and eluting in a NaCl gradient. Folded BamA was separated from unfolded and degraded BamA, as judged by SDS- PAGE, and used for reconstitution into liposomes containing E. coli polar lipid or DMPC, as required.  
+
+## Expression and purification of SurA  
+
+SurA with an N- terminal 6x His- tag and a TEV cleavage site was expressed and purified using a modified protocol described previously60. Briefly, SurA was expressed in E. coli BL21(DE3) cells and was purified on a \(5~\mathrm{mL}\) HisTrap FF column (GE Healthcare). SurA was denatured on- column in \(25~\mathrm{mM}\) Tris- HCl pH 7.2, \(6M\) guanidine- HCl, washed in the same
+
+<--- Page Split --->
+
+buffer and then refolded on- column in \(25~\mathrm{mM}\) Tris- HCl pH 7.2, \(150~\mathrm{mM}\) NaCl, \(20~\mathrm{mM}\) imidazole before elution in \(25~\mathrm{mM}\) Tris- HCl pH 7.2, \(150~\mathrm{mM}\) NaCl, \(500~\mathrm{mM}\) imidazole. The His- tag was cleaved by addition of His- tagged TEV protease and \(14.3~\mathrm{mM}\) 2- mercaptoethanol, produced as previously described<sup>31</sup>, and the cleaved His- tag and TEV protease were removed on a \(5~\mathrm{mL}\) HisTrap FF column. Purified SurA was dialysed against 5 L TBS pH 8.0, concentrated to \(\sim 200~\mu \mathrm{M}\) using Vivaspin 20 MWCO \(10~\mathrm{kDa}\) concentrators (Sartorius, UK), aliquoted, snap- frozen in liquid nitrogen, and stored at \(- 80~^\circ \mathrm{C}\) .  
+
+## Monoclonal antibody Fab production  
+
+Fabs were cloned and expressed in \(E\) . coli as previously described<sup>61,62</sup>. Cell paste containing the expressed Fab was resuspended in PBS buffer containing \(25~\mathrm{mM}\) EDTA and \(1~\mathrm{mM}\) PMSF. The mixture was homogenised and then passed twice through a microfluidiser. The suspension was then centrifuged at \(21,500g\) for \(60~\mathrm{min}\) . The supernatant was loaded onto a Protein G column equilibrated with PBS at \(5~\mathrm{mL / min}\) . The column was washed with PBS to baseline and proteins were eluted with \(0.6\%\) (v/v) acetic acid. Fractions containing Fabs, assayed by SDS- PAGE, were pooled and loaded onto a \(50~\mathrm{mL}\) SP Sepharose column equilibrated in \(20~\mathrm{mM}\) MES, pH 5.5. The column was washed with \(20~\mathrm{mM}\) MES, pH 5.5 for 2 column volumes and the protein was then eluted with a linear gradient to \(0.5\mathrm{M}\) NaCl in the same buffer. For final purification, Fab- containing fractions from the ion exchange column were concentrated and run on a Superdex 75 size exclusion column (GE Healthcare) in PBS buffer.  
+
+## Reconstitution of BAM complex variants and BamA into \(E\) . coli polar lipid proteoliposomes  
+
+\(E\) . coli polar lipid extract, purchased as powder from Avanti Polar Lipids (Alabaster, AL), was dissolved in \(80:20\) (v/v) chloroform/methanol at \(20~\mathrm{mg / mL}\) . Appropriate volumes were dried to thin films in clean Pyrex tubes at \(42~^\circ \mathrm{C}\) under \(\mathrm{N}_2\) gas, and were further dried by vacuum desiccation for at least 3 hours. WT BAM, BAM- LL and BAM- P5L in TBS pH 8.0, \(0.05\%\) (w/v) DDM were mixed with \(E\) . coli polar lipid extract films solubilized in TBS pH 8.0, \(0.05\%\) (w/v) DDM in a 1:2 (w/w) ratio. For formation of BAM- Fab1 proteoliposomes, a 2- fold molar excess of Fab1 was added to WT BAM, BAM- P5L or BAM- LL in TBS pH 8.0, \(0.05\%\) (w/v) DDM before mixing with lipid. For BamA proteoliposomes, refolded BamA was added to \(E\) . coli polar lipid films solubilised in TBS pH 8.0, \(0.1\%\) (w/v) LDAO in a 1:2 (w/w) ratio. Empty liposomes were prepared by mixing lipid with an equivalent volume of buffer. To remove detergent and promote liposome formation, the mixtures were dialyzed against \(2~\mathrm{L}\) of \(20~\mathrm{mM}\) Tris- HCl pH 8.0, \(150~\mathrm{mM}\) KCl using 12- 14 kDa MWCO D- Tube™ Maxi Dialyzers (Merck) at room temperature for 48 hours with a total of four buffer changes. Following dialysis, the
+
+<--- Page Split --->
+
+proteoliposomes were pelleted twice by ultracentrifugation at 100,000 \(g\) for 30 mins at \(4^{\circ}C\) (the supernatants referred to as wash 1 and wash 2 in Supplementary Figures) and were resuspended in TBS pH 8.0. Protein concentration was determined using a BCA assay (ThermoScientific) and successful reconstitution was determined by SDS- PAGE.  
+
+## Fluorescein-C5-maleimide labelling of free thiols in BAM disulphide variants  
+
+WT BAM, BAM- LL and BAM- P5L proteoliposome preparations (containing 5 \(\mu \mathrm{M}\) BAM) in TBS pH 8.0 were treated with 1 mM TCEP or 0.1 mM diamide, along with an untreated control, for 45 mins at room temperature. The proteoliposomes were then diluted 10- fold into TBS pH 7.5, 8 M urea containing 100 \(\mu \mathrm{M}\) fluorescein- C5- maleimide and were incubated overnight at \(25^{\circ}C\) . The products of the labelling reaction were then analysed by SDS- PAGE on \(15\%\) (w/v) acrylamide/bis- acrylamide (37.5:1) Tris- tricine SDS- PAGE gels run at \(60\mathrm{mA}\) per gel for 90 mins at \(25^{\circ}C\) , and imaged under 460 nm light using an Alliance Q9 Advanced gel doc (UVITEC, Cambridge, UK). Subsequently gels were stained with Coomassie Blue to visualise all protein bands.  
+
+## BAM-mediated folding of OMPs by SDS-PAGE band-shift assays  
+
+Solutions of \(20\mu \mathrm{M}\) tOmpA or OmpX denatured in TBS pH 8.0 containing 8 M urea were diluted 5- fold into a \(20\mu \mathrm{M}\) solution of SurA. This mixture was then immediately diluted 2- fold into BAM, BamA or empty proteoliposomes to initiate the folding reaction, maintained at 25 \(^\circ \mathrm{C}\) . Final concentrations were \(1\mu \mathrm{M}\) BAM, \(2\mu \mathrm{M}\) tOmpA/OmpX, \(10\mu \mathrm{M}\) SurA, \(0.8\mathrm{M}\) urea in TBS pH 8.0. DTT was included in the relevant folding reactions at a final concentration of 25 mM. Samples of the folding reaction were taken periodically and were quenched in SDS- PAGE loading buffer (final concentrations: \(50\mathrm{mM}\) Tris- HCl pH 6.8, \(10\%\) (v/v) glycerol, \(1.5\%\) (w/v) SDS, \(0.001\%\) (w/v) bromophenol blue). The samples, including a boiled control (10 mins at \(>95^{\circ}C\) ), were run on \(15\%\) (w/v) SDS- PAGE gels as described above. The gels were stained in InstantBlue™ (Experion) and were imaged using an Alliance Q9 Advanced gel doc (UVITEC, Cambridge, UK). Folded and unfolded band intensities were quantified using ImageJ software (Fiji) and were plotted as a fraction folded ( \(\mathrm{I_F / (I_F + I_{UF})}\) ) against time. Folding data were fitted to a single exponential function in Igor Pro (V8.04) and initial rates calculated by applying a linear fit to data within the first \(5\%\) of the time- course (540 seconds).  
+
+## CryoEM grid preparation  
+
+Samples for grid preparation were prepared as follows. Purified BAM- LL or BAM- P5L in 50 mM Tris- HCl pH 8.0, \(150\mathrm{mM}\) NaCl and \(0.05\%\) (w/v) DDM were diluted to \(3.3\mathrm{mg / mL}\) or 2.3
+
+<--- Page Split --->
+
+mg/mL, respectively. For the BAM- Fab1 complex, purified WT BAM was mixed with a 2- fold molar excess of Fab1 and run on a Superdex 200 10/300 column in TBS pH 8.0, 0.05% (w/v) DDM to isolate a stoichiometric complex from excess free Fab1. Fractions corresponding to the complex were concentrated to 4.8 \(\mu \mathrm{M}\) in Vivaspin 500 concentrator MWCO 30k (Sartorius). To assemble the Fab1- bound BAM- LL complex, stock solutions of purified BAM- LL and Fab1 were first diluted to 5.9 \(\mu \mathrm{M}\) in 20 mM Tris- HCl pH 8.0, 150 mM NaCl and 0.05% (w/v) DDM and mixed in a 1:1 molar ratio, before dilution in detergent- free buffer to a total protein concentration of 0.9 mg/mL and a total DDM concentration of 0.03% (w/v). The detergent concentration was lowered to combat a tendency for very thin ice on the resulting grids.  
+
+CryoEM grids were prepared as follows. For the BAM- Fab1 complex, 4 \(\mu \mathrm{L}\) protein was applied to gold UltraUfoil R2/2 200 mesh grids, previously glow discharged for 60 sec at 20 mA in a GlowQube Plus (Electron Microscopy Sciences) in the presence of amylamine vapor. For BAM- LL, BAM- P5L and BAM- LL in complex with Fab1, 3 \(\mu \mathrm{L}\) of sample was applied to copper QUANTIFOIL R1.2/1.3 300 mesh, copper QUANTIFOIL R0.6/1 400 mesh and gold UltraUfoil R1.2/1.3 300 mesh grids (Electron Microscopy Sciences), respectively, that were previously glow discharged for 30 sec at 60 mA in a GlowQube Plus (Electron Microscopy Sciences). Grids were blotted for 6 sec with Whatman #1 filter paper at 4 °C and 80- 100% relative humidity, before plunge freezing in liquid ethane using a Vitrobot Mark IV (ThermoFisher).  
+
+## CryoEM Imaging  
+
+Data were collected on a 300 KeV Titan Krios (ThermoFisher) EM in the Astbury Biostructure Laboratory in automated fashion using EPU software (ThermoFisher). Micrographs were recorded on an energy- filtered K2 detector (Gatan inc.) in counting mode, using a 100 \(\mu \mathrm{m}\) objective aperture. For BAM- LL, 6,456 micrographs were collected from a single grid over two sessions. For the Fab1- bound BAM- LL complex, 2,780 micrographs were collected from a single grid. For BAM- P5L, two grids were imaged in separate sessions, resulting in 2150 total micrographs. For the BAM- Fab1 complex, a single grid was imaged over three sessions, resulting in 4197 total micrographs. Full data collection parameters for each sample are shown in Supplementary Table 4.  
+
+## Image Processing  
+
+All processing was performed in RELION 3.0<sup>63</sup> (BAM- LL, BAM- Fab1, Fab1- bound BAM- LL) or 3.1<sup>64</sup> (BAM- P5L) unless otherwise stated. Dose- fractionated micrographs were motion- corrected and dose- weighted by MotionCor<sup>65</sup>, before estimation of contrast transfer function parameters by Gct<sup>66</sup> using the motion corrected and dose- weighted micrographs,
+
+<--- Page Split --->
+
+apart from the BAM- Fab1 complex where motion corrected, but non- dose weighted, micrographs were used.  
+
+For BAM- LL, the two datasets were initially processed separately in a similar manner (Supplementary Fig. 6). For dataset 1, 299,458 particles were first picked using the general model in crYOLO 1.3.5<sup>67</sup>, and extracted in 300 pixel (321 Å) boxes with two- fold binning, before removal of false positives through two rounds of 2D classification. The resulting 234,598 particles were then used to generate an initial model by stochastic gradient descent<sup>68</sup>, which was used as the starting model for a 3D classification. Two high resolution classes corresponding to different conformations of BAM- LL were obtained, one termed lateral- closed (86,615 particles) and one lateral- open (83,803 particles). Particles corresponding to each class were then re- extracted unbinned, and autorefined with a mask excluding bulk solvent. After masking and sharpening, resolutions of 5.0 Å (lateral- closed) and 5.9 Å (lateral- open) were obtained. Processing of dataset 2 proceeded similarly and resulted in comparable resolutions for both conformations. To achieve higher resolution, one round of CTF refinement followed by Bayesian polishing were then employed for each dataset, following which the particles corresponding to the same conformation were combined, resulting in 160,118 lateral- closed and 141,612 lateral- open particles. Finally these particle stacks were subject to separate non- uniform refinements in cryoSPARC v2.2.0<sup>68,69</sup>. Masking and sharpening of the resulting half- maps in RELION resulted in resolutions of 4.1 Å (lateral- closed) and 4.8 Å (lateral- open). B- factors of - 107 Å<sup>2</sup> and - 127 Å<sup>2</sup> were applied to the final lateral- closed and lateral- open reconstructions, respectively. Local resolution was estimated using RELION.  
+
+For the BAM- Fab1 complex (Supplementary Fig. 8), particles were autopicked in RELION 3<sup>63</sup> using class averages from a previous reconstruction<sup>8</sup> filtered to 30 Å as search templates. Individual particles were extracted in 350 pixel (374.5 Å) boxes and culled with multiple rounds of 2D and 3D classification. The resulting particle stack containing 131,853 particles was further refined using the non- uniform refinement function in CryoSPARC v2.2.0<sup>68,69</sup>. The reconstruction was performed on independent subsets and final resolution of 5.2 Å determined by 'gold standard' FSC<sup>70</sup>. A B- factor of - 167 Å<sup>2</sup> was applied to the final reconstruction.  
+
+For BAM- P5L (Supplementary Figs. 9 and 10), particles were picked in crYOLO 1.4.1 using the general model. For dataset 1: 41, 316 particles were picked and extracted in a 280 pixel (300 Å) box, for dataset 2: 54, 532 particles were picked and extracted into 352 pixel (300 Å) boxes. Both used twofold binning. The extracted particles were combined into a single dataset and the resulting 95,848 particles passed through 2D classification. The best 21, 483 particles were used to construct an initial model by stochastic gradient descent<sup>68</sup>, which was used as a reference for 3D classification of the 43,280 good particles from 2D
+
+<--- Page Split --->
+
+classification. The resulting 24, 101 particles were autorefined, and re- extracted as unbinned particles and subject to 3D classification using the autorefined model as the reference. The resulting 19,044 particles were autorefined with a mask to a resolution of 10.3 Å. A B- factor of - 671 Ų was applied to the final reconstruction  
+
+For the Fab1- bound BAM- LL complex (Supplementary Fig. 11), particles were picked in crYOLO 1.4.1 using a model trained with 11 handpicked micrographs spanning the defoci range. The resulting 162,844 particles were extracted in 300 (321 Å) pixel boxes with twofold binning. One round of 2D classification was used to cull the particle set to 108,096 particles which was then subject to 3D classification, using an initial model generated by stochastic gradient descent<sup>68</sup> from the best 32,645 particles in that stack as a template. From this 3D classification run, only one conformer was observed, corresponding to a lateral- open, BAM- LL bound to Fab1. The 71,675 particles in the highest resolution class were autorefined, re- extracted as unbinned particles and subject to 3D classification using the autorefined model as the reference, further culling the particle stack. Autorefinement and sharpening of the resulting 61,777 good particles gave a resolution of 7.3 Å. Finally, one round of CTF refinement followed by Bayesian polishing was carried out, and the resulting particle stacks were subject to non- uniform refinement in cryoSPARC v2.2.0<sup>68,69</sup>. Masking and sharpening of the resulting half- maps in RELION resulted in a resolution of 7.1 Å. A B- factor of - 274 Ų was applied to the final reconstruction.  
+
+## CryoEM model building and refinement  
+
+For LL- BAM in the lateral- closed cryoEM map, an existing crystal structure of intact BAM in a lateral- closed conformation (PDB ID: 5D0O<sup>5</sup>) was first edited to both remove the two natural cysteines in BamA and to insert the lid- lock disulphide bond. This starting model was fitted to the density as a rigid body in Chimera<sup>71</sup>, before performing several iterations of real- space refinement in PHENIX 1.14<sup>72</sup> with secondary structure restraints followed by manual refinement in COOT<sup>73</sup>, until satisfactory geometry and fit between model and map was obtained as assessed using MolProbity<sup>74</sup>. The extracellular region of eL6 (BamA<sub>675- 702</sub>, C- terminal globular domains of BamC (BamC<sub>89- 344</sub>), and regions at the chain termini of BamABCDE were insufficiently resolved and were not modelled. The final model contains BamA<sub>24- 675, 702- 810</sub> BamB<sub>31- 391</sub>, BamC<sub>30- 85</sub>, BamD<sub>27- 244</sub>, BamE<sub>29- 111</sub>.  
+
+As the resolution of the other structures was insufficient for the above approach, Molecular Dynamics Flexible Fitting (MDFF)<sup>40</sup> was used to flexibly fit these conformations. For BAM- LL lateral- open, cascade MDFF (cMDFF) simulations of the lateral- closed atomic model with BamA truncated after residue 809 were first used to derive an initial fit to the lid- lock lateral- open cryoEM map. Here, a series of Gaussian blurred density maps were generated using the volutil function in VMD (halfwidths \(\sigma = 0, 1, \ldots , 6 \text{Å}\) ). The atomic model was then simulated in vacuum and subject to an external potential derived from most blurred density
+
+<--- Page Split --->
+
+map, causing it to be flexibly fit into the density. 2 ps of minimisation followed by 100 ps of equilibration were run with a gscale of 1.0 defining the strength of the external potential derived from the density map. Consecutive 100 ps simulations were then run into maps of decreasing blurring, where the end coordinates from the previous simulation were used as input for the next, until reaching the unblurred map. At each step, isomerism, chirality and secondary structure restraints were applied. Several repeats were run, taking advantage of the stochastic nature of the simulation to generate different fits. Additionally, a second MDFF simulation was also run into the unblurred map using PDB- 5LJO<sup>8</sup> as a starting model, to derive better conformations for BamA<sub>720- 734</sub> and BamA<sub>807, 808</sub>. These models were then manually combined to give best mainchain fit to the density, before minimising against the unblurred map for 40 ps. In the combined model, BamA<sub>429- 440</sub>, corresponding to eL1 and the extracellular sides of \(\beta 1\) and \(\beta 2\) , was fitting into micelle density rather than protein density due to the low resolution in this region. A final set of 500 ps MDFF simulations were therefore run with this combined model against the unblurred map, in which BamA<sub>429- 440</sub> was not subject to the external potential. The best fitting structure from these runs was then minimised for 40 ps against the unblurred map and real space refined in PHENIX 1.14<sup>72</sup> with secondary structure restraints to generate the final atomic model.  
+
+For the Fab1- bound wild- type BAM complex, an initial model was created from the BAM complex PDB entry 5LJO<sup>8</sup>, with BamA<sub>687- 700</sub> from 5EKQ<sup>5</sup>, and the Fab1 crystal structure determined here (PDB 7BM5). The C- terminal globular domains of BamC were truncated, leaving only the lasso<sup>75</sup> region (residues 25- 83) resulting in a starting model containing BamA<sub>24- 806</sub>, BamB<sub>22- 392</sub>, BamC<sub>25- 83</sub>, BamD<sub>26- 243</sub>, and BamE<sub>24- 110</sub>. The starting model was fitted into each EM density as a rigid body using UCSF Chimera<sup>71</sup> and flexibly fit using cMDFF<sup>40</sup>. This was followed by real space refinement in PHENIX 1.14<sup>72</sup> using secondary structure restraints to generate the final atomic model, with the Fab1 crystal structure used as a reference model to generate additional restraints.  
+
+For the Fab1- bound lid- locked BAM complex, the final lid- locked lateral- open structure and the Fab1 crystal structure were rigid body fitted into the EM density using UCSF Chimera and flexibly fit using a round of MDFF into the unblurred map. This was followed by real space refinement in PHENIX 1.14 with secondary structure restraints to generate the final atomic model, with the Fab1 crystal structure and the final lid- locked lateral- open structures used as reference models to generate additional restraints. During the simulation eL1 of BamA (BamA<sub>429- 440</sub>) was not subject to the external potential to prevent overfitting to micelle density in this region. Model building statistics for all cryoEM conformers are shown in Supplementary Table 5.  
+
+## Crystallisation and structure determination of Fab1
+
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+
+Fab1 at 6.5 mg/mL was crystallised by the sitting drop vapour diffusion method in 96- well SWISSC1 3- drop plates at \(20^{\circ}C\) . Drops consisted of 100 nL protein and 100 nL crystallisation solution were dispensed using a Mosquito robot (TTP Labtech). Crystals were grown in 0.16 M lithium chloride, \(22\%\) (w/v) PEG6000, 0.1 M MES pH 6.0 and were harvested after 21 days. Crystals were cryo- protected in the crystallisation solution supplemented with \(20\%\) (v/v) ethylene glycol before flash- cooling into liquid nitrogen. X- ray data were collected at Diamond Light Source on beamline I24 from a single cryo- cooled crystal (100 K) using a Pilatus3 6M detector. Diffraction data were collected for a total of \(180^{\circ}\) up to a resolution of \(2.5 \AA\) with a \(0.2^{\circ}\) oscillation using an exposure time of 0.04 seconds at \(100\%\) transmission. X- ray diffraction data were indexed and integrated by autoPROC and STARANISO \(^{76}\) and were scaled to \(2.96 \AA\) in Aimless \(^{77}\) using the I24 beamline autoprocessing pipeline. The crystals belonged to a monoclinic space group \(P12_{1}1\) with unit cell parameters a = 92.0 Å, b = 130.1 Å, c = 138.9 Å, \(\alpha = 90.00^{\circ}\) , \(\beta = 106.1^{\circ}\) , \(\gamma = 90.00^{\circ}\) . The structure was solved by molecular replacement using Phaser \(^{78}\) and the C \(_{H}\) domain of the anti- NFG Fab as the search model (PDB accession number 1ZAN \(^{79}\) ). Crystallographic refinement was performed using PHENIX- 1.9 \(^{72,80}\) and model building was carried out in Coot \(^{73}\) . MolProbity \(^{74}\) was used for structure validation and quality assessment. The final model coordinates and structure factors are deposited in the PDB under the accession number 7BM5.  
+
+## Reconstitution of BamA and different BAM complexes into DMPC proteoliposomes  
+
+DMPC (dIC14:0PC), purchased as powder from Avanti Polar Lipids (Alabaster, AL), was dissolved in \(80:20\) (v/v) chloroform/methanol mixture at \(25 \text{mg/mL}\) . Appropriate volumes were dried to thin films in clean Pyrex tubes at \(42^{\circ}C\) under \(\mathsf{N}_2\) gas, and were further dried by vacuum desiccation for \(>3\) hours. BAM WT, BAM- LL and BAM- P5L or a 2:1 (mol/mol) mixture of Fab1 and BAM in TBS pH 8.0, \(0.05\%\) (w/v) DDM were mixed with DMPC lipid solubilized in TBS pH 8.0, \(0.05\%\) (w/v) DMD at a lipid to protein ratio (LPR) of 1600:1 (mol/mol). For BamA, DMPC lipid was first solubilised in TBS pH 8.0, \(0.1\%\) (w/v) LDAO. Empty liposomes were prepared by mixing DDM- solubilised lipid with an equivalent volume of buffer. Dialysis was performed as described for the preparation of E. coli polar lipid proteoliposomes, except that a temperature of \(30^{\circ}C\) was used (above the DMPC transition temperature). Following dialysis, the proteoliposomes were pelleted twice by ultracentrifugation at \(100,000 \text{g}\) for 30 min at \(4^{\circ}C\) and resuspended in TBS pH 8.0. The proteoliposomes were then extruded with 21 passes through a \(0.1 \mu \text{m}\) polycarbonate membrane using a mini- extruder (Avanti) pre- equilibrated at \(30^{\circ}C\) . Following ultracentrifugation as before, proteoliposomes were resuspended in TBS pH 8.0, protein concentration was determined using a BCA assay (ThermoScientific) and successful reconstitution was confirmed using SDS- PAGE.
+
+<--- Page Split --->
+
+## Probing lipid disorder using laurdan  
+
+Probing lipid disorder using laurdanLaurdan (Cambridge Bioscience) dissolved in DMSO was added to a final concentration of \(4.2 \mu M\) (final DMSO concentration of \(0.15\%\) (v/v)) to a \(0.8 \mu M\) suspension of BAM-, BamA- or empty- DMPC proteoliposomes (LPR 1600:1 mol/mol). The proteoliposomes were incubated at \(25 ^{\circ} C\) overnight to allow random partitioning of the laurdan probe into the membrane. Fluorescence emission was measured at \(440 nm\) and \(490 nm\) for a total time of 10 sec following excitation of laurdan fluorescence at \(340 nm\) in quartz cuvettes using a PTI QuantaMaster fluorimeter with a \(1 nm\) bandwidth and 1 second integration time. Excitation and emission slit widths were set to \(0.1 nm\) . Spectra were acquired at increasing temperature intervals from \(6 ^{\circ} C\) to \(40 ^{\circ} C\) , and to test reversibility, from \(40 ^{\circ} C\) to \(6 ^{\circ} C\) , allowing the sample to equilibrate at each temperature for 3 min. Generalised polarisation (GP) \(^{46}\) was calculated from the ratio of fluorescence intensity at \(440 nm\) and \(490 nm\) , averaged over the 10 second acquisition, using the formula GP = \((l_{440} - l_{490}) / (l_{440} + l_{490})\) , and was plotted against temperature. Mid- points and gradients of the transitions were determined by calculating the first derivative of the curve.  
+
+## Data availability  
+
+Data availabilityRaw micrographs for each dataset are deposited at EMPIAR under accession numbers XXXX (BAM- LL), XXXX (BAM Fab1 complex), XXXX (BAM- P5L), XXXX (BAM- LL Fab1 complex). The final density maps are deposited in the EMDB under accession numbers XXXX (BAM- LL lateral- closed), XXXX (BAM- LL lateral- open), XXXX (BAM Fab1 complex), XXXX (BAM- P5L) and XXXX (BAM- LL Fab1 complex). Final model coordinates have been deposited in the PDB under accession numbers XXXX (BAM- LL lateral- closed), XXXX (BAM- LL lateral- open), XXXX (BAM Fab1 complex) and XXXX (BAM- LL Fab1 complex). The crystal structure of Fab1 has been deposited in the PDB under accession number 7BM5, and crystallographic data are available at https://doi.org/10.2210/pdb7BM5/pdb. Data supporting this study are freely available at the University of Leeds Data Repository: https://doi.org/10.5518/835.  
+
+## Acknowledgements  
+
+AcknowledgementsWe thank members of the Radford, Ranson, Brockwell and Rutherford labs for helpful discussions, and Nasir Khan for technical support. CryoEM data were collected at the Astbury Biostructure Laboratory, funded by the University of Leeds and the Wellcome Trust (108466/Z/15/Z). We thank Diamond Light Source for access to Beamline i24 (MX19248). P.W and M.G.I acknowledge funding from the Medical Research Council UK
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+(MR/P018491/1). S.H and J.E.H are funded by the White Rose BBSRC DTP (BB/M011151/1) J.M. and A.J.H acknowledge support from the Wellcome Trust (222373/Z/21/Z and 105220/Z/14/Z, respectively). B.S acknowledges support from the BBSRC (BB/N007603/1 and BB/T000635/1). For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. J.W. is funded by an EOS Excellence in Research Program of the FWO and FRS-FNRS (G0G0818N). SER holds a Royal Society Professorial Fellowship (RSRP/R1/211057).  
+
+## Author contributions  
+
+P.W, S.F.H, M.G.I and A.J.H designed and performed the experiments and analysed the data. P.W, S.F.H, J.M.M, A.J.H, B.S and C.C.P carried out BAM functional assays. P.W prepared protein samples for cryoEM. S.F.H, M.G.I and J.M.M performed cryoEM experiments and determined BAM cryoEM structures. P.W solved the X-ray structure of Fab1. P.W, S.F.H, J.E.H, B.S, C.C.P and J.M.W produced proteins required for the study. J.E.H developed the BAM laurdan fluorescence assay. K.M.S and S.T.R developed and produced the anti- BamA Fab fragment (Fab1). S.E.R, N.A.R and D.J.B supervised the research. P.W, S.F.H and M.G.I wrote the manuscript with comments and edits provided from all authors.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 | Disulphide-locked BamA variants and Fab1 binding impair BAM-mediated OMP folding in vitro. (a) BAM-P5L (G393C/G584C) is expected to lock BamA in the lateral-open conformation (PDB code 5LJO<sup>8</sup>), while (b) BAM-LL (E435C/S665C) is expected to lock BamA in the lateral-closed conformation (PDB code 5DOO<sup>6</sup>). BamA POTRAs 1-4 and BamBCDE are rendered semi-transparent for emphasis on the BamA \(\beta\) -barrel and POTRA-5. The position of the disulphide bond is shown as a yellow bar. Figure made in PyMOL v1.7.2.3. (c and d) Quantification of folded and unfolded bands from SDS-PAGE band-shift </center>
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+assays (Supplementary Figs. 3 and 4) plotted as fraction folded against time for tOmpA or OmpX, respectively. Data are fitted to a single exponential function. (e and f) The initial rates of folding (determined by applying a linear fit to the first \(5\%\) of folding data) normalised as a percentage of the initial rate obtained for WT BAM, are shown for (e) tOmpA and (f) OmpX folding (see also Supplementary Table 1). Folding assays were repeated to assess reproducibility, with errors for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE), whilst "BamA" is just BamA alone.
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+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 | CryoEM resolves two conformations of BAM-LL in detergent. (a) 4.1 A cryoEM map of the BAM-LL lateral-closed conformation at a contour of \(10\sigma\) , coloured by subunit. The lateral-gate is closed and POTRA-5 does not block the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA-5 of BamA. \(\beta 1\) and \(\beta 16\) contact to close the gate. (c) The same density viewed from the periplasmic side, showing the open lumen of the BamA barrel in this conformation. (d) 4.8 Å cryoEM map of the BAM-LL lateral-open conformation at a contour of \(10\sigma\) , coloured by subunit. The lateral-gate is open and POTRA-5 occludes the BamA barrel (schematic inset). (e) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on segmented density for the barrel and POTRA-5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel to contact eL6. (f) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA-5 in this conformation. Fig. made in UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. </center>
+
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+![](images/Figure_3.jpg)
+
+<center>Fig. 3 | Fab1-bound BAM is in a lateral-open conformation. (a) 5.1 Å cryoEM map of the BAM-Fab1 complex in a lateral-open conformation at a contour of \(10\sigma\) , coloured by subunit. The lateral-gate is fully-open and POTRA-5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA-5 of BamA. \(\beta 1\) is in a conformation that makes limited contact with \(\beta 16\) . (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA-5 in this conformation. Panels made using UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d) Close up of the BamA-Fab1 interface region highlighting the Fab1 CDRs (red) interacting with eL4 of BamA (dark blue). Other regions of BamA are rendered semi-transparent to highlight eL4. Heavy and light chains of Fab1 are coloured cyan and pink, respectively. (e) The \(\mathrm{V_L}\) and \(\mathrm{V_H}\) domains of Fab1 variable form a complementary binding surface for eL4 of BamA involving residues Y550, E554 and H555. </center>
+
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+![](images/Figure_4.jpg)
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+<center>Fig. 4 | Additive effect of BAM inhibition by disulphide-locking and binding of Fab1. (a) 7.1 Å cryoEM map of the Fab1-bound LL-BAM in a lateral-open conformation at a contour of 9.5 σ, coloured by subunit. The lateral-gate is open and POTRA-5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the β-barrel and </center>
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+POTRA- 5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel to contact eL6. (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Structural panels made using UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d and e) Quantification of SDS- PAGE band- shift assays shown in Supplementary Fig. 13 for (d) tOmpA and (e) OmpX folding catalysed by BAM- P5L (green), BAM- LL (blue) and WT BAM (black), each with and without Fab1 (solid and open circles, respectively). (f and g) The initial rates, calculated by applying a linear fit to the first 5% of fitted folding data, were normalised to that of WT BAM, and are shown for (f) tOmpA and (g) OmpX folding (see also Supplementary Table 1). Folding assays were conducted twice for reproducibility with data for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE).
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 | BAM variants reduce the phase transition temperature of DMPC liposomes. Global lipid phase transition behaviour for each BAM variant and BamA in DMPC proteoliposomes, with an empty liposomes control measured using laurdan fluorescence. (a) The ratio of laurdan fluorescence at \(440 \text{nm}\) and \(490 \text{nm}\) was plotted as generalised polarisation (GP, see Methods) against temperature for \(0.8 \mu \text{M BAM/BamA proteoliposome}\) suspensions at a \(1600:1\) (mol/mol) lipid-to-protein ratio (LPR) with added laurdan (at a \(305:1\) lipid-to-laurdan ratio) in TBS pH 8.0. (b) The first derivative of data shown in (a) showing the transition temperature for each liposome suspension as the point of steepest (most negative) gradient. Whilst empty DMPC (grey) and BamA proteoliposomes (purple) have a transition temperature of \(24 \text{‰}\) , the presence of WT BAM (black), BAM-Fab1 (red), BAM-P5L (green), BAM-LL (blue), BAM-P5L + Fab1 (orange) and BAM-LL + Fab1 (yellow) </center>
+
+<--- Page Split --->
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+792 broaden the phase transition and lower the transition temperature. Figures labelled with 793 “BAM” refer to the full BAM complex (BamABCDE), whilst “BamA” is just BamA alone.
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+932 2782- 2794 (2018).933 57. Ricci, D. P., Hagan, C. L., Kahne, D. & Silhavy, T. J. Activation of the Escherichia coli \(\beta\) - barrel assembly machine (Bam) is required for essential components to interact properly with substrate. Proc. Natl. Acad. Sci. U.S.A. 109, 3487- 3491 (2012).936 58. Roman- Hernandez, G., Peterson, J. H. & Bernstein, H. D. Reconstitution of bacterial autotransporter assembly using purified components. Elife 3, e04234 (2014).937 59. Hartmann, J.- B., Zahn, M., Burmann, I. M., Bibow, S. & Hiller, S. Sequence- specific solution NMR assignments of the \(\beta\) - barrel insertase BamA to monitor its conformational ensemble at the atomic level. J. Am. Chem. Soc. 140, 11252- 11260 (2018).942 60. Calabrese, A. N. et al. Inter- domain dynamics in the chaperone SurA and multi- site binding to its outer membrane protein clients. Nat. Commun. 11, 1- 16 (2020).944 61. Simmons, L. C. et al. Expression of full- length immunoglobulins in Escherichia coli: Rapid and efficient production of aglycosylated antibodies. J. Immunol. Methods, 263, 133- 147 (2002).946 62. Lombana, T. N., Dillon, M., Bevers, J. & Spiess, C. Optimizing antibody expression by using the naturally occurring framework diversity in a live bacterial antibody display system. Sci. Rep. (2015).950 63. Zivanov, J. et al. New tools for automated high- resolution cryo- EM structure determination in RELION- 3. Elife 7, (2018).952 64. Zivanov, J., Nakane, T. & Scheres, S. H. W. Estimation of high- order aberrations and anisotropic magnification from cryo- EM data sets in RELION- 3.1. IUCrJ 7, 253- 267 (2020).955 65. Zheng, S. Q. et al. MotionCor2: Anisotropic correction of beam- induced motion for improved cryo- electron microscopy. Nat. Methods 14, 331- 332 (2017).956 66. Zhang, K. Gctf: Real- time CTF determination and correction. J. Struct. Biol. 193, 1- 12 (2016).957 67. Wagner, T. et al. SPHIRE- crYOLO is a fast and accurate fully automated particle picker for cryo- EM. Commun. Biol. 2, 1- 13 (2019).961 68. Punjani, A., Rubinstein, J. L., Fleet, D. J. & Brubaker, M. A. CryoSPARC: Algorithms for rapid unsupervised cryo- EM structure determination. Nat. Methods 14, 290- 296 (2017).964 69. Punjani, A., Zhang, H. & Fleet, D. J. Non- uniform refinement: Adaptive regularization improves single particle cryo- EM reconstruction. Nat. Methods 17, 1214- 1221 (2020).965 70. Henderson, R. et al. Outcome of the first electron microscopy validation task force meeting. in Structure 20, 205- 214 (2012).968 71. Pettersen, E. F. et al. UCSF Chimera?A visualization system for exploratory research and analysis. J. Comput. Chem. 25, 1605- 1612 (2004).970 72. Afonine, P. V. et al. Real- space refinement in PHENIX for cryo- EM and crystallography. Acta Crystallogr. Sect. D Struct. Biol. 74, 531- 544 (2018).972 73. Emsley, P. & Cowtan, K. Coot: Model- building tools for molecular graphics. Acta Crystallogr. Sect. D Biol. Crystallogr. 60, 2126- 2132 (2004).974 74. Chen, V. B. et al. MolProbity: All- atom structure validation for macromolecular crystallography. Acta Crystallogr. Sect. D Biol. Crystallogr. 66, 12- 21 (2010).976 75. Kim, K. H., Aulakh, S. & Paetzel, M. Crystal structure of \(\beta\) - barrel assembly machinery BamCD protein complex. J. Biol. Chem. 286, 39116- 39121 (2011).
+
+<--- Page Split --->
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+978 76. Tickle, I.J., Flensburg, C., Keller, P., Paciorek, W., Sharff, A. & Vonrhein, C., 979 Bricogne, G. STARANISO. (2018). 980 77. Evans, P. R. & Murshudov, G. N. How good are my data and what is the resolution? 981 Acta Crystallogr. D. Biol. Crystallogr. 69, 1204- 1214 (2013). 982 78. McCoy, A. J. et al. Phaser crystallographic software. J. Appl. Crystallogr. 40, 658- 674 983 (2007). 984 79. Covaceuszach, S. et al. Dissecting NGF interactions with TrkA and p75 receptors by 985 structural and functional studies of an anti- NGF neutralizing antibody. J. Mol. Biol. 986 381, 881- 896 (2008). 987 80. Adams, P. D. et al. PHENIX: A comprehensive Python- based system for 988 macromolecular structure solution. Acta Crystallogr. Sect. D Biol. Crystallogr. 66, 989 213- 221 (2010). 990
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+Disulphide- locked BamA variants and Fab1 binding impair BAM- mediated OMP folding in vitro. (a) BAM- P5L (G393C/G584C) is expected to lock BamA in the lateral- open conformation (PDB code 5LJ08), while (b) BAM- LL (E435C/S665C) is expected to lock BamA in the lateral- closed conformation (PDB code
+
+<--- Page Split --->
+
+5D006). BamA POTRAs 1- 4 and BamBCDE are rendered semi- transparent for emphasis on the BamA β- barrel and POTRA- 5. The position of the disulphide bond is shown as a yellow bar. Figure made in PyMOL v1.7.2.3. (c and d) Quantification of folded and unfolded bands from SDS- PAGE band- shift assays (Supplementary Figs. 3 and 4) plotted as fraction folded against time for tOmpA or OmpX, respectively. Data are fitted to a single exponential function. (e and f) The initial rates of folding (determined by applying a linear fit to the first 5% of folding data) normalised as a percentage of the initial rate obtained for WT BAM, are shown for (e) tOmpA and (f) OmpX folding (see also Supplementary Table 1). Folding assays were repeated to assess reproducibility, with errors for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE), whilst "BamA" is just BamA alone.  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+CryoEM resolves two conformations of BAM- LL in detergent. (a) 4.1 723 Å cryoEM map of the BAM- LL lateral- closed conformation at a contour of 10 σ, coloured by subunit. The lateral- gate is closed and POTRA- 5 does not block the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA- 5 of BamA. β1 and β16 contact to close the gate. (c) The same density viewed from the
+
+<--- Page Split --->
+
+periplasmic side, showing the open lumen of the BamA barrel in this conformation. (d) 4.8 Å cryoEM map of the BAM- LL lateral-open conformation at a contour of 10 σ, coloured by subunit. The lateral- gate is open and POTRA- 5 occludes the BamA barrel (schematic inset). (e) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on segmented density for the barrel and POTRA- 5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel to contact eL6. (f) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Fig. made in UCSF ChimeraX76. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>  
+
+Fab1- bound BAM is in a lateral- open conformation. (a) 5.1 Å cryoEM map of the BAM- Fab1 complex in a lateral- open conformation at a contour of 10 σ, coloured by subunit. The lateral- gate is fully- open and
+
+<--- Page Split --->
+
+POTRA- 5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA- 5 of BamA. \(\beta 1\) is in a conformation that makes limited contact with \(\beta 16\) . (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Panels made using UCSF ChimeraX76. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d) Close up of the BamA- Fab1 interface region highlighting the Fab1 CDRs (red) interacting with eL4 of BamA (dark blue). Other regions of BamA are rendered semi- transparent to highlight eL4. Heavy and light chains of Fab1 are coloured cyan and pink, respectively. (e) The VL and VH domains of Fab1 variable form a complementary binding surface for eL4 of BamA involving residues Y550, E554 and H555.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4 </center>  
+
+Additive effect of BAM inhibition by disulphide- locking and binding of Fab1. (a) 7.1 Å cryoEM map of the Fab1- bound LL- BAM in a lateral- open conformation at a contour of 9.5 σ, coloured by subunit. The lateral- gate is open and POTRA- 5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the β- barrel and POTRA- 5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel
+
+<--- Page Split --->
+
+to contact eL6. (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Structural panels made using UCSF ChimeraX76. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d and e) Quantification of SDS- PAGE band- shift assays shown in Supplementary Fig. 13 for (d) tOmpA and (e) OmpX folding catalysed by BAM- P5L (green), BAM- LL (blue) and WT BAM (black), each with and without Fab1 (solid and open circles, respectively). (f and g) The initial rates, calculated by applying a linear fit to the first \(5\%\) of fitted folding data, were normalised to that of WT BAM, and are shown for (f) tOmpA and (g) OmpX folding (see also Supplementary Table 1). Folding assays were conducted twice for reproducibility with data for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE).
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5 </center>  
+
+![PLACEHOLDER_42_1]
+
+
+<--- Page Split --->
+
+305:1 lipid- to- laurdan ratio) in TBS pH 8.0. (b) The first derivative of data shown in (a) showing the transition temperature for each liposome suspension as the point of steepest (most negative) gradient. Whilst empty DMPC (grey) and BamA proteoliposomes (purple) have a transition temperature of \(24^{\circ}C\) , the presence of WT BAM (black), BAM- Fab1 (red), BAM- P5L (green), BAM- LL (blue), BAM- P5L + Fab1 (orange) and BAM- LL + Fab1 (yellow) broaden the phase transition and lower the transition temperature. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE), whilst "BamA" is just BamA alone.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryInformationsubmitted.pdf ValidationReports.pdf
+
+<--- Page Split --->

preprint/preprint__07090632be97150b9482692b3758503018ba474d5a059546c8cd240472d00789/preprint__07090632be97150b9482692b3758503018ba474d5a059546c8cd240472d00789_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 106, 904, 177]]<|/det|>
+# The role of membrane destabilisation and protein dynamics in BAM catalysed OMP folding.  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 580, 848]]<|/det|>
+Paul White University of Leeds  Samuel Haysom University of Leeds https://orcid.org/0000- 0002- 8769- 090X  Matthew ladanza University of Leeds  Anna Higgins University of Leeds  Jonathan Machin University of Leeds  Jim Home University of Leeds https://orcid.org/0000- 0001- 5260- 2634  Bob Schiffrin University of Leeds  Charlotte Carpenter-Platt University of Leeds  James Whitehouse University of Leeds  Kelly Storek Genentech Inc  Steven Rutherford Genentech Inc https://orcid.org/0000- 0002- 4758- 4248  David Brockwell University of Leeds https://orcid.org/0000- 0002- 0802- 5937  Neil Ranson University of Leeds https://orcid.org/0000- 0002- 3640- 5275  Sheena Radford ( s.e.radford@leeds.ac.uk ) University of Leeds https://orcid.org/0000- 0002- 3079- 8039  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 882, 101, 899]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 918, 870, 939]]<|/det|>
+Keywords: outer membrane proteins (OMPs), \(\beta\) - barrel assembly machinery (BAM), OMP folding.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[44, 46, 327, 64]]<|/det|>
+**Posted Date:** February 2nd, 2021 
+
+<|ref|>text<|/ref|><|det|>[[44, 85, 465, 102]]<|/det|>
+**DOI:** https://doi.org/10.21203/rs.3.rs-155135/v1 
+
+<|ref|>text<|/ref|><|det|>[[44, 122, 909, 163]]<|/det|>
+**License:** © This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License 
+
+<|ref|>text<|/ref|><|det|>[[44, 201, 949, 241]]<|/det|>
+**Version of Record:** A version of this preprint was published at Nature Communications on July 7th, 2021.
+See the published version at https://doi.org/10.1038/s41467-021-24432-x.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[71, 80, 884, 540]]<|/det|>
+1 The role of membrane destabilisation and protein dynamics in BAM catalysed OMP folding 3 4 Paul White1\\*, Samuel F. Haysom1\\*, Matthew G. Iadanza1\\*, Anna J. Higgins1, Jonathan M. Machin1, Jim E. Horne1#, Bob Schiffrin1, Charlotte Carpenter-Platt1, James M. Whitehouse1, Kelly M. Storek2, Steven T. Rutherford2, David J. Brockwell1, Neil A. Ranson1\\*, Sheena E. Radford1\* 8 9 1 Astbury Centre for Structural Molecular Biology, School of Molecular and Cellular Biology, 10 Faculty of Biological Sciences, University of Leeds, Leeds, LS2 9JT, UK 11 2 Department of Infectious Diseases, Genentech Inc., South San Francisco, CA 94080 12 4 Contributed equally 13 \* Current affiliation Scientific Computing Department, Science and Technology Facilities 14 Council, Research Complex at Harwell, Didcot, OX11 0FA, UK 15 # Current affiliation: Department of Biochemistry, University of Oxford, Oxford, OX1 3QU, UK 16 17 \*Correspondence: n.a.ranson@leeds.ac.uk; s.e.radford@leeds.ac.uk 18
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[70, 83, 197, 100]]<|/det|>
+## 19 Abstract  
+
+<|ref|>text<|/ref|><|det|>[[115, 110, 882, 362]]<|/det|>
+The folding of \(\beta\) - barrel outer membrane proteins (OMPs) in Gram- negative bacteria is catalysed by the \(\beta\) - barrel assembly machinery (BAM). How lateral opening in the \(\beta\) - barrel of the major subunit BamA assists in OMP folding, and the contribution of membrane disruption to BAM catalysis remain unresolved. Here, we use an anti- BamA monoclonal antibody fragment (Fab1) and two disulphide- crosslinked BAM variants (lid- locked (LL), and POTRA- 5- locked (P5L)) to dissect these roles. Despite being lethal in vivo, we show that all complexes catalyse folding in vitro, albeit less efficiently than wild- type BAM. CryoEM revealed that while Fab1 and BAM- P5L trap an open- barrel state, BAM- LL contains a mixture of closed and contorted, partially- open structures. Finally, all three complexes globally destabilise the lipid bilayer, while BamA does not, revealing that the BAM lipoproteins are required for this function. Together the results provide new insights into the role of BAM structure and lipid dynamics in OMP folding.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[66, 108, 883, 320]]<|/det|>
+Outer membrane proteins (OMPs) in Gram negative bacteria are functionally diverse, but share a common \(\beta\) - barrel fold involving between 8 and 36 \(\beta\) - strands<sup>1</sup>. The folding and membrane insertion of OMPs is catalysed by the essential \(\beta\) - barrel assembly machinery (BAM)<sup>2- 4</sup> which in E. coli comprises five proteins (BamABCDE). The major conserved subunit, BamA, is a 16- stranded Omp85 family member that contains five N- terminal polypeptide transport associated (POTRA) domains that extend into the periplasm to scaffold four lipoprotein BamB- E<sup>5- 8</sup>, all of which are required for maximally- efficient OMP folding<sup>9,10</sup>. BAM is essential for bacterial survival, highly conserved, and surface accessible via the extracellular loops of BamA, making the complex an attractive target for small molecule<sup>11- 13</sup>, peptide<sup>14,15</sup> and antibody- based antibiotics<sup>16,17</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[66, 328, 883, 728]]<|/det|>
+BAM exists in an ensemble of conformations, with one of the most notable differences between published structures occurring around the seam or 'lateral gate' involving \(\beta\) - strands 1 ( \(\beta 1\) ) and 16 ( \(\beta 16\) ) in the BamA barrel<sup>6- 18,20</sup>. In the 'lateral- open' conformation, as captured by cryoEM of the intact complex<sup>8</sup> and X- ray crystallography of the BamACDE subcomplex<sup>5,6</sup>, \(\beta 1\) and \(\beta 16\) are separated. In contrast, crystal structures of the intact BAM complex are in a 'lateral- closed' conformation in both in the absence<sup>6,7</sup> or presence of substrates<sup>21,22</sup>, wherein \(\beta 1\) and \(\beta 16\) are hydrogen bonded, albeit with fewer hydrogen bonds than exist between the other strands in the barrel<sup>1</sup>. The POTRA domains are also dynamically organised, with motions of POTRA- 5 being tightly correlated with gate conformation, with POTRA- 5 plugging entrance to the BamA \(\beta\) - barrel lumen only in the lateral- open state<sup>18</sup>. These conformational changes are essential for cell viability as disulphide bonds that purportedly lock BamA in either conformation have a lethal phenotype that is rescued by reducing agent<sup>6,19</sup>. Such variants include those that lock the lateral gate closed (e.g. G433C/N805C linking \(\beta 1\) to \(\beta 16^{8,19}\) , or E435C/S665C locking extracellular loop 1 (eL1) to eL6<sup>6,19</sup>), or those that lock the BamA lateral gate in an open conformation by introducing a disulphide bond between POTRA- 5 and \(\beta\) - turn between \(\beta 8\) and \(\beta 9\) at the base of the barrel (e.g. G393C/G584C<sup>6</sup>). Disulphide bonds which restrict flexibility between POTRA domains 2 and 3 also impair growth<sup>23</sup>; how, or if, these motions correlate with structural changes at the BamA \(\beta\) - barrel is unclear.  
+
+<|ref|>text<|/ref|><|det|>[[66, 736, 883, 903]]<|/det|>
+Models of BAM- catalysed OMP insertion and folding broadly invoke two distinct roles for BAM (reviewed in<sup>24</sup>). Firstly conformational changes in BAM, and protein- protein interactions between BAM and substrate OMPs are thought to be involved in catalysing folding<sup>25- 29</sup>. These models all involve a folding intermediate in which the C- terminal \(\beta\) - strand of the substrate is associated with BamA- \(\beta 1\) , as supported by crosslinking<sup>26,27</sup>, a recent cryoEM structure of a hybrid barrel formed between BAM and tBamA (the transmembrane domain of a BamA substrate)<sup>29</sup>, and crystal structures of BAM covalently tethered to the C- terminal \(\beta\) - strands of OMP substrates OmpA and OmpLA<sup>22</sup>. Variations of these models include the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 81, 881, 356]]<|/det|>
+'barrel elongation'<sup>25</sup> and 'swing'<sup>27</sup> models which suggest that folding begins in the periplasm, and also 'budding' models<sup>1,3,25</sup> wherein OMPs are thought to enter the lumen of the BamA barrel and fold via sequential addition of \(\beta\) - hairpin units<sup>26</sup>. This is akin to the role proposed for the mitochondrial homologue Sam50 of the sorting and assembly machinery (SAM) complex<sup>26</sup>. An alternative model proposes that BAM may disorder its lipid environment, lowering the kinetic barrier to OMP folding, potentially allowing OMPs to fold and insert into the outer membrane without direct interaction with the \(\beta 1 - \beta 16\) seam. This 'BamA- assisted' model<sup>18,30- 32</sup> is supported by molecular dynamics (MD) simulations which show lipid disordering and bilayer thinning by BamA<sup>20,25,30- 35</sup>, and by BAM- mediated distortion of a nanodisc<sup>18</sup>. Both protein dynamics and lipid disordering may act synergistically to maximise the efficiency of OMP folding, and different OMPs may depend on each effect to different degrees. However, little mechanistic insight is available, beyond that which has been inferred from the observation of a lethal phenotype.  
+
+<|ref|>text<|/ref|><|det|>[[112, 363, 881, 718]]<|/det|>
+Here, we investigate the roles of BAM structure/dynamics and membrane stability in OMP folding by exploiting two disulphide- locked variants termed lid- lock (LL) and POTRA- 5- lock (P5L) which are lethal in vivo<sup>6,19</sup>, and purportedly lock BamA's barrel closed and open, respectively. We also investigate a bactericidal Fab fragment (Fab1), that binds to eL4 of BamA<sup>16</sup>. We report cryoEM structures for the two disulphide locked BAM variants and the BAM- Fab1 complex, revealing that BAM- P5L and Fab1 stabilise a lateral- open conformation, whilst BAM- LL adopts both a lateral- closed state and a distorted, partially- open conformation. Despite being lethal in vivo, the two disulphide variants and the Fab1- BAM complex are all able to catalyse the folding of the 8- stranded OMPs OmpX and tOmpA (the transmembrane region of OmpA) in vitro, though less efficiently than wild- type BAM, and by combining Fab1 and disulphide- locking, BAM is further inactivated. We also demonstrate that all BAM variants studied lower the phase transition temperature of their lipid environment, but that BamA alone does not, providing direct experimental evidence that lipid disordering by BAM requires the presence of its lipoproteins. The results provide new insights into the structural features of BAM's catalytic mechanism and suggest that even subtle disruption of BAM activity may provide an effective route to the development of novel antibiotics.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 84, 189, 100]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 111, 774, 130]]<|/det|>
+## Disulphide-locked and Fab1-bound BAM can catalyse OMP folding in vitro  
+
+<|ref|>text<|/ref|><|det|>[[110, 135, 881, 916]]<|/det|>
+To assess the relationship between bacterial lethality and the catalytic ability of BAM we determined the in vitro folding activity of two paired cysteine mutations in BamA that are bactericidal<sup>6,19</sup>. In the BAM- P5L variant (BamA G393C/G584C)<sup>6</sup>, tethering of POTRA- 5 to the base of the BamA barrel is expected to stabilise a lateral- open conformation (Fig. 1a). By contrast, the BAM- LL variant, (BamA E435C/S665C)<sup>19</sup> is expected to lock eL1 to eL6, and stabilise a lateral- closed conformation (Fig. 1b). The BAM- LL and BAM- P5L variants were made in a BAM construct in which the two Cys of BamA that naturally form a disulphide bond (C690 and C700), are replaced with Ser (Cys- free BAM). This variant is able to complement WT BamA in E. coli<sup>19,36</sup> and has little effect on BAM- catalysed OMP folding rates in vitro<sup>9</sup>. We also investigated how a bactericidal anti- BamA binding antibody Fab fragment, known as Fab<sup>16,37</sup>, affects OMP folding in vitro. BAM- P5L, BAM- LL and the BAM- Fab1 complex were each reconstituted into liposomes comprised of E. coli polar lipids, and their ability to fold the 8- stranded OMPs, OmpX and tOmpA, in the presence of SurA was determined by SDS- PAGE band- shift assays<sup>38</sup>. In each case, BamA was folded (as judged by a band- shift relative to the boiled (denatured) BamA band) and all four BAM lipoproteins were present (Supplementary Fig. 1). Interestingly, Fab1 formed a stable, SDS- resistant complex with BamA (Supplementary Fig. 1b), consistent with its IC<sub>50</sub> of 0.095 nM determined for \(\Delta waaD E. coli^{16}\) . Disulphide bond formation in BAM- P5L and BAM- LL was confirmed by the lack of fluorescein- C5- maleimide labelling, and electrophoretic band- shifts in oxidising/reducing conditions (Supplementary Fig. 2). Both tOmpA or OmpX do not fold spontaneously into the liposomes formed from E. coli polar lipids, but fold rapidly and efficiently into liposomes formed from the same lipids containing WT BAM (Fig. 1c and d). Remarkably, considering their in vivo lethality<sup>6,16,19</sup>, the efficiency of folding and membrane insertion of tOmpA and OmpX is reduced, but not abolished, by BAM- P5L, BAM- LL and BAM- Fab1, with folding yields of \(\sim 50\%\) for tOmpA and \(\sim 15 - 30\%\) for OmpX after 3 hours at 25 °C (note that tOmpA folds more rapidly than OmpX with WT BAM) (Fig. 1c and d, and Supplementary Fig. 3 and 4). Relative to WT BAM, the initial rates of folding for BAM- Fab1, BAM- LL and BAM- P5L ranged from 16- 20% for tOmpA, and 8- 29% for OmpX (Fig. 1e and f, respectively, and Supplementary Table 1). When the disulphide bond in BAM- P5L and BAM- LL is reduced with DTT, folding activity surpassed that of WT BAM. This effect was not observed for WT BAM, or Cys- free BAM (Supplementary Fig. 5). Folding into proteoliposomes containing BamA alone was much slower than observed with BAM- P5L, BAM- LL, or BAM- Fab1, with initial folding rates for both substrates reaching \(\sim 3\%\) of that WT BAM, highlighting the importance of the accessory lipoproteins for efficient catalysis of folding of these OMPs<sup>39</sup>. Importantly, the inhibited BAM variants were able to fold their OMP substrates to 80- 100% completion after 24 hours, whilst incubation with BamA alone resulted in folding yields of only 50% and 16% for tOmpA and OmpX, respectively, after 24
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 81, 880, 165]]<|/det|>
+hours (note that both substrates were unable to fold into empty liposomes even on these extended timescales) (Supplementary Table 2). Collectively, these results show that although both Fab1 binding and disulphide- locking of BamA are lethal in vivo<sup>6,16,19</sup>, the BAM- catalysed folding of OmpX and tOmpA is only partially inhibited in vitro.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 203, 512, 220]]<|/det|>
+## Lid-locked BAM exists in two conformations  
+
+<|ref|>text<|/ref|><|det|>[[113, 225, 881, 844]]<|/det|>
+To understand the molecular basis of inhibition, we determined the structure of BAM- LL in DDM detergent micelles using cryoEM. We predicted, based on the lethality of this mutation and the crystal/cryoEM structures of BAM in its different conformational states<sup>5- 8</sup>, that the formation of a disulphide bond between C435 and C665 would trap BAM in a lateral- closed state (Fig. 1b). However, 3D classification of cryoEM data of this construct revealed two distinct, approximately equally populated, structures (Fig. 2 and Supplementary Fig. 6). The first structure (at 4.1 Å resolution) is similar to the crystal structure of intact BAM in the lateral- closed conformation, with pairing of β1 and β16 (Fig. 2a,b) and displacement of POTRA- 5 from beneath the barrel (Fig. 2c). The second structure (at 4.8 Å) has β1 and β16 separated (Fig. 2d, e) and POTRA- 5 occludes the periplasmic face of the BamA barrel (Fig. 2f), and is thus consistent with a lateral- open conformation. In all previous lateral- open structures<sup>5,6,8</sup>, extracellular loop 1 (eL1) bends away from the BamA β- barrel, separating the lid- lock cysteine positions (C435 and C665) by \(\sim 20\) Å. Given the unequivocal in vitro biochemical evidence for formation of the lid- lock disulphide (Supplementary Fig. 2), eL1 must be distorted to allow disulphide bond formation with eL6. However, poor resolution in this region of the map, itself indicative of mobility, prevented modelling of this new eL1 conformation. We therefore used molecular dynamics- based flexible fitting (MDFF)<sup>40</sup> to morph the lateral- closed BAM- LL atomic model into the density observed in the second conformation, whilst maintaining the disulphide link. This generated a chemically plausible loop conformation (Fig. 2e), but this is not constrained by the EM density. The difference between eL1 conformations in the two BAM- LL structures is striking, and suggests that this region must be highly malleable to allow disulphide bond formation within the BamA β- barrel. Interestingly, the 'contorted open' BAM- LL structure closely resembles a recent structure of WT BAM in saponin nanodiscs<sup>22</sup> in which eL1 adopts this inward conformation in the absence of disulphide tethering. In accord with this idea, eL1 can adopt a wide range of conformations in lateral- open BAM structures (Supplementary Fig. 7). Overall, these data suggest that the lid- lock disulphide biases the conformational ensemble toward a lateral- closed conformation, but cannot completely pull the conformational equilibrium over to that state, consistent with BAM adopting only the lateral- open state in DDM detergent<sup>8</sup>.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 82, 630, 100]]<|/det|>
+## Fab1-bound BAM and BAM-P5L adopt a lateral-open state  
+
+<|ref|>text<|/ref|><|det|>[[115, 110, 882, 675]]<|/det|>
+Inspired by the findings that MAB1 (and Fab1) binding is lethal in vivo \(^{16}\) and also retards OMP folding rates in vitro (Figure 1), we next investigated the effect of Fab1 binding on the conformation of BAM using cryoEM. The structure of BAM in complex with a bactericidal molecule (Fab1) was solved in DDM micelles to 5.1 Å resolution. The cryoEM map contained unambiguous density for Fab1 bound to the extracellular region of BamA (Fig. 3a, Supplementary Fig. 8), and revealed that BAM is in a lateral-open conformation when bound to Fab1, as defined by the position of POTRA- 5, the shape of the BamA \(\beta\) - barrel, and the orientation of \(\beta 1\) and \(\beta 16\) (Fig. 3b and c). The structure of Fab1 alone was also solved by X- ray diffraction to \(\sim 3.0\) Å resolution and this structure was flexibly fitted into the EM density map (Supplementary Table 3). In agreement with mutagenesis data \(^{16}\) , Fab1 binds specifically to eL4 (Fig. 3d) (contributing 98% of the total interface area of 934 Å \(^{2}\) as determined by PISA interface analysis \(^{41}\) ), and the complementarity determining regions (CDRs) bind to residues Y550, E554 and H555 in BamA (Fig. 3e). Interestingly, a BamA- specific nanobody (nanoE6) has also been found to bind eL4 (involving E554) and also influences dynamics in the lateral gate \(^{17}\) . However, since binding of Fab1 to BAM (and nanoE6 to BamA \(^{17}\) ) does not drastically alter the conformation of eL4 from that seen in lateral- closed structures, how Fab1 binding stabilises a lateral- open conformation remains obscure. Finally, we determined the cryoEM structure of BAM- P5L at lower resolution (10.3 Å; Supplementary Figs. 9 and 10), and although the conformation of the lateral gate is not clearly observed at this resolution (Supplementary Fig. 10a), POTRA- 5 unambiguously occludes the BamA barrel suggesting that BAM- P5L is in a "lateral- open"- like state (Supplementary Fig. 10b). Cross- correlation of the BAM- P5L, WT BAM \(^{8}\) (open) and BAM- LL (closed) density maps, as well as comparison of the shapes of the BamA barrel in the different structures add further evidence that BAM- P5L is indeed in a lateral- open state, as expected from the design of the Cys mutants, (Supplementary Figure 10d,e).  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 712, 718, 730]]<|/det|>
+## Fab1 binding to disulphide-locked BAM further inhibits OMP folding  
+
+<|ref|>text<|/ref|><|det|>[[115, 740, 882, 905]]<|/det|>
+As BAM can populate a lateral- open conformation in the presence or absence of Fab1, we determined the cryoEM structure of BAM- LL bound to Fab1 to ascertain whether Fab1 binding could further stabilise a lateral- open conformation, potentially further blocking the conformational changes required for BAM's catalytic action. In contrast with BAM- LL, the cryoEM structure of the BAM- LL: Fab1 complex (at 7.1 Å resolution) contains a single structure which is in a lateral- open conformation (Fig. 4a, Supplementary Fig. 11), consistent with Fab1 biasing BamA's conformational equilibrium towards a lateral- open state (Fig. 4b) in which POTRA- 5 occludes the barrel (Fig. 4c). Further evidence for the lateral
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 416]]<|/det|>
+closed state being incompatible with Fab1 binding was observed by SDS- PAGE, where the SDS- resistant BamA- Fab1 band observed for WT BAM- Fab1 was weaker for BAM- LL- Fab1, with a compensating increase in the band corresponding to non- complexed BamA, suggestive of the BAM- LL- Fab1 complex being less stable under SDS- PAGE conditions (Supplementary Fig. 12a). Interestingly, since MAB1 binds to BAM in the E. coli OM<sup>16</sup>, this suggests that a lateral- open conformation is formed in situ in the OM, consistent with previous data<sup>36</sup>. Conversely, the Fab1- bound BAM- P5L complex produces an SDS- resistant band, consistent with stable binding to its lateral- open state (Supplementary Fig. 12b). tOmpA and OmpX folding assays revealed that the addition of Fab1 to BAM- P5L or BAM- LL each resulted in increased inhibition, with folding yields of \(\sim 10 - 20\%\) for tOmpA (Fig. 4d, Supplementary Fig. 13a) and \(5 - 10\%\) for OmpX (Fig. 4e, Supplementary Fig. 13b) after 3 hours at \(25^{\circ}C\) , and initial folding rates of only \(1 - 3\%\) and \(1 - 6\%\) of that of WT BAM for tOmpA and OmpX, respectively (Fig. 4f and g). This additive inhibition could arise from a synergistic reduction in conformational dynamics within the BAM complex, or from Fab1 binding and disulphide locking inhibiting distinct mechanisms of BAM- mediated folding catalysis.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 454, 647, 473]]<|/det|>
+## BAM lipoproteins mediate destabilisation of the lipid bilayer  
+
+<|ref|>text<|/ref|><|det|>[[115, 482, 881, 904]]<|/det|>
+In vitro studies have shown that spontaneous OMP folding rates and efficiencies are increased in membranes with decreased thickness, increased fluidity, or containing bilayer defects<sup>42- 45</sup>. As well as directly interacting with its substrate OMPs<sup>27,29</sup>, BAM is also thought to reduce the stability of the lipid bilayer to facilitate folding, due to asymmetry in the hydrophobic thickness of the BamA \(\beta\) - barrel (which is narrowest in the vicinity of the lateral gate)<sup>18,32</sup>. Evidence for membrane destabilisation has been provided by molecular dynamics (MD) simulations of BamA in lipid bilayers<sup>20,24,25,30- 35</sup> and by cryoEM and MD simulations of BAM in nanodiscs formed from E. coli polar lipids<sup>18</sup>. To determine how the different conformational states of BAM affect bilayer stability more directly, we measured the effect of the different BAM complexes studied above on the lipid phase transition of liposomes formed from 1,2- dimyristoyl- sn- glycero- 3- phosphocholine (DMPC, \(d / C_{14:0}PC\) ) using the fluorescent lipid probe laurdan (Supplementary Fig. 14), the fluorescence emission spectrum of which depends on lipid phase<sup>46</sup>. DMPC was chosen for these experiments as it undergoes a gel- liquid phase transition with a midpoint of \(\sim 24^{\circ}C\) , compared with \(\sim 3^{\circ}C\) for E. coli polar lipid<sup>47</sup> and BAM has been shown to be active in DMPC liposomes<sup>48</sup>. As expected, a phase transition for empty DMPC liposomes was observed at \(24^{\circ}C\) (Fig. 5a, see also Supplementary Fig. 15). Interestingly, the transition phase temperature (T<sub>m</sub>) was not affected by the presence of BamA alone (Fig. 5a), demonstrating that the asymmetric BamA \(\beta\) - barrel does not itself cause this global perturbation of the lipid bilayer, at least as judged by this assay. By contrast, in all proteoliposomes containing the full BAM complex,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 185]]<|/det|>
+regardless of whether that complex is inhibited, the gel- liquid phase transition occurred at a lower temperature ( \(\sim 22 - 23^{\circ}C\) ) and over a broader temperature range (Fig. 5b). These results thus demonstrate that BAM disrupts bilayer stability independently of the structure of the \(\beta 1 - \beta 16\) seam and shows that the BamB- E lipoproteins are essential for this perturbation of the membrane.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 232, 220, 248]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[111, 252, 881, 912]]<|/det|>
+Protein- protein interactions between BAM and substrate OMPs, and lipid disordering have both been implicated as important features in BAM function<sup>3,24</sup>, but how these different facets of BAM are balanced to enable OMP folding remained unclear. Here, we have used structural, biochemical and kinetic refolding analyses to dissect these two roles, at least for the 8- stranded OMPs, tOmpA and OmpX. BAM is well- known to be conformationally dynamic, with cryo- EM and X- ray structures capturing the complex in lateral- open<sup>5,6,8</sup> and lateral- closed<sup>6,7,21,22</sup> conformations, and a recent cryoEM, MD and single molecule FRET study demonstrating dynamics of the complex in nanodiscs<sup>18</sup>. Furthermore, recent X- ray structures have demonstrated that the C- terminal strand of the OMP substrates tOMPa and OMPLA forms an antiparallel \(\beta\) - strand pairing with lateral- closed BamA \(\beta 1\) , possibly capturing an early stage intermediate in OMP assembly<sup>22</sup>. A recent cryoEM structure of a BAM:tBamA complex revealed that the tBamA substrate forms a \(\beta\) - strand pairing with lateral- open BamA \(\beta 1\) of BAM, whilst making a side- chain mediated interface involving BamA \(\beta 16\) , to form a hybrid barrel<sup>29</sup> that presumably mimics a late- stage assembly intermediate. This observation is consistent with crosslinking studies of EspP<sup>27</sup> and LptD<sup>28</sup> to BAM, and Por1 to SAM<sup>26</sup>. Given these insights, it is perhaps unsurprising that trapping BamA in the BAM complex in an open or closed conformation by disulphide bonding has a profound effect on bacterial viability, akin to the observations found using nanobodies<sup>17</sup>, small molecules and peptidomimetic antibiotics, which also have a lethal outcome<sup>11,12</sup>. Remarkably, we show here that this in vivo lethality masks a more subtle effect on BAM activity that is revealed by in vitro activity assays. Both disulphide- locking and Fab1 binding inhibit, but do not abolish, BAM- catalysed folding of tOmpA and OmpX in vitro (Fig. 1, and Supplementary Tables 1 and 2). The finding that these inhibitory effects are distinct and additive (Fig. 4) highlights the importance of different, presumably parallel, facets of BAM action for OMP folding catalysis. Our cryoEM structures confirm that in solution, both BAM- P5L and Fab1 lock BamA in a lateral- open conformation (Figs. 3, 4, and Supplementary Fig. 10). Presumably this prevents substrate access and pairing to BamA \(\beta 1\) which recent structures suggest initially occurs to a lateral- closed conformation<sup>22</sup>. It may also inhibit substrate binding by occlusion of entry to the BamA barrel by POTRA- 5. Consistent with this, it has recently been shown that the BAM substrate, RcsF, binds in the lumen of the BamA \(\beta\) - barrel only in the lateral- closed conformation<sup>21</sup>, and that the essential mediator of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 81, 881, 416]]<|/det|>
+LPS assembly, LptD, contacts the internal lumen of BamA during folding<sup>28</sup>. An inability to assemble larger and essential BAM-dependent substrates, such as LptD, could explain why disulphide locking/Fab1 binding are lethal in vivo<sup>6,16,19</sup>, despite smaller OMPs potentially remaining able to fold and insert into the OM, albeit more slowly than with WT BAM. For the latter OMPs, lethality may result from a reduced flux through the OMP biogenesis pathway when BAM is impaired, inducing cell envelope stress caused by accumulation of unfolded OMPs in the periplasmid. Indeed, increased envelope stress was observed upon addition of MAB1 to \(\Delta \text{waaD} E\) . coli<sup>16</sup>. Moreover, a small molecule inhibitor of the regulator of sigma E protease (RseP)<sup>49</sup>, that is a key component of this pathway, has a lethal outcome by blocking the \(\sigma^{\mathrm{F}}\) stress response that normally responds to envelope stress by increasing BAM expression<sup>50</sup>, decreasing OMP expression<sup>51</sup>, and increasing protein degradation<sup>52</sup>. The extent to which the folding of larger OMPs is inhibited by the BAM variants examined here remains unclear, but we speculate that for these proteins there could be a greater dependence on a direct interaction with BAM for successful insertion and folding, with BAM being unable to destabilise membranes sufficiently to allow larger OMPs to fold solely via this route.  
+
+<|ref|>text<|/ref|><|det|>[[115, 424, 881, 677]]<|/det|>
+Despite the apparent incompatibility of BAM- LL's disulphide bond and a lateral- open conformation<sup>6,8</sup>, both open- like and closed structures are present in approximately equal populations in solution. The BAM- LL structures presented here thus provide direct evidence that at least \(\beta 1\) and \(\beta 2\) of BamA are malleable in the lateral- open state, being able to bend inwards towards the barrel lumen (Supplementary Fig. 7). Such plasticity appears to be functionally relevant, especially considering the more severe outward motion observed when BAM is engaged with tBamA as a substrate<sup>29</sup> (Supplementary Fig. 7). Such an extended conformation would presumably be impossible in BAM- LL, perhaps explaining the partial inhibitory effects observed here for OmpX and tOmpA. Superposition of all the lateral- open BAM structures reported to date thus support a model in which the N- terminal half of the BamA barrel is conformationally dynamic, whilst the C- terminal half provides a stable scaffold that supports these functionally important conformational changes.  
+
+<|ref|>text<|/ref|><|det|>[[115, 685, 881, 913]]<|/det|>
+Lipid destabilisation by BAM has been proposed previously as a potentially important facet of the catalysis of OMP folding and insertion into the OM<sup>3,25,53</sup>. This has been supported by MD simulations that reveal destabilisation of the membrane surrounding BamA<sup>20,24,25,30- 35</sup>, and a recent cryoEM structure of BAM in a nanodiscs containing \(E\) . coli polar lipids that shows distortion of the bilayer adjacent to the lateral gate<sup>18</sup>. Whilst these effects are localised to the BamA barrel, the laurdan fluorescence data provide direct biochemical evidence that BAM causes global destabilisation of a bilayer, as revealed by a reduction in the lipid phase transition temperature of DMPC liposomes (Fig. 5). They also reveal that this is mediated by lipoproteins BamB- E, since BamA alone had no discernible effect. This is consistent with cryoEM structures which have identified interactions between BamB, BamD and BamE and detergent micelles<sup>8</sup> as well as with lipid in nanodiscs<sup>18</sup>, whilst BamC is
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 185]]<|/det|>
+thought to span the membrane necessary for surface exposure of the two C- terminal helix- grip domains54. In addition to the roles of BamB- E in substrate recognition15,55, in mediating BAM oligomerisation into 'precincts'56, and coordinating conformational changes in BamA36,57, the results presented here highlight the importance of these lipoproteins in mediating changes in membrane stability.  
+
+<|ref|>text<|/ref|><|det|>[[115, 194, 882, 509]]<|/det|>
+In summary, the results presented allow different facets of BAM- mediated catalysis of OMP folding and membrane insertion to be discerned. By structural analysis of Fab1- bound and two different disulphide locked BAM complexes we reveal a remarkable structural malleability of the BamA barrel, and show that interconversion between these different structures is not essential for folding and membrane insertion of the 8- stranded tOmpA and OmpX substrates in vitro. In addition, we provide direct biochemical evidence that BAM causes global destabilisation of a lipid bilayer and reveal that this is not endowed by asymmetry in the depth of the BamA barrel, but instead requires the presence of BamB- E, demonstrating a new role for its lipoproteins. Finally, by demonstrating a significant, but reduced folding capacity of the Fab1- bound and disulphide- locked BAM variants in vitro, we provide evidence in support of models that suggest that bacterial viability depends on a delicate balance between the rates of OMP synthesis and their chaperone- dependent delivery to BAM, with the catalytic power of BAM to insert OMPs into the OM. Perturbing this balance thus offers exciting opportunities to create new antibacterial agents by targeting the different protein complexes required for OMP biogenesis.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 84, 198, 100]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 111, 770, 130]]<|/det|>
+## Expression and purification of WT and disulphide-locked BAM complexes  
+
+<|ref|>text<|/ref|><|det|>[[118, 138, 881, 263]]<|/det|>
+BAM- LL (BamA(E435C/S665C/C690S/C700S)BCDE- His) and BAM- P5L (BamA(G393C/G584C/C690S/C700S)BCDE- His) in a pTrc99a vector were generated using Q5 site- directed mutagenesis (New England BioLabs) using plasmid pJH114 (kindly provided by Harris Bernstein58) as a template. WT BAM, BAM- LL and BAM- P5L were expressed in E. coli BL21(DE3) cells and were purified from the membrane fraction using a combination of Ni- affinity and size exclusion chromatography, as described previously8.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 300, 616, 319]]<|/det|>
+## Expression and purification of BamA, OmpX and tOmpA  
+
+<|ref|>text<|/ref|><|det|>[[116, 327, 882, 536]]<|/det|>
+BamA, OmpX and tOmpA were expressed as inclusion bodies in E. coli BL21(DE3) cells, using a procedure modified from McMorran et al.50. Briefly, inclusion bodies were solubilised in \(25~\mathrm{mM}\) Tris- HCl pH 8.0, \(6M\) guanidine- HCl and were centrifuged (20,000 g, \(20\mathrm{min}\) , \(4^{\circ}\mathrm{C}\) ) to remove remaining insoluble material. The solubilised inclusion bodies were purified by SEC using a Superdex 75 HiLoad 26/60 column (GE Healthcare) for tOmpA and OmpX, and Sephacryl 200 26/60 column for BamA, equilibrated in \(25~\mathrm{mM}\) Tris- HCl pH 8.0, \(6M\) guanidine- HCl. For folding experiments, OmpX and tOmpA were buffer exchanged into Tris- buffered saline (TBS, \(20~\mathrm{mM}\) Tris- HCl, \(150~\mathrm{mM}\) NaCl) pH 8.0, \(8M\) urea using ZebaTM Spin Desalting Columns, \(7k\) MWCO, \(0.5~\mathrm{mL}\) (Thermo Scientific). BamA was refolded in LDAO detergent prior to reconstitution into proteoliposomes, as described previously59.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 575, 288, 592]]<|/det|>
+## Refolding of BamA  
+
+<|ref|>text<|/ref|><|det|>[[116, 601, 882, 747]]<|/det|>
+BamA was refolded as described by Hartmann et al.59. Briefly, BamA added dropwise into ice- cold \(50~\mathrm{mM}\) Tris- HCl pH 8.0, \(300~\mathrm{mM}\) NaCl, \(500~\mathrm{mM}\) arginine, \(0.5\%\) (w/v) LDAO, \(10~\mathrm{mM}\) DTT whilst rapidly stirring. Following 24 hours incubation, BamA was dialysed against 50 mM Tris- HCl pH 8.0, \(0.1\%\) (w/v) LDAO overnight before loading on a \(5~\mathrm{mL}\) HiTrap Q (GE Healthcare) anion exchange column and eluting in a NaCl gradient. Folded BamA was separated from unfolded and degraded BamA, as judged by SDS- PAGE, and used for reconstitution into liposomes containing E. coli polar lipid or DMPC, as required.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 785, 437, 803]]<|/det|>
+## Expression and purification of SurA  
+
+<|ref|>text<|/ref|><|det|>[[116, 812, 882, 893]]<|/det|>
+SurA with an N- terminal 6x His- tag and a TEV cleavage site was expressed and purified using a modified protocol described previously60. Briefly, SurA was expressed in E. coli BL21(DE3) cells and was purified on a \(5~\mathrm{mL}\) HisTrap FF column (GE Healthcare). SurA was denatured on- column in \(25~\mathrm{mM}\) Tris- HCl pH 7.2, \(6M\) guanidine- HCl, washed in the same
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 227]]<|/det|>
+buffer and then refolded on- column in \(25~\mathrm{mM}\) Tris- HCl pH 7.2, \(150~\mathrm{mM}\) NaCl, \(20~\mathrm{mM}\) imidazole before elution in \(25~\mathrm{mM}\) Tris- HCl pH 7.2, \(150~\mathrm{mM}\) NaCl, \(500~\mathrm{mM}\) imidazole. The His- tag was cleaved by addition of His- tagged TEV protease and \(14.3~\mathrm{mM}\) 2- mercaptoethanol, produced as previously described<sup>31</sup>, and the cleaved His- tag and TEV protease were removed on a \(5~\mathrm{mL}\) HisTrap FF column. Purified SurA was dialysed against 5 L TBS pH 8.0, concentrated to \(\sim 200~\mu \mathrm{M}\) using Vivaspin 20 MWCO \(10~\mathrm{kDa}\) concentrators (Sartorius, UK), aliquoted, snap- frozen in liquid nitrogen, and stored at \(- 80~^\circ \mathrm{C}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 266, 446, 284]]<|/det|>
+## Monoclonal antibody Fab production  
+
+<|ref|>text<|/ref|><|det|>[[115, 293, 881, 542]]<|/det|>
+Fabs were cloned and expressed in \(E\) . coli as previously described<sup>61,62</sup>. Cell paste containing the expressed Fab was resuspended in PBS buffer containing \(25~\mathrm{mM}\) EDTA and \(1~\mathrm{mM}\) PMSF. The mixture was homogenised and then passed twice through a microfluidiser. The suspension was then centrifuged at \(21,500g\) for \(60~\mathrm{min}\) . The supernatant was loaded onto a Protein G column equilibrated with PBS at \(5~\mathrm{mL / min}\) . The column was washed with PBS to baseline and proteins were eluted with \(0.6\%\) (v/v) acetic acid. Fractions containing Fabs, assayed by SDS- PAGE, were pooled and loaded onto a \(50~\mathrm{mL}\) SP Sepharose column equilibrated in \(20~\mathrm{mM}\) MES, pH 5.5. The column was washed with \(20~\mathrm{mM}\) MES, pH 5.5 for 2 column volumes and the protein was then eluted with a linear gradient to \(0.5\mathrm{M}\) NaCl in the same buffer. For final purification, Fab- containing fractions from the ion exchange column were concentrated and run on a Superdex 75 size exclusion column (GE Healthcare) in PBS buffer.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 580, 880, 619]]<|/det|>
+## Reconstitution of BAM complex variants and BamA into \(E\) . coli polar lipid proteoliposomes  
+
+<|ref|>text<|/ref|><|det|>[[115, 628, 881, 901]]<|/det|>
+\(E\) . coli polar lipid extract, purchased as powder from Avanti Polar Lipids (Alabaster, AL), was dissolved in \(80:20\) (v/v) chloroform/methanol at \(20~\mathrm{mg / mL}\) . Appropriate volumes were dried to thin films in clean Pyrex tubes at \(42~^\circ \mathrm{C}\) under \(\mathrm{N}_2\) gas, and were further dried by vacuum desiccation for at least 3 hours. WT BAM, BAM- LL and BAM- P5L in TBS pH 8.0, \(0.05\%\) (w/v) DDM were mixed with \(E\) . coli polar lipid extract films solubilized in TBS pH 8.0, \(0.05\%\) (w/v) DDM in a 1:2 (w/w) ratio. For formation of BAM- Fab1 proteoliposomes, a 2- fold molar excess of Fab1 was added to WT BAM, BAM- P5L or BAM- LL in TBS pH 8.0, \(0.05\%\) (w/v) DDM before mixing with lipid. For BamA proteoliposomes, refolded BamA was added to \(E\) . coli polar lipid films solubilised in TBS pH 8.0, \(0.1\%\) (w/v) LDAO in a 1:2 (w/w) ratio. Empty liposomes were prepared by mixing lipid with an equivalent volume of buffer. To remove detergent and promote liposome formation, the mixtures were dialyzed against \(2~\mathrm{L}\) of \(20~\mathrm{mM}\) Tris- HCl pH 8.0, \(150~\mathrm{mM}\) KCl using 12- 14 kDa MWCO D- Tube™ Maxi Dialyzers (Merck) at room temperature for 48 hours with a total of four buffer changes. Following dialysis, the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 164]]<|/det|>
+proteoliposomes were pelleted twice by ultracentrifugation at 100,000 \(g\) for 30 mins at \(4^{\circ}C\) (the supernatants referred to as wash 1 and wash 2 in Supplementary Figures) and were resuspended in TBS pH 8.0. Protein concentration was determined using a BCA assay (ThermoScientific) and successful reconstitution was determined by SDS- PAGE.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 201, 790, 220]]<|/det|>
+## Fluorescein-C5-maleimide labelling of free thiols in BAM disulphide variants  
+
+<|ref|>text<|/ref|><|det|>[[115, 229, 882, 416]]<|/det|>
+WT BAM, BAM- LL and BAM- P5L proteoliposome preparations (containing 5 \(\mu \mathrm{M}\) BAM) in TBS pH 8.0 were treated with 1 mM TCEP or 0.1 mM diamide, along with an untreated control, for 45 mins at room temperature. The proteoliposomes were then diluted 10- fold into TBS pH 7.5, 8 M urea containing 100 \(\mu \mathrm{M}\) fluorescein- C5- maleimide and were incubated overnight at \(25^{\circ}C\) . The products of the labelling reaction were then analysed by SDS- PAGE on \(15\%\) (w/v) acrylamide/bis- acrylamide (37.5:1) Tris- tricine SDS- PAGE gels run at \(60\mathrm{mA}\) per gel for 90 mins at \(25^{\circ}C\) , and imaged under 460 nm light using an Alliance Q9 Advanced gel doc (UVITEC, Cambridge, UK). Subsequently gels were stained with Coomassie Blue to visualise all protein bands.  
+
+<|ref|>sub_title<|/ref|><|det|>[[117, 454, 687, 473]]<|/det|>
+## BAM-mediated folding of OMPs by SDS-PAGE band-shift assays  
+
+<|ref|>text<|/ref|><|det|>[[115, 482, 882, 794]]<|/det|>
+Solutions of \(20\mu \mathrm{M}\) tOmpA or OmpX denatured in TBS pH 8.0 containing 8 M urea were diluted 5- fold into a \(20\mu \mathrm{M}\) solution of SurA. This mixture was then immediately diluted 2- fold into BAM, BamA or empty proteoliposomes to initiate the folding reaction, maintained at 25 \(^\circ \mathrm{C}\) . Final concentrations were \(1\mu \mathrm{M}\) BAM, \(2\mu \mathrm{M}\) tOmpA/OmpX, \(10\mu \mathrm{M}\) SurA, \(0.8\mathrm{M}\) urea in TBS pH 8.0. DTT was included in the relevant folding reactions at a final concentration of 25 mM. Samples of the folding reaction were taken periodically and were quenched in SDS- PAGE loading buffer (final concentrations: \(50\mathrm{mM}\) Tris- HCl pH 6.8, \(10\%\) (v/v) glycerol, \(1.5\%\) (w/v) SDS, \(0.001\%\) (w/v) bromophenol blue). The samples, including a boiled control (10 mins at \(>95^{\circ}C\) ), were run on \(15\%\) (w/v) SDS- PAGE gels as described above. The gels were stained in InstantBlue™ (Experion) and were imaged using an Alliance Q9 Advanced gel doc (UVITEC, Cambridge, UK). Folded and unfolded band intensities were quantified using ImageJ software (Fiji) and were plotted as a fraction folded ( \(\mathrm{I_F / (I_F + I_{UF})}\) ) against time. Folding data were fitted to a single exponential function in Igor Pro (V8.04) and initial rates calculated by applying a linear fit to data within the first \(5\%\) of the time- course (540 seconds).  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 834, 338, 852]]<|/det|>
+## CryoEM grid preparation  
+
+<|ref|>text<|/ref|><|det|>[[115, 861, 881, 901]]<|/det|>
+Samples for grid preparation were prepared as follows. Purified BAM- LL or BAM- P5L in 50 mM Tris- HCl pH 8.0, \(150\mathrm{mM}\) NaCl and \(0.05\%\) (w/v) DDM were diluted to \(3.3\mathrm{mg / mL}\) or 2.3
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 290]]<|/det|>
+mg/mL, respectively. For the BAM- Fab1 complex, purified WT BAM was mixed with a 2- fold molar excess of Fab1 and run on a Superdex 200 10/300 column in TBS pH 8.0, 0.05% (w/v) DDM to isolate a stoichiometric complex from excess free Fab1. Fractions corresponding to the complex were concentrated to 4.8 \(\mu \mathrm{M}\) in Vivaspin 500 concentrator MWCO 30k (Sartorius). To assemble the Fab1- bound BAM- LL complex, stock solutions of purified BAM- LL and Fab1 were first diluted to 5.9 \(\mu \mathrm{M}\) in 20 mM Tris- HCl pH 8.0, 150 mM NaCl and 0.05% (w/v) DDM and mixed in a 1:1 molar ratio, before dilution in detergent- free buffer to a total protein concentration of 0.9 mg/mL and a total DDM concentration of 0.03% (w/v). The detergent concentration was lowered to combat a tendency for very thin ice on the resulting grids.  
+
+<|ref|>text<|/ref|><|det|>[[115, 300, 881, 507]]<|/det|>
+CryoEM grids were prepared as follows. For the BAM- Fab1 complex, 4 \(\mu \mathrm{L}\) protein was applied to gold UltraUfoil R2/2 200 mesh grids, previously glow discharged for 60 sec at 20 mA in a GlowQube Plus (Electron Microscopy Sciences) in the presence of amylamine vapor. For BAM- LL, BAM- P5L and BAM- LL in complex with Fab1, 3 \(\mu \mathrm{L}\) of sample was applied to copper QUANTIFOIL R1.2/1.3 300 mesh, copper QUANTIFOIL R0.6/1 400 mesh and gold UltraUfoil R1.2/1.3 300 mesh grids (Electron Microscopy Sciences), respectively, that were previously glow discharged for 30 sec at 60 mA in a GlowQube Plus (Electron Microscopy Sciences). Grids were blotted for 6 sec with Whatman #1 filter paper at 4 °C and 80- 100% relative humidity, before plunge freezing in liquid ethane using a Vitrobot Mark IV (ThermoFisher).  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 547, 266, 564]]<|/det|>
+## CryoEM Imaging  
+
+<|ref|>text<|/ref|><|det|>[[115, 574, 881, 759]]<|/det|>
+Data were collected on a 300 KeV Titan Krios (ThermoFisher) EM in the Astbury Biostructure Laboratory in automated fashion using EPU software (ThermoFisher). Micrographs were recorded on an energy- filtered K2 detector (Gatan inc.) in counting mode, using a 100 \(\mu \mathrm{m}\) objective aperture. For BAM- LL, 6,456 micrographs were collected from a single grid over two sessions. For the Fab1- bound BAM- LL complex, 2,780 micrographs were collected from a single grid. For BAM- P5L, two grids were imaged in separate sessions, resulting in 2150 total micrographs. For the BAM- Fab1 complex, a single grid was imaged over three sessions, resulting in 4197 total micrographs. Full data collection parameters for each sample are shown in Supplementary Table 4.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 800, 279, 816]]<|/det|>
+## Image Processing  
+
+<|ref|>text<|/ref|><|det|>[[115, 826, 881, 907]]<|/det|>
+All processing was performed in RELION 3.0<sup>63</sup> (BAM- LL, BAM- Fab1, Fab1- bound BAM- LL) or 3.1<sup>64</sup> (BAM- P5L) unless otherwise stated. Dose- fractionated micrographs were motion- corrected and dose- weighted by MotionCor<sup>65</sup>, before estimation of contrast transfer function parameters by Gct<sup>66</sup> using the motion corrected and dose- weighted micrographs,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 879, 121]]<|/det|>
+apart from the BAM- Fab1 complex where motion corrected, but non- dose weighted, micrographs were used.  
+
+<|ref|>text<|/ref|><|det|>[[115, 131, 881, 550]]<|/det|>
+For BAM- LL, the two datasets were initially processed separately in a similar manner (Supplementary Fig. 6). For dataset 1, 299,458 particles were first picked using the general model in crYOLO 1.3.5<sup>67</sup>, and extracted in 300 pixel (321 Å) boxes with two- fold binning, before removal of false positives through two rounds of 2D classification. The resulting 234,598 particles were then used to generate an initial model by stochastic gradient descent<sup>68</sup>, which was used as the starting model for a 3D classification. Two high resolution classes corresponding to different conformations of BAM- LL were obtained, one termed lateral- closed (86,615 particles) and one lateral- open (83,803 particles). Particles corresponding to each class were then re- extracted unbinned, and autorefined with a mask excluding bulk solvent. After masking and sharpening, resolutions of 5.0 Å (lateral- closed) and 5.9 Å (lateral- open) were obtained. Processing of dataset 2 proceeded similarly and resulted in comparable resolutions for both conformations. To achieve higher resolution, one round of CTF refinement followed by Bayesian polishing were then employed for each dataset, following which the particles corresponding to the same conformation were combined, resulting in 160,118 lateral- closed and 141,612 lateral- open particles. Finally these particle stacks were subject to separate non- uniform refinements in cryoSPARC v2.2.0<sup>68,69</sup>. Masking and sharpening of the resulting half- maps in RELION resulted in resolutions of 4.1 Å (lateral- closed) and 4.8 Å (lateral- open). B- factors of - 107 Å<sup>2</sup> and - 127 Å<sup>2</sup> were applied to the final lateral- closed and lateral- open reconstructions, respectively. Local resolution was estimated using RELION.  
+
+<|ref|>text<|/ref|><|det|>[[115, 558, 881, 724]]<|/det|>
+For the BAM- Fab1 complex (Supplementary Fig. 8), particles were autopicked in RELION 3<sup>63</sup> using class averages from a previous reconstruction<sup>8</sup> filtered to 30 Å as search templates. Individual particles were extracted in 350 pixel (374.5 Å) boxes and culled with multiple rounds of 2D and 3D classification. The resulting particle stack containing 131,853 particles was further refined using the non- uniform refinement function in CryoSPARC v2.2.0<sup>68,69</sup>. The reconstruction was performed on independent subsets and final resolution of 5.2 Å determined by 'gold standard' FSC<sup>70</sup>. A B- factor of - 167 Å<sup>2</sup> was applied to the final reconstruction.  
+
+<|ref|>text<|/ref|><|det|>[[115, 763, 881, 907]]<|/det|>
+For BAM- P5L (Supplementary Figs. 9 and 10), particles were picked in crYOLO 1.4.1 using the general model. For dataset 1: 41, 316 particles were picked and extracted in a 280 pixel (300 Å) box, for dataset 2: 54, 532 particles were picked and extracted into 352 pixel (300 Å) boxes. Both used twofold binning. The extracted particles were combined into a single dataset and the resulting 95,848 particles passed through 2D classification. The best 21, 483 particles were used to construct an initial model by stochastic gradient descent<sup>68</sup>, which was used as a reference for 3D classification of the 43,280 good particles from 2D
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 165]]<|/det|>
+classification. The resulting 24, 101 particles were autorefined, and re- extracted as unbinned particles and subject to 3D classification using the autorefined model as the reference. The resulting 19,044 particles were autorefined with a mask to a resolution of 10.3 Å. A B- factor of - 671 Ų was applied to the final reconstruction  
+
+<|ref|>text<|/ref|><|det|>[[115, 173, 882, 487]]<|/det|>
+For the Fab1- bound BAM- LL complex (Supplementary Fig. 11), particles were picked in crYOLO 1.4.1 using a model trained with 11 handpicked micrographs spanning the defoci range. The resulting 162,844 particles were extracted in 300 (321 Å) pixel boxes with twofold binning. One round of 2D classification was used to cull the particle set to 108,096 particles which was then subject to 3D classification, using an initial model generated by stochastic gradient descent<sup>68</sup> from the best 32,645 particles in that stack as a template. From this 3D classification run, only one conformer was observed, corresponding to a lateral- open, BAM- LL bound to Fab1. The 71,675 particles in the highest resolution class were autorefined, re- extracted as unbinned particles and subject to 3D classification using the autorefined model as the reference, further culling the particle stack. Autorefinement and sharpening of the resulting 61,777 good particles gave a resolution of 7.3 Å. Finally, one round of CTF refinement followed by Bayesian polishing was carried out, and the resulting particle stacks were subject to non- uniform refinement in cryoSPARC v2.2.0<sup>68,69</sup>. Masking and sharpening of the resulting half- maps in RELION resulted in a resolution of 7.1 Å. A B- factor of - 274 Ų was applied to the final reconstruction.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 525, 465, 542]]<|/det|>
+## CryoEM model building and refinement  
+
+<|ref|>text<|/ref|><|det|>[[115, 552, 882, 761]]<|/det|>
+For LL- BAM in the lateral- closed cryoEM map, an existing crystal structure of intact BAM in a lateral- closed conformation (PDB ID: 5D0O<sup>5</sup>) was first edited to both remove the two natural cysteines in BamA and to insert the lid- lock disulphide bond. This starting model was fitted to the density as a rigid body in Chimera<sup>71</sup>, before performing several iterations of real- space refinement in PHENIX 1.14<sup>72</sup> with secondary structure restraints followed by manual refinement in COOT<sup>73</sup>, until satisfactory geometry and fit between model and map was obtained as assessed using MolProbity<sup>74</sup>. The extracellular region of eL6 (BamA<sub>675- 702</sub>, C- terminal globular domains of BamC (BamC<sub>89- 344</sub>), and regions at the chain termini of BamABCDE were insufficiently resolved and were not modelled. The final model contains BamA<sub>24- 675, 702- 810</sub> BamB<sub>31- 391</sub>, BamC<sub>30- 85</sub>, BamD<sub>27- 244</sub>, BamE<sub>29- 111</sub>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 770, 881, 914]]<|/det|>
+As the resolution of the other structures was insufficient for the above approach, Molecular Dynamics Flexible Fitting (MDFF)<sup>40</sup> was used to flexibly fit these conformations. For BAM- LL lateral- open, cascade MDFF (cMDFF) simulations of the lateral- closed atomic model with BamA truncated after residue 809 were first used to derive an initial fit to the lid- lock lateral- open cryoEM map. Here, a series of Gaussian blurred density maps were generated using the volutil function in VMD (halfwidths \(\sigma = 0, 1, \ldots , 6 \text{Å}\) ). The atomic model was then simulated in vacuum and subject to an external potential derived from most blurred density
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 437]]<|/det|>
+map, causing it to be flexibly fit into the density. 2 ps of minimisation followed by 100 ps of equilibration were run with a gscale of 1.0 defining the strength of the external potential derived from the density map. Consecutive 100 ps simulations were then run into maps of decreasing blurring, where the end coordinates from the previous simulation were used as input for the next, until reaching the unblurred map. At each step, isomerism, chirality and secondary structure restraints were applied. Several repeats were run, taking advantage of the stochastic nature of the simulation to generate different fits. Additionally, a second MDFF simulation was also run into the unblurred map using PDB- 5LJO<sup>8</sup> as a starting model, to derive better conformations for BamA<sub>720- 734</sub> and BamA<sub>807, 808</sub>. These models were then manually combined to give best mainchain fit to the density, before minimising against the unblurred map for 40 ps. In the combined model, BamA<sub>429- 440</sub>, corresponding to eL1 and the extracellular sides of \(\beta 1\) and \(\beta 2\) , was fitting into micelle density rather than protein density due to the low resolution in this region. A final set of 500 ps MDFF simulations were therefore run with this combined model against the unblurred map, in which BamA<sub>429- 440</sub> was not subject to the external potential. The best fitting structure from these runs was then minimised for 40 ps against the unblurred map and real space refined in PHENIX 1.14<sup>72</sup> with secondary structure restraints to generate the final atomic model.  
+
+<|ref|>text<|/ref|><|det|>[[115, 447, 881, 633]]<|/det|>
+For the Fab1- bound wild- type BAM complex, an initial model was created from the BAM complex PDB entry 5LJO<sup>8</sup>, with BamA<sub>687- 700</sub> from 5EKQ<sup>5</sup>, and the Fab1 crystal structure determined here (PDB 7BM5). The C- terminal globular domains of BamC were truncated, leaving only the lasso<sup>75</sup> region (residues 25- 83) resulting in a starting model containing BamA<sub>24- 806</sub>, BamB<sub>22- 392</sub>, BamC<sub>25- 83</sub>, BamD<sub>26- 243</sub>, and BamE<sub>24- 110</sub>. The starting model was fitted into each EM density as a rigid body using UCSF Chimera<sup>71</sup> and flexibly fit using cMDFF<sup>40</sup>. This was followed by real space refinement in PHENIX 1.14<sup>72</sup> using secondary structure restraints to generate the final atomic model, with the Fab1 crystal structure used as a reference model to generate additional restraints.  
+
+<|ref|>text<|/ref|><|det|>[[115, 643, 881, 825]]<|/det|>
+For the Fab1- bound lid- locked BAM complex, the final lid- locked lateral- open structure and the Fab1 crystal structure were rigid body fitted into the EM density using UCSF Chimera and flexibly fit using a round of MDFF into the unblurred map. This was followed by real space refinement in PHENIX 1.14 with secondary structure restraints to generate the final atomic model, with the Fab1 crystal structure and the final lid- locked lateral- open structures used as reference models to generate additional restraints. During the simulation eL1 of BamA (BamA<sub>429- 440</sub>) was not subject to the external potential to prevent overfitting to micelle density in this region. Model building statistics for all cryoEM conformers are shown in Supplementary Table 5.  
+
+<|ref|>sub_title<|/ref|><|det|>[[117, 869, 568, 886]]<|/det|>
+## Crystallisation and structure determination of Fab1
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 81, 881, 480]]<|/det|>
+Fab1 at 6.5 mg/mL was crystallised by the sitting drop vapour diffusion method in 96- well SWISSC1 3- drop plates at \(20^{\circ}C\) . Drops consisted of 100 nL protein and 100 nL crystallisation solution were dispensed using a Mosquito robot (TTP Labtech). Crystals were grown in 0.16 M lithium chloride, \(22\%\) (w/v) PEG6000, 0.1 M MES pH 6.0 and were harvested after 21 days. Crystals were cryo- protected in the crystallisation solution supplemented with \(20\%\) (v/v) ethylene glycol before flash- cooling into liquid nitrogen. X- ray data were collected at Diamond Light Source on beamline I24 from a single cryo- cooled crystal (100 K) using a Pilatus3 6M detector. Diffraction data were collected for a total of \(180^{\circ}\) up to a resolution of \(2.5 \AA\) with a \(0.2^{\circ}\) oscillation using an exposure time of 0.04 seconds at \(100\%\) transmission. X- ray diffraction data were indexed and integrated by autoPROC and STARANISO \(^{76}\) and were scaled to \(2.96 \AA\) in Aimless \(^{77}\) using the I24 beamline autoprocessing pipeline. The crystals belonged to a monoclinic space group \(P12_{1}1\) with unit cell parameters a = 92.0 Å, b = 130.1 Å, c = 138.9 Å, \(\alpha = 90.00^{\circ}\) , \(\beta = 106.1^{\circ}\) , \(\gamma = 90.00^{\circ}\) . The structure was solved by molecular replacement using Phaser \(^{78}\) and the C \(_{H}\) domain of the anti- NFG Fab as the search model (PDB accession number 1ZAN \(^{79}\) ). Crystallographic refinement was performed using PHENIX- 1.9 \(^{72,80}\) and model building was carried out in Coot \(^{73}\) . MolProbity \(^{74}\) was used for structure validation and quality assessment. The final model coordinates and structure factors are deposited in the PDB under the accession number 7BM5.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 516, 850, 536]]<|/det|>
+## Reconstitution of BamA and different BAM complexes into DMPC proteoliposomes  
+
+<|ref|>text<|/ref|><|det|>[[113, 545, 881, 902]]<|/det|>
+DMPC (dIC14:0PC), purchased as powder from Avanti Polar Lipids (Alabaster, AL), was dissolved in \(80:20\) (v/v) chloroform/methanol mixture at \(25 \text{mg/mL}\) . Appropriate volumes were dried to thin films in clean Pyrex tubes at \(42^{\circ}C\) under \(\mathsf{N}_2\) gas, and were further dried by vacuum desiccation for \(>3\) hours. BAM WT, BAM- LL and BAM- P5L or a 2:1 (mol/mol) mixture of Fab1 and BAM in TBS pH 8.0, \(0.05\%\) (w/v) DDM were mixed with DMPC lipid solubilized in TBS pH 8.0, \(0.05\%\) (w/v) DMD at a lipid to protein ratio (LPR) of 1600:1 (mol/mol). For BamA, DMPC lipid was first solubilised in TBS pH 8.0, \(0.1\%\) (w/v) LDAO. Empty liposomes were prepared by mixing DDM- solubilised lipid with an equivalent volume of buffer. Dialysis was performed as described for the preparation of E. coli polar lipid proteoliposomes, except that a temperature of \(30^{\circ}C\) was used (above the DMPC transition temperature). Following dialysis, the proteoliposomes were pelleted twice by ultracentrifugation at \(100,000 \text{g}\) for 30 min at \(4^{\circ}C\) and resuspended in TBS pH 8.0. The proteoliposomes were then extruded with 21 passes through a \(0.1 \mu \text{m}\) polycarbonate membrane using a mini- extruder (Avanti) pre- equilibrated at \(30^{\circ}C\) . Following ultracentrifugation as before, proteoliposomes were resuspended in TBS pH 8.0, protein concentration was determined using a BCA assay (ThermoScientific) and successful reconstitution was confirmed using SDS- PAGE.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 111, 440, 129]]<|/det|>
+## Probing lipid disorder using laurdan  
+
+<|ref|>text<|/ref|><|det|>[[115, 138, 881, 430]]<|/det|>
+Probing lipid disorder using laurdanLaurdan (Cambridge Bioscience) dissolved in DMSO was added to a final concentration of \(4.2 \mu M\) (final DMSO concentration of \(0.15\%\) (v/v)) to a \(0.8 \mu M\) suspension of BAM-, BamA- or empty- DMPC proteoliposomes (LPR 1600:1 mol/mol). The proteoliposomes were incubated at \(25 ^{\circ} C\) overnight to allow random partitioning of the laurdan probe into the membrane. Fluorescence emission was measured at \(440 nm\) and \(490 nm\) for a total time of 10 sec following excitation of laurdan fluorescence at \(340 nm\) in quartz cuvettes using a PTI QuantaMaster fluorimeter with a \(1 nm\) bandwidth and 1 second integration time. Excitation and emission slit widths were set to \(0.1 nm\) . Spectra were acquired at increasing temperature intervals from \(6 ^{\circ} C\) to \(40 ^{\circ} C\) , and to test reversibility, from \(40 ^{\circ} C\) to \(6 ^{\circ} C\) , allowing the sample to equilibrate at each temperature for 3 min. Generalised polarisation (GP) \(^{46}\) was calculated from the ratio of fluorescence intensity at \(440 nm\) and \(490 nm\) , averaged over the 10 second acquisition, using the formula GP = \((l_{440} - l_{490}) / (l_{440} + l_{490})\) , and was plotted against temperature. Mid- points and gradients of the transitions were determined by calculating the first derivative of the curve.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 469, 260, 485]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[115, 496, 881, 725]]<|/det|>
+Data availabilityRaw micrographs for each dataset are deposited at EMPIAR under accession numbers XXXX (BAM- LL), XXXX (BAM Fab1 complex), XXXX (BAM- P5L), XXXX (BAM- LL Fab1 complex). The final density maps are deposited in the EMDB under accession numbers XXXX (BAM- LL lateral- closed), XXXX (BAM- LL lateral- open), XXXX (BAM Fab1 complex), XXXX (BAM- P5L) and XXXX (BAM- LL Fab1 complex). Final model coordinates have been deposited in the PDB under accession numbers XXXX (BAM- LL lateral- closed), XXXX (BAM- LL lateral- open), XXXX (BAM Fab1 complex) and XXXX (BAM- LL Fab1 complex). The crystal structure of Fab1 has been deposited in the PDB under accession number 7BM5, and crystallographic data are available at https://doi.org/10.2210/pdb7BM5/pdb. Data supporting this study are freely available at the University of Leeds Data Repository: https://doi.org/10.5518/835.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 763, 295, 780]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[115, 790, 881, 898]]<|/det|>
+AcknowledgementsWe thank members of the Radford, Ranson, Brockwell and Rutherford labs for helpful discussions, and Nasir Khan for technical support. CryoEM data were collected at the Astbury Biostructure Laboratory, funded by the University of Leeds and the Wellcome Trust (108466/Z/15/Z). We thank Diamond Light Source for access to Beamline i24 (MX19248). P.W and M.G.I acknowledge funding from the Medical Research Council UK
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 81, 882, 260]]<|/det|>
+(MR/P018491/1). S.H and J.E.H are funded by the White Rose BBSRC DTP (BB/M011151/1) J.M. and A.J.H acknowledge support from the Wellcome Trust (222373/Z/21/Z and 105220/Z/14/Z, respectively). B.S acknowledges support from the BBSRC (BB/N007603/1 and BB/T000635/1). For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. J.W. is funded by an EOS Excellence in Research Program of the FWO and FRS-FNRS (G0G0818N). SER holds a Royal Society Professorial Fellowship (RSRP/R1/211057).  
+
+<|ref|>sub_title<|/ref|><|det|>[[120, 278, 305, 295]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[115, 306, 882, 492]]<|/det|>
+P.W, S.F.H, M.G.I and A.J.H designed and performed the experiments and analysed the data. P.W, S.F.H, J.M.M, A.J.H, B.S and C.C.P carried out BAM functional assays. P.W prepared protein samples for cryoEM. S.F.H, M.G.I and J.M.M performed cryoEM experiments and determined BAM cryoEM structures. P.W solved the X-ray structure of Fab1. P.W, S.F.H, J.E.H, B.S, C.C.P and J.M.W produced proteins required for the study. J.E.H developed the BAM laurdan fluorescence assay. K.M.S and S.T.R developed and produced the anti- BamA Fab fragment (Fab1). S.E.R, N.A.R and D.J.B supervised the research. P.W, S.F.H and M.G.I wrote the manuscript with comments and edits provided from all authors.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[112, 78, 870, 760]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 760, 881, 904]]<|/det|>
+<center>Fig. 1 | Disulphide-locked BamA variants and Fab1 binding impair BAM-mediated OMP folding in vitro. (a) BAM-P5L (G393C/G584C) is expected to lock BamA in the lateral-open conformation (PDB code 5LJO<sup>8</sup>), while (b) BAM-LL (E435C/S665C) is expected to lock BamA in the lateral-closed conformation (PDB code 5DOO<sup>6</sup>). BamA POTRAs 1-4 and BamBCDE are rendered semi-transparent for emphasis on the BamA \(\beta\) -barrel and POTRA-5. The position of the disulphide bond is shown as a yellow bar. Figure made in PyMOL v1.7.2.3. (c and d) Quantification of folded and unfolded bands from SDS-PAGE band-shift </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[60, 81, 883, 271]]<|/det|>
+assays (Supplementary Figs. 3 and 4) plotted as fraction folded against time for tOmpA or OmpX, respectively. Data are fitted to a single exponential function. (e and f) The initial rates of folding (determined by applying a linear fit to the first \(5\%\) of folding data) normalised as a percentage of the initial rate obtained for WT BAM, are shown for (e) tOmpA and (f) OmpX folding (see also Supplementary Table 1). Folding assays were repeated to assess reproducibility, with errors for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE), whilst "BamA" is just BamA alone.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 81, 880, 490]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 504, 881, 863]]<|/det|>
+<center>Fig. 2 | CryoEM resolves two conformations of BAM-LL in detergent. (a) 4.1 A cryoEM map of the BAM-LL lateral-closed conformation at a contour of \(10\sigma\) , coloured by subunit. The lateral-gate is closed and POTRA-5 does not block the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA-5 of BamA. \(\beta 1\) and \(\beta 16\) contact to close the gate. (c) The same density viewed from the periplasmic side, showing the open lumen of the BamA barrel in this conformation. (d) 4.8 Å cryoEM map of the BAM-LL lateral-open conformation at a contour of \(10\sigma\) , coloured by subunit. The lateral-gate is open and POTRA-5 occludes the BamA barrel (schematic inset). (e) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on segmented density for the barrel and POTRA-5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel to contact eL6. (f) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA-5 in this conformation. Fig. made in UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 80, 875, 550]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 575, 881, 866]]<|/det|>
+<center>Fig. 3 | Fab1-bound BAM is in a lateral-open conformation. (a) 5.1 Å cryoEM map of the BAM-Fab1 complex in a lateral-open conformation at a contour of \(10\sigma\) , coloured by subunit. The lateral-gate is fully-open and POTRA-5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA-5 of BamA. \(\beta 1\) is in a conformation that makes limited contact with \(\beta 16\) . (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA-5 in this conformation. Panels made using UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d) Close up of the BamA-Fab1 interface region highlighting the Fab1 CDRs (red) interacting with eL4 of BamA (dark blue). Other regions of BamA are rendered semi-transparent to highlight eL4. Heavy and light chains of Fab1 are coloured cyan and pink, respectively. (e) The \(\mathrm{V_L}\) and \(\mathrm{V_H}\) domains of Fab1 variable form a complementary binding surface for eL4 of BamA involving residues Y550, E554 and H555. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 80, 870, 789]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 791, 880, 894]]<|/det|>
+<center>Fig. 4 | Additive effect of BAM inhibition by disulphide-locking and binding of Fab1. (a) 7.1 Å cryoEM map of the Fab1-bound LL-BAM in a lateral-open conformation at a contour of 9.5 σ, coloured by subunit. The lateral-gate is open and POTRA-5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the β-barrel and </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[66, 81, 883, 377]]<|/det|>
+POTRA- 5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel to contact eL6. (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Structural panels made using UCSF ChimeraX<sup>76</sup>. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d and e) Quantification of SDS- PAGE band- shift assays shown in Supplementary Fig. 13 for (d) tOmpA and (e) OmpX folding catalysed by BAM- P5L (green), BAM- LL (blue) and WT BAM (black), each with and without Fab1 (solid and open circles, respectively). (f and g) The initial rates, calculated by applying a linear fit to the first 5% of fitted folding data, were normalised to that of WT BAM, and are shown for (f) tOmpA and (g) OmpX folding (see also Supplementary Table 1). Folding assays were conducted twice for reproducibility with data for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE).
+
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+<|ref|>image<|/ref|><|det|>[[122, 100, 820, 680]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 685, 880, 912]]<|/det|>
+<center>Fig. 5 | BAM variants reduce the phase transition temperature of DMPC liposomes. Global lipid phase transition behaviour for each BAM variant and BamA in DMPC proteoliposomes, with an empty liposomes control measured using laurdan fluorescence. (a) The ratio of laurdan fluorescence at \(440 \text{nm}\) and \(490 \text{nm}\) was plotted as generalised polarisation (GP, see Methods) against temperature for \(0.8 \mu \text{M BAM/BamA proteoliposome}\) suspensions at a \(1600:1\) (mol/mol) lipid-to-protein ratio (LPR) with added laurdan (at a \(305:1\) lipid-to-laurdan ratio) in TBS pH 8.0. (b) The first derivative of data shown in (a) showing the transition temperature for each liposome suspension as the point of steepest (most negative) gradient. Whilst empty DMPC (grey) and BamA proteoliposomes (purple) have a transition temperature of \(24 \text{‰}\) , the presence of WT BAM (black), BAM-Fab1 (red), BAM-P5L (green), BAM-LL (blue), BAM-P5L + Fab1 (orange) and BAM-LL + Fab1 (yellow) </center>
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+<--- Page Split --->
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+792 broaden the phase transition and lower the transition temperature. Figures labelled with 793 “BAM” refer to the full BAM complex (BamABCDE), whilst “BamA” is just BamA alone.
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+796 1. Horne, J. E., Brockwell, D. J. & Radford, S. E. Role of the lipid bilayer in outer 797 membrane protein folding in Gram-negative bacteria. J. Biol. Chem. 295, 10340- 798 10367 (2020). 799 2. Noinaj, N., Gumbart, J. C. & Buchanan, S. K. The \(\beta\) - barrel assembly machinery in 800 motion. Nat. Rev. Microbiol. 15, 197- 204 (2017). 801 3. Konovalova, A., Kahne, D. E. & Silhavy, T. J. Outer membrane biogenesis. Annu. 802 Rev. Microbiol. 71, 539- 556 (2017). 803 4. Voulhoux, R., Bos, M. P., Geurtsen, J., Mols, M. & Tommassen, J. Role of a highly 804 conserved bacterial protein in outer membrane protein assembly. Science 299, 262- 805 265 (2003). 806 5. Bakelar, J., Buchanan, S. K. & Noinaj, N. The structure of the \(\beta\) - barrel assembly 807 machinery complex. Science 351, 180- 186 (2016). 808 6. Gu, Y. et al. Structural basis of outer membrane protein insertion by the BAM 809 complex. Nature 531, 64 (2016). 810 7. Han, L. et al. Structure of the BAM complex and its implications for biogenesis of 811 outer-membrane proteins. Nat. Struct. Mol. Biol. 23, 192- 196 (2016). 812 8. Iadanza, M. G. et al. Lateral opening in the intact \(\beta\) - barrel assembly machinery 813 captured by cryo- EM. Nat. Commun. 7, 12865 (2016). 814 9. Hart, E. M., Gupta, M., Wühr, M. & Silhavy, T. J. The synthetic phenotype of \(\Delta\) BamB 815 \(\Delta\) BamE double mutants results from a lethal jamming of the BAM complex by the 816 lipoprotein RcsF. MBio 10, (2019). 817 10. Tata, M. & Konovalova, A. Improper coordination of BamA and BamD results in BAM 818 complex jamming by a lipoprotein substrate. MBio 10, (2019). 819 11. Luther, A. et al. Chimeric peptidomimetic antibiotics against Gram- negative bacteria. 820 Nature 576, 452- 458 (2019). 821 12. Imai, Y. et al. A new antibiotic selectively kills Gram- negative pathogens. Nature 576, 822 459- 464 (2019). 823 13. Hart, E. M. et al. A small- molecule inhibitor of BamA impervious to efflux and the outer 824 membrane permeability barrier. Proc. Natl. Acad. Sci. U.S.A. 116, 21748- 21757 825 (2019). 826 14. Urfer, M. et al. A peptidomimetic antibiotic targets outer membrane proteins and 827 disrupts selectively the outer membrane in Escherichia coli. J. Biol. Chem. 291, 1921- 828 32 (2016). 829 15. Hagan, C. L., Wzorek, J. S. & Kahne, D. Inhibition of the \(\beta\) - barrel assembly machine 830 by a peptide that binds BamD. Proc. Natl. Acad. Sci. U.S.A. 112, 2011- 6 (2015). 831 16. Storek, K. M. et al. Monoclonal antibody targeting the \(\beta\) - barrel assembly machine of 832 Escherichia coli is bactericidal. Proc. Natl. Acad. Sci. U.S.A. 115, 3692- 3697 (2018). 833 17. Kaur, H. et al. Identification of conformation- selective nanobodies against the 834 membrane protein insertase BamA by an integrated structural biology approach. J. 835 Biomol. NMR 73, 375- 384 (2019). 836 18. Iadanza, M. G. et al. Distortion of the bilayer and dynamics of the BAM complex in 837 lipid nanodiscs. Commun. Biol. 3, 766 (2020). 838 19. Noinaj, N., Kuszak, A. J., Balusek, C., Gumbart, J. C. & Buchanan, S. K. Lateral 839 opening and exit pore formation are required for BamA function. Structure 22, 1055-
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+840 1062 (2014).841 20. Doerner, P. A. & Sousa, M. C. Extreme dynamics in the BamA \(\beta\) - barrel seam.842 Biochemistry 56, 3142- 3149 (2017).843 21. Rodriguez-Alonso, R. et al. Structural insight into the formation of lipoprotein- \(\beta\) - barrel844 complexes. Nat. Chem. Biol. 16, 1019- 1025 (2020).845 22. Xiao, L. et al. Structures of the \(\beta\) - barrel assembly machine recognizing outer846 membrane protein substrates. FASEB J. 35, e21207 (2021).847 23. Warner, L. R., Gatzewa- Topalova, P. Z., Doerner, P. A., Pardi, A. & Sousa, M. C.848 Flexibility in the periplasmic domain of BamA is important for function. Structure 25,849 94- 106 (2017).850 24. Lundquist, K., Billings, E., Bi, M., Wellnitz, J. & Noinaj, N. The assembly of \(\beta\) - barrel851 membrane proteins by BAM and SAM. Mol. Microbiol. (2020).852 25. Schiffrin, B., Brockwell, D. J. & Radford, S. E. Outer membrane protein folding from853 an energy landscape perspective. BMC Biol. 15, 123 (2017).854 26. Hohr, A. I. C. et al. Membrane protein insertion through a mitochondrial \(\beta\) - barrel gate.855 Science. 359, (2018).856 27. Doyle, M. T. & Bernstein, H. D. Bacterial outer membrane proteins assemble via857 asymmetric interactions with the BamA \(\beta\) - barrel. Nat. Commun. 10, 3358 (2019).858 28. Lee, J. et al. Formation of a \(\beta\) - barrel membrane protein is catalyzed by the interior859 surface of the assembly machine protein BamA. Elife 8, (2019).860 29. Tomasek, D. et al. Structure of a nascent membrane protein as it folds on the BAM861 complex. Nature 583, 473- 478 (2020).862 30. Noinaj, N. et al. Structural insight into the biogenesis of \(\beta\) - barrel membrane proteins.863 Nature 501, 385- 390 (2013).864 31. Schiffrin, B. et al. Effects of periplasmic chaperones and membrane thickness on865 BamA- catalyzed outer- membrane protein folding. J. Mol. Biol. 429, 3776- 3792 (2017).866 32. Liu, J. & Gumbart, J. C. Membrane thinning and lateral gating are consistent features867 of BamA across multiple species. PLOS Comput. Biol. 16, e1008355 (2020).868 33. Patel, G. J. & Kleinschmidt, J. H. The lipid bilayer- inserted membrane protein BamA869 of Escherichia coli facilitates insertion and folding of outer membrane protein A from870 its complex with Skp. Biochemistry 52, 3794- 3986 (2013).871 34. Gessmann, D. et al. Outer membrane \(\beta\) - barrel protein folding is physically controlled872 by periplasmic lipid head groups and BamA. Proc. Natl. Acad. Sci. U.S.A. 111, 5878- 873 (2014).874 35. Tiwari, P. B. & Mahalakshmi, R. Interplay of protein primary sequence, lipid875 membrane, and chaperone in \(\beta\) - barrel assembly. Protein Sci. (2021).876 36. Rigel, N. W., Ricci, D. P. & Silhavy, T. J. Conformation- specific labelling of BamA and877 suppressor analysis suggest a cyclic mechanism for \(\beta\) - barrel assembly in Escherichia878 coli. Proc. Natl. Acad. Sci. U.S.A. 110, 5151- 5156 (2013).879 37. Storek, K. M. et al. The Escherichia coli \(\beta\) - barrel assembly machinery is sensitized to880 perturbations under high membrane fluidity. J. Bacteriol. 201, e00517- 18 (2019).881 38. Schüßler A., Herwig S., Kleinschmidt J.H. (2019) Kinetics of Insertion and Folding of882 Outer Membrane Proteins by Gel Electrophoresis. In: Kleinschmidt J. (eds) Lipid-883 Protein Interactions. Methods in Molecular Biology, vol 2003. Humana, New York, NY.884 39. Hagan, C. L., Westwood, D. B. & Kahne, D. Bam lipoproteins assemble BamA in vitro.
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+885 Biochemistry 52, 6108- 6113 (2013). 886 40. Trabuco, L. G., Villa, E., Mitra, K., Frank, J. & Schulten, K. Flexible fitting of atomic 887 structures into electron microscopy maps using molecular dynamics. Structure 16, 888 673- 683 (2008). 889 41. Krissinel, E. Stock- based detection of protein oligomeric states in jsPISA. Nucleic 890 Acids Res. 43, W314- W319 (2015). 891 42. Kleinschmidt, J. H. Folding of \(\beta\) - barrel membrane proteins in lipid bilayers - 892 Unassisted and assisted folding and insertion. Biochim. Biophys. Acta - Biomembr. 893 1848, 1927- 1943 (2015). 894 43. Burgess, N. K., Dao, T. P., Stanley, A. M. & Fleming, K. G. \(\beta\) - barrel proteins that 895 reside in the Escherichia coli outer membrane in vivo demonstrate varied folding 896 behavior in vitro. J. Biol. Chem. 283, 26748- 26758 (2008). 897 44. Andersen, K. K., Wang, H. & Otzen, D. E. A kinetic analysis of the folding and 898 unfolding of OmpA in urea and guanidinium chloride: Single and parallel pathways. 899 Biochemistry 51, 8371- 8383 (2012). 900 45. Danoff, E. J. & Fleming, K. G. Membrane defects accelerate outer membrane \(\beta\) - barrel 901 protein folding. Biochemistry 54, 97- 99 (2015). 902 46. Parasassi, T., De Stasio, G., Ravagnan, G., Rusch, R. M. & Gratton, E. Quantitation 903 of lipid phases in phospholipid vesicles by the generalized polarization of Laurdan 904 fluorescence. Biophys. J. 60, 179- 89 (1991). 905 47. Bonora, S., Markarian, S. A., Trinchero, A. & Grigorian, K. R. DSC study on the effect 906 of dimethylsulfoxide (DMSO) and diethylsulfoxide (DESO) on phospholipid liposomes. 907 Thermochim. Acta 433, 19- 26 (2005). 908 48. Hussain, S. & Bernstein, H. D. The Bam complex catalyzes efficient insertion of 909 bacterial outer membrane proteins into membrane vesicles of variable lipid 910 composition. J. Biol. Chem. 293, 2959- 2973 (2018). 911 49. Konovalova, A. et al. Inhibitor of intramembrane protease RseP blocks the \(\sigma \in\) 912 response causing lethal accumulation of unfolded outer membrane proteins. Proc. 913 Natl. Acad. Sci. U.S.A. 115, E6614- E6621 (2018). 914 50. Dartigalongue, C., Missiakas, D. & Raina, S. Characterization of the Escherichia coli 915 \(\sigma \in\) regulon. J. Biol. Chem. 276, 20866- 20875 (2001). 916 51. Johansen, J., Rasmussen, A. A., Overgaard, M. & Valentin- Hansen, P. Conserved 917 small non- coding RNAs that belong to the \(\sigma \in\) regulon: Role in down- regulation of 918 outer membrane proteins. J. Mol. Biol. 364, 1- 8 (2006). 919 52. Rhodius, V. A., Suh, W. C., Nonaka, G., West, J. & Gross, C. A. Conserved and 920 variable functions of the \(\sigma \in\) stress response in related genomes. PLoS Biol. 4, 0043- 921 0059 (2006). 922 53. Rollauer, S. E., Sooreshjani, M. A., Noinaj, N. & Buchanan, S. K. Outer membrane 923 protein biogenesis in Gram- negative bacteria. Philosophical Transactions of the Royal 924 Society B: Biological Sciences 370, (2015). 925 54. Webb, C. T. et al. Dynamic association of BAM complex modules includes surface 926 exposure of the lipoprotein BamC. J. Mol. Biol. 422, 545- 555 (2012). 927 55. Lee, J. et al. Substrate binding to BamD triggers a conformational change in BamA to 928 control membrane insertion. Proc. Natl. Acad. Sci. U.S.A. 115, 2359 LP - 2364 929 (2018). 930 56. Gunasinghe, S. D. et al. The WD40 protein BamB mediates coupling of BAM 931 complexes into assembly precincts in the bacterial outer membrane. Cell Rep. 23,
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+932 2782- 2794 (2018).933 57. Ricci, D. P., Hagan, C. L., Kahne, D. & Silhavy, T. J. Activation of the Escherichia coli \(\beta\) - barrel assembly machine (Bam) is required for essential components to interact properly with substrate. Proc. Natl. Acad. Sci. U.S.A. 109, 3487- 3491 (2012).936 58. Roman- Hernandez, G., Peterson, J. H. & Bernstein, H. D. Reconstitution of bacterial autotransporter assembly using purified components. Elife 3, e04234 (2014).937 59. Hartmann, J.- B., Zahn, M., Burmann, I. M., Bibow, S. & Hiller, S. Sequence- specific solution NMR assignments of the \(\beta\) - barrel insertase BamA to monitor its conformational ensemble at the atomic level. J. Am. Chem. Soc. 140, 11252- 11260 (2018).942 60. Calabrese, A. N. et al. Inter- domain dynamics in the chaperone SurA and multi- site binding to its outer membrane protein clients. Nat. Commun. 11, 1- 16 (2020).944 61. Simmons, L. C. et al. Expression of full- length immunoglobulins in Escherichia coli: Rapid and efficient production of aglycosylated antibodies. J. Immunol. Methods, 263, 133- 147 (2002).946 62. Lombana, T. N., Dillon, M., Bevers, J. & Spiess, C. Optimizing antibody expression by using the naturally occurring framework diversity in a live bacterial antibody display system. Sci. Rep. (2015).950 63. Zivanov, J. et al. New tools for automated high- resolution cryo- EM structure determination in RELION- 3. Elife 7, (2018).952 64. Zivanov, J., Nakane, T. & Scheres, S. H. W. Estimation of high- order aberrations and anisotropic magnification from cryo- EM data sets in RELION- 3.1. IUCrJ 7, 253- 267 (2020).955 65. Zheng, S. Q. et al. MotionCor2: Anisotropic correction of beam- induced motion for improved cryo- electron microscopy. Nat. Methods 14, 331- 332 (2017).956 66. Zhang, K. Gctf: Real- time CTF determination and correction. J. Struct. Biol. 193, 1- 12 (2016).957 67. Wagner, T. et al. SPHIRE- crYOLO is a fast and accurate fully automated particle picker for cryo- EM. Commun. Biol. 2, 1- 13 (2019).961 68. Punjani, A., Rubinstein, J. L., Fleet, D. J. & Brubaker, M. A. CryoSPARC: Algorithms for rapid unsupervised cryo- EM structure determination. Nat. Methods 14, 290- 296 (2017).964 69. Punjani, A., Zhang, H. & Fleet, D. J. Non- uniform refinement: Adaptive regularization improves single particle cryo- EM reconstruction. Nat. Methods 17, 1214- 1221 (2020).965 70. Henderson, R. et al. Outcome of the first electron microscopy validation task force meeting. in Structure 20, 205- 214 (2012).968 71. Pettersen, E. F. et al. UCSF Chimera?A visualization system for exploratory research and analysis. J. Comput. Chem. 25, 1605- 1612 (2004).970 72. Afonine, P. V. et al. Real- space refinement in PHENIX for cryo- EM and crystallography. Acta Crystallogr. Sect. D Struct. Biol. 74, 531- 544 (2018).972 73. Emsley, P. & Cowtan, K. Coot: Model- building tools for molecular graphics. Acta Crystallogr. Sect. D Biol. Crystallogr. 60, 2126- 2132 (2004).974 74. Chen, V. B. et al. MolProbity: All- atom structure validation for macromolecular crystallography. Acta Crystallogr. Sect. D Biol. Crystallogr. 66, 12- 21 (2010).976 75. Kim, K. H., Aulakh, S. & Paetzel, M. Crystal structure of \(\beta\) - barrel assembly machinery BamCD protein complex. J. Biol. Chem. 286, 39116- 39121 (2011).
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+978 76. Tickle, I.J., Flensburg, C., Keller, P., Paciorek, W., Sharff, A. & Vonrhein, C., 979 Bricogne, G. STARANISO. (2018). 980 77. Evans, P. R. & Murshudov, G. N. How good are my data and what is the resolution? 981 Acta Crystallogr. D. Biol. Crystallogr. 69, 1204- 1214 (2013). 982 78. McCoy, A. J. et al. Phaser crystallographic software. J. Appl. Crystallogr. 40, 658- 674 983 (2007). 984 79. Covaceuszach, S. et al. Dissecting NGF interactions with TrkA and p75 receptors by 985 structural and functional studies of an anti- NGF neutralizing antibody. J. Mol. Biol. 986 381, 881- 896 (2008). 987 80. Adams, P. D. et al. PHENIX: A comprehensive Python- based system for 988 macromolecular structure solution. Acta Crystallogr. Sect. D Biol. Crystallogr. 66, 989 213- 221 (2010). 990
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+<|ref|>image_caption<|/ref|><|det|>[[44, 849, 115, 868]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 889, 953, 956]]<|/det|>
+Disulphide- locked BamA variants and Fab1 binding impair BAM- mediated OMP folding in vitro. (a) BAM- P5L (G393C/G584C) is expected to lock BamA in the lateral- open conformation (PDB code 5LJ08), while (b) BAM- LL (E435C/S665C) is expected to lock BamA in the lateral- closed conformation (PDB code
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 45, 955, 271]]<|/det|>
+5D006). BamA POTRAs 1- 4 and BamBCDE are rendered semi- transparent for emphasis on the BamA β- barrel and POTRA- 5. The position of the disulphide bond is shown as a yellow bar. Figure made in PyMOL v1.7.2.3. (c and d) Quantification of folded and unfolded bands from SDS- PAGE band- shift assays (Supplementary Figs. 3 and 4) plotted as fraction folded against time for tOmpA or OmpX, respectively. Data are fitted to a single exponential function. (e and f) The initial rates of folding (determined by applying a linear fit to the first 5% of folding data) normalised as a percentage of the initial rate obtained for WT BAM, are shown for (e) tOmpA and (f) OmpX folding (see also Supplementary Table 1). Folding assays were repeated to assess reproducibility, with errors for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE), whilst "BamA" is just BamA alone.  
+
+<|ref|>image<|/ref|><|det|>[[72, 295, 884, 770]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 802, 117, 821]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 841, 930, 956]]<|/det|>
+CryoEM resolves two conformations of BAM- LL in detergent. (a) 4.1 723 Å cryoEM map of the BAM- LL lateral- closed conformation at a contour of 10 σ, coloured by subunit. The lateral- gate is closed and POTRA- 5 does not block the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA- 5 of BamA. β1 and β16 contact to close the gate. (c) The same density viewed from the
+
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+<|ref|>text<|/ref|><|det|>[[40, 44, 944, 247]]<|/det|>
+periplasmic side, showing the open lumen of the BamA barrel in this conformation. (d) 4.8 Å cryoEM map of the BAM- LL lateral-open conformation at a contour of 10 σ, coloured by subunit. The lateral- gate is open and POTRA- 5 occludes the BamA barrel (schematic inset). (e) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on segmented density for the barrel and POTRA- 5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel to contact eL6. (f) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Fig. made in UCSF ChimeraX76. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked.  
+
+<|ref|>image<|/ref|><|det|>[[60, 260, 901, 817]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 863, 117, 881]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 903, 946, 947]]<|/det|>
+Fab1- bound BAM is in a lateral- open conformation. (a) 5.1 Å cryoEM map of the BAM- Fab1 complex in a lateral- open conformation at a contour of 10 σ, coloured by subunit. The lateral- gate is fully- open and
+
+<--- Page Split --->
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+POTRA- 5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the barrel and POTRA- 5 of BamA. \(\beta 1\) is in a conformation that makes limited contact with \(\beta 16\) . (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Panels made using UCSF ChimeraX76. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d) Close up of the BamA- Fab1 interface region highlighting the Fab1 CDRs (red) interacting with eL4 of BamA (dark blue). Other regions of BamA are rendered semi- transparent to highlight eL4. Heavy and light chains of Fab1 are coloured cyan and pink, respectively. (e) The VL and VH domains of Fab1 variable form a complementary binding surface for eL4 of BamA involving residues Y550, E554 and H555.
+
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+<|ref|>image_caption<|/ref|><|det|>[[43, 800, 118, 820]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 840, 955, 955]]<|/det|>
+Additive effect of BAM inhibition by disulphide- locking and binding of Fab1. (a) 7.1 Å cryoEM map of the Fab1- bound LL- BAM in a lateral- open conformation at a contour of 9.5 σ, coloured by subunit. The lateral- gate is open and POTRA- 5 occludes the BamA barrel (schematic inset). (b) Cartoon representation of the corresponding atomic model at the lateral gate, superimposed on the segmented density for the β- barrel and POTRA- 5 of BamA. To satisfy the disulphide in this conformation, eL1 must bend back into the barrel
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[39, 44, 945, 293]]<|/det|>
+to contact eL6. (c) The same density viewed from the periplasmic side, showing that the BamA lumen is blocked by POTRA- 5 in this conformation. Structural panels made using UCSF ChimeraX76. Segmenting and colouring performed with corresponding atomic models. Less well resolved regions and the micelle have been masked. (d and e) Quantification of SDS- PAGE band- shift assays shown in Supplementary Fig. 13 for (d) tOmpA and (e) OmpX folding catalysed by BAM- P5L (green), BAM- LL (blue) and WT BAM (black), each with and without Fab1 (solid and open circles, respectively). (f and g) The initial rates, calculated by applying a linear fit to the first \(5\%\) of fitted folding data, were normalised to that of WT BAM, and are shown for (f) tOmpA and (g) OmpX folding (see also Supplementary Table 1). Folding assays were conducted twice for reproducibility with data for replicate initial rate measurements listed in Supplementary Table 1. Folding yields after 24 hours are reported in Supplementary Table 2. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[75, 68, 830, 300]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 800, 120, 820]]<|/det|>
+<center>Figure 5 </center>  
+
+<|ref|>image<|/ref|><|det|>[[75, 460, 830, 770]]<|/det|>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 44, 944, 200]]<|/det|>
+305:1 lipid- to- laurdan ratio) in TBS pH 8.0. (b) The first derivative of data shown in (a) showing the transition temperature for each liposome suspension as the point of steepest (most negative) gradient. Whilst empty DMPC (grey) and BamA proteoliposomes (purple) have a transition temperature of \(24^{\circ}C\) , the presence of WT BAM (black), BAM- Fab1 (red), BAM- P5L (green), BAM- LL (blue), BAM- P5L + Fab1 (orange) and BAM- LL + Fab1 (yellow) broaden the phase transition and lower the transition temperature. Figures labelled with "BAM" refer to the full BAM complex (BamABCDE), whilst "BamA" is just BamA alone.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 223, 310, 251]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 274, 765, 295]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 312, 441, 358]]<|/det|>
+SupplementaryInformationsubmitted.pdf ValidationReports.pdf
+
+<--- Page Split --->

preprint/preprint__07208eea83c232a05dca70cd64270d5ee1a24fdbc00dcd03cf4ddc8b21562a44/images_list.json

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+    "caption": "Figure 1: Schematic diagram of a remote focusing system implemented in light-sheet microscopy and its performance. a) Three different modalities to acquire volumetric imaging of the sample along the focus direction. Either the sample or objective lens can be moved for axial refocusing. Alternatively, both the sample and objective lens can remain stationary by using a remote focusing system. b) Implementation of the remote-focusing system on the detection arm of the light sheet microscope. In this configuration, objective lenses 1 and 2 are pupil-matched through two lenses to form a perfect imaging system. Combined with mirror M3 and a polarizing beam splitter (PBS), the whole system works as a remote focusing system. The novel design of this remote-focusing system is implementation in the detection arm for unpolarized fluorescent light emitted from the sample. To do this, two tilted mirrors M1 and M2 are utilized to direct both S and P-polarized beams toward Objective lens 2 and then combine the reflected beams from mirror M3 to create an image by S and P-polarized beams onto the camera by focusing through the tube lens. The mirror M3 is attached to the linear focus actuator (LFA), moving back and forth to scan the sample in the Z-direction to acquire a 3D image. In the illumination arm, the generated light sheet by a cylindrical lens is translated by a galvanometric scan mirror (GSM) along the detection arm. To focus the detection path on the plane of the light sheet, the synchronization of GSM and LFA is carried out by sawtooth signals. Simultaneous dual-channel imaging of the cell is achieved in \\(40 \\mu \\mathrm{m} \\times 150 \\mu \\mathrm{m}\\) FOV over \\(70 \\mu \\mathrm{m}\\) in the Z-direction. c) The polarization state of the incoming beams changes after reflection from mirror M3 (S to P, and P to S). d) The reflected beams from mirror M3 have a different polarization state compared to the incoming beams; therefore, they exist from a different side of the PBS than the incoming beams. e) The point spread function (PSF) of 200 nm beads formed by S, P, and S+P polarized beams. The microscope performs at the diffraction limit, \\(394 \\mathrm{nm}\\) resolution, for S, P, and S+P in the lateral directions (X-Y), while it maintains a resolution of \\(654 \\mathrm{nm}\\) in the axial direction (Z).",
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+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2: Ray tracing of the setup and resolution assessment. a) Ray tracing of the detection path. L: image size, f: effective focal length, S: image or object position relative to the lens, unit: mm. b) Calibration of lateral magnification at various object positions, a target illuminated by a white light LED is imaged for magnification measurement. c) Maximum intensity projections of data acquired on \\(200 \\mathrm{nm}\\) beads from 10 slices spaced \\(500 \\mathrm{nm}\\) in the Z-direction. The images show orthogonal views of the MIPs across scan range for S,P and S+P. The elongated PSF in the Z direction exhibits less resolution in the axial direction controlled by the light sheet waist. d) The FWHM of the \\(200 \\mathrm{nm}\\) beads in the lateral and axial directions over the scan range. The minimum lateral resolution, \\(394 \\mathrm{nm}\\) , occurs at the center of the scan range and increases by moving away from the center. These plots show a constant axial resolution of \\(650 \\mathrm{nm}\\) over the axial scan range. The microscope functions in the scan range of \\(70 \\mu \\mathrm{m}\\) .",
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+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3: Dual-Color volumetric imaging of live RBL cells. (a-d) Dual-color volumetric imaging of granule motions in a live RBL-2H3 GFP-FasL cell, where the cell membrane is labeled with IgE-CF640R and granules contain GFP-FasL, at an imaging speed of \\(\\sim 0.6\\) volumes \\((80\\times 15\\times 40\\) \\(\\mu \\mathrm{m}^3\\) in XYZ) per second for 80 volumes, for a total imaging time of \\(\\sim 2\\) minutes. (a) Maximum intensity projection views of the cell images at one-time point and overlay with representative trajectories of granule movement (orange lines). (b) Time series of the trajectories in a. (c, d) Histograms of estimated diffusion coefficients and velocities of all trajectories found in cell 1 and cell 2. (e-g) Dual-color volumetric imaging of live RBL-2H3 GFP-FasL cell, where the cell membrane is labeled with CellMask DeepRed and the granules contain GFP-FasL using an imaging speed of \\(\\sim 8.3\\) volumes/s for 80 volumes for a total time of \\(10\\mathrm{s}\\) . (e) Maximum intensity projection views of the cell images at one-time point and overlay with representative trajectories of granule movement (orange lines). (f) Time series of the trajectories in e. (g) Histograms of estimated diffusion coefficients of all trajectories in the cell. (h) Cumulative probability of the estimated diffusion coefficients under normal (a-d) and stressed (e-g) imaging conditions. 400-500 trajectories with a diffusion coefficient \\(>0.001\\mu \\mathrm{m}^2 /\\mathrm{s}\\) from four cells under each condition are selected.",
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preprint/preprint__07208eea83c232a05dca70cd64270d5ee1a24fdbc00dcd03cf4ddc8b21562a44/preprint__07208eea83c232a05dca70cd64270d5ee1a24fdbc00dcd03cf4ddc8b21562a44.mmd

@@ -0,0 +1,336 @@
+
+# Axial de-scanning using remote focusing in the detection arm of light-sheet microscopy  
+
+Tommy Chakraborty tchakraborty@umn.edu  
+
+University of New Mexico  HASSAN DIBAJI  University of New Mexico  Ali KAZEMI NASABAN SHOTORBAN  University of New Mexico  https://orcid.org/0000- 0002- 8513- 1784  
+
+MAHSA HABIBI  University of New Mexico  
+
+RACHEL GRATTAN  Comprehensive Cancer Center, University of New Mexico Health Sciences Center,  
+
+SHAYNA LUCERO  Comprehensive Cancer Center, University of New Mexico Health Sciences Center,  
+
+DAVID SCHODT  University of New Mexico  
+
+Keith A. Lidke  The University of New Mexico  https://orcid.org/0000- 0002- 9328- 4318  
+
+JONATHAN PETRUCCELLI  Department of Physics, University at Albany- State University of New York  
+
+DIANE LIDKE  Comprehensive Cancer Center, University of New Mexico Health Sciences Center,  
+
+SHENG LIU  University of New Mexico  
+
+Article  
+
+Keywords:  
+
+Posted Date: October 3rd, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3338831/v1
+
+<--- Page Split --->
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: Yes there is potential Competing Interest. T.C. and H.D. have filed a patent application (United States Patent and Trademark Office application number 63/397,714) for the remote focusing setup mentioned here.  
+
+Version of Record: A version of this preprint was published at Nature Communications on June 12th, 2024. See the published version at https://doi.org/10.1038/s41467-024-49291-0.
+
+<--- Page Split --->
+
+# Axial de-scanning using remote focusing in the detection arm of light-sheet microscopy  
+
+HASSAN DIBAJI \(^{1}\) , ALI KAZEMI NASABAN SHOTORBAN \(^{1}\) , MAHSA HABIBI \(^{1}\) , RACHEL M GRATTAN \(^{2,3}\) , SHAYNA LUCERO \(^{2,3}\) , DAVID J. SCHODT \(^{1}\) , KEITH A. LIDKE \(^{1,2}\) , JONATHAN PETRUCCELLI \(^{4}\) , DIANE S. LIDKE \(^{2,3}\) , SHENG LIU \(^{1}\) , AND TONMOY CHAKRABORTY \(^{1,2,*}\)  
+
+\(^{1}\) Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA \(^{2}\) Comprehensive Cancer Center, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, 87131, USA \(^{3}\) Department of Pathology, University of New Mexico Health Science Center, Albuquerque, NM, USA \(^{4}\) Department of Physics, University at Albany- State University of New York, 1400 Washington Avenue, Albany, NY 12222, USA \(^*\) tchakraborty@unm.edu  
+
+Abstract: The ability to image at high speeds is necessary in biological imaging to capture fast- moving or transient events or to efficiently image large samples. However, due to the lack of rigidity of biological specimens, carrying out fast, high- resolution volumetric imaging without moving and agitating the sample has been a challenging problem. Pupil- matched remote focusing has been promising for high NA imaging systems with their low aberrations and wavelength independence, making it suitable for multicolor imaging. However, owing to the incoherent and unpolarized nature of the fluorescence signal, manipulating this emission light through remote focusing is challenging. Therefore, remote focusing has been primarily limited to the illumination arm, using polarized laser light for facilitating coupling in and out of the remote focusing optics. Here we introduce a novel optical design that can de- scan the axial focus movement in the detection arm of a microscope. Our method splits the fluorescence signal into S and P- polarized light and lets them pass through the remote focusing module separately and combines them with the camera. This allows us to use only one focusing element to perform aberration- free, multi- color, volumetric imaging without (a) compromising the fluorescent signal and (b) needing to perform sample/detection- objective translation. We demonstrate the capabilities of this scheme by acquiring fast dual- color 4D (3D space + time) image stacks, with an axial range of \(70 \mu \mathrm{m}\) and camera limited acquisition speed. Owing to its general nature, we believe this technique will find its application to many other microscopy techniques that currently use an adjustable Z- stage to carry out volumetric imaging such as confocal, 2- photon, and light sheet variants.  
+
+## MAIN  
+
+Fast 3D positioning or scanning of an optical system's focal point or focal plane has the potential to transform many areas of BioPhotonics, especially those that require studying the complex dynamics of living organisms. Processes like investigation of neuronal activities of the brain, blood flow in the heart, and cell signaling require high- speed volumetric imaging \(^{1 - 3}\) . However, volumetric imaging requires an axial scan either through the translation of the sample or the detection objective lens (Fig. 1a). Such axial translations result in imaging modalities that are often slow with speeds limited to a few hundred \(\mathrm{Hz}^{4 - 6}\) . Additionally, with fragile samples, such as an expanded sample in hydrogel \(^{7}\) , fast movements of the sample stage may agitate the sample and induce distortions when collecting volumetric images. To avoid the slow translation of bulky objectives or the sample stages, several attempts, employing variable- focus (vari- focus) lenses, mechanical mirrors, and acousto- optics modulators have been proposed to refocus the light for 3D imaging. However, they all suffer from unacceptable aberrations introduced by the focusing elements. A large category of those techniques utilize different types of tunable lenses such as ferroelectric liquid crystal (LC), acoustic waves (TAG lens), and acoustic optics modulators (AOM) \(^{8}\) to achieve fast focal shifts (~1kHz). Ferroelectric LC and TAG lenses introduce a focal shift by varying the gradient of the refractive index of the liquid medium, however, the generated phase variation only approximates the defocus phase, leading to increased spherical aberration at large focal shifts \(^{9 - 11}\) . AOM- based vari- focus techniques on the other hand use two AOMs with counterpropagating acoustic waves to cancel out the transverse scan but can only achieve focus shift in one dimension (acting as a cylindrical lens) \(^{12,13}\) .  
+
+Adaptive optics- based vari- focus techniques overcome these limitations through accurate wavefront control using either a spatial light modulator (SLM) or a deformable mirror (DM), which can achieve a response rate of ~1 kHz and 20 kHz respectively. However, SLMs are polarization and wavelength- dependent and cannot model a continuous wavefront of the defocus phase due to its limited phase modulation depth. Large phase shifts are generated through multiple phase- wrapping of \(2\pi\) . With finite fly- back at the phase- wrapping borders, part of the incident light is not correctly modulated and results in decreased intensity at the focus \(^{14}\) . DMs are not polarization and wavelength- dependent and can model a continuous defocus wavefront. However, the axial scan range of a DM is limited by the
+
+<--- Page Split --->
+
+stroke length of the DM actuators. For example, for an objective with a numerical aperture (NA) of 0.8, the maximum axial scan range that DM based techniques can generate is \(- 40 \mu \mathrm{m}^{15}\) . Furthermore, using DM for focus control requires accurate alignment and complicated calibration of the DM to reduce the aberrations caused by imaging samples out of the nominal focal plane of the objective<sup>9</sup>.  
+
+Unlike the adaptive optics or DM- based approaches that require correcting the defocus plane- by- plane, pupil- matched remote focusing (pmRF), pioneered by Botcherby et al.<sup>16,17</sup>, instantaneously corrects defocus across 3D volumes for high- NA optics thereby conserving the microscope's temporal bandwidth<sup>16- 26</sup>. In addition, because pmRF allows precise mapping of the wavefront coupled into the back- pupil of the objective, where the angular magnification is unity, such techniques have been routinely used to carry out aberration- free high- quality axial focus control<sup>16- 26</sup>. In pmRF techniques, a fast axial scan is achieved by the translation of a small mirror in front of the remote objective using a focus actuator<sup>18,19,23</sup> or by a lateral scan of a galvo mirror in combination to a step or tilted mirror at the remote objective<sup>27</sup>. Because of the fast response time of the focus actuator or the galvo mirror, an axial scan rate of 1- 5 kHz or 12 kHz can be achieved respectively. However, current pmRF techniques for focus control are primarily limited to the illumination path. This is because pmRF uses the concept of optical isolators<sup>28</sup>, where the polarization of the returning beam is rotated orthogonally to the incoming beam so that it can be separated from the incoming beam at the polarized beam splitter (PBS) (Supplementary Fig. 1a). This configuration ensures minimum light loss through the pmRF module but requires the incoming beam to be polarized, which is why this method is primarily used in the illumination arm where illumination laser light is usually polarized in nature and its manipulation through the optical isolator can be easily done. In the detection arm, however, the emitted fluorescence is unpolarized in nature. To the best of our knowledge, because, using purely linear optical elements, lossless conversion of unpolarized light into a single polarized state is not yet possible<sup>29,30</sup> (Supplementary Note 1), manipulating the fluorescent light using the optical isolators is unfeasible. As a result, microscopes that use pmRF to carry out axial scanning, incur 50% light loss due to one state of the polarized light being discarded after the PBS<sup>16,21,24</sup> (Supplementary Fig. 1a).  
+
+A straightforward method to mitigate this problem is to have another copy of the pmRF module at the unused port of the PBS (Supplementary Fig. 1b) to collect the other half of the fluorescent light. However, this would require precise synchronization of two linear- focus- actuators (LFA), which is not only a difficult task at high speeds but also will be expensive since this method warrants two such LFAs. In this article, we present a novel optical design that overcomes these problems and presents a modular setup that can perform remote focusing on the detection arm of a fluorescent microscope without incurring polarization- induced losses. When attached to a light- sheet microscope, this technique allows optical refocusing without requiring the movement of the sample, or the detection objective (Fig. 1b and Supplementary Fig. 1c). As a result the microscope can acquire 3D volumetric data limited by camera speed. This technique is applicable to many other microscopy techniques that currently use an adjustable \(Z\) - stage to carry out volumetric imaging such as confocal, 2- photon, and light sheet variants.  
+
+## Results  
+
+## Concept and microscope layout  
+
+Optical axial- refocusing: Our refocusing unit is shown in Fig. 1b. Here, the water immersion detection objective (Obj1) is pupil matched to a second air objective (Obj2) through two intermediate lenses following the original design by Botcherby et al.<sup>16,17</sup>. However, unlike traditional refocusing geometry, we split the collected unpolarized fluorescence into S and P- polarized light using a polarizing beam splitter cube (PBS) in the infinity space of Obj2. The generated orthogonal paths are then projected onto Obj2 using two angled mirrors M1 and M2. Because of this angular launch in infinity space, Obj2 forms two distinct laterally shifted images at its nominal focal plane. A small mirror placed on an LFA reflects the light back through the path it came from where a quarter wave plate (QWP) converts the S- polarized light to P on its way back (and P- polarized light to S) after being reflected from the mirror (Fig. 1c). When the returning light (in each arm) reaches the PBS, it now acts as an optical valve where the S path (which was initially P) gets reflected while the P- polarized light (which was initially S) gets transmitted by the PBS. As a result, both S and P polarized light exits the PBS through the fourth and unused face of the PBS cube (Fig. 1d). This light after passing through a tube lens forms identical images, one with S and another with P, at the sCMOS camera. A precise alignment using mirrors M1 and M2 overlays the two images, thereby resulting in a combined image by simply an incoherent addition without any interference artifacts.  
+
+There are a few important design considerations that need to be considered for our de- scanning setup. Firstly, it is essential that mirror M3 consistently moves in parallel with the focal plane of Obj2 during the LFA's oscillatory motion. This prevents any unwanted focal shifts between the S and P paths, ensuring that the resulting image from
+
+<--- Page Split --->
+
+both S and P polarizations remain focused on the camera at the same time. This arrangement ensures that both beams return through their incoming paths, resulting in easier alignment for overlaying the final images formed by the S and P- polarized beams.  
+
+Secondly, it is advantageous that 0 (angle between S and P polarized beam hitting the Obj2) (Supplementary Fig. 2) be as small as possible because this directly controls the distance between the two focal points at M3 (depicted by \(\Delta L\) in Fig. 1c). A smaller \(\Delta L\) ensures: (1) a smaller mirror could be utilized to carry out the remote- focusing, reducing the inertial load on the LFA, and enhancing its efficiency; (2) The alignment becomes less sensitive to tip- tilt misalignment of M3; and (3) This guarantees that both images fit within Obj2's field of view (FOV).  
+
+Thirdly, there exists an inverse relationship between the angle \(\theta\) and the distance between Obj2 and the PBS (inset of Supplementary Fig.2). Therefore, this gives us an option: either adhere to the 4f system or minimize \(\theta\) . We found that for our matching objectives Obj1 and Obj2 the 4f system (with matching lenses L1 and L2) resulted in a \(\theta\) of \(20^{\circ}\) (inset of Supplementary Fig.2). However, operating in this range poses a risk as it is challenging to ensure that both reflected beams are entirely captured by Obj2. Hence, there is a balance between adhering to the 4f system and minimizing the angle \(\theta\) . We found that with our current design, we can still achieve diffraction limited resolution (Fig. 1e).  
+
+Finally, because we generated two identical images on the camera using S and P- polarized light, it was crucial to overlay these images with precision higher than the diffraction- limited resolution to produce the final image. To do this, we developed a cross- correlation- based algorithm that quantifies the shift between overlayed S and P images in real- time with sub- pixel accuracy, allowing interactive adjustment of the mirrors M1 and M2 during system alignment.  
+
+Implementation in a light- sheet system: In order to test the performance of our design we implemented this setup into the detection arm of a light- sheet microscope with orthogonal illumination and detection objectives. The system layout is shown in (Fig.1b and Supplementary Fig.2). The sample is illuminated by a sheet of light generated with a cylindrical lens in the illumination arm, and the emitted fluorescence from the sample is collected by the detection objective lens, which is set orthogonal to the illumination objective lens to capture 2D information from the sample. A galvanometric scan mirror (GSM) in the illumination arm translates the light- sheet in the Z- direction. Because the position of the LFA in the detection arm determines the focal plane of the detection objective lens, we synchronized the GSM and LFA with the sawtooth signal to ensure that the detection path is always focused on the plane of the light- sheet (Supplementary Fig.3). This allowed us to carry out volumetric imaging by acquiring a sequence of images from different focal planes. The LFA moves back and forth rapidly, synchronized with the movement of the GSM enabling us to quickly collect 3D image stacks.  
+
+The optical correction of defocus in our high- NA microscope allowed fast de- scanning of a 3D volume over an axial range of \(\sim 70 \mu \mathrm{m}\) at speeds limited primarily by the camera framerate ( \(\sim\) in our case 799 camera frames/s at \(2304 \times 256\) pixels using Hamamatsu Orca- fusion BT). We employed a dual- color imaging strategy by partitioning the FOV, enabling simultaneous capture of two distinct fluorescent labels within each slice without sacrificing imaging speed. To do this we used a pair of dichroic mirrors to separate the emitted wavelengths from the two labels into side- by- side dual- color images (Supplementary Fig.2). Once acquired, these separate image sets are then precisely registered and merged to generate 4D (X, Y, Z, and \(\lambda\) ) stacks. By sequentially capturing 4D stacks, we generated 5D (X, Y, Z, \(\lambda\) , and time) datasets that allowed us to track the dynamic behavior of biological processes. It is important to note that our setup is wavelength- independent, an attribute not feasible with technologies like diffractive tunable lenses or spatial light modulators.  
+
+## Characterization of the optical system  
+
+To understand the image formation of the proposed setup, we simulated the ray tracing of the detection path (Fig. 2a). The ray tracing assumes all rays satisfy paraxial approximation and all lenses are simple lenses. The detection objective is a water immersion objective, we calculated its effective focal length as \(f_{\mathrm{obj}} = f_{\mathrm{Tube}} n / M_{\mathrm{obj}}\) , where \(f_{\mathrm{Tube}}\) is the focal length of the designed tube lens, \(M_{\mathrm{obj}}\) is the magnification of the objective, and \(n\) is the refractive index of water. Here we have \(f_{\mathrm{obj}}\) equal to 6.65 mm. The pmRF module (from the beam splitter to LFA) is modeled two times to simulate the forward and backward transmission through the module. The LFA is omitted from the simulation, instead, we change the distance between the two copies of the pmRF objectives so that the distance \((S_{3})\) of the image plane to the second pmRF objective remains as a constant. We simulated with an object of \(100 \mu \mathrm{m}\) , the image size after the pmRF objective is \(\sim 140 \mu \mathrm{m}\) , indicating a lateral magnification of 1.4, which is close to the requirement of perfect imaging with \(M_{\mathrm{lateral}} = n_{\mathrm{water}} / n_{\mathrm{air}} = 1.33\) . The small deviation is limited by the geometry of the pmRF
+
+<--- Page Split --->
+
+module: the separation \((\Delta L)\) of the S and P- images formed by the pmRF objective is approximate to \(\Delta L = f_{\mathrm{RFobj}}\theta\) where \(f_{\mathrm{RFobj}} = 10 \mathrm{mm}\) is the effective focal length of the RF objective and \(\theta\) is the angle between the S and P- polarized rays meeting at the RF objective. The larger the \(\Delta L\) , the larger the aberration introduced by the pmRF objective. To reduce \(\Delta L\) , the pmRF objective is located \(\sim 500 \mathrm{mm}\) from the PBS, therefore, the pmRF module is no longer an exact 4f system, the magnification, \(M_{\mathrm{lateral}}\) , varies with the axial position of the object. Furthermore, the beam path from the detection objective to the tube lens is also not a 4f system, where the tube lens is \(\sim 100 \mathrm{mm}\) away from the detection objective. The combination of the two non- 4f systems can partially reduce the axial dependence of the magnification. Fig. 2b shows the change of the lateral magnification with respect to the galvo position (the axial position of the light sheet) from both ray tracing and the experimental data. There is a \(\sim 5\%\) magnification change over an axial range of \(80 \mu \mathrm{m}\) . This magnification change can be further reduced by optimizing the axial position of the tube lens.  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1: Schematic diagram of a remote focusing system implemented in light-sheet microscopy and its performance. a) Three different modalities to acquire volumetric imaging of the sample along the focus direction. Either the sample or objective lens can be moved for axial refocusing. Alternatively, both the sample and objective lens can remain stationary by using a remote focusing system. b) Implementation of the remote-focusing system on the detection arm of the light sheet microscope. In this configuration, objective lenses 1 and 2 are pupil-matched through two lenses to form a perfect imaging system. Combined with mirror M3 and a polarizing beam splitter (PBS), the whole system works as a remote focusing system. The novel design of this remote-focusing system is implementation in the detection arm for unpolarized fluorescent light emitted from the sample. To do this, two tilted mirrors M1 and M2 are utilized to direct both S and P-polarized beams toward Objective lens 2 and then combine the reflected beams from mirror M3 to create an image by S and P-polarized beams onto the camera by focusing through the tube lens. The mirror M3 is attached to the linear focus actuator (LFA), moving back and forth to scan the sample in the Z-direction to acquire a 3D image. In the illumination arm, the generated light sheet by a cylindrical lens is translated by a galvanometric scan mirror (GSM) along the detection arm. To focus the detection path on the plane of the light sheet, the synchronization of GSM and LFA is carried out by sawtooth signals. Simultaneous dual-channel imaging of the cell is achieved in \(40 \mu \mathrm{m} \times 150 \mu \mathrm{m}\) FOV over \(70 \mu \mathrm{m}\) in the Z-direction. c) The polarization state of the incoming beams changes after reflection from mirror M3 (S to P, and P to S). d) The reflected beams from mirror M3 have a different polarization state compared to the incoming beams; therefore, they exist from a different side of the PBS than the incoming beams. e) The point spread function (PSF) of 200 nm beads formed by S, P, and S+P polarized beams. The microscope performs at the diffraction limit, \(394 \mathrm{nm}\) resolution, for S, P, and S+P in the lateral directions (X-Y), while it maintains a resolution of \(654 \mathrm{nm}\) in the axial direction (Z). </center>
+
+<--- Page Split --->
+
+To quantify the performance of the proposed scheme, we used full width at half max (FWHM) measurements of 3D point spread function (PSF) to validate that the incoherent addition of S and P images was not compromising the resolution. To do this, we measured the PSF of each polarization component individually and compared it with the PSF of the unified S+P image. As illustrated in Fig.1e, both the S and P- polarized images rendered onto the camera exhibit identical FHWM, resulting in an equivalent resolution for the combined S+P image. Further quantification involving 10 randomly chosen beads, reveals that the microscope achieved diffraction- limited resolutions: \(394 \pm 31 \mathrm{nm}\) laterally (X- Y) and \(654 \pm 130 \mathrm{nm}\) axially (Z). These measurements were performed in proximity to the nominal focal plane (MIP of 10 slices, each separated 500 nm).  
+
+To evaluate the performance of the de- scanning system, we imaged 3D volumes of \(200 \mathrm{nm}\) beads embedded in a \(2\%\)  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2: Ray tracing of the setup and resolution assessment. a) Ray tracing of the detection path. L: image size, f: effective focal length, S: image or object position relative to the lens, unit: mm. b) Calibration of lateral magnification at various object positions, a target illuminated by a white light LED is imaged for magnification measurement. c) Maximum intensity projections of data acquired on \(200 \mathrm{nm}\) beads from 10 slices spaced \(500 \mathrm{nm}\) in the Z-direction. The images show orthogonal views of the MIPs across scan range for S,P and S+P. The elongated PSF in the Z direction exhibits less resolution in the axial direction controlled by the light sheet waist. d) The FWHM of the \(200 \mathrm{nm}\) beads in the lateral and axial directions over the scan range. The minimum lateral resolution, \(394 \mathrm{nm}\) , occurs at the center of the scan range and increases by moving away from the center. These plots show a constant axial resolution of \(650 \mathrm{nm}\) over the axial scan range. The microscope functions in the scan range of \(70 \mu \mathrm{m}\) . </center>  
+
+agarose cube across the scan range and accessed the quality of the generated PSFs. Fig. 2c shows the maximum intensity projection (MIP) of beads (from 10 axial slices, each slice spaced \(500 \mathrm{nm}\) ) separated by \(30 \mu \mathrm{m}\) for S, P, and S+P across the scan range, after 10 iterations of Richardson- Lucy (RL) deconvolution. We found that our remote focusing setup demonstrated close to diffraction- limited performance over a scan range of \(\sim 70 \mathrm{um}\) . As evident from
+
+<--- Page Split --->
+
+the 'S' and 'P' images the quality of the beads visually appears similar across the entire scan range thereby resulting in an identical 'S+P' image. In the axial direction (the \(YZ\) view) the PSFs are limited by the Gaussian light sheet's waist (beads from red boxes in \(XY\) view), which was determined by the tradeoff that exists between the FOV and \(Z\) resolution. We found that in order to image an entire cell, we needed a lightsheet that would generate a FOV of \(\sim 8\) \(\mu \mathrm{m}\) (Supplementary Fig. 4). As a result, we reduced the NA of the illumination objective and chose a light sheet whose waist was at FWHMz of \(\sim 650 \mathrm{nm}\) after deconvolution (850 nm before deconvolution).  
+
+Figure 2d displays the measured FWHMs from \(200 \mathrm{nm}\) beads after RL deconvolution for S, P, and S+P polarize images in the lateral (XY) and axial (Z) directions across the entire scan range. The figure shows a minimum lateral FWHM of \(394 \mathrm{nm}\) at the center of the scan range which slowly increases as the beads move away from the nominal focal plane. This can be attributed to residue index mismatch aberrations that were not corrected by the remote focusing system<sup>21</sup>. Additionally, we found that the S polarization path suffered more in lateral resolution compared to the P polarization path and the trend is different along \(X\) and \(Y\) directions. This asymmetric FWHMs (X-Y) across scan range (Z) and the discrepancy between S and P paths is likely due to field- dependent aberrations from Obj2, where the S and P images were formed at different field points of Obj2 (Fig. 1b). Furthermore, our microscope shows a constant axial FWHM of \(\sim 650 \mathrm{nm}\) over the entire scan range as the axial resolution is mainly determined by the lightsheet waist.  
+
+## Fast 3D live cell imaging  
+
+As a first demonstration of the 3D cellular imaging capabilities, we monitored the 3D motion of secretory granules in living mast cells. Mast cells possess distinct secretory granules that contain the mediators of the allergic response and are released upon mast cell activation by allergen<sup>31</sup>. These granules are distributed across the cytosol and have been shown to undergo both Brownian diffusion and directed motion<sup>31</sup>. Upon activation of the membrane receptor, FcεRI, via crosslinking by multivalent antigen<sup>32,33</sup>, the granules undergo increased directed motion that moves them to the plasma membrane where they will fuse and release mediators that regulate allergic responses<sup>31,34</sup>.  
+
+We applied the developed system for dual- color, volumetric imaging of live cells and tracked the 3D motion of green fluorescent protein- labeled Fas ligand (GFP- FasL) loaded secretory granules in the cytosol of RBL- 2H3 mast cells<sup>31</sup>. IgE- bound FcεRI was simultaneously imaged by addition of anti- DNP IgE- CF640R. With addition of the antigen- mimic, DNP- conjugated to BSA (DNP- BSA), FcεRI aggregates and undergoes endocytosis as seen in Figure 3a. During data acquisition, the light sheet is parallel to the \(XY\) plane and scans along the \(Z\) direction. Within the lightsheet region, the \(XY\) and \(XZ\) maximum intensity projections (Fig.3a) of the cell image show GFP- FasL granules in three dimensions. The cells were imaged at \(\sim 0.6\) volumes \((80 \times 15 \times 40 \mu \mathrm{m}^3\) in \(XYZ\) per second for 80 volumes, for a total imaging time of \(\sim 2\) minutes (Fig.3a- d). To quantify the granule dynamics, isolated granules were identified and tracked in 3D using the U- track3D software<sup>35</sup>. We calculated the mean square displacement (MSD) of each trajectory over time and extracted the diffusion coefficient, \(D\) , and velocity, \(v\) , by fitting the MSD curve with \(MSD(t) = 6Dt^2 + v^2 t^2 + o\) , where \(o\) is an offset related to localization and tracking uncertainties<sup>36,37</sup> (Fig.3c,d). We found that most granules undergo Brownian Diffusion and a few exhibited directed motion, consistent with granules being transported along the microtubules (Fig.3a,b)<sup>31</sup>. The measured transport velocities of the two trajectories indicated in Fig.3a,b are \(\sim 0.1 \mu \mathrm{m / s}\) , consistent with previous work that performed tracking in 2D<sup>31</sup>.  
+
+To test the limits of the new system in terms of speed, we set out to image Brownian motion on the microscopic level. For this, we stressed the cells by incubating them in Hank's balanced salt solution (HBSS) (Method) at room temperature for over 1 hour, which induced cell blebbing. This also caused more rapid diffusion of the granules that we were able to capture using an imaging speed of \(\sim 8.3\) volumes/s for 80 volumes for a total time of \(10 \mathrm{s}\) . With this imaging speed, we retained good signal- to- noise and the ability to track the 3D motion of individual granules (Fig 3e- g). Under these non- physiological conditions, average granule diffusion was increased by \(\sim 41\) times (Fig.3h). Two tracks shown in Fig. 3e have diffusion coefficients of \(0.41 \mu \mathrm{m}^2 / \mathrm{s}\) and \(0.64 \mu \mathrm{m}^2 / \mathrm{s}\) .
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3: Dual-Color volumetric imaging of live RBL cells. (a-d) Dual-color volumetric imaging of granule motions in a live RBL-2H3 GFP-FasL cell, where the cell membrane is labeled with IgE-CF640R and granules contain GFP-FasL, at an imaging speed of \(\sim 0.6\) volumes \((80\times 15\times 40\) \(\mu \mathrm{m}^3\) in XYZ) per second for 80 volumes, for a total imaging time of \(\sim 2\) minutes. (a) Maximum intensity projection views of the cell images at one-time point and overlay with representative trajectories of granule movement (orange lines). (b) Time series of the trajectories in a. (c, d) Histograms of estimated diffusion coefficients and velocities of all trajectories found in cell 1 and cell 2. (e-g) Dual-color volumetric imaging of live RBL-2H3 GFP-FasL cell, where the cell membrane is labeled with CellMask DeepRed and the granules contain GFP-FasL using an imaging speed of \(\sim 8.3\) volumes/s for 80 volumes for a total time of \(10\mathrm{s}\) . (e) Maximum intensity projection views of the cell images at one-time point and overlay with representative trajectories of granule movement (orange lines). (f) Time series of the trajectories in e. (g) Histograms of estimated diffusion coefficients of all trajectories in the cell. (h) Cumulative probability of the estimated diffusion coefficients under normal (a-d) and stressed (e-g) imaging conditions. 400-500 trajectories with a diffusion coefficient \(>0.001\mu \mathrm{m}^2 /\mathrm{s}\) from four cells under each condition are selected. </center>
+
+<--- Page Split --->
+
+## Discussion  
+
+In this work, we developed an axial scanning module in the detection path of a light- sheet microscope utilizing the pmRF technique proposed by Botcherby et al.16,17. While inheriting all the benefits from the pmRF technique, such as fast scanning and all- optical aberration compensation (no wavefront control element), our design overcomes a critical limitation of the original pmRF technique, as in, the loss of \(50\%\) of the emitted fluorescence in the detection path21,24,38. Here we engineered a new optical design, where we split the emitted fluorescence into S and P polarized light to carryout remote focusing and then seamlessly combine them to achieve minimum light loss. We demonstrated our implementation of the developed scanning module through a light- sheet microscope with two orthogonally arranged objectives. We can perform simultaneous two- color imaging at 8.3 volumes ( \(80\times 15\times 40\mu \mathrm{m}^{3}\) in XYZ) per second with a lateral resolution of \(394\mathrm{nm}\) and an axial resolution of \(650\mathrm{nm}\) (after deconvolution). As our method is fully optical, the imaging speed scales with advancements in LFA technology and camera acquisition speed.  
+
+The S and P polarized beams are directed at an oblique angle into the remote objective (Fig. 1b). This angled approach creates two separate images at the mirror attached to the LFA (M3). However, there are limitations to this angular arrangement. The two images formed away from the optical axis are prone to aberrations. To reduce the image separation, the remote objective must be positioned further from the PBS to reduce the incident angles of S and P- polarized lights. However, this increased distance breaks the 4f configuration between the two objectives (detection and remote objectives) that is critical to achieving aberration- free imaging. Future studies will investigate into more compact designs that will better satisfy the 4f condition and will reduce the separation between the two foci at M3.  
+
+Of note, our approach offers several advantages over the existing axial refocusing methods. First, it provides an extended, aberration- free scan range for high numerical aperture (NA) optics. This is a significant benefit when compared to techniques based on deformable mirrors (DMs), where our method approximately doubles the axial scan range of DMs15. Second, it is wavelength independent, which makes it suited for simultaneous multicolor imaging when compared to SLMs and tunable lenses. Additionally, unlike SLMs which depend on polarization, our arrangement is not dependent on the polarization of the fluorescence. Furthermore, unlike SLMs, which are typically slow (especially the nematic liquid crystal ones), and even their faster counterparts (ferroelectrics) tend to be less effective, our method allows for imaging speed that are only limited by the sCMOS's framerate.  
+
+Although recent advancements in single- objective oblique plane microscopy (OPM) have achieved speeds comparable to our method, our technique presents several notable advantages. In OPM, the de- scanning of the returning fluorescent light leads to skewed images. Before these images can be viewed, they require intensive de- skewing processes23,39- 43. On the other hand, our approach captures 3D volumes in a conventional orthogonal setup. This is achieved by recording high- speed images while sweeping the light- sheet through the sample. Each frame captured by the camera represents an optical cross- section of the specimen. As a result, the 3D image stacks generated using our method are immediately available for viewing. They may benefit from an optional deconvolution, but there's no delay caused by necessary post- processing. Furthermore, the OPM setup necessitates a third objective, which in the latest setups require expensive objectives like 'Snouty' or 'King Snout'2,39- 42. Our setup on the other hand does not have this requirement and our secondary objective performs the role of a tertiary objective. Moreover, while not demonstrated explicitly here, our method can be employed to achieve isotropic resolution, a feat the OPM cannot achieve.  
+
+Compared with the original Botcherby's remote focusing setup, our pmRF module folds the beam path between the detection and the remote objectives. This configuration complicated the optical alignment. A potential solution is to arrange both objectives inline in a 4f configuration. Furthermore, we note that although an all- optical design has its merit of simplicity and robustness, using an objective lens in the pmRF module introduces \(\sim 30 - 40\%\) light loss (Supplementary Fig.5) compared with the axial scanning techniques based on DMs, future development of objective with high- transmission efficiency is desirable.  
+
+Finally, it is our firm belief that owing to its generalized design, we envision our method has the potential to transform many popular microscope modalities like confocal, 2- photon, and the rapidly emerging field of light sheet microscopy, by reinventing how they perform scanning in the axial dimension.  
+
+## Acknowledgements  
+
+This work was supported by University of New Mexico (Start- up Grant) (TC), NIH R35GM151152 (TC), NIH P30CA118100 (TC and KL) and NIH R35GM126934 (DSL). We thank Derek Rinaldi for generating the IgE
+
+<--- Page Split --->
+
+CF640R. This work was conducted with support from the University of New Mexico Office of the Vice President for Research Program for Enhancing Research Capacity, was supported by grants from NVIDIA and utilized an NVIDIA A6000 GPU.  
+
+## Author contributions  
+
+T.C. conceived the idea of lossless remote focusing in detection arm. H.D. and T.C. designed and built the remote focusing unit. H.D. and T.C. designed, built, and operated the microscope. H.D. and Sh.Li performed image analysis. Sh. Li and J.P. have theoretically demonstrated that achieving \(100\%\) conversion from unpolarized to polarized light is not feasible. D.J.S and K.A.L provided the MATLAB code for the fine alignment. H.D., T.C. and M.H. designed the chamber and sample holder. D.S.L., Sh.Lu., and R.M.G prepared RBL cells for imaging. H.D. imaged RBL cells labeled with DeepRed CellMask. H.D. and A.K.N.Sh imaged the RBL cells labeled with IgE- CF640R. H.D., Sh.Li., and T.C. wrote the manuscript. All authors read and provided feedback on the final manuscript.  
+
+## Competing interests  
+
+T.C. and H.D. have filed a patent application (United States Patent and Trademark Office application number 63/397,714) for the remote focusing setup mentioned here.  
+
+## Methods  
+
+## Optical setup  
+
+The illumination arm consists of two laser sources (Coherent Sapphire \(488~\mathrm{nm}\) and Obis LX \(637~\mathrm{nm}\) ) which were combined with a dichroic beam splitter (LM01- 503- 25, Semrock). To clean up the beams, the beams were focused through a \(50 - \mu \mathrm{m}\) pinhole (P50D, Thorlabs) by a \(45 - \mathrm{mm}\) achromatic doublet (AC254- 045- A, Thorlabs) and then recollimated using a \(150 - \mathrm{mm}\) achromatic doublet (AC254- 150- A- ML, Thorlabs). The original beams were expanded by 9 folds with a \(3\times\) Galilean beam expander (GBE03- A) before being focused with a cylindrical lens (ACY254- 50- A, Thorlabs), onto a resonant mirror galvanometer (CRS \(4\mathrm{kHz}\) , Cambridge Technology), driven by a 12- volt power supply (A12MT400, Acopian), to wobble the light sheet. One- dimensional focus was then recollimated with a 100- mm achromatic doublet (AC254- 100- A- ML, Thorlabs) and hit the galvanometric scan mirror (GSM) (GVS111, Thorlabs), driven by a 15- volt power supply (GPS011, Thorlabs), for rapid shifting of the light sheet along the detection arm. This galvanometric mirror was conjugated to the back pupil of the objective lens (Nikon \(40\times 0.8\mathrm{NA}\) ) through \(100 - \mathrm{mm}\) and \(200 - \mathrm{mm}\) achromatic doublet (AC508- 100- A- ML and AC508- 200- A- ML, Thorlabs).  
+
+In the detection arm, the same objective lens (Nikon \(40\times 0.8\mathrm{NA}\) ) in an orthogonal setup was used and pupil- matched to the scanning objective lens (Nikon Plan Apo \(20\times 0.75\mathrm{NA}\) ) through a \(200 - \mathrm{mm}\) tube lens (TTL200- A, Thorlabs) and a \(300 - \mathrm{mm}\) achromatic doublet (AC508- 300- A- ML, Thorlabs). A \(50:50\) polarizing beam splitter (PBS) (10FC16PB.3, Newport), splits the beam in S and P polarized light. Using mirrors M1 and M2 these light paths where then launched at an angle towards the Obj2 (Supplementary Fig.2). It is extremely critical to minimize the angle of the launch. Both experiment and simulation predicted that we used 8 degrees as the launch angle (called 0) (Fig.2a, inset of Supplementary Fig.2). The S and P polarized light passed through a quarter waveplate (AQWP10M, Thorlabs) and were focused onto a mirror positioned at the focus of the scanning objective lens. The mirror (PF03- 03- P01 - 07.0 mm Protected Silver Mirror, Thorlabs) was attached to a voice coil with a travel of \(10\mathrm{mm}\) , positional repeatability of fewer than 50 nanometers, and a response time of fewer than 3 milliseconds (LFA- 2010, Equipment Solutions). Then the reflected light was recaptured by the same scanning objective lens and quarter- wave plate to rotate the beam's polarization state. Afterward, the light was directed toward an sCMOS camera (Hamamatsu Orca- fusion BT) by reflecting from the same cube polarizing beam splitter and a \(300 - \mathrm{mm}\) achromatic doublet (AC508- 300- A- ML, Thorlabs). For emission filters, we used two long- pass filters (FF01- 525/30- 25, and BLP01- 647R- 25, Semrock), for blue, and far- red, respectively. To image dual channels simultaneously, the field of view (FOV) was separated into half using dichroic mirrors (DMLP605R, Thorlabs) between the \(300 - \mathrm{mm}\) achromatic doublet and the camera. We immersed the specimen and the illumination and detection objectives in a chamber designed using Adobe Inventor and machined through Protolabs (R). The LFA and GSM, in the detection and illumination arms respectively, were synchronized together to always keep the translated light sheet in the focus of the detection objective lens to acquire a 3D stack of the specimen.
+
+<--- Page Split --->
+
+## Overlaying S and P images with sub-pixel accuracy  
+
+Two identical images - - one corresponding to S and another to P polarized light - - are formed at the camera and added incoherently to generate the final image. We used a custom- written MATLAB script to monitor the offset between the two images in near real- time while adjusting the positions of M1 and M2 (Supplementary Fig.6).  
+
+The offset between the two images using a cross- correlation- based algorithm as was used in Wester, M.J. et al44, which achieves sub- pixel accuracy by fitting second- order polynomials through the peak of the scaled cross- correlation between the S and P polarized images.  
+
+Initially, an image is acquired as a reference by obstructing one optical path (either S or P). Subsequently, the alternative optical path is used to collect new images. The shift between each new image and the reference image is then measured using the method described in Wester, M.J. et al44 and is available as the MIC_Reg3DTrans.findStackOffset method in the matlab- instrument- control toolbox45. And while new images are collecting, mirrors M1 and M2 are adjusted to minimize the shift.  
+
+## Microscope control  
+
+A Dell Precision 7920 computer with two processors Intel(R) Xenon(R) Silver 4210R CPU having a processing speed of 2.40 GHz and \(2.39\mathrm{GHz}\) and was integrated with 128 GB RAM was used to acquire the microscope's data. An NVIDIA Quadro RTX 4000 Graphics processing unit (GPU) with dedicated memory of 8 GB and shared memory of 63.8 GB (GPU memory of 71.8 GB) was also integrated into the system. 64- bit operating system \(\times 64\) - based processor facilities the system to operate. LabView 2020 64- bit allowed us to work with the required software, including the LabView Run- Time Engine, Vision Run- Time Module, Vision Development Module, and other required drivers like NI- RIO drivers (National Instruments). DCAM- API software was used for the Active Silicon Firebird frame- grabber to actively interfere with the scientific complementary metal- oxide semiconductor (sCMOS) camera (ORCA- Fusion BT Digital CMOS camera, model: C15440- 20UP) manufactured by Hamamatsu, Japan. It generated deterministic transistor logic (TTL) trigger sequences through 150 Watts shutter instrument (100- 240 V\~50/60 Hz; model: MP- 285A) with a field programmable gate array (FPGA) (PCIe 7852R, National Instruments). The generated triggers controlled the resonant mirror galvanometers, placement of the stage, voice coils, blanking and modulation of laser, firing camera, and other external triggers. K- Hyper Terminal software facilitated engaging LFA with the system hardware. Some key features along with some routines under the agreement of material transfer were licensed by the Howard Hughes Medical Institute's Janelia Farms Research Campus.  
+
+## Sample preparation  
+
+Bead sample:200 nm beads embedded in \(2\%\) agarose gel was used for microscope resolution assessment. To make \(2\%\) agarose gel, 2 g of agarose powder (A9045- 25G, SIGMA life science) was mixed with \(100\mathrm{mL}\) water and swirled thoroughly before putting into the microwave oven to heat. Once the solution boiled and got completely clear and the agarose was dissolved, we should remove the solution from the oven and let it cool down. Then, \(200\mathrm{nm}\) beads (YG, Polysciences) were mixed with water with a ratio of \(1 / 100\) to form a solution of the \(200\mathrm{nm}\) beads. It was sonicated before mixing with the molten \(2\%\) agarose gel with a volumetric ratio of \(1 / 10\) . Then this molten combination was poured into the cubic mold where the sample holder was placed there and sat there for a few minutes to dry and form a \(1\mathrm{cm}^3\) cubic sample (200 nm beads embedded into \(2\%\) agarose gel) attached to the sample holder.  
+
+Cell samples: RBL- 2H3 GFP- FasL cells were cultured in Gibco Minimum Essential Media (MEM) media supplemented with \(10\%\) heat- inactivated Fetal Bovine Serum (FBS), \(1\%\) Penicillin/Streptomycin, and \(1\%\) L- glutamine \(^{31}\) . The cells were primed with \(1\mu \mathrm{g / ml}\) anti- DNP- IgE \(^{46}\) (Fig. 3e- g) or anti- DNP- IgE- CF640R (Fig. 3a- d) and seeded at a density of \(100,000\) cells per well in 12 well dish over \(5\mathrm{mm}\) glass coverslips and incubated with \(5\%\) \(\mathrm{CO_2}\) at \(37^{\circ}\mathrm{C}\) overnight. IgE- CF640R was prepared using CF640R NHS- ester (Biotium #92108). For fast imaging experiments, the cellular membranes of anti- DNP- IgE primed cells were labeled with CellMask™ Deep Red Plasma Membrane Stain (Thermo Fisher Scientific #C10046, \(5\mathrm{mg / ml}\) , 1000X) according to manufacturer's instruction for 10 minutes in modified Hank's balanced salt solution (HBSS) (additional \(10\mathrm{mM}\) Hepes, \(0.05\%\) w/v BSA, \(5.45\mathrm{mM}\) glucose, 0.88
+
+<--- Page Split --->
+
+mM MgSO4, \(1.79\mathrm{mM}\) CaCl2, \(16.67\mathrm{mM}\) NaHCO3) and rinsed with HBSS. Cells were stimulated with \(1\mu \mathrm{g / ml}\) DNPBSA in the sample chamber. Data was acquired in 2 min captures for up to 15 minutes post antigen treatment.  
+
+## Sample mounting  
+
+Cells samples on \(5\mathrm{mm}\) coverslips were loaded onto the holder as depicted in Supplementary Fig.7. In the sample holder, two metal wires were designed to clamp the coverslip tightly. This sample holder was attached to the XYZ Translation Stage with Standard Micrometers using a rotation mount. As a result, the coverslip had four degrees of freedom, including the translation on the \(X - Y - Z\) axis to locate the cells while imaging and the rotation around the X- axis to face the coverslip with the desired angle relative to the illumination and detection objectives. Here, the coverslips were faced 8 degrees relative to the optic axis of the detection objective (Supplementary Fig.7). In order to minimize the buffer volume for live cell imaging, the \(6\mathrm{ml}\) chamber was designed to immerse the sample, illumination, and detection of objective lenses into it (Supplementary Fig.7).  
+
+## Image processing pipeline  
+
+Data were analyzed with the custom script written in Matlab. The procedure for quantifying the microscope's resolution from fluorescence bead data is as follows: 1) A 3D- PSF model was generated from the raw data. 2) The light- sheet region was cropped from each slice of the raw data. The width of the light- sheet region was defined by the distance to the waist of the light- sheet where the axial resolution increases by 2 times. We sat the light- sheet width to be \(\sim 6\mathrm{mm}\) . Note that the light- sheet region translated along its width direction (the \(Y\) - axis) while it was being scanned in the axial direction (Z- axis relative to the detection objective) (Supplementary Fig.8). Therefore, the light- sheet region to be cropped was also shifted in \(Y\) accordingly (Supplementary Video 1). 3) the cropped region was deconvolved with the 3D- PSF model using Richard- Lucy deconvolution from ImageJ. 4) the deconvolved data stack was divided into segments with an axial dimension of \(5\mu \mathrm{m}\) . For each segment, candidate beads were selected and their FWHMs along each dimension were estimated from Gaussian fitting of their intensity profiles along that dimension. 5) the measured FWHMs were used to quantify the resolution of the microscope as shown in Fig. 2d.  
+
+Dual- color live- cell data was processed as follows: 1) cell signal from each color channel was cropped with a user- selected region. 2) for each color channel, the XYZ drifts of the data stack at each time point relative to the reference data stack were estimated, where the maximum- intensity projection (MIP) along each dimension of the two data stacks was generated and the 2D shift between each pair of the MIP images was calculated through cross- correlation. 3) an average of the XYZ shifts from both channels was used to correct the drift between time points. 4) the XYZ shift between the two- color channels was calculated by first averaging over the time dimension for each color channel, then estimating the shift from the MIP images as in step 3. Then register the two channels by applying the estimated shift. 5) after drift correction and channel registration, the resulting image stacks were deconvolved with the 3D- PSF model generated from the bead data using Richard- Lucy deconvolution from Matlab. 6) to reduce noise and correct photobleaching, the deconvolved images were subtracted by a background value with negative pixel values set to zero and divided by a normalization factor equal to the 99.95 quantiles of all pixel values in the corresponding time points and color channel.  
+
+## Quantification of Light-sheet dimension  
+
+To quantify the light- sheet dimension, bead data in agarose gel were collected at different slit widths. At each slit width, we estimated the FWHMs in XYZ for all selected beads as described above, however, here we used the full FOV of the color channel for bead imaging. As the position of the light- sheet waist shifted in y with respect to the axial dimension, we corrected the y coordinates of the selected bead by \(y_{Cor}^{\prime} = y_{Cor} - az_{Cor}\) , where \(a\) is the y shift by moving one pixel in \(Z\) (Supplementary Fig.8). Then we fitted the \(FWHM_{Z}\) verse \(y_{Cor}^{\prime}\) for all selected beads with a polynomial function (Supplementary Fig.4). The length of the light- sheet was found when the \(FWHM_{Z}\) was twice the minimum from the polynomial fit.  
+
+## Magnification calibration
+
+<--- Page Split --->
+
+One brightfield image of the calibration target was captured at each of the galvo positions from \(- 40\) to \(40\mu \mathrm{m}\) with a step size of \(10\mu \mathrm{m}\) . The target image consisted of parallel line segments, we cropped a region of \(700\mathrm{x}700\) pixels from each image (Supplementary Fig.9a- b). We then calculated the affine transformation (from the Dipimage toolbox) of each image with respect to a reference image. The zoom factors from affine transformation were used to quantify the relative magnification between each image to the reference image. The absolute magnification of one image was calculated as follows: crop a narrow section of multiple parallel lines, obtain the intensity profile by averaging over the line dimension, smooth the intensity profile by applying a running average with a window size of 30 pixels, find all peaks from the smoothed intensity profile (Supplementary Fig.9c), calculate the average distance (in pixels, denoted as \(\Delta d\) ) between consecutive peaks, as the distance between consecutive parallel lines is \(10\mathrm{mm}\) , then the pixel size at the sample plane can be estimated from \(10 / \Delta d\) mm, therefore the magnification can be calculated from the pixel size of the camera divided by pixel size at the sample plane.  
+
+## Ray tracing  
+
+Ray tracing was based on geometric optics with paraxial approximation. The ray propagation was calculated using the ABCD matrices. Two matrices were used, the translation matrix,  
+
+\[M_{d} = \left[ \begin{array}{cc}1 & 0\\ d / n & 1 \end{array} \right],\]  
+
+and the matrix of a thin lens,  
+
+\[M_{f} = \left[ \begin{array}{cc}1 & -n / f\\ 0 & 1 \end{array} \right],\]  
+
+where \(d\) is the translation distance, \(f\) is the focal length of the thin lens and \(n\) is the refractive index of the propagation medium. For our system, \(n\) is 1.33 before the detection objective (including the objective) and \(n\) equals 1 for the rest of the ray tracing. The starting point of each ray was represented by a vector of \([n\alpha ,y]^{T}\) , where \(\alpha\) and \(y\) are the angle and the y position of the ray with respect to the optical axis. The propagation of the ray is then calculated from  
+
+\[\left[ \begin{array}{c}n\alpha '\\ y' \end{array} \right] = M\left[ \begin{array}{c}n\alpha '\\ y \end{array} \right].\]  
+
+For a defined FOV, we selected three field points, two mark the edge of the FOV and one at the optical axis. For each field point, we generated three rays at different angles that will intersect three points at the pupil plane, where two points mark the edge of the pupil and one at the center of the pupil. Rays from the same field point were colored the same. The optical axis after the polarizing beam splitter was rotated by 45 degree to be along the splitting plane of the PBS. The ray tracing after the PBS was done by first transforming the ray coordinates to the ones defined by the optical axis and propagating the ray with the ABCD matrix, then transforming back to the global coordinates. Except for the distance between the tube lens and the detection objective (denoted as \(d_{1}\) ), the rest distances between consecutive optical elements were measured with a ruler. The angle between the chief rays of the S and P- polarization \((\theta\) in Fig.2a) was set when the input and output beam diameters at the remote focusing objective were minimum. The distance \(d_{1}\) was set when the relative magnifications from ray tracing match with the measured ones (Fig. 2b). The central position of the scan range, the distance of the objective to the detection objective (denoted as \(S_{1}\) ), was set when the absolute magnification from ray tracing matches with measured one. Here \(S_{1} = 6.695\mathrm{mm}\) , which was \(45\mu \mathrm{m}\) away from the designed focal plane of the detection objective.  
+
+## References  
+
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+
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+
+45. matlab-instrument-control. (2023).  
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+46. Liu, F. T. et al. Monoclonal dinitrophenyl-specific murine IgE antibody: preparation, isolation, and characterization. J. Immunol. 124, 2728-2737 (1980).
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryVideo1. avi SupplementaryFileSept1. pdf
+
+<--- Page Split --->

preprint/preprint__07208eea83c232a05dca70cd64270d5ee1a24fdbc00dcd03cf4ddc8b21562a44/preprint__07208eea83c232a05dca70cd64270d5ee1a24fdbc00dcd03cf4ddc8b21562a44_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 107, 860, 177]]<|/det|>
+# Axial de-scanning using remote focusing in the detection arm of light-sheet microscopy  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 280, 240]]<|/det|>
+Tommy Chakraborty tchakraborty@umn.edu  
+
+<|ref|>text<|/ref|><|det|>[[44, 270, 640, 380]]<|/det|>
+University of New Mexico  HASSAN DIBAJI  University of New Mexico  Ali KAZEMI NASABAN SHOTORBAN  University of New Mexico  https://orcid.org/0000- 0002- 8513- 1784  
+
+<|ref|>text<|/ref|><|det|>[[44, 384, 280, 426]]<|/det|>
+MAHSA HABIBI  University of New Mexico  
+
+<|ref|>text<|/ref|><|det|>[[44, 431, 761, 472]]<|/det|>
+RACHEL GRATTAN  Comprehensive Cancer Center, University of New Mexico Health Sciences Center,  
+
+<|ref|>text<|/ref|><|det|>[[44, 476, 761, 519]]<|/det|>
+SHAYNA LUCERO  Comprehensive Cancer Center, University of New Mexico Health Sciences Center,  
+
+<|ref|>text<|/ref|><|det|>[[44, 523, 280, 565]]<|/det|>
+DAVID SCHODT  University of New Mexico  
+
+<|ref|>text<|/ref|><|det|>[[44, 570, 677, 612]]<|/det|>
+Keith A. Lidke  The University of New Mexico  https://orcid.org/0000- 0002- 9328- 4318  
+
+<|ref|>text<|/ref|><|det|>[[44, 616, 692, 658]]<|/det|>
+JONATHAN PETRUCCELLI  Department of Physics, University at Albany- State University of New York  
+
+<|ref|>text<|/ref|><|det|>[[44, 662, 761, 704]]<|/det|>
+DIANE LIDKE  Comprehensive Cancer Center, University of New Mexico Health Sciences Center,  
+
+<|ref|>text<|/ref|><|det|>[[44, 709, 280, 750]]<|/det|>
+SHENG LIU  University of New Mexico  
+
+<|ref|>text<|/ref|><|det|>[[44, 792, 103, 810]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 830, 137, 848]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 867, 317, 886]]<|/det|>
+Posted Date: October 3rd, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 905, 473, 924]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3338831/v1
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 44, 916, 87]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 105, 937, 171]]<|/det|>
+Additional Declarations: Yes there is potential Competing Interest. T.C. and H.D. have filed a patent application (United States Patent and Trademark Office application number 63/397,714) for the remote focusing setup mentioned here.  
+
+<|ref|>text<|/ref|><|det|>[[42, 207, 917, 250]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on June 12th, 2024. See the published version at https://doi.org/10.1038/s41467-024-49291-0.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[118, 89, 875, 137]]<|/det|>
+# Axial de-scanning using remote focusing in the detection arm of light-sheet microscopy  
+
+<|ref|>text<|/ref|><|det|>[[115, 150, 797, 204]]<|/det|>
+HASSAN DIBAJI \(^{1}\) , ALI KAZEMI NASABAN SHOTORBAN \(^{1}\) , MAHSA HABIBI \(^{1}\) , RACHEL M GRATTAN \(^{2,3}\) , SHAYNA LUCERO \(^{2,3}\) , DAVID J. SCHODT \(^{1}\) , KEITH A. LIDKE \(^{1,2}\) , JONATHAN PETRUCCELLI \(^{4}\) , DIANE S. LIDKE \(^{2,3}\) , SHENG LIU \(^{1}\) , AND TONMOY CHAKRABORTY \(^{1,2,*}\)  
+
+<|ref|>text<|/ref|><|det|>[[115, 208, 861, 272]]<|/det|>
+\(^{1}\) Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA \(^{2}\) Comprehensive Cancer Center, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, 87131, USA \(^{3}\) Department of Pathology, University of New Mexico Health Science Center, Albuquerque, NM, USA \(^{4}\) Department of Physics, University at Albany- State University of New York, 1400 Washington Avenue, Albany, NY 12222, USA \(^*\) tchakraborty@unm.edu  
+
+<|ref|>text<|/ref|><|det|>[[115, 280, 882, 514]]<|/det|>
+Abstract: The ability to image at high speeds is necessary in biological imaging to capture fast- moving or transient events or to efficiently image large samples. However, due to the lack of rigidity of biological specimens, carrying out fast, high- resolution volumetric imaging without moving and agitating the sample has been a challenging problem. Pupil- matched remote focusing has been promising for high NA imaging systems with their low aberrations and wavelength independence, making it suitable for multicolor imaging. However, owing to the incoherent and unpolarized nature of the fluorescence signal, manipulating this emission light through remote focusing is challenging. Therefore, remote focusing has been primarily limited to the illumination arm, using polarized laser light for facilitating coupling in and out of the remote focusing optics. Here we introduce a novel optical design that can de- scan the axial focus movement in the detection arm of a microscope. Our method splits the fluorescence signal into S and P- polarized light and lets them pass through the remote focusing module separately and combines them with the camera. This allows us to use only one focusing element to perform aberration- free, multi- color, volumetric imaging without (a) compromising the fluorescent signal and (b) needing to perform sample/detection- objective translation. We demonstrate the capabilities of this scheme by acquiring fast dual- color 4D (3D space + time) image stacks, with an axial range of \(70 \mu \mathrm{m}\) and camera limited acquisition speed. Owing to its general nature, we believe this technique will find its application to many other microscopy techniques that currently use an adjustable Z- stage to carry out volumetric imaging such as confocal, 2- photon, and light sheet variants.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 544, 162, 558]]<|/det|>
+## MAIN  
+
+<|ref|>text<|/ref|><|det|>[[115, 565, 882, 799]]<|/det|>
+Fast 3D positioning or scanning of an optical system's focal point or focal plane has the potential to transform many areas of BioPhotonics, especially those that require studying the complex dynamics of living organisms. Processes like investigation of neuronal activities of the brain, blood flow in the heart, and cell signaling require high- speed volumetric imaging \(^{1 - 3}\) . However, volumetric imaging requires an axial scan either through the translation of the sample or the detection objective lens (Fig. 1a). Such axial translations result in imaging modalities that are often slow with speeds limited to a few hundred \(\mathrm{Hz}^{4 - 6}\) . Additionally, with fragile samples, such as an expanded sample in hydrogel \(^{7}\) , fast movements of the sample stage may agitate the sample and induce distortions when collecting volumetric images. To avoid the slow translation of bulky objectives or the sample stages, several attempts, employing variable- focus (vari- focus) lenses, mechanical mirrors, and acousto- optics modulators have been proposed to refocus the light for 3D imaging. However, they all suffer from unacceptable aberrations introduced by the focusing elements. A large category of those techniques utilize different types of tunable lenses such as ferroelectric liquid crystal (LC), acoustic waves (TAG lens), and acoustic optics modulators (AOM) \(^{8}\) to achieve fast focal shifts (~1kHz). Ferroelectric LC and TAG lenses introduce a focal shift by varying the gradient of the refractive index of the liquid medium, however, the generated phase variation only approximates the defocus phase, leading to increased spherical aberration at large focal shifts \(^{9 - 11}\) . AOM- based vari- focus techniques on the other hand use two AOMs with counterpropagating acoustic waves to cancel out the transverse scan but can only achieve focus shift in one dimension (acting as a cylindrical lens) \(^{12,13}\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 805, 881, 908]]<|/det|>
+Adaptive optics- based vari- focus techniques overcome these limitations through accurate wavefront control using either a spatial light modulator (SLM) or a deformable mirror (DM), which can achieve a response rate of ~1 kHz and 20 kHz respectively. However, SLMs are polarization and wavelength- dependent and cannot model a continuous wavefront of the defocus phase due to its limited phase modulation depth. Large phase shifts are generated through multiple phase- wrapping of \(2\pi\) . With finite fly- back at the phase- wrapping borders, part of the incident light is not correctly modulated and results in decreased intensity at the focus \(^{14}\) . DMs are not polarization and wavelength- dependent and can model a continuous defocus wavefront. However, the axial scan range of a DM is limited by the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 882, 147]]<|/det|>
+stroke length of the DM actuators. For example, for an objective with a numerical aperture (NA) of 0.8, the maximum axial scan range that DM based techniques can generate is \(- 40 \mu \mathrm{m}^{15}\) . Furthermore, using DM for focus control requires accurate alignment and complicated calibration of the DM to reduce the aberrations caused by imaging samples out of the nominal focal plane of the objective<sup>9</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 161, 882, 438]]<|/det|>
+Unlike the adaptive optics or DM- based approaches that require correcting the defocus plane- by- plane, pupil- matched remote focusing (pmRF), pioneered by Botcherby et al.<sup>16,17</sup>, instantaneously corrects defocus across 3D volumes for high- NA optics thereby conserving the microscope's temporal bandwidth<sup>16- 26</sup>. In addition, because pmRF allows precise mapping of the wavefront coupled into the back- pupil of the objective, where the angular magnification is unity, such techniques have been routinely used to carry out aberration- free high- quality axial focus control<sup>16- 26</sup>. In pmRF techniques, a fast axial scan is achieved by the translation of a small mirror in front of the remote objective using a focus actuator<sup>18,19,23</sup> or by a lateral scan of a galvo mirror in combination to a step or tilted mirror at the remote objective<sup>27</sup>. Because of the fast response time of the focus actuator or the galvo mirror, an axial scan rate of 1- 5 kHz or 12 kHz can be achieved respectively. However, current pmRF techniques for focus control are primarily limited to the illumination path. This is because pmRF uses the concept of optical isolators<sup>28</sup>, where the polarization of the returning beam is rotated orthogonally to the incoming beam so that it can be separated from the incoming beam at the polarized beam splitter (PBS) (Supplementary Fig. 1a). This configuration ensures minimum light loss through the pmRF module but requires the incoming beam to be polarized, which is why this method is primarily used in the illumination arm where illumination laser light is usually polarized in nature and its manipulation through the optical isolator can be easily done. In the detection arm, however, the emitted fluorescence is unpolarized in nature. To the best of our knowledge, because, using purely linear optical elements, lossless conversion of unpolarized light into a single polarized state is not yet possible<sup>29,30</sup> (Supplementary Note 1), manipulating the fluorescent light using the optical isolators is unfeasible. As a result, microscopes that use pmRF to carry out axial scanning, incur 50% light loss due to one state of the polarized light being discarded after the PBS<sup>16,21,24</sup> (Supplementary Fig. 1a).  
+
+<|ref|>text<|/ref|><|det|>[[115, 451, 882, 596]]<|/det|>
+A straightforward method to mitigate this problem is to have another copy of the pmRF module at the unused port of the PBS (Supplementary Fig. 1b) to collect the other half of the fluorescent light. However, this would require precise synchronization of two linear- focus- actuators (LFA), which is not only a difficult task at high speeds but also will be expensive since this method warrants two such LFAs. In this article, we present a novel optical design that overcomes these problems and presents a modular setup that can perform remote focusing on the detection arm of a fluorescent microscope without incurring polarization- induced losses. When attached to a light- sheet microscope, this technique allows optical refocusing without requiring the movement of the sample, or the detection objective (Fig. 1b and Supplementary Fig. 1c). As a result the microscope can acquire 3D volumetric data limited by camera speed. This technique is applicable to many other microscopy techniques that currently use an adjustable \(Z\) - stage to carry out volumetric imaging such as confocal, 2- photon, and light sheet variants.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 605, 170, 618]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 627, 336, 641]]<|/det|>
+## Concept and microscope layout  
+
+<|ref|>text<|/ref|><|det|>[[115, 648, 882, 852]]<|/det|>
+Optical axial- refocusing: Our refocusing unit is shown in Fig. 1b. Here, the water immersion detection objective (Obj1) is pupil matched to a second air objective (Obj2) through two intermediate lenses following the original design by Botcherby et al.<sup>16,17</sup>. However, unlike traditional refocusing geometry, we split the collected unpolarized fluorescence into S and P- polarized light using a polarizing beam splitter cube (PBS) in the infinity space of Obj2. The generated orthogonal paths are then projected onto Obj2 using two angled mirrors M1 and M2. Because of this angular launch in infinity space, Obj2 forms two distinct laterally shifted images at its nominal focal plane. A small mirror placed on an LFA reflects the light back through the path it came from where a quarter wave plate (QWP) converts the S- polarized light to P on its way back (and P- polarized light to S) after being reflected from the mirror (Fig. 1c). When the returning light (in each arm) reaches the PBS, it now acts as an optical valve where the S path (which was initially P) gets reflected while the P- polarized light (which was initially S) gets transmitted by the PBS. As a result, both S and P polarized light exits the PBS through the fourth and unused face of the PBS cube (Fig. 1d). This light after passing through a tube lens forms identical images, one with S and another with P, at the sCMOS camera. A precise alignment using mirrors M1 and M2 overlays the two images, thereby resulting in a combined image by simply an incoherent addition without any interference artifacts.  
+
+<|ref|>text<|/ref|><|det|>[[116, 859, 882, 902]]<|/det|>
+There are a few important design considerations that need to be considered for our de- scanning setup. Firstly, it is essential that mirror M3 consistently moves in parallel with the focal plane of Obj2 during the LFA's oscillatory motion. This prevents any unwanted focal shifts between the S and P paths, ensuring that the resulting image from
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 89, 882, 133]]<|/det|>
+both S and P polarizations remain focused on the camera at the same time. This arrangement ensures that both beams return through their incoming paths, resulting in easier alignment for overlaying the final images formed by the S and P- polarized beams.  
+
+<|ref|>text<|/ref|><|det|>[[115, 140, 882, 215]]<|/det|>
+Secondly, it is advantageous that 0 (angle between S and P polarized beam hitting the Obj2) (Supplementary Fig. 2) be as small as possible because this directly controls the distance between the two focal points at M3 (depicted by \(\Delta L\) in Fig. 1c). A smaller \(\Delta L\) ensures: (1) a smaller mirror could be utilized to carry out the remote- focusing, reducing the inertial load on the LFA, and enhancing its efficiency; (2) The alignment becomes less sensitive to tip- tilt misalignment of M3; and (3) This guarantees that both images fit within Obj2's field of view (FOV).  
+
+<|ref|>text<|/ref|><|det|>[[115, 221, 882, 309]]<|/det|>
+Thirdly, there exists an inverse relationship between the angle \(\theta\) and the distance between Obj2 and the PBS (inset of Supplementary Fig.2). Therefore, this gives us an option: either adhere to the 4f system or minimize \(\theta\) . We found that for our matching objectives Obj1 and Obj2 the 4f system (with matching lenses L1 and L2) resulted in a \(\theta\) of \(20^{\circ}\) (inset of Supplementary Fig.2). However, operating in this range poses a risk as it is challenging to ensure that both reflected beams are entirely captured by Obj2. Hence, there is a balance between adhering to the 4f system and minimizing the angle \(\theta\) . We found that with our current design, we can still achieve diffraction limited resolution (Fig. 1e).  
+
+<|ref|>text<|/ref|><|det|>[[115, 316, 882, 375]]<|/det|>
+Finally, because we generated two identical images on the camera using S and P- polarized light, it was crucial to overlay these images with precision higher than the diffraction- limited resolution to produce the final image. To do this, we developed a cross- correlation- based algorithm that quantifies the shift between overlayed S and P images in real- time with sub- pixel accuracy, allowing interactive adjustment of the mirrors M1 and M2 during system alignment.  
+
+<|ref|>text<|/ref|><|det|>[[115, 388, 882, 550]]<|/det|>
+Implementation in a light- sheet system: In order to test the performance of our design we implemented this setup into the detection arm of a light- sheet microscope with orthogonal illumination and detection objectives. The system layout is shown in (Fig.1b and Supplementary Fig.2). The sample is illuminated by a sheet of light generated with a cylindrical lens in the illumination arm, and the emitted fluorescence from the sample is collected by the detection objective lens, which is set orthogonal to the illumination objective lens to capture 2D information from the sample. A galvanometric scan mirror (GSM) in the illumination arm translates the light- sheet in the Z- direction. Because the position of the LFA in the detection arm determines the focal plane of the detection objective lens, we synchronized the GSM and LFA with the sawtooth signal to ensure that the detection path is always focused on the plane of the light- sheet (Supplementary Fig.3). This allowed us to carry out volumetric imaging by acquiring a sequence of images from different focal planes. The LFA moves back and forth rapidly, synchronized with the movement of the GSM enabling us to quickly collect 3D image stacks.  
+
+<|ref|>text<|/ref|><|det|>[[115, 562, 882, 710]]<|/det|>
+The optical correction of defocus in our high- NA microscope allowed fast de- scanning of a 3D volume over an axial range of \(\sim 70 \mu \mathrm{m}\) at speeds limited primarily by the camera framerate ( \(\sim\) in our case 799 camera frames/s at \(2304 \times 256\) pixels using Hamamatsu Orca- fusion BT). We employed a dual- color imaging strategy by partitioning the FOV, enabling simultaneous capture of two distinct fluorescent labels within each slice without sacrificing imaging speed. To do this we used a pair of dichroic mirrors to separate the emitted wavelengths from the two labels into side- by- side dual- color images (Supplementary Fig.2). Once acquired, these separate image sets are then precisely registered and merged to generate 4D (X, Y, Z, and \(\lambda\) ) stacks. By sequentially capturing 4D stacks, we generated 5D (X, Y, Z, \(\lambda\) , and time) datasets that allowed us to track the dynamic behavior of biological processes. It is important to note that our setup is wavelength- independent, an attribute not feasible with technologies like diffractive tunable lenses or spatial light modulators.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 730, 381, 745]]<|/det|>
+## Characterization of the optical system  
+
+<|ref|>text<|/ref|><|det|>[[115, 752, 882, 905]]<|/det|>
+To understand the image formation of the proposed setup, we simulated the ray tracing of the detection path (Fig. 2a). The ray tracing assumes all rays satisfy paraxial approximation and all lenses are simple lenses. The detection objective is a water immersion objective, we calculated its effective focal length as \(f_{\mathrm{obj}} = f_{\mathrm{Tube}} n / M_{\mathrm{obj}}\) , where \(f_{\mathrm{Tube}}\) is the focal length of the designed tube lens, \(M_{\mathrm{obj}}\) is the magnification of the objective, and \(n\) is the refractive index of water. Here we have \(f_{\mathrm{obj}}\) equal to 6.65 mm. The pmRF module (from the beam splitter to LFA) is modeled two times to simulate the forward and backward transmission through the module. The LFA is omitted from the simulation, instead, we change the distance between the two copies of the pmRF objectives so that the distance \((S_{3})\) of the image plane to the second pmRF objective remains as a constant. We simulated with an object of \(100 \mu \mathrm{m}\) , the image size after the pmRF objective is \(\sim 140 \mu \mathrm{m}\) , indicating a lateral magnification of 1.4, which is close to the requirement of perfect imaging with \(M_{\mathrm{lateral}} = n_{\mathrm{water}} / n_{\mathrm{air}} = 1.33\) . The small deviation is limited by the geometry of the pmRF
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 883, 255]]<|/det|>
+module: the separation \((\Delta L)\) of the S and P- images formed by the pmRF objective is approximate to \(\Delta L = f_{\mathrm{RFobj}}\theta\) where \(f_{\mathrm{RFobj}} = 10 \mathrm{mm}\) is the effective focal length of the RF objective and \(\theta\) is the angle between the S and P- polarized rays meeting at the RF objective. The larger the \(\Delta L\) , the larger the aberration introduced by the pmRF objective. To reduce \(\Delta L\) , the pmRF objective is located \(\sim 500 \mathrm{mm}\) from the PBS, therefore, the pmRF module is no longer an exact 4f system, the magnification, \(M_{\mathrm{lateral}}\) , varies with the axial position of the object. Furthermore, the beam path from the detection objective to the tube lens is also not a 4f system, where the tube lens is \(\sim 100 \mathrm{mm}\) away from the detection objective. The combination of the two non- 4f systems can partially reduce the axial dependence of the magnification. Fig. 2b shows the change of the lateral magnification with respect to the galvo position (the axial position of the light sheet) from both ray tracing and the experimental data. There is a \(\sim 5\%\) magnification change over an axial range of \(80 \mu \mathrm{m}\) . This magnification change can be further reduced by optimizing the axial position of the tube lens.  
+
+<|ref|>image<|/ref|><|det|>[[128, 280, 863, 675]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 686, 883, 886]]<|/det|>
+<center>Figure 1: Schematic diagram of a remote focusing system implemented in light-sheet microscopy and its performance. a) Three different modalities to acquire volumetric imaging of the sample along the focus direction. Either the sample or objective lens can be moved for axial refocusing. Alternatively, both the sample and objective lens can remain stationary by using a remote focusing system. b) Implementation of the remote-focusing system on the detection arm of the light sheet microscope. In this configuration, objective lenses 1 and 2 are pupil-matched through two lenses to form a perfect imaging system. Combined with mirror M3 and a polarizing beam splitter (PBS), the whole system works as a remote focusing system. The novel design of this remote-focusing system is implementation in the detection arm for unpolarized fluorescent light emitted from the sample. To do this, two tilted mirrors M1 and M2 are utilized to direct both S and P-polarized beams toward Objective lens 2 and then combine the reflected beams from mirror M3 to create an image by S and P-polarized beams onto the camera by focusing through the tube lens. The mirror M3 is attached to the linear focus actuator (LFA), moving back and forth to scan the sample in the Z-direction to acquire a 3D image. In the illumination arm, the generated light sheet by a cylindrical lens is translated by a galvanometric scan mirror (GSM) along the detection arm. To focus the detection path on the plane of the light sheet, the synchronization of GSM and LFA is carried out by sawtooth signals. Simultaneous dual-channel imaging of the cell is achieved in \(40 \mu \mathrm{m} \times 150 \mu \mathrm{m}\) FOV over \(70 \mu \mathrm{m}\) in the Z-direction. c) The polarization state of the incoming beams changes after reflection from mirror M3 (S to P, and P to S). d) The reflected beams from mirror M3 have a different polarization state compared to the incoming beams; therefore, they exist from a different side of the PBS than the incoming beams. e) The point spread function (PSF) of 200 nm beads formed by S, P, and S+P polarized beams. The microscope performs at the diffraction limit, \(394 \mathrm{nm}\) resolution, for S, P, and S+P in the lateral directions (X-Y), while it maintains a resolution of \(654 \mathrm{nm}\) in the axial direction (Z). </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 117, 883, 242]]<|/det|>
+To quantify the performance of the proposed scheme, we used full width at half max (FWHM) measurements of 3D point spread function (PSF) to validate that the incoherent addition of S and P images was not compromising the resolution. To do this, we measured the PSF of each polarization component individually and compared it with the PSF of the unified S+P image. As illustrated in Fig.1e, both the S and P- polarized images rendered onto the camera exhibit identical FHWM, resulting in an equivalent resolution for the combined S+P image. Further quantification involving 10 randomly chosen beads, reveals that the microscope achieved diffraction- limited resolutions: \(394 \pm 31 \mathrm{nm}\) laterally (X- Y) and \(654 \pm 130 \mathrm{nm}\) axially (Z). These measurements were performed in proximity to the nominal focal plane (MIP of 10 slices, each separated 500 nm).  
+
+<|ref|>text<|/ref|><|det|>[[115, 254, 883, 270]]<|/det|>
+To evaluate the performance of the de- scanning system, we imaged 3D volumes of \(200 \mathrm{nm}\) beads embedded in a \(2\%\)  
+
+<|ref|>image<|/ref|><|det|>[[120, 285, 860, 707]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 723, 870, 831]]<|/det|>
+<center>Figure 2: Ray tracing of the setup and resolution assessment. a) Ray tracing of the detection path. L: image size, f: effective focal length, S: image or object position relative to the lens, unit: mm. b) Calibration of lateral magnification at various object positions, a target illuminated by a white light LED is imaged for magnification measurement. c) Maximum intensity projections of data acquired on \(200 \mathrm{nm}\) beads from 10 slices spaced \(500 \mathrm{nm}\) in the Z-direction. The images show orthogonal views of the MIPs across scan range for S,P and S+P. The elongated PSF in the Z direction exhibits less resolution in the axial direction controlled by the light sheet waist. d) The FWHM of the \(200 \mathrm{nm}\) beads in the lateral and axial directions over the scan range. The minimum lateral resolution, \(394 \mathrm{nm}\) , occurs at the center of the scan range and increases by moving away from the center. These plots show a constant axial resolution of \(650 \mathrm{nm}\) over the axial scan range. The microscope functions in the scan range of \(70 \mu \mathrm{m}\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 835, 882, 895]]<|/det|>
+agarose cube across the scan range and accessed the quality of the generated PSFs. Fig. 2c shows the maximum intensity projection (MIP) of beads (from 10 axial slices, each slice spaced \(500 \mathrm{nm}\) ) separated by \(30 \mu \mathrm{m}\) for S, P, and S+P across the scan range, after 10 iterations of Richardson- Lucy (RL) deconvolution. We found that our remote focusing setup demonstrated close to diffraction- limited performance over a scan range of \(\sim 70 \mathrm{um}\) . As evident from
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 88, 882, 177]]<|/det|>
+the 'S' and 'P' images the quality of the beads visually appears similar across the entire scan range thereby resulting in an identical 'S+P' image. In the axial direction (the \(YZ\) view) the PSFs are limited by the Gaussian light sheet's waist (beads from red boxes in \(XY\) view), which was determined by the tradeoff that exists between the FOV and \(Z\) resolution. We found that in order to image an entire cell, we needed a lightsheet that would generate a FOV of \(\sim 8\) \(\mu \mathrm{m}\) (Supplementary Fig. 4). As a result, we reduced the NA of the illumination objective and chose a light sheet whose waist was at FWHMz of \(\sim 650 \mathrm{nm}\) after deconvolution (850 nm before deconvolution).  
+
+<|ref|>text<|/ref|><|det|>[[115, 190, 882, 336]]<|/det|>
+Figure 2d displays the measured FWHMs from \(200 \mathrm{nm}\) beads after RL deconvolution for S, P, and S+P polarize images in the lateral (XY) and axial (Z) directions across the entire scan range. The figure shows a minimum lateral FWHM of \(394 \mathrm{nm}\) at the center of the scan range which slowly increases as the beads move away from the nominal focal plane. This can be attributed to residue index mismatch aberrations that were not corrected by the remote focusing system<sup>21</sup>. Additionally, we found that the S polarization path suffered more in lateral resolution compared to the P polarization path and the trend is different along \(X\) and \(Y\) directions. This asymmetric FWHMs (X-Y) across scan range (Z) and the discrepancy between S and P paths is likely due to field- dependent aberrations from Obj2, where the S and P images were formed at different field points of Obj2 (Fig. 1b). Furthermore, our microscope shows a constant axial FWHM of \(\sim 650 \mathrm{nm}\) over the entire scan range as the axial resolution is mainly determined by the lightsheet waist.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 365, 287, 380]]<|/det|>
+## Fast 3D live cell imaging  
+
+<|ref|>text<|/ref|><|det|>[[115, 393, 882, 481]]<|/det|>
+As a first demonstration of the 3D cellular imaging capabilities, we monitored the 3D motion of secretory granules in living mast cells. Mast cells possess distinct secretory granules that contain the mediators of the allergic response and are released upon mast cell activation by allergen<sup>31</sup>. These granules are distributed across the cytosol and have been shown to undergo both Brownian diffusion and directed motion<sup>31</sup>. Upon activation of the membrane receptor, FcεRI, via crosslinking by multivalent antigen<sup>32,33</sup>, the granules undergo increased directed motion that moves them to the plasma membrane where they will fuse and release mediators that regulate allergic responses<sup>31,34</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 494, 882, 700]]<|/det|>
+We applied the developed system for dual- color, volumetric imaging of live cells and tracked the 3D motion of green fluorescent protein- labeled Fas ligand (GFP- FasL) loaded secretory granules in the cytosol of RBL- 2H3 mast cells<sup>31</sup>. IgE- bound FcεRI was simultaneously imaged by addition of anti- DNP IgE- CF640R. With addition of the antigen- mimic, DNP- conjugated to BSA (DNP- BSA), FcεRI aggregates and undergoes endocytosis as seen in Figure 3a. During data acquisition, the light sheet is parallel to the \(XY\) plane and scans along the \(Z\) direction. Within the lightsheet region, the \(XY\) and \(XZ\) maximum intensity projections (Fig.3a) of the cell image show GFP- FasL granules in three dimensions. The cells were imaged at \(\sim 0.6\) volumes \((80 \times 15 \times 40 \mu \mathrm{m}^3\) in \(XYZ\) per second for 80 volumes, for a total imaging time of \(\sim 2\) minutes (Fig.3a- d). To quantify the granule dynamics, isolated granules were identified and tracked in 3D using the U- track3D software<sup>35</sup>. We calculated the mean square displacement (MSD) of each trajectory over time and extracted the diffusion coefficient, \(D\) , and velocity, \(v\) , by fitting the MSD curve with \(MSD(t) = 6Dt^2 + v^2 t^2 + o\) , where \(o\) is an offset related to localization and tracking uncertainties<sup>36,37</sup> (Fig.3c,d). We found that most granules undergo Brownian Diffusion and a few exhibited directed motion, consistent with granules being transported along the microtubules (Fig.3a,b)<sup>31</sup>. The measured transport velocities of the two trajectories indicated in Fig.3a,b are \(\sim 0.1 \mu \mathrm{m / s}\) , consistent with previous work that performed tracking in 2D<sup>31</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[115, 713, 882, 816]]<|/det|>
+To test the limits of the new system in terms of speed, we set out to image Brownian motion on the microscopic level. For this, we stressed the cells by incubating them in Hank's balanced salt solution (HBSS) (Method) at room temperature for over 1 hour, which induced cell blebbing. This also caused more rapid diffusion of the granules that we were able to capture using an imaging speed of \(\sim 8.3\) volumes/s for 80 volumes for a total time of \(10 \mathrm{s}\) . With this imaging speed, we retained good signal- to- noise and the ability to track the 3D motion of individual granules (Fig 3e- g). Under these non- physiological conditions, average granule diffusion was increased by \(\sim 41\) times (Fig.3h). Two tracks shown in Fig. 3e have diffusion coefficients of \(0.41 \mu \mathrm{m}^2 / \mathrm{s}\) and \(0.64 \mu \mathrm{m}^2 / \mathrm{s}\) .
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[130, 92, 876, 734]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[125, 742, 901, 878]]<|/det|>
+<center>Figure 3: Dual-Color volumetric imaging of live RBL cells. (a-d) Dual-color volumetric imaging of granule motions in a live RBL-2H3 GFP-FasL cell, where the cell membrane is labeled with IgE-CF640R and granules contain GFP-FasL, at an imaging speed of \(\sim 0.6\) volumes \((80\times 15\times 40\) \(\mu \mathrm{m}^3\) in XYZ) per second for 80 volumes, for a total imaging time of \(\sim 2\) minutes. (a) Maximum intensity projection views of the cell images at one-time point and overlay with representative trajectories of granule movement (orange lines). (b) Time series of the trajectories in a. (c, d) Histograms of estimated diffusion coefficients and velocities of all trajectories found in cell 1 and cell 2. (e-g) Dual-color volumetric imaging of live RBL-2H3 GFP-FasL cell, where the cell membrane is labeled with CellMask DeepRed and the granules contain GFP-FasL using an imaging speed of \(\sim 8.3\) volumes/s for 80 volumes for a total time of \(10\mathrm{s}\) . (e) Maximum intensity projection views of the cell images at one-time point and overlay with representative trajectories of granule movement (orange lines). (f) Time series of the trajectories in e. (g) Histograms of estimated diffusion coefficients of all trajectories in the cell. (h) Cumulative probability of the estimated diffusion coefficients under normal (a-d) and stressed (e-g) imaging conditions. 400-500 trajectories with a diffusion coefficient \(>0.001\mu \mathrm{m}^2 /\mathrm{s}\) from four cells under each condition are selected. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 190, 104]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[115, 117, 882, 264]]<|/det|>
+In this work, we developed an axial scanning module in the detection path of a light- sheet microscope utilizing the pmRF technique proposed by Botcherby et al.16,17. While inheriting all the benefits from the pmRF technique, such as fast scanning and all- optical aberration compensation (no wavefront control element), our design overcomes a critical limitation of the original pmRF technique, as in, the loss of \(50\%\) of the emitted fluorescence in the detection path21,24,38. Here we engineered a new optical design, where we split the emitted fluorescence into S and P polarized light to carryout remote focusing and then seamlessly combine them to achieve minimum light loss. We demonstrated our implementation of the developed scanning module through a light- sheet microscope with two orthogonally arranged objectives. We can perform simultaneous two- color imaging at 8.3 volumes ( \(80\times 15\times 40\mu \mathrm{m}^{3}\) in XYZ) per second with a lateral resolution of \(394\mathrm{nm}\) and an axial resolution of \(650\mathrm{nm}\) (after deconvolution). As our method is fully optical, the imaging speed scales with advancements in LFA technology and camera acquisition speed.  
+
+<|ref|>text<|/ref|><|det|>[[115, 277, 882, 380]]<|/det|>
+The S and P polarized beams are directed at an oblique angle into the remote objective (Fig. 1b). This angled approach creates two separate images at the mirror attached to the LFA (M3). However, there are limitations to this angular arrangement. The two images formed away from the optical axis are prone to aberrations. To reduce the image separation, the remote objective must be positioned further from the PBS to reduce the incident angles of S and P- polarized lights. However, this increased distance breaks the 4f configuration between the two objectives (detection and remote objectives) that is critical to achieving aberration- free imaging. Future studies will investigate into more compact designs that will better satisfy the 4f condition and will reduce the separation between the two foci at M3.  
+
+<|ref|>text<|/ref|><|det|>[[115, 393, 882, 510]]<|/det|>
+Of note, our approach offers several advantages over the existing axial refocusing methods. First, it provides an extended, aberration- free scan range for high numerical aperture (NA) optics. This is a significant benefit when compared to techniques based on deformable mirrors (DMs), where our method approximately doubles the axial scan range of DMs15. Second, it is wavelength independent, which makes it suited for simultaneous multicolor imaging when compared to SLMs and tunable lenses. Additionally, unlike SLMs which depend on polarization, our arrangement is not dependent on the polarization of the fluorescence. Furthermore, unlike SLMs, which are typically slow (especially the nematic liquid crystal ones), and even their faster counterparts (ferroelectrics) tend to be less effective, our method allows for imaging speed that are only limited by the sCMOS's framerate.  
+
+<|ref|>text<|/ref|><|det|>[[115, 523, 882, 685]]<|/det|>
+Although recent advancements in single- objective oblique plane microscopy (OPM) have achieved speeds comparable to our method, our technique presents several notable advantages. In OPM, the de- scanning of the returning fluorescent light leads to skewed images. Before these images can be viewed, they require intensive de- skewing processes23,39- 43. On the other hand, our approach captures 3D volumes in a conventional orthogonal setup. This is achieved by recording high- speed images while sweeping the light- sheet through the sample. Each frame captured by the camera represents an optical cross- section of the specimen. As a result, the 3D image stacks generated using our method are immediately available for viewing. They may benefit from an optional deconvolution, but there's no delay caused by necessary post- processing. Furthermore, the OPM setup necessitates a third objective, which in the latest setups require expensive objectives like 'Snouty' or 'King Snout'2,39- 42. Our setup on the other hand does not have this requirement and our secondary objective performs the role of a tertiary objective. Moreover, while not demonstrated explicitly here, our method can be employed to achieve isotropic resolution, a feat the OPM cannot achieve.  
+
+<|ref|>text<|/ref|><|det|>[[115, 698, 882, 787]]<|/det|>
+Compared with the original Botcherby's remote focusing setup, our pmRF module folds the beam path between the detection and the remote objectives. This configuration complicated the optical alignment. A potential solution is to arrange both objectives inline in a 4f configuration. Furthermore, we note that although an all- optical design has its merit of simplicity and robustness, using an objective lens in the pmRF module introduces \(\sim 30 - 40\%\) light loss (Supplementary Fig.5) compared with the axial scanning techniques based on DMs, future development of objective with high- transmission efficiency is desirable.  
+
+<|ref|>text<|/ref|><|det|>[[115, 800, 882, 844]]<|/det|>
+Finally, it is our firm belief that owing to its generalized design, we envision our method has the potential to transform many popular microscope modalities like confocal, 2- photon, and the rapidly emerging field of light sheet microscopy, by reinventing how they perform scanning in the axial dimension.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 860, 252, 873]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[115, 873, 881, 902]]<|/det|>
+This work was supported by University of New Mexico (Start- up Grant) (TC), NIH R35GM151152 (TC), NIH P30CA118100 (TC and KL) and NIH R35GM126934 (DSL). We thank Derek Rinaldi for generating the IgE
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 881, 133]]<|/det|>
+CF640R. This work was conducted with support from the University of New Mexico Office of the Vice President for Research Program for Enhancing Research Capacity, was supported by grants from NVIDIA and utilized an NVIDIA A6000 GPU.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 149, 265, 162]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[115, 163, 881, 265]]<|/det|>
+T.C. conceived the idea of lossless remote focusing in detection arm. H.D. and T.C. designed and built the remote focusing unit. H.D. and T.C. designed, built, and operated the microscope. H.D. and Sh.Li performed image analysis. Sh. Li and J.P. have theoretically demonstrated that achieving \(100\%\) conversion from unpolarized to polarized light is not feasible. D.J.S and K.A.L provided the MATLAB code for the fine alignment. H.D., T.C. and M.H. designed the chamber and sample holder. D.S.L., Sh.Lu., and R.M.G prepared RBL cells for imaging. H.D. imaged RBL cells labeled with DeepRed CellMask. H.D. and A.K.N.Sh imaged the RBL cells labeled with IgE- CF640R. H.D., Sh.Li., and T.C. wrote the manuscript. All authors read and provided feedback on the final manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 280, 258, 293]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[115, 293, 881, 322]]<|/det|>
+T.C. and H.D. have filed a patent application (United States Patent and Trademark Office application number 63/397,714) for the remote focusing setup mentioned here.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 351, 177, 365]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 380, 210, 396]]<|/det|>
+## Optical setup  
+
+<|ref|>text<|/ref|><|det|>[[115, 408, 882, 578]]<|/det|>
+The illumination arm consists of two laser sources (Coherent Sapphire \(488~\mathrm{nm}\) and Obis LX \(637~\mathrm{nm}\) ) which were combined with a dichroic beam splitter (LM01- 503- 25, Semrock). To clean up the beams, the beams were focused through a \(50 - \mu \mathrm{m}\) pinhole (P50D, Thorlabs) by a \(45 - \mathrm{mm}\) achromatic doublet (AC254- 045- A, Thorlabs) and then recollimated using a \(150 - \mathrm{mm}\) achromatic doublet (AC254- 150- A- ML, Thorlabs). The original beams were expanded by 9 folds with a \(3\times\) Galilean beam expander (GBE03- A) before being focused with a cylindrical lens (ACY254- 50- A, Thorlabs), onto a resonant mirror galvanometer (CRS \(4\mathrm{kHz}\) , Cambridge Technology), driven by a 12- volt power supply (A12MT400, Acopian), to wobble the light sheet. One- dimensional focus was then recollimated with a 100- mm achromatic doublet (AC254- 100- A- ML, Thorlabs) and hit the galvanometric scan mirror (GSM) (GVS111, Thorlabs), driven by a 15- volt power supply (GPS011, Thorlabs), for rapid shifting of the light sheet along the detection arm. This galvanometric mirror was conjugated to the back pupil of the objective lens (Nikon \(40\times 0.8\mathrm{NA}\) ) through \(100 - \mathrm{mm}\) and \(200 - \mathrm{mm}\) achromatic doublet (AC508- 100- A- ML and AC508- 200- A- ML, Thorlabs).  
+
+<|ref|>text<|/ref|><|det|>[[115, 591, 882, 884]]<|/det|>
+In the detection arm, the same objective lens (Nikon \(40\times 0.8\mathrm{NA}\) ) in an orthogonal setup was used and pupil- matched to the scanning objective lens (Nikon Plan Apo \(20\times 0.75\mathrm{NA}\) ) through a \(200 - \mathrm{mm}\) tube lens (TTL200- A, Thorlabs) and a \(300 - \mathrm{mm}\) achromatic doublet (AC508- 300- A- ML, Thorlabs). A \(50:50\) polarizing beam splitter (PBS) (10FC16PB.3, Newport), splits the beam in S and P polarized light. Using mirrors M1 and M2 these light paths where then launched at an angle towards the Obj2 (Supplementary Fig.2). It is extremely critical to minimize the angle of the launch. Both experiment and simulation predicted that we used 8 degrees as the launch angle (called 0) (Fig.2a, inset of Supplementary Fig.2). The S and P polarized light passed through a quarter waveplate (AQWP10M, Thorlabs) and were focused onto a mirror positioned at the focus of the scanning objective lens. The mirror (PF03- 03- P01 - 07.0 mm Protected Silver Mirror, Thorlabs) was attached to a voice coil with a travel of \(10\mathrm{mm}\) , positional repeatability of fewer than 50 nanometers, and a response time of fewer than 3 milliseconds (LFA- 2010, Equipment Solutions). Then the reflected light was recaptured by the same scanning objective lens and quarter- wave plate to rotate the beam's polarization state. Afterward, the light was directed toward an sCMOS camera (Hamamatsu Orca- fusion BT) by reflecting from the same cube polarizing beam splitter and a \(300 - \mathrm{mm}\) achromatic doublet (AC508- 300- A- ML, Thorlabs). For emission filters, we used two long- pass filters (FF01- 525/30- 25, and BLP01- 647R- 25, Semrock), for blue, and far- red, respectively. To image dual channels simultaneously, the field of view (FOV) was separated into half using dichroic mirrors (DMLP605R, Thorlabs) between the \(300 - \mathrm{mm}\) achromatic doublet and the camera. We immersed the specimen and the illumination and detection objectives in a chamber designed using Adobe Inventor and machined through Protolabs (R). The LFA and GSM, in the detection and illumination arms respectively, were synchronized together to always keep the translated light sheet in the focus of the detection objective lens to acquire a 3D stack of the specimen.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 473, 105]]<|/det|>
+## Overlaying S and P images with sub-pixel accuracy  
+
+<|ref|>text<|/ref|><|det|>[[115, 119, 882, 164]]<|/det|>
+Two identical images - - one corresponding to S and another to P polarized light - - are formed at the camera and added incoherently to generate the final image. We used a custom- written MATLAB script to monitor the offset between the two images in near real- time while adjusting the positions of M1 and M2 (Supplementary Fig.6).  
+
+<|ref|>text<|/ref|><|det|>[[115, 176, 882, 220]]<|/det|>
+The offset between the two images using a cross- correlation- based algorithm as was used in Wester, M.J. et al44, which achieves sub- pixel accuracy by fitting second- order polynomials through the peak of the scaled cross- correlation between the S and P polarized images.  
+
+<|ref|>text<|/ref|><|det|>[[115, 231, 882, 308]]<|/det|>
+Initially, an image is acquired as a reference by obstructing one optical path (either S or P). Subsequently, the alternative optical path is used to collect new images. The shift between each new image and the reference image is then measured using the method described in Wester, M.J. et al44 and is available as the MIC_Reg3DTrans.findStackOffset method in the matlab- instrument- control toolbox45. And while new images are collecting, mirrors M1 and M2 are adjusted to minimize the shift.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 323, 252, 337]]<|/det|>
+## Microscope control  
+
+<|ref|>text<|/ref|><|det|>[[114, 347, 882, 582]]<|/det|>
+A Dell Precision 7920 computer with two processors Intel(R) Xenon(R) Silver 4210R CPU having a processing speed of 2.40 GHz and \(2.39\mathrm{GHz}\) and was integrated with 128 GB RAM was used to acquire the microscope's data. An NVIDIA Quadro RTX 4000 Graphics processing unit (GPU) with dedicated memory of 8 GB and shared memory of 63.8 GB (GPU memory of 71.8 GB) was also integrated into the system. 64- bit operating system \(\times 64\) - based processor facilities the system to operate. LabView 2020 64- bit allowed us to work with the required software, including the LabView Run- Time Engine, Vision Run- Time Module, Vision Development Module, and other required drivers like NI- RIO drivers (National Instruments). DCAM- API software was used for the Active Silicon Firebird frame- grabber to actively interfere with the scientific complementary metal- oxide semiconductor (sCMOS) camera (ORCA- Fusion BT Digital CMOS camera, model: C15440- 20UP) manufactured by Hamamatsu, Japan. It generated deterministic transistor logic (TTL) trigger sequences through 150 Watts shutter instrument (100- 240 V\~50/60 Hz; model: MP- 285A) with a field programmable gate array (FPGA) (PCIe 7852R, National Instruments). The generated triggers controlled the resonant mirror galvanometers, placement of the stage, voice coils, blanking and modulation of laser, firing camera, and other external triggers. K- Hyper Terminal software facilitated engaging LFA with the system hardware. Some key features along with some routines under the agreement of material transfer were licensed by the Howard Hughes Medical Institute's Janelia Farms Research Campus.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 593, 255, 608]]<|/det|>
+## Sample preparation  
+
+<|ref|>text<|/ref|><|det|>[[115, 622, 882, 746]]<|/det|>
+Bead sample:200 nm beads embedded in \(2\%\) agarose gel was used for microscope resolution assessment. To make \(2\%\) agarose gel, 2 g of agarose powder (A9045- 25G, SIGMA life science) was mixed with \(100\mathrm{mL}\) water and swirled thoroughly before putting into the microwave oven to heat. Once the solution boiled and got completely clear and the agarose was dissolved, we should remove the solution from the oven and let it cool down. Then, \(200\mathrm{nm}\) beads (YG, Polysciences) were mixed with water with a ratio of \(1 / 100\) to form a solution of the \(200\mathrm{nm}\) beads. It was sonicated before mixing with the molten \(2\%\) agarose gel with a volumetric ratio of \(1 / 10\) . Then this molten combination was poured into the cubic mold where the sample holder was placed there and sat there for a few minutes to dry and form a \(1\mathrm{cm}^3\) cubic sample (200 nm beads embedded into \(2\%\) agarose gel) attached to the sample holder.  
+
+<|ref|>text<|/ref|><|det|>[[115, 761, 882, 882]]<|/det|>
+Cell samples: RBL- 2H3 GFP- FasL cells were cultured in Gibco Minimum Essential Media (MEM) media supplemented with \(10\%\) heat- inactivated Fetal Bovine Serum (FBS), \(1\%\) Penicillin/Streptomycin, and \(1\%\) L- glutamine \(^{31}\) . The cells were primed with \(1\mu \mathrm{g / ml}\) anti- DNP- IgE \(^{46}\) (Fig. 3e- g) or anti- DNP- IgE- CF640R (Fig. 3a- d) and seeded at a density of \(100,000\) cells per well in 12 well dish over \(5\mathrm{mm}\) glass coverslips and incubated with \(5\%\) \(\mathrm{CO_2}\) at \(37^{\circ}\mathrm{C}\) overnight. IgE- CF640R was prepared using CF640R NHS- ester (Biotium #92108). For fast imaging experiments, the cellular membranes of anti- DNP- IgE primed cells were labeled with CellMask™ Deep Red Plasma Membrane Stain (Thermo Fisher Scientific #C10046, \(5\mathrm{mg / ml}\) , 1000X) according to manufacturer's instruction for 10 minutes in modified Hank's balanced salt solution (HBSS) (additional \(10\mathrm{mM}\) Hepes, \(0.05\%\) w/v BSA, \(5.45\mathrm{mM}\) glucose, 0.88
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 89, 881, 120]]<|/det|>
+mM MgSO4, \(1.79\mathrm{mM}\) CaCl2, \(16.67\mathrm{mM}\) NaHCO3) and rinsed with HBSS. Cells were stimulated with \(1\mu \mathrm{g / ml}\) DNPBSA in the sample chamber. Data was acquired in 2 min captures for up to 15 minutes post antigen treatment.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 137, 240, 152]]<|/det|>
+## Sample mounting  
+
+<|ref|>text<|/ref|><|det|>[[115, 166, 882, 285]]<|/det|>
+Cells samples on \(5\mathrm{mm}\) coverslips were loaded onto the holder as depicted in Supplementary Fig.7. In the sample holder, two metal wires were designed to clamp the coverslip tightly. This sample holder was attached to the XYZ Translation Stage with Standard Micrometers using a rotation mount. As a result, the coverslip had four degrees of freedom, including the translation on the \(X - Y - Z\) axis to locate the cells while imaging and the rotation around the X- axis to face the coverslip with the desired angle relative to the illumination and detection objectives. Here, the coverslips were faced 8 degrees relative to the optic axis of the detection objective (Supplementary Fig.7). In order to minimize the buffer volume for live cell imaging, the \(6\mathrm{ml}\) chamber was designed to immerse the sample, illumination, and detection of objective lenses into it (Supplementary Fig.7).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 312, 297, 327]]<|/det|>
+## Image processing pipeline  
+
+<|ref|>text<|/ref|><|det|>[[115, 338, 882, 500]]<|/det|>
+Data were analyzed with the custom script written in Matlab. The procedure for quantifying the microscope's resolution from fluorescence bead data is as follows: 1) A 3D- PSF model was generated from the raw data. 2) The light- sheet region was cropped from each slice of the raw data. The width of the light- sheet region was defined by the distance to the waist of the light- sheet where the axial resolution increases by 2 times. We sat the light- sheet width to be \(\sim 6\mathrm{mm}\) . Note that the light- sheet region translated along its width direction (the \(Y\) - axis) while it was being scanned in the axial direction (Z- axis relative to the detection objective) (Supplementary Fig.8). Therefore, the light- sheet region to be cropped was also shifted in \(Y\) accordingly (Supplementary Video 1). 3) the cropped region was deconvolved with the 3D- PSF model using Richard- Lucy deconvolution from ImageJ. 4) the deconvolved data stack was divided into segments with an axial dimension of \(5\mu \mathrm{m}\) . For each segment, candidate beads were selected and their FWHMs along each dimension were estimated from Gaussian fitting of their intensity profiles along that dimension. 5) the measured FWHMs were used to quantify the resolution of the microscope as shown in Fig. 2d.  
+
+<|ref|>text<|/ref|><|det|>[[115, 510, 882, 698]]<|/det|>
+Dual- color live- cell data was processed as follows: 1) cell signal from each color channel was cropped with a user- selected region. 2) for each color channel, the XYZ drifts of the data stack at each time point relative to the reference data stack were estimated, where the maximum- intensity projection (MIP) along each dimension of the two data stacks was generated and the 2D shift between each pair of the MIP images was calculated through cross- correlation. 3) an average of the XYZ shifts from both channels was used to correct the drift between time points. 4) the XYZ shift between the two- color channels was calculated by first averaging over the time dimension for each color channel, then estimating the shift from the MIP images as in step 3. Then register the two channels by applying the estimated shift. 5) after drift correction and channel registration, the resulting image stacks were deconvolved with the 3D- PSF model generated from the bead data using Richard- Lucy deconvolution from Matlab. 6) to reduce noise and correct photobleaching, the deconvolved images were subtracted by a background value with negative pixel values set to zero and divided by a normalization factor equal to the 99.95 quantiles of all pixel values in the corresponding time points and color channel.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 711, 395, 726]]<|/det|>
+## Quantification of Light-sheet dimension  
+
+<|ref|>text<|/ref|><|det|>[[115, 738, 882, 848]]<|/det|>
+To quantify the light- sheet dimension, bead data in agarose gel were collected at different slit widths. At each slit width, we estimated the FWHMs in XYZ for all selected beads as described above, however, here we used the full FOV of the color channel for bead imaging. As the position of the light- sheet waist shifted in y with respect to the axial dimension, we corrected the y coordinates of the selected bead by \(y_{Cor}^{\prime} = y_{Cor} - az_{Cor}\) , where \(a\) is the y shift by moving one pixel in \(Z\) (Supplementary Fig.8). Then we fitted the \(FWHM_{Z}\) verse \(y_{Cor}^{\prime}\) for all selected beads with a polynomial function (Supplementary Fig.4). The length of the light- sheet was found when the \(FWHM_{Z}\) was twice the minimum from the polynomial fit.  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 862, 295, 876]]<|/det|>
+## Magnification calibration
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 89, 883, 260]]<|/det|>
+One brightfield image of the calibration target was captured at each of the galvo positions from \(- 40\) to \(40\mu \mathrm{m}\) with a step size of \(10\mu \mathrm{m}\) . The target image consisted of parallel line segments, we cropped a region of \(700\mathrm{x}700\) pixels from each image (Supplementary Fig.9a- b). We then calculated the affine transformation (from the Dipimage toolbox) of each image with respect to a reference image. The zoom factors from affine transformation were used to quantify the relative magnification between each image to the reference image. The absolute magnification of one image was calculated as follows: crop a narrow section of multiple parallel lines, obtain the intensity profile by averaging over the line dimension, smooth the intensity profile by applying a running average with a window size of 30 pixels, find all peaks from the smoothed intensity profile (Supplementary Fig.9c), calculate the average distance (in pixels, denoted as \(\Delta d\) ) between consecutive peaks, as the distance between consecutive parallel lines is \(10\mathrm{mm}\) , then the pixel size at the sample plane can be estimated from \(10 / \Delta d\) mm, therefore the magnification can be calculated from the pixel size of the camera divided by pixel size at the sample plane.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 274, 200, 289]]<|/det|>
+## Ray tracing  
+
+<|ref|>text<|/ref|><|det|>[[115, 301, 880, 331]]<|/det|>
+Ray tracing was based on geometric optics with paraxial approximation. The ray propagation was calculated using the ABCD matrices. Two matrices were used, the translation matrix,  
+
+<|ref|>equation<|/ref|><|det|>[[440, 329, 558, 361]]<|/det|>
+\[M_{d} = \left[ \begin{array}{cc}1 & 0\\ d / n & 1 \end{array} \right],\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 360, 304, 374]]<|/det|>
+and the matrix of a thin lens,  
+
+<|ref|>equation<|/ref|><|det|>[[435, 371, 561, 401]]<|/det|>
+\[M_{f} = \left[ \begin{array}{cc}1 & -n / f\\ 0 & 1 \end{array} \right],\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 400, 881, 460]]<|/det|>
+where \(d\) is the translation distance, \(f\) is the focal length of the thin lens and \(n\) is the refractive index of the propagation medium. For our system, \(n\) is 1.33 before the detection objective (including the objective) and \(n\) equals 1 for the rest of the ray tracing. The starting point of each ray was represented by a vector of \([n\alpha ,y]^{T}\) , where \(\alpha\) and \(y\) are the angle and the y position of the ray with respect to the optical axis. The propagation of the ray is then calculated from  
+
+<|ref|>equation<|/ref|><|det|>[[440, 458, 556, 489]]<|/det|>
+\[\left[ \begin{array}{c}n\alpha '\\ y' \end{array} \right] = M\left[ \begin{array}{c}n\alpha '\\ y \end{array} \right].\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 487, 882, 678]]<|/det|>
+For a defined FOV, we selected three field points, two mark the edge of the FOV and one at the optical axis. For each field point, we generated three rays at different angles that will intersect three points at the pupil plane, where two points mark the edge of the pupil and one at the center of the pupil. Rays from the same field point were colored the same. The optical axis after the polarizing beam splitter was rotated by 45 degree to be along the splitting plane of the PBS. The ray tracing after the PBS was done by first transforming the ray coordinates to the ones defined by the optical axis and propagating the ray with the ABCD matrix, then transforming back to the global coordinates. Except for the distance between the tube lens and the detection objective (denoted as \(d_{1}\) ), the rest distances between consecutive optical elements were measured with a ruler. The angle between the chief rays of the S and P- polarization \((\theta\) in Fig.2a) was set when the input and output beam diameters at the remote focusing objective were minimum. The distance \(d_{1}\) was set when the relative magnifications from ray tracing match with the measured ones (Fig. 2b). The central position of the scan range, the distance of the objective to the detection objective (denoted as \(S_{1}\) ), was set when the absolute magnification from ray tracing matches with measured one. Here \(S_{1} = 6.695\mathrm{mm}\) , which was \(45\mu \mathrm{m}\) away from the designed focal plane of the detection objective.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 705, 196, 718]]<|/det|>
+## References  
+
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+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[42, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 333, 177]]<|/det|>
+SupplementaryVideo1. avi SupplementaryFileSept1. pdf
+
+<--- Page Split --->

preprint/preprint__074d5ca947dfa0b3c0d61ffc91ee2ad07daa2a3b9cd623deb20d79df8add57d4/images_list.json

@@ -0,0 +1,47 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1: Temporal behaviour of the fractions of Searches (red, left \\(y\\) -axis) and General News (blue, right \\(y\\) -axis) for the keyword coronavirus in Italy from early December 2019 to the end of August 2020. Searches are reported as a percentage of the maximum observed in the monitored period. General News is represented by the daily fraction of articles containing at least three keyword occurrences (see Materials and Methods). The Improved Model (black line) leverages the past General News and Searches, together with present Searches, to infer the dynamics of General News.",
+    "footnote": [],
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+    "caption": "Figure 2: The ranked components of \\(\\mathbf{S}_{tot}\\) (centre red), representing coronavirus sub-domains sorted by total news demand over the observed time. On the sides of each keyword, a tag indicates the rank in \\(\\mathbf{N}_{tot}\\) for General News, on the left, and in \\(\\mathbf{FN}_{tot}\\) for Fake News, on the right. Tags are distanced from the centre by the amount of rank mismatch to Searches ranks. Tags are coloured to highlight the rank closest to the Searches rank: blue for General News and green for Fake News.",
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+    "caption": "Figure 3: The time series of news annotated as Fake, normalised through the total number of coronavirus-related News compared with the Combined Index for disinformation. The Combined Index is defined as a linear combination of the weighted modelling error for the local fitting of News within the improved Vector Auto-Regression model and the cosine distance between the semantic vectors of Searches and News. The parameters of the combination were fitted in the training set and then tested in the validation set.",
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preprint/preprint__074d5ca947dfa0b3c0d61ffc91ee2ad07daa2a3b9cd623deb20d79df8add57d4/preprint__074d5ca947dfa0b3c0d61ffc91ee2ad07daa2a3b9cd623deb20d79df8add57d4.mmd

@@ -0,0 +1,337 @@
+
+# Assessing disinformation through the dynamics of supply and demand in the news ecosystem  
+
+Pietro Gravino ( \(\boxed{ \begin{array}{r l} \end{array} }\) pietro.gravino@sony.com) Sony CSL Paris Giulio Prevedello Sony CSL Paris Martina Galletti Sony CSL Paris Vittorio Loreto Sony CSL Paris  
+
+## Article  
+
+Keywords: SARS- CoV- 2, social dialogue, information technology  
+
+Posted Date: June 1st, 2021  
+
+DOI: https://doi.org/10.21203/rs.3. rs- 577571/v1  
+
+License: © \(\circledast\) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Version of Record: A version of this preprint was published at Nature Human Behaviour on May 23rd, 2022. See the published version at https://doi.org/10.1038/s41562- 022- 01353- 3.
+
+<--- Page Split --->
+
+# Assessing disinformation through the dynamics of supply and demand in the news ecosystem  
+
+Pietro Gravino\*a, Giulio Prevedelloa, Martina Gallettia, and Vittorio Loretoa,b,c  
+
+aSony Computer Science Laboratories, 75005 Paris, France bSapienza University of Rome, Physics Department, 00185, Rome, Italy cComplexity Science Hub Vienna, A- 1080 Vienna, Austria \*Corresponding author: pietro.gravino@sony.com  
+
+May 31, 2021  
+
+## Abstract  
+
+Social dialogue, the foundation of our democracies, is currently threatened by disinformation and partisanship, with their disrupting role on individual and collective awareness and detrimental effects on decision- making processes. Despite a great deal of attention to the news sphere itself, little is known about the subtle interplay between the offer and the demand for information. Still, a broader perspective on the news ecosystem, including both the producers and the consumers of information, is needed to build new tools to assess the health of the infosphere. Here, we combine in the same framework news supply, as mirrored by a fairly complete Italian news database - partially annotated for fake news, and news demand, as captured through the Google Trends data for Italy. Our investigation focuses on the temporal and semantic interplay of news, fake news, and searches in several domains, including the virus SARS- CoV- 2 pandemic. Two main results emerge. First, disinformation is extremely reactive to people's interests and tends to thrive, especially when there is a mismatch between what people are interested in and what news outlets provide. Second, a suitably defined index can assess the level of disinformation only based on the available volumes of news and searches. Although our results mainly concern the Coronavirus subject, we provide hints that the same findings can have more general applications. We contend these results can be a powerful asset in informing campaigns against disinformation and providing news outlets and institutions with potentially relevant strategies.
+
+<--- Page Split --->
+
+## Introduction  
+
+The Covid- 19 crisis evidenced once more that disinformation stands as one of the major plagues of the Information Age. In the last decades, many national and international institutions started to implement a vast plethora of strategies to tackle this issue [14] and mitigate its effects. Still, the mechanisms underlying the role and phenomenology of disinformation are largely unclear.  
+
+Only in recent times the complex ecosystem of information massively attracted the interest of the scientific community. Disinformation went under investigation, from its very definition [13] to its psychological mechanisms [3], and its spreading dynamics [7]. Detection and forecast of disinformation were also among the relevant topics explored by the scientific community [28]. These studies raised questions about how to identify statistical markers in the news content [8] or about the diffusion mechanisms [33].  
+
+A meaningful part of the research effort focused on the impact of disinformation on diverse fields of human activities, such as consumers' behaviour [34], political elections [2], sustainability [31] or health [20]. During the Covid- 19 pandemic, particularly, the effect of disinformation on social behaviours became so compelling that the term "Infodemic" made a comeback from the SARS epidemic of 2003 [25], to describe the spreading of false or incorrect information about the virus SARS- CoV- 2. The consequences were disastrous [17] and led to dangerous behaviours that further aggravated the epidemic crisis.  
+
+While disinformation is always under the spotlight, the complex ecosystem of information, which is the substrate for disinformation, attracted much less interest. It is important to stress that the infosphere relies on the subtle interplay of two types of actors: news producers on the one hand and news consumers on the other. In this structure, the supply and the demand of information stand in a market- like relationship. The study of their interplay is essential to unveil the mechanisms of information dynamics. It also provides a broader view in which disinformation can be contextualised and analysed.  
+
+The news supply can be identified with the overall news production, mainly consisting of officially recognised newspapers. The general news production had been primarily studied in linguistics [10], while analyses of news content [21] and coverage [26, 29] were often focusing on particular countries or topics. Other works investigated the impacts of news and its consumption on, for example, reading behaviour [30], finance [12], and political opinions [16].  
+
+News demand, instead, is more difficult to pinpoint. In the literature, surveys and lab studies are usual procedures of investigation [32, 30, 18], but, unlike general news production, they cannot scale up to the population level. Thus, different solutions have to be adopted. The tracking of reading behaviours, for example, had been used to study the demands and interests of readers [4]. However, such a methodology is biased by the very existence of news since the interest for topics not covered by news cannot be recorded.  
+
+An independent way to track people interests that gained popularity in the
+
+<--- Page Split --->
+
+scientific community is the Google Trends service \(^{1}\) [19]. It provides an index proportional to the number of searches made with the Google Search engine, enabling the quantitative comparison of searched queries. In the last decade, Google Trends has been mainly used as a marker, and a predictor, of people's behaviours in different contexts, like finance [9, 24], epidemiology [22, 11] or socio- economic indicators [6, 5]. Interestingly, its intrinsic value as a proxy for people's interest was perhaps overlooked. In the framework of news, the Google Trends index has been mainly adopted for forecasting [35], without delving into the comprehension of the dynamics of the news ecosystem.  
+
+Here we comprehend, in a unique framework, the supply and demand for information and analyse their dynamical interplay with the final goal of understanding the main mechanisms of the information ecosystem dynamics and extracting hints about the determinants of disinformation. To this end, we focused on the general production of news in Italy, from early December 2019 to the end of August 2020, as the reference for the news supply. For the same period, the Google Trend index served as a proxy for the general public's information demand.  
+
+We adopted Vector Auto- Regression (VAR) models to study the interplay between news demand and supply, evidencing different causal relationships for distinct subjects. We presented an improved modelling scheme that allows for a quantitative description of the dependencies in the time series evolution for information demand and supply.  
+
+The new framework also permitted to study and compare the disinformation dynamics within the general information system, highlighting behavioural differences in reactivity and modelling efficacy. We observed, in particular, that the semantic misalignment between information supply and demand is higher than the misalignment between disinformation supply and demand.  
+
+These discrepancies could be exploited to aggregate a disinformation risk indicator that is independent of fake news annotations. We contend this index could provide a reliable and independent assessment tool for the news supply's health status.  
+
+## Results  
+
+## Dynamics of news supply and demand  
+
+Information systems feature two main drivers: news supply and news demand. As a reference for the news supply, we looked at the whole Italian production of information, termed General News, from early December 2019 to the end of August 2020. For the same period, the Google Trend index served as a proxy for the news demand from the Italian general public, thus termed Searches (refer to Materials and Methods for more details).  
+
+To investigate the nature of the relation between supply and demand of news about a certain subject, six keywords, referring to the most searched subjects
+
+<--- Page Split --->
+
+in Italy over the entire observation period, were selected: coronavirus, regional, playstation, papa francesco, eurovision, sondaggi (Supplemental Fig. S1)). General News and Searches for coronavirus are reported in Fig. 1. For each keyword, the time series of the daily appearances in the General News and the daily volume of queries in the Searches were simultaneously fit by Vector Auto- Regression (VAR) linear modelling [15]. VAR models with different lag parameters, which encapsulate the system's memory, were considered, and the best parameters were identified via the Akaike criterion [1] (see Materials and Methods). For all keywords, best- fitting lags ranged between 2 and 4, suggesting a typical, short- memory timescale in the system (see Supplemental Fig. S2)).  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1: Temporal behaviour of the fractions of Searches (red, left \(y\) -axis) and General News (blue, right \(y\) -axis) for the keyword coronavirus in Italy from early December 2019 to the end of August 2020. Searches are reported as a percentage of the maximum observed in the monitored period. General News is represented by the daily fraction of articles containing at least three keyword occurrences (see Materials and Methods). The Improved Model (black line) leverages the past General News and Searches, together with present Searches, to infer the dynamics of General News. </center>  
+
+Within the VAR framework, we performed the test for Granger- causality [15] to illustrate which time series, between General News and Searches, contributed more to the prediction of the other, and if any contribution was significant. For the majority of keywords, the contribution of past Searches to present General News was most significant (i.e. coronavirus, regional, playstation, papa francesco) (see Supplemental Fig. S2)). We could safely assume that Searches anticipates General News and use this assumption to improve the model of the temporal behaviour of the latter. We modified the VAR equation for the evo
+
+<--- Page Split --->
+
+
+Table 1: The parameters and the \(R^{2}\) resulting from the improved linear model of equation 1 for the 4 selected keywords. As a reference, in brackets, we report the value for \(R^{2}\) of a trivial model with equation \(N(t) = \alpha N(t - 1)\) , i.e., a model where every day depends only on the day before. The value of \(R^{2}\) of the improved linear model is systematically larger than that of the trivial model. Starred values are those not significantly different from zero.   
+
+<table><tr><td></td><td>coronavirus</td><td>regionali</td><td>playstation</td><td>papa francesco</td></tr><tr><td>α1</td><td>0.82</td><td>0.65</td><td>0.18</td><td>0.54</td></tr><tr><td>α2</td><td></td><td>0.26</td><td>0.19</td><td></td></tr><tr><td>β0</td><td>0.070</td><td>0.0082</td><td>0.00055</td><td>0.0038</td></tr><tr><td>β1</td><td>-0.034</td><td>0.003*</td><td>0.00035</td><td></td></tr><tr><td>β2</td><td></td><td>-0.0064</td><td>0.00068</td><td></td></tr><tr><td>R²</td><td>0.996 (0.991)</td><td>0.89 (0.86)</td><td>0.54 (0.29)</td><td>0.73 (0.63)</td></tr></table>  
+
+lution of General News by inserting Searches' role. More precisely, let \(S(t)\) and \(N(t)\) be, respectively, the values of Searches and General News at day \(t\) , then the new equation for the evolution of \(N(t)\) reads:  
+
+\[N(t) = \sum_{i = 1}^{d}(\alpha_{i}N(t - i) + \beta_{i}S(t - i)) + \beta_{0}S(t). \quad (1)\]  
+
+where the coefficients \(\alpha_{i}\) , \(\beta_{0}\) and \(\beta_{i}\) were fitted, while the Akaike criterion provides the optimal lag \(d\) . This Improved Model closely reproduced the data, particularly in correspondence with the peaks (Fig. 1 for coronavirus and Supplemental Fig. S3).  
+
+The model's parameters also provided a quantitative insight on the interplay between General News and Searches (Tab. 1):  
+
+\(\alpha_{1}\) was larger than other \(\alpha\) parameters, indicating a strong dependence of General News on the previous day activity. This evidence is a sign of an inertial behaviour of the news supply. \(\beta_{0}\) , the weight of present Searches, was typically larger than other \(\beta\) parameters and significantly non- zero, supporting the assumption of present Searches role for the Improved Model. The remaining parameters were smaller though almost always significant. For two keywords (coronavirus and regionali), the parameters \(\beta_{d}\) (for \(d \geq 1\) ) were negative. This result suggests that General News depends on the different quotient of Searches, together with the volume of Searches itself.  
+
+Of note, a direct comparison between \(\alpha\) and \(\beta\) parameters was not possible, as Searches and General News were scaled differently (Google Trends does not disclose the absolute scale of queries volume).
+
+<--- Page Split --->
+
+## The different behaviours of General News and Fake News  
+
+The Improved Model quantifies the information supply dynamics and enables the comparison between General News and disinformation supply. We applied this methodology to the topic coronavirus, since it dominated the landscape of information (Supplemental Fig. S1), and due to the direct impact of disinformation on the response to the 2020 pandemic. To this end, we extended our analysis to the news items that were annotated as false or misleading, thus named Fake News (see Material and Methods).  
+
+We exploited the Improved Model 1 to compare General News and Fake News through their best- fitting coefficients \(\alpha\) and \(\beta\) . To this end, we paralleled the variable \(N(t)\) , the daily proportion of coronavirus- related General News at day \(t\) , and \(FN(t)\) , the daily proportion of coronavirus- related Fake News at day \(t\) (Tab. 2).  
+
+Compared to General News, coronavirus- related Fake News shows a meaningfully lower Inertia term, \(\alpha_{1}\) , and a non- significant \(\beta_{1}\) indicating a greater reactivity to \(S(t)\) . These pieces of evidence and the lower prediction score (adjusted \(R^{2}\) ) suggest that disinformation presents a different behaviour than General News, to the points that it distorts the dynamics of the news ecosystem and leads to impaired modelling performance.  
+
+Table 2: Coefficients from the Improved Model fitting of General News and of Fake News having at least one occurrence of the keyword coronavirus (see Materials and Methods). Starred coefficients do not differ significantly from zero.   
+
+<table><tr><td></td><td>General News</td><td>Fake News</td></tr><tr><td>α1 (Inertia)</td><td>0.860 ± 0.016</td><td>0.758 ± 0.039</td></tr><tr><td>β0</td><td>0.460 ± 0.035</td><td>0.294 ± 0.086</td></tr><tr><td>β1</td><td>-0.248 ± 0.042</td><td>-0.081* ± 0.091</td></tr><tr><td>R²</td><td>0.995</td><td>0.931</td></tr></table>  
+
+Another difference in the behaviour of news and disinformation emerged at a semantic level. We focused on the most queried keywords searched together with coronavirus in Google Search (see Materials and Methods). Each of these related queries provided a time series of news demand about a sub- domain that co- occurs with, and therefore is semantically linked to, coronavirus. We quantified the co- occurrence of these terms with the coronavirus keyword also in the news items, for both General News and Fake News. In this way, we defined \(\mathbf{S}(t), \mathbf{N}(t), \mathbf{FN}(t)\) as the daily semantic vectors for coronavirus- related Searches, General News, and Fake News, respectively. Each vector has seventeen entries, one per sub- domain (see Materials and Methods for more details).  
+
+We calculated \(\mathbf{S}_{tot} = \sum_{t} \mathbf{S}(t)\) and sort its components to rank the different sub- domains by the total news demand over the period considered (Fig. 2). To assess the difference between information and disinformation with respect to the matching of news demand for different sub- domains, we challenged the
+
+<--- Page Split --->
+
+components' rankings of \(\mathbf{N}_{tot} = \sum_{t}\mathbf{N}(t)\) and \(\mathbf{FN}_{tot} = \sum_{t}\mathbf{FN}(t)\) against the corresponding ones of \(\mathbf{S}_{tot}\) (Fig. 2).  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 2: The ranked components of \(\mathbf{S}_{tot}\) (centre red), representing coronavirus sub-domains sorted by total news demand over the observed time. On the sides of each keyword, a tag indicates the rank in \(\mathbf{N}_{tot}\) for General News, on the left, and in \(\mathbf{FN}_{tot}\) for Fake News, on the right. Tags are distanced from the centre by the amount of rank mismatch to Searches ranks. Tags are coloured to highlight the rank closest to the Searches rank: blue for General News and green for Fake News. </center>  
+
+Given the coronavirus- related keywords ranked from the Searches as a reference, Fake News ranking shows fewer and minor mismatches compared to General News. We quantified this difference in behaviour through Spearman's Correlation. \(\mathbf{S}_{tot}\) and \(\mathbf{N}_{tot}\) components resulted positively correlated ( \(r = 0.52\) , with a p- value of 0.031) but \(\mathbf{S}_{tot}\) and \(\mathbf{FN}_{tot}\) correlated more ( \(r = 0.67\) , with a p- value of 0.0032).  
+
+The semantic difference in the behaviour of Fake News and General News holds not only at the aggregated level but also at a daily level. This was mea
+
+<--- Page Split --->
+
+sured through the cosine distance \(\mathrm{d}(\cdot ,\cdot)\) on their daily vectors \(\mathbf{S}(t)\) , \(\mathbf{N}(t)\) and \(\mathbf{FN}(t)\) (see Materials and Methods). Again, Searches were taken as reference and we calculated its cosine distance from General News, \(\mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))\) , and from Fake News, \(\mathrm{d}(\mathbf{S}(t),\mathbf{FN}(t))\) . The daily relative difference between the cosine distances of Searches- Fake News and Searches- General News  
+
+\[\frac{\mathrm{d}(\mathbf{S}(t),\mathbf{FN}(t)) - \mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))}{\mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))} \quad (2)\]  
+
+resulted in negatives values in most days \(t\) (Supplemental Fig. S5)). In fact, both the Mean \((- 0.13)\) and Median \((- 0.15)\) were negative, indicating that the cosine distance Searches- Fake News is generally smaller than that of Searches- General News. This result shows how Fake News meets news demand better than General News.  
+
+## Independent detection of Fake News concentration  
+
+The observed differences between General News and Fake News dynamics can be exploited to assess disinformation about the topic coronavirus.  
+
+The difference in modelling Fake and General News suggests that when Fake News concentration on a topic rises, the General News dynamics, which includes Fake News, becomes perturbed. We hypothesise that this perturbation is expected to impair the General News modelling performance. To test this hypothesis, the Improved Model was fit to General News locally on a time window of 14 days, sliding over the entire data time range (see Materials and Methods). For each window, centred in \(t\) , we computed the local modelling error defined as:  
+
+\[E(t) = (1 - R^{2}(t))\cdot \langle N\rangle (t), \quad (3)\]  
+
+where \(R^{2}(t)\) , the \(R^{2}\) score for the model fitted to the window, is weighted by \(\langle N\rangle (t)\) , the average volume of news produced in that time window.  
+
+Although formulated without exploiting disinformation annotations, \(E(t)\) significantly correlates with the concentration of Fake News on the coronavirus subject, \(FN(t) / N(t)\) (Spearman's \(r = 0.47\) , with a p- value of \(3.9\cdot 10^{- 13}\) (see Materials and Methods). This result supports the hypothesis that loss of predictability from the General News dynamics co- occurs with disinformation spikes. As a consequence, \(E(t)\) stands as a very promising proxy for the concentration of disinformation about the topic coronavirus.  
+
+The semantic difference between General News and Fake News suggests that disinformation might receive greater attention thanks to its ability to match the news demand semantically unsatisfied. We hypothesized that as General News becomes more semantically distant from Searches, Fake News would fill that gap. This hypothesis was tested all over the time range measuring the daily cosine distance between the semantic vectors of Searches and General News \(K(t) = \mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))\) . We then checked the correlation of \(K(t)\) with the daily concentration of Fake News, \(FN(t) / N(t)\) , about coronavirus. The correlation turns out to be positive and significant (Spearman's \(r = 0.58\) , with a p- value of
+
+<--- Page Split --->
+
+\(1.6 \cdot 10^{- 21}\) ), supporting the hypothesis. This result allows us to adopt \(K\) as a second independent indicator for Fake News concentration assessment.  
+
+To test the effectiveness of our indicators \(E\) and \(K\) in assessing disinformation concentration, we combined them in a Combined Index for disinformation (see Material and Methods). We fit them linearly on a training set composed of approximately the first \(25\%\) of data from the time series, providing the best linear combination of the two (see Fig. 3).  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3: The time series of news annotated as Fake, normalised through the total number of coronavirus-related News compared with the Combined Index for disinformation. The Combined Index is defined as a linear combination of the weighted modelling error for the local fitting of News within the improved Vector Auto-Regression model and the cosine distance between the semantic vectors of Searches and News. The parameters of the combination were fitted in the training set and then tested in the validation set. </center>  
+
+The Combined Index was then tested against the validation set, achieving substantial accuracy (reduced chi- squared statistic of 0.945). All these findings suggest that the Combined Index provides a valuable measure for detecting disinformation concerning SARS- CoV- 2.  
+
+The methodology could also be applied to different topics, and to the aggregation of several topics, to assess the health status of the news ecosystem at a more general level. To challenge this claim, we considered the set of the 4 keywords modelled. We aggregated them to create a synthetic macro- topic, for which they individually represented the analogous of the related queries we have seen before. We judged the adoption of the first indicator, i.e. the weighted modelling error for the local fitting, to be pointless since the macro- subject dynamics is largely dominated by the topic coronavirus. This would have resulted
+
+<--- Page Split --->
+
+in an indicator similar to the modelling of the coronavirus component alone. We thus focused only on the second indicator, i.e., the cosine distance between the semantic vectors of Searches and News, where the components of the vectors are now the values of General News, Fake News, and Searches for the 4 keywords. The daily value of cosine distance between General News and Searches of the synthetic subject correlates positively and meaningfully with the concentration of disinformation on the synthetic subject (Spearman's correlation of 0.44 with p- value \(= 1.8 \cdot 10^{- 11}\) ). This result supports the plausibility of the application of our methodology in wider contexts.  
+
+## Discussion  
+
+Information quality is a fundamental challenge for the Information Age, especially during a pandemic. Studying the general news system and comparing it with the subset of news labelled as disinformation, we found that pandemic- related Fake News production seems more reactive and precise than General News supply in addressing people's news demand. We exploited such a difference to develop an index for vulnerability of specific topics to disinformation takeover.  
+
+The analysis of Searches and General News for coronavirus and a set of other coronavirus- unrelated highly queried keywords exposed the relation between supply and demand of news: (i) a linear modelling scheme was effective in almost all cases; (ii) the memory of the process seems to be very short (2- 4 days) in all cases; (iii) causality was more commonly directed from Searches to General News (e.g. for coronavirus). Thanks to these considerations, an improved descriptive model could be developed to better describe the relationship between supply and demand for information. This modelling framework allowed us to discern how the inertia of news suppliers is one of the main traits of the dynamics for all the studied keywords. Also, the negative dependence on previous days Searches observed in some cases suggests a dynamics where the trend of the interest is more important than the interest itself for news producers.  
+
+The comparison of coronavirus- related General News and Fake News through the improved linear model's lens exposed that Fake News feature lower inertia and a different dependence on Searches, quantifying their more reactive behaviour. We can speculate that this behavioural difference could be a consequence of the different production environments of General News and Fake News. The firsts are mainly produced by a large and well- established community of professional journalists while the latter are the outcome of by a scattered multitude of small, unorganized actors. The community size effect might be responsible for the different inertial behaviour observed.  
+
+The semantic analysis revealed another key difference between the dynamics of General News and Fake News. Looking at the shares of the most queried keywords co- occurring with coronavirus we discovered that Fake News is better aligned to Searches than General News not only at a cumulative level but also daily over the entire observation period. This result suggests that disinformation
+
+<--- Page Split --->
+
+tends to be more semantically precise than information in matching people's interests. This difference might be explained considering the different aims of the two communities. While they are both interested in answering people's demand for information, general news producers also have the ambition for complete coverage of topics, while Fake News producers can focus on chasing the people's attention.  
+
+We exploited the modelling and the semantic mismatch between General News and Fake News to detect bursts of disinformation on coronavirus. It is worth mentioning how this measure was performed without any information about FakeNews, looking instead only at the time- series of General News and Searches. The modelling difference resulted in a destabilizing effect of Fake News peaks on the modelling of General News as a function of Searches. Such a perturbation was measured as the local weighted modelling error in the Improved Model for General News as a function of Searches. A higher value of this indicator means that the normal relation between General News and Searches has been altered, probably by Fake News presence. The semantic difference was estimated from daily misalignment itself between General News and Searches. In this case, a higher value of this indicator means that semantic imprecision leaves an unsatisfied interest in readers, possibly fostering Fake News.  
+
+The positive and meaningful correlation of both indicators with Fake News concentration on Coronavirus supports both the hypothesis: (i) disinformation perturbs the normal relation between General News and Searches and (ii) is fueled by the semantic misalignment between the two.  
+
+We blend the two markers into a single Combined Index for disinformation by adopting a training set for its definition and testing it on a validation set with good results. Given its independence from Fake News annotations and the hints supporting a possible generalization of the result to other topics, the Combined Index can be a powerful tool for journalists and editors as well as for news monitoring authorities to detect in real- time vulnerabilities to disinformation. Our results also suggest, as a possible strategy to face these vulnerabilities, a timely refocus of General News supply to better meet the information demand of the public.  
+
+Information vulnerabilities are a major risk factor for our societies, as they have a direct impact on individuals. For example, the solution to the Coronavirus crisis depends mainly on individual behaviours which, in turn, are directly affected by the news. The approach presented here, far from being conclusive, represents a first contribution towards a deeper understanding of the phenomenology of disinformation as part of the information ecosystem's general dynamics. Further studies will be needed to test the conclusions and to generalize the results to different countries, languages, domains, and time periods. Moreover, the diffusion layer should be added to the analysis of the dynamics of the infosphere, with particular attention to the social media spreading of news. In our opinion, a paradigm shift in facing disinformation is no more an option, is a necessity for information societies. We contend that the presented work contributes to the shift of scientific research towards a more concrete view, aiming to provide policymakers with knowledge and tools to fight disinformation.
+
+<--- Page Split --->
+
+## Materials and Methods  
+
+## Searches Data  
+
+The information demand about a specific subject was obtained from Google Trends, a platform providing access to an anonymous sample of actual search requests made in Google Search engine, from a selected location and time interval.  
+
+For each given keyword, Google Search returns a time- series with values proportional to the number of times the keyword was searched each day. Since Google Search does not disclose the actual number of searches, the time series values are rendered as percentages of the maximum number returned. As a result, data consist of integers ranging in the interval \((0,100)\) . The time series of one keyword was referred to as the "Searches" for that keyword and provided a measure of the interest it received.  
+
+The use of "pytrends" library for Python \(^2\) enabled the interaction with the Google Trends platform. The terms from Supplemental Fig. S1 were requested separately, for the time ranging from the 6th of December 2019 to the 31st of August 2020 in Italy. These were: coronavirus, regionali (regional elections), playstation, papa francesco (Pope Francesco), eurovision (the European music contest), sondaggi (polls).  
+
+Google Trends also provided information about queries most searched with a specific keyword. In particular, the most popular queries related to the keyword coronavirus (e.g., coronavirus news ) were gathered. Such list is capped by Google Trends at a maximum of 25 related keywords, ordered by most searched to least, and denoted \(q_{1}(t),\ldots ,q_{25}(t)\) respectively ( \(t\) indicating the time), with \(q_{0}(t)\) the time series of coronavirus searches.  
+
+To compare the searches of a given keyword with its related keywords, it is necessary to put them on the same scale. To this end, searched items were queried in pairs. In this way, Google Trends normalized the two resulting time series for the highest of the maximums of the two. Given the two times- series per request \((q_{i - 1}(t),q_{i}(t))\) , with \(i = 1,\ldots ,25\) , a coefficient \(\alpha_{i} = \max_{t}(q_{i - 1}(t)) / \max_{t}(q_{i}(t))\) was calculated. Thus, all the time series \(q_{i}\) could be set on the same scale of \(q_{0}\) , multiplying by \(\prod_{j = 1}^{i}\alpha_{j}\) . This procedure is needed not to lose resolution on keywords with a small number of queries. Having queried for pairs \((q_{0}(t),q_{i}(t))\) , would have resulted in a rounding at 0 performed by Google Trends.  
+
+coronavirus- related queries were then aggregated by summing up their time- series. Thus, coronavirus oggi (Coronavirus today), coronavirus notizie (Coronavirus news), coronavirus ultime (Coronavirus latest), coronavirus ultime notizie (Coronavirus latest news) and coronavirus news, were all aggregated into coronavirus news. Subsequently, we removed all the queries that returned the same search results as another query. These were coronavirus contagi (Coronavirus infections) and coronavirus in italia (Coronavirus in Italy), duplicates
+
+<--- Page Split --->
+
+of contagi coronavirus (Coronavirus infections), and coronavirus italia (Coronavirus Italy), respectively. Also, the query corona was excluded because it has other meanings in Italian, namely "crown", and it is also a famous brand of beer. Finally, the list of queries associated with coronavirus, ordered by the amount of searches, was: news, italia (Italy), lombardia (Lombardy), sintomi (symptoms), contagi (infections), casi (cases), morti (deaths), bollettino (bulletin), roma (Rome), dati (data), mondo (world), mappa (map), sicilia (Sicily), veneto, campania, decreto (decree), milano (Milan), piemonte (Piedmont).  
+
+## News Data  
+
+To analyse the news supply, we investigated the data provided by AGCOM, the Italian Authority for Communications Guarantees, which granted us access to the content of a vast number of Italian news sources published online and offline from the 6th of December 2019 to the 31st of August 2020 in Italy. These data included articles from printed and digital newspapers and information agencies, TV, radio sites, and scientific sources. Moreover, the data had a specific annotation for "fake news" sources. The list disinformation sources, vetted by the Authority, is provided by fact- checking organizations like bufale.net and butac.it. It had already been employed for other studies on disinformation [33].  
+
+After pre- processing the data for duplicates and incomplete logs elimination, the General News data consisted of almost 7 million entries from 554 different news sources. Each data entry has a unique ID and contains, among other information, the title and the content of the piece of news, its date, its source, and the annotation of belonging to the disinformation sources list).  
+
+Needing to imitate the rationale underlying Google Trends data, where daily search counts refer to the query of specific keywords, we sought to find counts of daily keywords also in the news data. To do so, given a keyword (e.g., coronavirus), we defined three different metrics: the piece of news containing the keyword at least once, those having the keyword at least three times, and finally, all the occurrences of a specific keyword. These three metrics were then normalized on the total number of news' sources per day to level the press activity during weekends. For each model, we chose the metric with the best modelling performances. For the improved version of the VAR model described in equation 1 from the Results section, the metric with at least three occurrences was selected, even if the other two showed similar performances. Instead, the most inclusive metric (at least one occurrence) was adopted when dealing with disinformation. This procedure was necessary to enhance the signal, given the low number of Fake News items encountered. For consistency, the overall General News was considered with the same metric (at least one occurrence) when comparing it with the Fake News time series.  
+
+Following the same rationale, we adopted the first metric to filter for the keywords related to the Coronavirus subject described in the previous subsection. To do so, we selected the piece of news containing the keyword coronavirus at least once, and, in this subset, we counted the ones featuring the desired related keyword at least once. The values found were normalized on the total
+
+<--- Page Split --->
+
+number of news pieces having the keyword coronavirus at least once per day to get a proxy for the share of Coronavirus piece of information focused on the related keyword sub- domain. We repeated this analysis for the subset of news mentioning the keyword coronavirus at least once and marked as Fake News in the data. We then used the values extracted from this analysis to investigate the disinformation supply in the Coronavirus context.  
+
+## Time Series Analysis  
+
+Time series of Searches and General News, from Supplemental Fig. S1, were investigated using the VAR model [15], using Python's statsmodels package for time series analysis [27]. Data were regularized via \(x \mapsto \log (1 + x)\) transformation before fitting. For the VAR modelling, the number of lags \(d\) was determined as the parameter that minimized the Akaike information criterion [1], with \(d\) ranging in the interval \((1, 14)\) . This modelling strategy was chosen to ensure the interpretability of the fitted model and its regression coefficients.  
+
+From the VAR model, we computed Granger- causality [15] to test whether queries' values provided meaningful information to the prediction of news volumes and vice versa. Since two tests were performed on the same data from a given subject (for the null hypotheses "Searches do not Granger- cause General News" and "General News do not Granger- cause Searches"), resulting p- values were corrected by the Holm- Bonferroni method [23] Thus, pairs of p- values in Supplemental Fig. S2 were multiplied by 2, to control for family- wise error rate and to maintain comparability.  
+
+In Fig. 1 and Supplemental Fig. S3, the Improved Models for regression of the General News were derived adjusting the VAR models to include Searches at time \(t\) (Supplemental Fig. S3). Lags were re- elaborated through the Akaike criterion as before, with similar results. These models were then compared against a null model that forecasts one day proportionally to the value of the day before to benchmark how beneficial the addition of regressing variables was to General News's prediction (see Tab. 1).  
+
+To assess the semantic misalignment between General News and Searches from Supplemental Fig. S5, the cosine distance was calculated as \(\mathrm{d}(\mathbf{S}(t), \mathbf{N}(t)) = 1 - \mathbf{S}(t) \cdot \mathbf{N}(t) / |\mathbf{S}(t)| |\mathbf{N}(t)|\) , on the vectors \(\mathbf{S}(t) = (S_{1}(t), \ldots , S_{k}(t))\) , \(\mathbf{N}(t) = (N_{1}(t), \ldots , N_{k}(t))\) where \(S_{i}(t)\) and \(N_{i}(t)\) represented the volumes of searches and news, respectively, at time \(t\) for the \(i\) - th keyword associated to coronavirus, with \(\cdot\) being the dot product and \(|\cdot |\) the Euclidean norm. Cosine distance was suitable to compare high- dimensional vectors at different scales, and returned values in \((0, 1)\) for vectors with non- negative entries such as \(\mathbf{S}(t)\) and \(\mathbf{N}(t)\) .  
+
+## Combined Index Validation  
+
+To define and validate the Combined Index from Fig. 3, we split the daily data from Fake News concentration on coronavirus into a training set (from the 29th of January 2020 to the 20th of March 2020) and a validation set (from the 21st of March 2020 on).
+
+<--- Page Split --->
+
+Thus, we defined the Combined Index as a linear combination of the two starting indexes that best fitted the Fake News concentration, using a linear model with Gaussian noise on the training data. The ordinary least squares estimate \(\hat{\sigma}\) for the variance of the Gaussian noise was then calculated as the Mean Squared Error (MSE) divided by the statistical degrees of freedom \(k\) (i.e., the number of observations minus 2, the number of parameters in the model).  
+
+To assess the predictive potential of the Combined Index, we adopted the trained model to forecast the concentration of Fake News in the validation set. This prediction's goodness was tested through the reduced chi- squared statistic, which is calculated as the MSE on the validation set divided by \(\hat{\sigma}\) . This statistic is approximately distributed as a \(\chi^{2}\) with as many degrees of freedom as the size of the validation set (i.e., 51), leading to a p- value of about 0.945. As such, the null hypothesis, that the concentration of Fake News for the keyword coronavirus is distributed in agreement with the trained model, cannot be rejected.  
+
+## Acknowledgements  
+
+The Authors wish to warmly thank Marco Delmastro of AGCOM for insightful discussions about the Italian news ecosystem as well as for providing the database of Italian news. The database was shared in the framework of the Task Force on "Digital Platforms and Big Data - Covid- 19 Emergency", established by the AGCOM to contribute, among other things, to the fight against online disinformation on issues related to the SARS- CoV- 2 crisis.  
+
+## References  
+
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+
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+
+<--- Page Split --->
+
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+
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+
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+
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+
+<--- Page Split --->
+
+[19] Seung- Pyo Jun, Hyoung Sun Yoo, and San Choi. Ten years of research change using google trends: From the perspective of big data utilizations and applications. Technological forecasting and social change, 130:69- 87, 2018.  
+
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+
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+
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+
+[23] Erich L Lehmann and Joseph P Romano. Testing statistical hypotheses. Springer- Verlag New York, 3 edition, 2006.  
+
+[24] Tobias Preis, Helen Susannah Moat, and H Eugene Stanley. Quantifying trading behavior in financial markets using google trends. Scientific reports, 3:1684, 2013.  
+
+[25] David J Rothkopf. When the buzz bites back. The Washington Post, 11:B1- B5, 2003.  
+
+[26] Andreas Schmidt, Ana Ivanova, and Mike S Schafer. Media attention for climate change around the world: A comparative analysis of newspaper coverage in 27 countries. Global Environmental Change, 23(5):1233- 1248, 2013.  
+
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+
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+
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+
+<--- Page Split --->
+
+[32] Marc Trussler and Stuart Soroka. Consumer demand for cynical and negative news frames. The International Journal of Press/Politics, 19(3):360- 379, 2014.  
+
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+
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+
+[35] Brian Weeks and Brian Southwell. The symbiosis of news coverage and aggregate online search behavior: Obama, rumors, and presidential politics. Mass communication and society, 13(4):341- 360, 2010.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+GravinoetalSl.pdf
+
+<--- Page Split --->

preprint/preprint__074d5ca947dfa0b3c0d61ffc91ee2ad07daa2a3b9cd623deb20d79df8add57d4/preprint__074d5ca947dfa0b3c0d61ffc91ee2ad07daa2a3b9cd623deb20d79df8add57d4_det.mmd

@@ -0,0 +1,458 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 933, 177]]<|/det|>
+# Assessing disinformation through the dynamics of supply and demand in the news ecosystem  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 448, 377]]<|/det|>
+Pietro Gravino ( \(\boxed{ \begin{array}{r l} \end{array} }\) pietro.gravino@sony.com) Sony CSL Paris Giulio Prevedello Sony CSL Paris Martina Galletti Sony CSL Paris Vittorio Loreto Sony CSL Paris  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 417, 102, 435]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 455, 597, 475]]<|/det|>
+Keywords: SARS- CoV- 2, social dialogue, information technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 494, 288, 512]]<|/det|>
+Posted Date: June 1st, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 531, 463, 550]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3. rs- 577571/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 568, 910, 610]]<|/det|>
+License: © \(\circledast\) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 648, 914, 690]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Human Behaviour on May 23rd, 2022. See the published version at https://doi.org/10.1038/s41562- 022- 01353- 3.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[216, 202, 781, 255]]<|/det|>
+# Assessing disinformation through the dynamics of supply and demand in the news ecosystem  
+
+<|ref|>text<|/ref|><|det|>[[243, 271, 752, 306]]<|/det|>
+Pietro Gravino\*a, Giulio Prevedelloa, Martina Gallettia, and Vittorio Loretoa,b,c  
+
+<|ref|>text<|/ref|><|det|>[[219, 319, 777, 405]]<|/det|>
+aSony Computer Science Laboratories, 75005 Paris, France bSapienza University of Rome, Physics Department, 00185, Rome, Italy cComplexity Science Hub Vienna, A- 1080 Vienna, Austria \*Corresponding author: pietro.gravino@sony.com  
+
+<|ref|>text<|/ref|><|det|>[[441, 430, 553, 447]]<|/det|>
+May 31, 2021  
+
+<|ref|>sub_title<|/ref|><|det|>[[465, 478, 530, 491]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[256, 498, 740, 817]]<|/det|>
+Social dialogue, the foundation of our democracies, is currently threatened by disinformation and partisanship, with their disrupting role on individual and collective awareness and detrimental effects on decision- making processes. Despite a great deal of attention to the news sphere itself, little is known about the subtle interplay between the offer and the demand for information. Still, a broader perspective on the news ecosystem, including both the producers and the consumers of information, is needed to build new tools to assess the health of the infosphere. Here, we combine in the same framework news supply, as mirrored by a fairly complete Italian news database - partially annotated for fake news, and news demand, as captured through the Google Trends data for Italy. Our investigation focuses on the temporal and semantic interplay of news, fake news, and searches in several domains, including the virus SARS- CoV- 2 pandemic. Two main results emerge. First, disinformation is extremely reactive to people's interests and tends to thrive, especially when there is a mismatch between what people are interested in and what news outlets provide. Second, a suitably defined index can assess the level of disinformation only based on the available volumes of news and searches. Although our results mainly concern the Coronavirus subject, we provide hints that the same findings can have more general applications. We contend these results can be a powerful asset in informing campaigns against disinformation and providing news outlets and institutions with potentially relevant strategies.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[216, 153, 362, 173]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[216, 184, 780, 259]]<|/det|>
+The Covid- 19 crisis evidenced once more that disinformation stands as one of the major plagues of the Information Age. In the last decades, many national and international institutions started to implement a vast plethora of strategies to tackle this issue [14] and mitigate its effects. Still, the mechanisms underlying the role and phenomenology of disinformation are largely unclear.  
+
+<|ref|>text<|/ref|><|det|>[[216, 260, 780, 366]]<|/det|>
+Only in recent times the complex ecosystem of information massively attracted the interest of the scientific community. Disinformation went under investigation, from its very definition [13] to its psychological mechanisms [3], and its spreading dynamics [7]. Detection and forecast of disinformation were also among the relevant topics explored by the scientific community [28]. These studies raised questions about how to identify statistical markers in the news content [8] or about the diffusion mechanisms [33].  
+
+<|ref|>text<|/ref|><|det|>[[216, 366, 780, 486]]<|/det|>
+A meaningful part of the research effort focused on the impact of disinformation on diverse fields of human activities, such as consumers' behaviour [34], political elections [2], sustainability [31] or health [20]. During the Covid- 19 pandemic, particularly, the effect of disinformation on social behaviours became so compelling that the term "Infodemic" made a comeback from the SARS epidemic of 2003 [25], to describe the spreading of false or incorrect information about the virus SARS- CoV- 2. The consequences were disastrous [17] and led to dangerous behaviours that further aggravated the epidemic crisis.  
+
+<|ref|>text<|/ref|><|det|>[[216, 486, 780, 606]]<|/det|>
+While disinformation is always under the spotlight, the complex ecosystem of information, which is the substrate for disinformation, attracted much less interest. It is important to stress that the infosphere relies on the subtle interplay of two types of actors: news producers on the one hand and news consumers on the other. In this structure, the supply and the demand of information stand in a market- like relationship. The study of their interplay is essential to unveil the mechanisms of information dynamics. It also provides a broader view in which disinformation can be contextualised and analysed.  
+
+<|ref|>text<|/ref|><|det|>[[216, 607, 780, 697]]<|/det|>
+The news supply can be identified with the overall news production, mainly consisting of officially recognised newspapers. The general news production had been primarily studied in linguistics [10], while analyses of news content [21] and coverage [26, 29] were often focusing on particular countries or topics. Other works investigated the impacts of news and its consumption on, for example, reading behaviour [30], finance [12], and political opinions [16].  
+
+<|ref|>text<|/ref|><|det|>[[216, 697, 780, 802]]<|/det|>
+News demand, instead, is more difficult to pinpoint. In the literature, surveys and lab studies are usual procedures of investigation [32, 30, 18], but, unlike general news production, they cannot scale up to the population level. Thus, different solutions have to be adopted. The tracking of reading behaviours, for example, had been used to study the demands and interests of readers [4]. However, such a methodology is biased by the very existence of news since the interest for topics not covered by news cannot be recorded.  
+
+<|ref|>text<|/ref|><|det|>[[238, 803, 780, 818]]<|/det|>
+An independent way to track people interests that gained popularity in the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 293]]<|/det|>
+scientific community is the Google Trends service \(^{1}\) [19]. It provides an index proportional to the number of searches made with the Google Search engine, enabling the quantitative comparison of searched queries. In the last decade, Google Trends has been mainly used as a marker, and a predictor, of people's behaviours in different contexts, like finance [9, 24], epidemiology [22, 11] or socio- economic indicators [6, 5]. Interestingly, its intrinsic value as a proxy for people's interest was perhaps overlooked. In the framework of news, the Google Trends index has been mainly adopted for forecasting [35], without delving into the comprehension of the dynamics of the news ecosystem.  
+
+<|ref|>text<|/ref|><|det|>[[216, 293, 780, 413]]<|/det|>
+Here we comprehend, in a unique framework, the supply and demand for information and analyse their dynamical interplay with the final goal of understanding the main mechanisms of the information ecosystem dynamics and extracting hints about the determinants of disinformation. To this end, we focused on the general production of news in Italy, from early December 2019 to the end of August 2020, as the reference for the news supply. For the same period, the Google Trend index served as a proxy for the general public's information demand.  
+
+<|ref|>text<|/ref|><|det|>[[216, 413, 780, 488]]<|/det|>
+We adopted Vector Auto- Regression (VAR) models to study the interplay between news demand and supply, evidencing different causal relationships for distinct subjects. We presented an improved modelling scheme that allows for a quantitative description of the dependencies in the time series evolution for information demand and supply.  
+
+<|ref|>text<|/ref|><|det|>[[216, 489, 780, 564]]<|/det|>
+The new framework also permitted to study and compare the disinformation dynamics within the general information system, highlighting behavioural differences in reactivity and modelling efficacy. We observed, in particular, that the semantic misalignment between information supply and demand is higher than the misalignment between disinformation supply and demand.  
+
+<|ref|>text<|/ref|><|det|>[[216, 564, 780, 624]]<|/det|>
+These discrepancies could be exploited to aggregate a disinformation risk indicator that is independent of fake news annotations. We contend this index could provide a reliable and independent assessment tool for the news supply's health status.  
+
+<|ref|>sub_title<|/ref|><|det|>[[216, 647, 303, 666]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[216, 679, 586, 697]]<|/det|>
+## Dynamics of news supply and demand  
+
+<|ref|>text<|/ref|><|det|>[[216, 705, 780, 795]]<|/det|>
+Information systems feature two main drivers: news supply and news demand. As a reference for the news supply, we looked at the whole Italian production of information, termed General News, from early December 2019 to the end of August 2020. For the same period, the Google Trend index served as a proxy for the news demand from the Italian general public, thus termed Searches (refer to Materials and Methods for more details).  
+
+<|ref|>text<|/ref|><|det|>[[216, 796, 780, 825]]<|/det|>
+To investigate the nature of the relation between supply and demand of news about a certain subject, six keywords, referring to the most searched subjects
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 309]]<|/det|>
+in Italy over the entire observation period, were selected: coronavirus, regional, playstation, papa francesco, eurovision, sondaggi (Supplemental Fig. S1)). General News and Searches for coronavirus are reported in Fig. 1. For each keyword, the time series of the daily appearances in the General News and the daily volume of queries in the Searches were simultaneously fit by Vector Auto- Regression (VAR) linear modelling [15]. VAR models with different lag parameters, which encapsulate the system's memory, were considered, and the best parameters were identified via the Akaike criterion [1] (see Materials and Methods). For all keywords, best- fitting lags ranged between 2 and 4, suggesting a typical, short- memory timescale in the system (see Supplemental Fig. S2)).  
+
+<|ref|>image<|/ref|><|det|>[[239, 336, 768, 565]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[216, 595, 780, 717]]<|/det|>
+<center>Figure 1: Temporal behaviour of the fractions of Searches (red, left \(y\) -axis) and General News (blue, right \(y\) -axis) for the keyword coronavirus in Italy from early December 2019 to the end of August 2020. Searches are reported as a percentage of the maximum observed in the monitored period. General News is represented by the daily fraction of articles containing at least three keyword occurrences (see Materials and Methods). The Improved Model (black line) leverages the past General News and Searches, together with present Searches, to infer the dynamics of General News. </center>  
+
+<|ref|>text<|/ref|><|det|>[[216, 730, 780, 850]]<|/det|>
+Within the VAR framework, we performed the test for Granger- causality [15] to illustrate which time series, between General News and Searches, contributed more to the prediction of the other, and if any contribution was significant. For the majority of keywords, the contribution of past Searches to present General News was most significant (i.e. coronavirus, regional, playstation, papa francesco) (see Supplemental Fig. S2)). We could safely assume that Searches anticipates General News and use this assumption to improve the model of the temporal behaviour of the latter. We modified the VAR equation for the evo
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[258, 258, 730, 380]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[215, 165, 781, 256]]<|/det|>
+Table 1: The parameters and the \(R^{2}\) resulting from the improved linear model of equation 1 for the 4 selected keywords. As a reference, in brackets, we report the value for \(R^{2}\) of a trivial model with equation \(N(t) = \alpha N(t - 1)\) , i.e., a model where every day depends only on the day before. The value of \(R^{2}\) of the improved linear model is systematically larger than that of the trivial model. Starred values are those not significantly different from zero.   
+
+<table><tr><td></td><td>coronavirus</td><td>regionali</td><td>playstation</td><td>papa francesco</td></tr><tr><td>α1</td><td>0.82</td><td>0.65</td><td>0.18</td><td>0.54</td></tr><tr><td>α2</td><td></td><td>0.26</td><td>0.19</td><td></td></tr><tr><td>β0</td><td>0.070</td><td>0.0082</td><td>0.00055</td><td>0.0038</td></tr><tr><td>β1</td><td>-0.034</td><td>0.003*</td><td>0.00035</td><td></td></tr><tr><td>β2</td><td></td><td>-0.0064</td><td>0.00068</td><td></td></tr><tr><td>R²</td><td>0.996 (0.991)</td><td>0.89 (0.86)</td><td>0.54 (0.29)</td><td>0.73 (0.63)</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[215, 404, 780, 450]]<|/det|>
+lution of General News by inserting Searches' role. More precisely, let \(S(t)\) and \(N(t)\) be, respectively, the values of Searches and General News at day \(t\) , then the new equation for the evolution of \(N(t)\) reads:  
+
+<|ref|>equation<|/ref|><|det|>[[333, 460, 778, 503]]<|/det|>
+\[N(t) = \sum_{i = 1}^{d}(\alpha_{i}N(t - i) + \beta_{i}S(t - i)) + \beta_{0}S(t). \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[216, 512, 780, 573]]<|/det|>
+where the coefficients \(\alpha_{i}\) , \(\beta_{0}\) and \(\beta_{i}\) were fitted, while the Akaike criterion provides the optimal lag \(d\) . This Improved Model closely reproduced the data, particularly in correspondence with the peaks (Fig. 1 for coronavirus and Supplemental Fig. S3).  
+
+<|ref|>text<|/ref|><|det|>[[216, 574, 780, 604]]<|/det|>
+The model's parameters also provided a quantitative insight on the interplay between General News and Searches (Tab. 1):  
+
+<|ref|>text<|/ref|><|det|>[[238, 613, 781, 787]]<|/det|>
+\(\alpha_{1}\) was larger than other \(\alpha\) parameters, indicating a strong dependence of General News on the previous day activity. This evidence is a sign of an inertial behaviour of the news supply. \(\beta_{0}\) , the weight of present Searches, was typically larger than other \(\beta\) parameters and significantly non- zero, supporting the assumption of present Searches role for the Improved Model. The remaining parameters were smaller though almost always significant. For two keywords (coronavirus and regionali), the parameters \(\beta_{d}\) (for \(d \geq 1\) ) were negative. This result suggests that General News depends on the different quotient of Searches, together with the volume of Searches itself.  
+
+<|ref|>text<|/ref|><|det|>[[216, 796, 780, 841]]<|/det|>
+Of note, a direct comparison between \(\alpha\) and \(\beta\) parameters was not possible, as Searches and General News were scaled differently (Google Trends does not disclose the absolute scale of queries volume).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[216, 154, 773, 171]]<|/det|>
+## The different behaviours of General News and Fake News  
+
+<|ref|>text<|/ref|><|det|>[[216, 179, 780, 286]]<|/det|>
+The Improved Model quantifies the information supply dynamics and enables the comparison between General News and disinformation supply. We applied this methodology to the topic coronavirus, since it dominated the landscape of information (Supplemental Fig. S1), and due to the direct impact of disinformation on the response to the 2020 pandemic. To this end, we extended our analysis to the news items that were annotated as false or misleading, thus named Fake News (see Material and Methods).  
+
+<|ref|>text<|/ref|><|det|>[[216, 286, 780, 361]]<|/det|>
+We exploited the Improved Model 1 to compare General News and Fake News through their best- fitting coefficients \(\alpha\) and \(\beta\) . To this end, we paralleled the variable \(N(t)\) , the daily proportion of coronavirus- related General News at day \(t\) , and \(FN(t)\) , the daily proportion of coronavirus- related Fake News at day \(t\) (Tab. 2).  
+
+<|ref|>text<|/ref|><|det|>[[216, 361, 780, 452]]<|/det|>
+Compared to General News, coronavirus- related Fake News shows a meaningfully lower Inertia term, \(\alpha_{1}\) , and a non- significant \(\beta_{1}\) indicating a greater reactivity to \(S(t)\) . These pieces of evidence and the lower prediction score (adjusted \(R^{2}\) ) suggest that disinformation presents a different behaviour than General News, to the points that it distorts the dynamics of the news ecosystem and leads to impaired modelling performance.  
+
+<|ref|>table<|/ref|><|det|>[[310, 530, 680, 626]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[216, 474, 780, 534]]<|/det|>
+Table 2: Coefficients from the Improved Model fitting of General News and of Fake News having at least one occurrence of the keyword coronavirus (see Materials and Methods). Starred coefficients do not differ significantly from zero.   
+
+<table><tr><td></td><td>General News</td><td>Fake News</td></tr><tr><td>α1 (Inertia)</td><td>0.860 ± 0.016</td><td>0.758 ± 0.039</td></tr><tr><td>β0</td><td>0.460 ± 0.035</td><td>0.294 ± 0.086</td></tr><tr><td>β1</td><td>-0.248 ± 0.042</td><td>-0.081* ± 0.091</td></tr><tr><td>R²</td><td>0.995</td><td>0.931</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[216, 640, 780, 791]]<|/det|>
+Another difference in the behaviour of news and disinformation emerged at a semantic level. We focused on the most queried keywords searched together with coronavirus in Google Search (see Materials and Methods). Each of these related queries provided a time series of news demand about a sub- domain that co- occurs with, and therefore is semantically linked to, coronavirus. We quantified the co- occurrence of these terms with the coronavirus keyword also in the news items, for both General News and Fake News. In this way, we defined \(\mathbf{S}(t), \mathbf{N}(t), \mathbf{FN}(t)\) as the daily semantic vectors for coronavirus- related Searches, General News, and Fake News, respectively. Each vector has seventeen entries, one per sub- domain (see Materials and Methods for more details).  
+
+<|ref|>text<|/ref|><|det|>[[216, 791, 780, 851]]<|/det|>
+We calculated \(\mathbf{S}_{tot} = \sum_{t} \mathbf{S}(t)\) and sort its components to rank the different sub- domains by the total news demand over the period considered (Fig. 2). To assess the difference between information and disinformation with respect to the matching of news demand for different sub- domains, we challenged the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[215, 155, 780, 188]]<|/det|>
+components' rankings of \(\mathbf{N}_{tot} = \sum_{t}\mathbf{N}(t)\) and \(\mathbf{FN}_{tot} = \sum_{t}\mathbf{FN}(t)\) against the corresponding ones of \(\mathbf{S}_{tot}\) (Fig. 2).  
+
+<|ref|>image<|/ref|><|det|>[[252, 220, 700, 590]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[215, 607, 781, 713]]<|/det|>
+<center>Figure 2: The ranked components of \(\mathbf{S}_{tot}\) (centre red), representing coronavirus sub-domains sorted by total news demand over the observed time. On the sides of each keyword, a tag indicates the rank in \(\mathbf{N}_{tot}\) for General News, on the left, and in \(\mathbf{FN}_{tot}\) for Fake News, on the right. Tags are distanced from the centre by the amount of rank mismatch to Searches ranks. Tags are coloured to highlight the rank closest to the Searches rank: blue for General News and green for Fake News. </center>  
+
+<|ref|>text<|/ref|><|det|>[[216, 725, 780, 816]]<|/det|>
+Given the coronavirus- related keywords ranked from the Searches as a reference, Fake News ranking shows fewer and minor mismatches compared to General News. We quantified this difference in behaviour through Spearman's Correlation. \(\mathbf{S}_{tot}\) and \(\mathbf{N}_{tot}\) components resulted positively correlated ( \(r = 0.52\) , with a p- value of 0.031) but \(\mathbf{S}_{tot}\) and \(\mathbf{FN}_{tot}\) correlated more ( \(r = 0.67\) , with a p- value of 0.0032).  
+
+<|ref|>text<|/ref|><|det|>[[216, 817, 780, 847]]<|/det|>
+The semantic difference in the behaviour of Fake News and General News holds not only at the aggregated level but also at a daily level. This was mea
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 156, 780, 232]]<|/det|>
+sured through the cosine distance \(\mathrm{d}(\cdot ,\cdot)\) on their daily vectors \(\mathbf{S}(t)\) , \(\mathbf{N}(t)\) and \(\mathbf{FN}(t)\) (see Materials and Methods). Again, Searches were taken as reference and we calculated its cosine distance from General News, \(\mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))\) , and from Fake News, \(\mathrm{d}(\mathbf{S}(t),\mathbf{FN}(t))\) . The daily relative difference between the cosine distances of Searches- Fake News and Searches- General News  
+
+<|ref|>equation<|/ref|><|det|>[[388, 238, 778, 273]]<|/det|>
+\[\frac{\mathrm{d}(\mathbf{S}(t),\mathbf{FN}(t)) - \mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))}{\mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))} \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[216, 283, 780, 359]]<|/det|>
+resulted in negatives values in most days \(t\) (Supplemental Fig. S5)). In fact, both the Mean \((- 0.13)\) and Median \((- 0.15)\) were negative, indicating that the cosine distance Searches- Fake News is generally smaller than that of Searches- General News. This result shows how Fake News meets news demand better than General News.  
+
+<|ref|>sub_title<|/ref|><|det|>[[216, 377, 707, 395]]<|/det|>
+## Independent detection of Fake News concentration  
+
+<|ref|>text<|/ref|><|det|>[[216, 402, 780, 432]]<|/det|>
+The observed differences between General News and Fake News dynamics can be exploited to assess disinformation about the topic coronavirus.  
+
+<|ref|>text<|/ref|><|det|>[[216, 433, 780, 552]]<|/det|>
+The difference in modelling Fake and General News suggests that when Fake News concentration on a topic rises, the General News dynamics, which includes Fake News, becomes perturbed. We hypothesise that this perturbation is expected to impair the General News modelling performance. To test this hypothesis, the Improved Model was fit to General News locally on a time window of 14 days, sliding over the entire data time range (see Materials and Methods). For each window, centred in \(t\) , we computed the local modelling error defined as:  
+
+<|ref|>equation<|/ref|><|det|>[[398, 551, 778, 569]]<|/det|>
+\[E(t) = (1 - R^{2}(t))\cdot \langle N\rangle (t), \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[216, 575, 780, 605]]<|/det|>
+where \(R^{2}(t)\) , the \(R^{2}\) score for the model fitted to the window, is weighted by \(\langle N\rangle (t)\) , the average volume of news produced in that time window.  
+
+<|ref|>text<|/ref|><|det|>[[216, 606, 781, 711]]<|/det|>
+Although formulated without exploiting disinformation annotations, \(E(t)\) significantly correlates with the concentration of Fake News on the coronavirus subject, \(FN(t) / N(t)\) (Spearman's \(r = 0.47\) , with a p- value of \(3.9\cdot 10^{- 13}\) (see Materials and Methods). This result supports the hypothesis that loss of predictability from the General News dynamics co- occurs with disinformation spikes. As a consequence, \(E(t)\) stands as a very promising proxy for the concentration of disinformation about the topic coronavirus.  
+
+<|ref|>text<|/ref|><|det|>[[216, 712, 781, 848]]<|/det|>
+The semantic difference between General News and Fake News suggests that disinformation might receive greater attention thanks to its ability to match the news demand semantically unsatisfied. We hypothesized that as General News becomes more semantically distant from Searches, Fake News would fill that gap. This hypothesis was tested all over the time range measuring the daily cosine distance between the semantic vectors of Searches and General News \(K(t) = \mathrm{d}(\mathbf{S}(t),\mathbf{N}(t))\) . We then checked the correlation of \(K(t)\) with the daily concentration of Fake News, \(FN(t) / N(t)\) , about coronavirus. The correlation turns out to be positive and significant (Spearman's \(r = 0.58\) , with a p- value of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 187]]<|/det|>
+\(1.6 \cdot 10^{- 21}\) ), supporting the hypothesis. This result allows us to adopt \(K\) as a second independent indicator for Fake News concentration assessment.  
+
+<|ref|>text<|/ref|><|det|>[[216, 188, 780, 263]]<|/det|>
+To test the effectiveness of our indicators \(E\) and \(K\) in assessing disinformation concentration, we combined them in a Combined Index for disinformation (see Material and Methods). We fit them linearly on a training set composed of approximately the first \(25\%\) of data from the time series, providing the best linear combination of the two (see Fig. 3).  
+
+<|ref|>image<|/ref|><|det|>[[277, 280, 712, 533]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[216, 552, 781, 658]]<|/det|>
+<center>Figure 3: The time series of news annotated as Fake, normalised through the total number of coronavirus-related News compared with the Combined Index for disinformation. The Combined Index is defined as a linear combination of the weighted modelling error for the local fitting of News within the improved Vector Auto-Regression model and the cosine distance between the semantic vectors of Searches and News. The parameters of the combination were fitted in the training set and then tested in the validation set. </center>  
+
+<|ref|>text<|/ref|><|det|>[[216, 670, 780, 730]]<|/det|>
+The Combined Index was then tested against the validation set, achieving substantial accuracy (reduced chi- squared statistic of 0.945). All these findings suggest that the Combined Index provides a valuable measure for detecting disinformation concerning SARS- CoV- 2.  
+
+<|ref|>text<|/ref|><|det|>[[216, 732, 780, 848]]<|/det|>
+The methodology could also be applied to different topics, and to the aggregation of several topics, to assess the health status of the news ecosystem at a more general level. To challenge this claim, we considered the set of the 4 keywords modelled. We aggregated them to create a synthetic macro- topic, for which they individually represented the analogous of the related queries we have seen before. We judged the adoption of the first indicator, i.e. the weighted modelling error for the local fitting, to be pointless since the macro- subject dynamics is largely dominated by the topic coronavirus. This would have resulted
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 293]]<|/det|>
+in an indicator similar to the modelling of the coronavirus component alone. We thus focused only on the second indicator, i.e., the cosine distance between the semantic vectors of Searches and News, where the components of the vectors are now the values of General News, Fake News, and Searches for the 4 keywords. The daily value of cosine distance between General News and Searches of the synthetic subject correlates positively and meaningfully with the concentration of disinformation on the synthetic subject (Spearman's correlation of 0.44 with p- value \(= 1.8 \cdot 10^{- 11}\) ). This result supports the plausibility of the application of our methodology in wider contexts.  
+
+<|ref|>sub_title<|/ref|><|det|>[[216, 315, 337, 335]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[216, 346, 780, 452]]<|/det|>
+Information quality is a fundamental challenge for the Information Age, especially during a pandemic. Studying the general news system and comparing it with the subset of news labelled as disinformation, we found that pandemic- related Fake News production seems more reactive and precise than General News supply in addressing people's news demand. We exploited such a difference to develop an index for vulnerability of specific topics to disinformation takeover.  
+
+<|ref|>text<|/ref|><|det|>[[216, 453, 780, 633]]<|/det|>
+The analysis of Searches and General News for coronavirus and a set of other coronavirus- unrelated highly queried keywords exposed the relation between supply and demand of news: (i) a linear modelling scheme was effective in almost all cases; (ii) the memory of the process seems to be very short (2- 4 days) in all cases; (iii) causality was more commonly directed from Searches to General News (e.g. for coronavirus). Thanks to these considerations, an improved descriptive model could be developed to better describe the relationship between supply and demand for information. This modelling framework allowed us to discern how the inertia of news suppliers is one of the main traits of the dynamics for all the studied keywords. Also, the negative dependence on previous days Searches observed in some cases suggests a dynamics where the trend of the interest is more important than the interest itself for news producers.  
+
+<|ref|>text<|/ref|><|det|>[[216, 634, 780, 770]]<|/det|>
+The comparison of coronavirus- related General News and Fake News through the improved linear model's lens exposed that Fake News feature lower inertia and a different dependence on Searches, quantifying their more reactive behaviour. We can speculate that this behavioural difference could be a consequence of the different production environments of General News and Fake News. The firsts are mainly produced by a large and well- established community of professional journalists while the latter are the outcome of by a scattered multitude of small, unorganized actors. The community size effect might be responsible for the different inertial behaviour observed.  
+
+<|ref|>text<|/ref|><|det|>[[216, 770, 780, 845]]<|/det|>
+The semantic analysis revealed another key difference between the dynamics of General News and Fake News. Looking at the shares of the most queried keywords co- occurring with coronavirus we discovered that Fake News is better aligned to Searches than General News not only at a cumulative level but also daily over the entire observation period. This result suggests that disinformation
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 247]]<|/det|>
+tends to be more semantically precise than information in matching people's interests. This difference might be explained considering the different aims of the two communities. While they are both interested in answering people's demand for information, general news producers also have the ambition for complete coverage of topics, while Fake News producers can focus on chasing the people's attention.  
+
+<|ref|>text<|/ref|><|det|>[[216, 248, 780, 444]]<|/det|>
+We exploited the modelling and the semantic mismatch between General News and Fake News to detect bursts of disinformation on coronavirus. It is worth mentioning how this measure was performed without any information about FakeNews, looking instead only at the time- series of General News and Searches. The modelling difference resulted in a destabilizing effect of Fake News peaks on the modelling of General News as a function of Searches. Such a perturbation was measured as the local weighted modelling error in the Improved Model for General News as a function of Searches. A higher value of this indicator means that the normal relation between General News and Searches has been altered, probably by Fake News presence. The semantic difference was estimated from daily misalignment itself between General News and Searches. In this case, a higher value of this indicator means that semantic imprecision leaves an unsatisfied interest in readers, possibly fostering Fake News.  
+
+<|ref|>text<|/ref|><|det|>[[216, 445, 780, 504]]<|/det|>
+The positive and meaningful correlation of both indicators with Fake News concentration on Coronavirus supports both the hypothesis: (i) disinformation perturbs the normal relation between General News and Searches and (ii) is fueled by the semantic misalignment between the two.  
+
+<|ref|>text<|/ref|><|det|>[[216, 505, 780, 640]]<|/det|>
+We blend the two markers into a single Combined Index for disinformation by adopting a training set for its definition and testing it on a validation set with good results. Given its independence from Fake News annotations and the hints supporting a possible generalization of the result to other topics, the Combined Index can be a powerful tool for journalists and editors as well as for news monitoring authorities to detect in real- time vulnerabilities to disinformation. Our results also suggest, as a possible strategy to face these vulnerabilities, a timely refocus of General News supply to better meet the information demand of the public.  
+
+<|ref|>text<|/ref|><|det|>[[216, 641, 780, 851]]<|/det|>
+Information vulnerabilities are a major risk factor for our societies, as they have a direct impact on individuals. For example, the solution to the Coronavirus crisis depends mainly on individual behaviours which, in turn, are directly affected by the news. The approach presented here, far from being conclusive, represents a first contribution towards a deeper understanding of the phenomenology of disinformation as part of the information ecosystem's general dynamics. Further studies will be needed to test the conclusions and to generalize the results to different countries, languages, domains, and time periods. Moreover, the diffusion layer should be added to the analysis of the dynamics of the infosphere, with particular attention to the social media spreading of news. In our opinion, a paradigm shift in facing disinformation is no more an option, is a necessity for information societies. We contend that the presented work contributes to the shift of scientific research towards a more concrete view, aiming to provide policymakers with knowledge and tools to fight disinformation.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[216, 153, 486, 172]]<|/det|>
+## Materials and Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[216, 185, 354, 202]]<|/det|>
+## Searches Data  
+
+<|ref|>text<|/ref|><|det|>[[216, 210, 780, 269]]<|/det|>
+The information demand about a specific subject was obtained from Google Trends, a platform providing access to an anonymous sample of actual search requests made in Google Search engine, from a selected location and time interval.  
+
+<|ref|>text<|/ref|><|det|>[[216, 270, 780, 375]]<|/det|>
+For each given keyword, Google Search returns a time- series with values proportional to the number of times the keyword was searched each day. Since Google Search does not disclose the actual number of searches, the time series values are rendered as percentages of the maximum number returned. As a result, data consist of integers ranging in the interval \((0,100)\) . The time series of one keyword was referred to as the "Searches" for that keyword and provided a measure of the interest it received.  
+
+<|ref|>text<|/ref|><|det|>[[216, 376, 780, 466]]<|/det|>
+The use of "pytrends" library for Python \(^2\) enabled the interaction with the Google Trends platform. The terms from Supplemental Fig. S1 were requested separately, for the time ranging from the 6th of December 2019 to the 31st of August 2020 in Italy. These were: coronavirus, regionali (regional elections), playstation, papa francesco (Pope Francesco), eurovision (the European music contest), sondaggi (polls).  
+
+<|ref|>text<|/ref|><|det|>[[216, 466, 780, 557]]<|/det|>
+Google Trends also provided information about queries most searched with a specific keyword. In particular, the most popular queries related to the keyword coronavirus (e.g., coronavirus news ) were gathered. Such list is capped by Google Trends at a maximum of 25 related keywords, ordered by most searched to least, and denoted \(q_{1}(t),\ldots ,q_{25}(t)\) respectively ( \(t\) indicating the time), with \(q_{0}(t)\) the time series of coronavirus searches.  
+
+<|ref|>text<|/ref|><|det|>[[216, 557, 780, 708]]<|/det|>
+To compare the searches of a given keyword with its related keywords, it is necessary to put them on the same scale. To this end, searched items were queried in pairs. In this way, Google Trends normalized the two resulting time series for the highest of the maximums of the two. Given the two times- series per request \((q_{i - 1}(t),q_{i}(t))\) , with \(i = 1,\ldots ,25\) , a coefficient \(\alpha_{i} = \max_{t}(q_{i - 1}(t)) / \max_{t}(q_{i}(t))\) was calculated. Thus, all the time series \(q_{i}\) could be set on the same scale of \(q_{0}\) , multiplying by \(\prod_{j = 1}^{i}\alpha_{j}\) . This procedure is needed not to lose resolution on keywords with a small number of queries. Having queried for pairs \((q_{0}(t),q_{i}(t))\) , would have resulted in a rounding at 0 performed by Google Trends.  
+
+<|ref|>text<|/ref|><|det|>[[216, 710, 780, 816]]<|/det|>
+coronavirus- related queries were then aggregated by summing up their time- series. Thus, coronavirus oggi (Coronavirus today), coronavirus notizie (Coronavirus news), coronavirus ultime (Coronavirus latest), coronavirus ultime notizie (Coronavirus latest news) and coronavirus news, were all aggregated into coronavirus news. Subsequently, we removed all the queries that returned the same search results as another query. These were coronavirus contagi (Coronavirus infections) and coronavirus in italia (Coronavirus in Italy), duplicates
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 278]]<|/det|>
+of contagi coronavirus (Coronavirus infections), and coronavirus italia (Coronavirus Italy), respectively. Also, the query corona was excluded because it has other meanings in Italian, namely "crown", and it is also a famous brand of beer. Finally, the list of queries associated with coronavirus, ordered by the amount of searches, was: news, italia (Italy), lombardia (Lombardy), sintomi (symptoms), contagi (infections), casi (cases), morti (deaths), bollettino (bulletin), roma (Rome), dati (data), mondo (world), mappa (map), sicilia (Sicily), veneto, campania, decreto (decree), milano (Milan), piemonte (Piedmont).  
+
+<|ref|>sub_title<|/ref|><|det|>[[216, 296, 323, 313]]<|/det|>
+## News Data  
+
+<|ref|>text<|/ref|><|det|>[[216, 320, 780, 456]]<|/det|>
+To analyse the news supply, we investigated the data provided by AGCOM, the Italian Authority for Communications Guarantees, which granted us access to the content of a vast number of Italian news sources published online and offline from the 6th of December 2019 to the 31st of August 2020 in Italy. These data included articles from printed and digital newspapers and information agencies, TV, radio sites, and scientific sources. Moreover, the data had a specific annotation for "fake news" sources. The list disinformation sources, vetted by the Authority, is provided by fact- checking organizations like bufale.net and butac.it. It had already been employed for other studies on disinformation [33].  
+
+<|ref|>text<|/ref|><|det|>[[216, 457, 780, 531]]<|/det|>
+After pre- processing the data for duplicates and incomplete logs elimination, the General News data consisted of almost 7 million entries from 554 different news sources. Each data entry has a unique ID and contains, among other information, the title and the content of the piece of news, its date, its source, and the annotation of belonging to the disinformation sources list).  
+
+<|ref|>text<|/ref|><|det|>[[216, 532, 780, 773]]<|/det|>
+Needing to imitate the rationale underlying Google Trends data, where daily search counts refer to the query of specific keywords, we sought to find counts of daily keywords also in the news data. To do so, given a keyword (e.g., coronavirus), we defined three different metrics: the piece of news containing the keyword at least once, those having the keyword at least three times, and finally, all the occurrences of a specific keyword. These three metrics were then normalized on the total number of news' sources per day to level the press activity during weekends. For each model, we chose the metric with the best modelling performances. For the improved version of the VAR model described in equation 1 from the Results section, the metric with at least three occurrences was selected, even if the other two showed similar performances. Instead, the most inclusive metric (at least one occurrence) was adopted when dealing with disinformation. This procedure was necessary to enhance the signal, given the low number of Fake News items encountered. For consistency, the overall General News was considered with the same metric (at least one occurrence) when comparing it with the Fake News time series.  
+
+<|ref|>text<|/ref|><|det|>[[216, 774, 780, 848]]<|/det|>
+Following the same rationale, we adopted the first metric to filter for the keywords related to the Coronavirus subject described in the previous subsection. To do so, we selected the piece of news containing the keyword coronavirus at least once, and, in this subset, we counted the ones featuring the desired related keyword at least once. The values found were normalized on the total
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[217, 157, 780, 248]]<|/det|>
+number of news pieces having the keyword coronavirus at least once per day to get a proxy for the share of Coronavirus piece of information focused on the related keyword sub- domain. We repeated this analysis for the subset of news mentioning the keyword coronavirus at least once and marked as Fake News in the data. We then used the values extracted from this analysis to investigate the disinformation supply in the Coronavirus context.  
+
+<|ref|>sub_title<|/ref|><|det|>[[217, 265, 419, 283]]<|/det|>
+## Time Series Analysis  
+
+<|ref|>text<|/ref|><|det|>[[217, 290, 780, 397]]<|/det|>
+Time series of Searches and General News, from Supplemental Fig. S1, were investigated using the VAR model [15], using Python's statsmodels package for time series analysis [27]. Data were regularized via \(x \mapsto \log (1 + x)\) transformation before fitting. For the VAR modelling, the number of lags \(d\) was determined as the parameter that minimized the Akaike information criterion [1], with \(d\) ranging in the interval \((1, 14)\) . This modelling strategy was chosen to ensure the interpretability of the fitted model and its regression coefficients.  
+
+<|ref|>text<|/ref|><|det|>[[217, 397, 780, 517]]<|/det|>
+From the VAR model, we computed Granger- causality [15] to test whether queries' values provided meaningful information to the prediction of news volumes and vice versa. Since two tests were performed on the same data from a given subject (for the null hypotheses "Searches do not Granger- cause General News" and "General News do not Granger- cause Searches"), resulting p- values were corrected by the Holm- Bonferroni method [23] Thus, pairs of p- values in Supplemental Fig. S2 were multiplied by 2, to control for family- wise error rate and to maintain comparability.  
+
+<|ref|>text<|/ref|><|det|>[[217, 517, 780, 622]]<|/det|>
+In Fig. 1 and Supplemental Fig. S3, the Improved Models for regression of the General News were derived adjusting the VAR models to include Searches at time \(t\) (Supplemental Fig. S3). Lags were re- elaborated through the Akaike criterion as before, with similar results. These models were then compared against a null model that forecasts one day proportionally to the value of the day before to benchmark how beneficial the addition of regressing variables was to General News's prediction (see Tab. 1).  
+
+<|ref|>text<|/ref|><|det|>[[217, 622, 780, 743]]<|/det|>
+To assess the semantic misalignment between General News and Searches from Supplemental Fig. S5, the cosine distance was calculated as \(\mathrm{d}(\mathbf{S}(t), \mathbf{N}(t)) = 1 - \mathbf{S}(t) \cdot \mathbf{N}(t) / |\mathbf{S}(t)| |\mathbf{N}(t)|\) , on the vectors \(\mathbf{S}(t) = (S_{1}(t), \ldots , S_{k}(t))\) , \(\mathbf{N}(t) = (N_{1}(t), \ldots , N_{k}(t))\) where \(S_{i}(t)\) and \(N_{i}(t)\) represented the volumes of searches and news, respectively, at time \(t\) for the \(i\) - th keyword associated to coronavirus, with \(\cdot\) being the dot product and \(|\cdot |\) the Euclidean norm. Cosine distance was suitable to compare high- dimensional vectors at different scales, and returned values in \((0, 1)\) for vectors with non- negative entries such as \(\mathbf{S}(t)\) and \(\mathbf{N}(t)\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[217, 761, 481, 779]]<|/det|>
+## Combined Index Validation  
+
+<|ref|>text<|/ref|><|det|>[[217, 787, 780, 847]]<|/det|>
+To define and validate the Combined Index from Fig. 3, we split the daily data from Fake News concentration on coronavirus into a training set (from the 29th of January 2020 to the 20th of March 2020) and a validation set (from the 21st of March 2020 on).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 248]]<|/det|>
+Thus, we defined the Combined Index as a linear combination of the two starting indexes that best fitted the Fake News concentration, using a linear model with Gaussian noise on the training data. The ordinary least squares estimate \(\hat{\sigma}\) for the variance of the Gaussian noise was then calculated as the Mean Squared Error (MSE) divided by the statistical degrees of freedom \(k\) (i.e., the number of observations minus 2, the number of parameters in the model).  
+
+<|ref|>text<|/ref|><|det|>[[216, 248, 780, 368]]<|/det|>
+To assess the predictive potential of the Combined Index, we adopted the trained model to forecast the concentration of Fake News in the validation set. This prediction's goodness was tested through the reduced chi- squared statistic, which is calculated as the MSE on the validation set divided by \(\hat{\sigma}\) . This statistic is approximately distributed as a \(\chi^{2}\) with as many degrees of freedom as the size of the validation set (i.e., 51), leading to a p- value of about 0.945. As such, the null hypothesis, that the concentration of Fake News for the keyword coronavirus is distributed in agreement with the trained model, cannot be rejected.  
+
+<|ref|>sub_title<|/ref|><|det|>[[217, 390, 436, 410]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[216, 421, 780, 512]]<|/det|>
+The Authors wish to warmly thank Marco Delmastro of AGCOM for insightful discussions about the Italian news ecosystem as well as for providing the database of Italian news. The database was shared in the framework of the Task Force on "Digital Platforms and Big Data - Covid- 19 Emergency", established by the AGCOM to contribute, among other things, to the fight against online disinformation on issues related to the SARS- CoV- 2 crisis.  
+
+<|ref|>sub_title<|/ref|><|det|>[[216, 535, 341, 555]]<|/det|>
+## References  
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+[7] Matteo Cinelli, Walter Quattrociocchi, Alessandro Galeazzi, Carlo Michele Valensise, Emanuele Brugnoli, Ana Lucia Schmidt, Paola Zola, Fabiana Zollo, and Antonio Scala. The covid- 19 social media infodemic, 2020.  
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+[13] Don Fallis. What is disinformation? Library Trends, 63(3):401- 426, 2015.  
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+[14] Daniel Funke and Daniela Flamini. A guide to anti- misinformation actions around the world, 2018.  
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+[15] James Douglas Hamilton. Time Series Analysis. Princeton University Press, 1 edition, 1994.  
+
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+[17] Md Saiful Islam, Tonmoy Sarkar, Sazzad Hossain Khan, Abu- Hena Mostofa Kamal, SM Murshid Hasan, Alamgir Kabir, Dalia Yeasmin, Mohammad Ariful Islam, Kamal Ibne Amin Chowdhury, Kazi Selim Anwar, et al. Covid- 19- related infodemic and its impact on public health: a global social media analysis. The American Journal of Tropical Medicine and Hygiene, 103(4):1621- 1629, 2020.  
+
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+[18] Shanto Iyengar, Helmut Norpoth, and Kyu S Hahn. Consumer demand for election news: The horserace sells. The Journal of Politics, 66(1):157- 175, 2004.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[215, 157, 780, 218]]<|/det|>
+[19] Seung- Pyo Jun, Hyoung Sun Yoo, and San Choi. Ten years of research change using google trends: From the perspective of big data utilizations and applications. Technological forecasting and social change, 130:69- 87, 2018.  
+
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+[20] Anna Kata. A postmodern pandora's box: anti- vaccination misinformation on the internet. Vaccine, 28(7):1709- 1716, 2010.  
+
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+[21] Maksym Korobchinsky, Liliya Chyrun, Lyubomyr Chyrun, and Victoria Vysotska. Peculiarities of content forming and analysis in internet newspaper covering music news. In 2017 12th International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT), volume 1, pages 52- 57. IEEE, 2017.  
+
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+[22] Vasileios Lampos, Andrew C Miller, Steve Crossan, and Christian Stefansen. Advances in nowcasting influenza- like illness rates using search query logs. Scientific reports, 5(1):1- 10, 2015.  
+
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+[23] Erich L Lehmann and Joseph P Romano. Testing statistical hypotheses. Springer- Verlag New York, 3 edition, 2006.  
+
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+[24] Tobias Preis, Helen Susannah Moat, and H Eugene Stanley. Quantifying trading behavior in financial markets using google trends. Scientific reports, 3:1684, 2013.  
+
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+[25] David J Rothkopf. When the buzz bites back. The Washington Post, 11:B1- B5, 2003.  
+
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+[26] Andreas Schmidt, Ana Ivanova, and Mike S Schafer. Media attention for climate change around the world: A comparative analysis of newspaper coverage in 27 countries. Global Environmental Change, 23(5):1233- 1248, 2013.  
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+[27] Skipper Seabold and Josef Perktold. statsmodels: Econometric and statistical modeling with python. In 9th Python in Science Conference, 2010.  
+
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+[28] Kai Shu, Amy Sliva, Suhang Wang, Jiliang Tang, and Huan Liu. Fake news detection on social media: A data mining perspective. ACM SIGKDD explorations newsletter, 19(1):22- 36, 2017.  
+
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+[29] Sharon R Sznitman and Nehama Lewis. Is cannabis an illicit drug or a medicine? a quantitative framing analysis of israeli newspaper coverage. International Journal of Drug Policy, 26(5):446- 452, 2015.  
+
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+[30] David Tewksbury. What do americans really want to know? tracking the behavior of news readers on the internet. Journal of communication, 53(4):694- 710, 2003.  
+
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+[31] Kathie M d'I Treen, Hywel TP Williams, and Saffron J O'Neill. Online misinformation about climate change. Wiley Interdisciplinary Reviews: Climate Change, 11(5):e665, 2020.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[216, 157, 780, 202]]<|/det|>
+[32] Marc Trussler and Stuart Soroka. Consumer demand for cynical and negative news frames. The International Journal of Press/Politics, 19(3):360- 379, 2014.  
+
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+[33] Michela Del Vicario, Walter Quattrociocchi, Antonio Scala, and Fabiana Zollo. Polarization and fake news: Early warning of potential misinformation targets. ACM Transactions on the Web (TWEB), 13(2):1- 22, 2019.  
+
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+[34] Marco Visentin, Gabriele Pizzi, and Marco Pichierri. Fake news, real problems for brands: The impact of content truthfulness and source credibility on consumers' behavioral intentions toward the advertised brands. Journal of Interactive Marketing, 45:99- 112, 2019.  
+
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+[35] Brian Weeks and Brian Southwell. The symbiosis of news coverage and aggregate online search behavior: Obama, rumors, and presidential politics. Mass communication and society, 13(4):341- 360, 2010.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 43, 311, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[61, 130, 237, 149]]<|/det|>
+GravinoetalSl.pdf
+
+<--- Page Split --->

preprint/preprint__075d82fd5d37a02cde8eab26a4d85528ea15df290443dfb4d60ca9ac191d6a24/images_list.json

@@ -0,0 +1,108 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig 1. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of withdrawing IRS after 5 years of sustained use. The blue shaded region represents the \\(95\\%\\) confidence interval around the predicted case counts from the adjusted regression model. Vertical bars represent the \\(95\\%\\) confidence interval around adjusted IRR.",
+    "footnote": [],
+    "bbox": [
+      [
+        112,
+        545,
+        875,
+        765
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig 2. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of restarting IRS with a single round. The blue shaded region represents the 95% CI around the predicted case counts from the adjusted regression model. Vertical bars represent the 95% CI around adjusted IRR.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        560,
+        880,
+        787
+      ]
+    ],
+    "page_idx": 7
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig 3. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of initiating and sustaining IRS. The blue shaded region represents the \\(95\\%\\) CI around the predicted case counts from the adjusted regression model. Vertical bars represent the \\(95\\%\\) CI around adjusted IRR.",
+    "footnote": [],
+    "bbox": [
+      [
+        112,
+        612,
+        880,
+        840
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig 4. Map of Uganda showing study sites and IRS districts.",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        110,
+        880,
+        530
+      ]
+    ],
+    "page_idx": 16
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 18
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2",
+    "footnote": [],
+    "bbox": [
+      [
+        44,
+        516,
+        951,
+        783
+      ]
+    ],
+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3",
+    "footnote": [],
+    "bbox": [
+      [
+        45,
+        45,
+        951,
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+      ]
+    ],
+    "page_idx": 30
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 31
+  }
+]

preprint/preprint__075d82fd5d37a02cde8eab26a4d85528ea15df290443dfb4d60ca9ac191d6a24/preprint__075d82fd5d37a02cde8eab26a4d85528ea15df290443dfb4d60ca9ac191d6a24.mmd

@@ -0,0 +1,409 @@
+
+# The impact of stopping and starting indoor residual spraying on malaria burden in 14 districts of Uganda  
+
+Jane Namuganga Infectious Diseases Research Collaboration Adrienne Epstein ( \(\boxed{}\) adrienne.epstein@ucsf.edu) University of California, San Francisco https://orcid.org/0000- 0002- 8253- 6102  
+
+Joaniter Nankabirwa Infectious Diseases Research Collaboration  
+
+Arthur Mpimbaza Infectious Diseases Research Collaboration  
+
+Moses Kiggundu Infectious Diseases Research Collaboration  
+
+Asadu Sserwanga Infectious Diseases Research Collaboration  
+
+James Kapisi Infectious Diseases Research Collaboration  
+
+Emmanuel Arinaitwe Infectious Diseases Research Collaboration  
+
+Samuel Gonahasa Infectious Diseases Research Collaboration  
+
+Jimmy Opigo National Malaria Control Division  
+
+Chris Ebong Infectious Diseases Research Collaboration  
+
+Sarah Staedke London School of Hygiene & Tropical Medicine  
+
+Josephat Shillul US President's Malaria Initiative - VectorLink Uganda Project  
+
+Michael Okia US President's Malaria Initiative - VectorLink Uganda Project  
+
+Damian Rutazaana National Malaria Control Division  
+
+Catherine Maiteki- Ssebuguzi
+
+<--- Page Split --->
+
+National Malaria Control Division  
+
+Kassahun Belay US President's Malaria Initiative, USAID  
+
+Moses Kamya Makerere University  
+
+Grant Dorsey University of California, San Francisco  
+
+Isabel Rodriguez- Barraquer University of California, San Francisco  
+
+## Article  
+
+Keywords: malaria, disease control, insecticide, vector control intervention  
+
+Posted Date: December 29th, 2020  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 126095/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 May 11th, 2021. See the published version at https://doi.org/10.1038/s41467- 021- 22896- 5.
+
+<--- Page Split --->
+
+# The impact of stopping and starting indoor residual spraying on malaria burden in 14 districts of Uganda  
+
+Jane F. Namuganga1\\*, Adrienne Epstein2\\*, Joaniter I. Nankabirwa1,3, Arthur Mpimbaza1,4, Moses Kiggundu1, Asadu Serwanga1, James Kapisi1, Emmanuel Arinaitwe1, Samuel Gonahasa1, Jimmy Opigo5, Chris Ebong1, Sarah G. Staedke6, Josephat Shililu7, Michael Okia7, Damian Rutazaanas, Catherine Maiteki- Ssebuguzi5, Kassahun Belay8, Moses R. Kamya1,3, Grant Dorsey9, Isabel Rodriquez- Barraquer9  
+
+1 Infectious Diseases Research Collaboration, Kampala, Uganda  
+
+2 Department of Epidemiology and Biostatistics, University of California San Francisco, San Francisco, California, United States of America  
+
+3 Department of Medicine, Makerere University, College of Health Sciences, Kampala, Uganda  
+
+4 Child Health and Development Centre, Makerere University, College of Health Sciences, Kampala, Uganda  
+
+5 National Malaria Control Division, Ministry of Health, Kampala, Uganda  
+
+6 London School of Hygiene and Tropical Medicine, London, United Kingdom  
+
+7 US President's Malaria Initiative - VectorLink Uganda Project, Kampala, Uganda  
+
+8 US President's Malaria Initiative, USAID/Uganda Senior Malaria Advisor  
+
+9 Department of Medicine, University of California San Francisco, San Francisco, California, United States of America  
+
+\*Adrienne.Epstein@ucsf.edu  
+
+\* These authors contributed equally to this work.
+
+<--- Page Split --->
+
+## 40 Abstract  
+
+The scale- up of malaria control efforts has led to marked reductions in malaria burden over the past twenty years, but progress has slowed. Implementation of indoor residual spraying (IRS) of insecticide, a proven vector control intervention, has been limited and difficult to sustain partly because questions remain on its added impact over widely accepted interventions such as bed nets. Using data from 14 enhanced surveillance health facilities in Uganda, a country with high bet net coverage yet high malaria burden, we estimate the impact of starting and stopping IRS. We show that stopping IRS resulted in a 5- fold increase in malaria incidence within 10 months, but reinstating IRS led to an over 5- fold decrease within 8 months. In areas where IRS was initiated and sustained, malaria incidence dropped by \(85\%\) after year 4. IRS could play a critical role in achieving global malaria targets, particularly in areas where progress has stalled.
+
+<--- Page Split --->
+
+## Introduction  
+
+Over the past twenty years the scale- up of malaria control efforts has led to marked reductions in morbidity and mortality \(^{1,2}\) . However, global progress has slowed in recent years, particularly in sub- Saharan Africa, which accounted for \(93\%\) of the world's 228 million cases in \(2018^{2}\) . Longlasting insecticidal nets (LLINs) and indoor residual spraying of insecticide (IRS) are the primary vector control interventions used for the prevention of malaria. The World Health Organization recommends universal coverage of LLINs for at- risk populations in sub- Saharan Africa, where the proportion of households owning at least one LLIN is estimated to have increased from \(47\%\) in 2010 to \(72\%\) in 2018. Until recently, pyrethroids were the only class of insecticides approved for use in LLINs and, given the emergence of widespread pyrethroid resistance \(^{3,4}\) , there is concern that the effectiveness of LLINs may be diminishing. Unlike LLINs, IRS has the advantage of utilizing multiple different classes of insecticides and combing IRS with LLINs may improve malaria control and slow the spread of pyrethroid resistance. However, few controlled trials have evaluated the effect of adding IRS to communities using LLINs and the evidence is mixed, with a few studies showing benefits when IRS included 'non- pyrethroid- like' insecticides \(^{5}\) . Other barriers to IRS delivery – including cost, logistics, and community acceptance – have limited its use \(^{6}\) , such that less than \(5\%\) of the population at risk in sub- Saharan Africa was protected by IRS in 2018, a decrease from over \(10\%\) coverage in \(2010^{2}\) .  
+
+Uganda is illustrative of a country where the burden of malaria remains high and progress has slowed in recent years \(^{2}\) . Malaria control efforts in Uganda have primarily focused on LLINs. In 2013- 14 it became the first country to implement a universal LLIN distribution campaign, which was repeated in 2017- 18. In 2018- 19, Uganda had the highest coverage of LLINs in the world,
+
+<--- Page Split --->
+
+with \(83\%\) of households reported owning at least one LLIN<sup>7</sup>. In contrast to LLINs, the implementation of IRS in Uganda has been focal and limited. In 2006, IRS was reintroduced into Uganda for the first time since the 1960s. In 2007- 09, the IRS program was shifted to 10 high burden districts in the north, leading to large reductions in malaria burden<sup>8,9</sup>. In 2014, the IRS program was relocated from these 10 northern districts to 14 districts in the eastern part of the country, where it has been sustained. The discontinuation of IRS in the 10 northern districts was followed by a marked resurgence in malaria cases<sup>10,11</sup>, prompting the implementation of a single round of IRS in these 10 districts in 2017.  
+
+In this study, we used data from a network of health facility- based malaria surveillance sites to evaluate the impact of different IRS delivery scenarios in 14 districts in Uganda. This study had three objectives: (1) to estimate the impact of withdrawing IRS after five years of sustained use on the burden of malaria in three sites in Northern Uganda; (2) to estimate the impact of restarting IRS with a single round three to four years after IRS was discontinued on the burden of malaria in nine sites in Northern Uganda; and (3) to estimate the impact of five years of sustained IRS on the burden of malaria in five sites in Northern and Eastern Uganda.  
+
+## Results  
+
+## Impact of withdrawing IRS after sustained use  
+
+Across the three sites included in the analysis, a total of 224,859 outpatient visits were observed (Table 1). During the baseline period, average monthly cases ranged from 104- 272 and TPR ranged from \(23.7\% - 25.9\%\) . This increased to 491- 751 and \(52.3\% - 78.0\%\) respectively, during the evaluation period (Supplementary Fig S1).
+
+<--- Page Split --->
+
+Monthly adjusted IRRs and \(95\%\) confidence intervals (CI) for the three sites combined are presented in Fig 1 and Supplementary Table S1. These results showed an initial reduction in malaria cases after the final round of IRS relative to the baseline period until (adjusted IRR in the first month after \(\mathrm{IRS} = 0.19\) , \(95\%\) CI 0.09- 0.42) about four to five months after the final IRS campaign when malaria cases began to increase. Over the 10- 31 months after IRS was stopped, the number of malaria cases increased by over 5- fold relative to the baseline period (adjusted \(\mathrm{IRR} = 5.24\) , \(95\%\) CI 3.67- 7.50). This corresponds to predicted case counts of near zero immediately following final IRS campaign followed by an increase to about 1000 cases per month at each site (Fig 1). These results were consistent when considering only laboratory- confirmed cases unadjusted for testing rates (Supplementary Fig S2).  
+
+![](images/Figure_1.jpg)
+
+<center>Fig 1. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of withdrawing IRS after 5 years of sustained use. The blue shaded region represents the \(95\%\) confidence interval around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) confidence interval around adjusted IRR. </center>  
+
+## Impact of restarting IRS with a single round  
+
+A total of 858,380 outpatient visits were recorded across the analysis period for the nine sites. (Table 2). Mean monthly malaria cases ranged from 643- 1,569 and the TPR ranged from \(56.5\%\) -
+
+<--- Page Split --->
+
+84.7% during the baseline period. These ranges were 501- 762 and 48.5%- 72.0% respectively during the evaluation period. Temporal trends of laboratory- confirmed malaria cases over time for the individual health facilities are presented in Supplementary Fig S3.  
+
+Monthly adjusted IRRs and 95% CI for the nine sites combined are presented in Fig 2 and Supplementary Table S2. The single round of IRS led to a reduction in malaria cases until approximately 23 months post- IRS. Over the 8- 12 months after the single round of IRS, malaria cases decreased by over 5- fold relative to the baseline period (adjusted \(\mathrm{IRR} = 0.17\) , 95% CI 0.15- 0.20). After 23 months following the single round of IRS, malaria cases returned to a level similar to the baseline period before the single round of IRS (adjusted IRR for months \(23 - 31 = 1.06\) , 95% CI 0.92- 1.21). These results were consistent when considering only laboratory- confirmed cases unadjusted for testing rates (Supplementary Fig S4).  
+
+![](images/Figure_2.jpg)
+
+<center>Fig 2. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of restarting IRS with a single round. The blue shaded region represents the 95% CI around the predicted case counts from the adjusted regression model. Vertical bars represent the 95% CI around adjusted IRR. </center>  
+
+## Impact of initiating and sustaining IRS  
+
+In total, 574,587 outpatient visits were observed across the five sites included in the analysis.  
+
+(Table 3). During the baseline period, average monthly malaria cases adjusted for testing rates
+
+<--- Page Split --->
+
+ranged from 286- 657 and the TPR ranged from \(25.4\% - 67.0\%\) . This range decreased to 85- 289 for malaria cases and \(13.8\% - 45.3\%\) for the TPR during the evaluation period. Temporal trends of laboratory- confirmed malaria cases over time for the individual health facilities are presented in Supplementary Fig S5.  
+
+Monthly adjusted IRRs and \(95\%\) CI for the five sites combined are presented in Fig 3 and Supplementary Table S3. There was a modest overall reduction in malaria case counts in the first three years after IRS was initiated relative to the baseline period, with some peaks in case counts returning to near baseline levels just prior to when rounds of IRS were administered. However, after the third year of sustained use, malaria case counts dropped substantially and remained low relative to the period before IRS was initiated. In the \(4^{\text{th}}\) and \(5^{\text{th}}\) year after IRS was initiated and sustained, malaria cases dropped by \(85\%\) (adjusted \(\mathrm{IRR} = 0.15\) , \(95\%\) CI 0.12- 0.18). These results were consistent when considering only laboratory- confirmed cases unadjusted for testing rates (Supplementary Fig S6).  
+
+![](images/Figure_3.jpg)
+
+<center>Fig 3. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of initiating and sustaining IRS. The blue shaded region represents the \(95\%\) CI around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) CI around adjusted IRR. </center>
+
+<--- Page Split --->
+
+## Discussion  
+
+Uganda has been exceptionally successful in scaling- up coverage of LLINs. Following the mass distribution campaigns to deliver free LLINs in 2013- 14 and 2017- 18, \(90\%\) and \(83\%\) of households respectively reported ownership of at least one LLIN \(^{7,12}\) . However, despite this success, the burden of malaria remains high in much of the country. Uganda had the \(3^{\text{rd}}\) highest number of malaria cases reported in 2018, with reported case incidence increasing since \(2014^{2}\) . If Uganda is to achieve the goals established by the World Health Organization’s Global Technical Strategy for malaria including reducing malaria case incidence by at least \(90\%\) by 2030 as compared with \(2015^{13}\) , additional malaria control measures will be needed. This report highlights the critical role of IRS in substantially reducing the burden of malaria in areas where transmission remains high despite deployment of LLINs. Withdrawing IRS after five years of sustained use in three districts in northern Uganda resulted in a more than 5- fold increase in malaria cases within 10 months. Re- starting IRS with a single round in nine districts in Northern Uganda approximately three years after IRS had been stopped led to a transient but important (more than a 5- fold) decrease in malaria cases within 8- 12 months, returning to pre- IRS levels after 23 months. Initiating and sustaining IRS in five districts in Eastern Uganda led to a gradual reduction in malaria cases reaching almost a 7- fold reduction after 4- 5 years.  
+
+Robust evidence supports the widespread use of LLINs for malaria control. In a systematic review of clinical trials conducted between 1987 and 2001, insecticide treated nets reduced all cause child mortality by \(17\%\) and the incidence of uncomplicated \(P\) . falciparum malaria by almost half \(^{14}\) . However, there is concern that the effectiveness of LLINs may be diminishing due to widespread resistance to pyrethroids which until recently were the only class of insecticides
+
+<--- Page Split --->
+
+approved for LLINs. Similar to many other African countries, high- level resistance to pyrethroids among the principle Anopheles vectors has been reported recently throughout Uganda \(^{15 - 17}\) . In addition, behavioral changes in vector biting activity following the introduction of LLINs have been reported which could present new challenges for malaria control \(^{18 - 20}\) . Finally, the effectiveness of LLINs may be further compromised by poor adherence and waning coverage in the setting of free distribution campaigns done intermittently. In Uganda, less than \(18\%\) of households reported adequate coverage (defined as at least one LLIN per 2 residents) three years after the 2013- 14 distribution campaign \(^{21}\) and adequate coverage decreased from \(71\%\) to \(51\%\) between 6 and 18 months following the 2017- 18 distribution campaign \(^{22}\) . Although the World Health Organization recommends mass distribution campaigns every three years, mounting evidence suggests that LLINs should be distributed more frequently to sustain high coverage \(^{23 - 29}\) .  
+
+Given concerns about the current effectiveness of pyrethroid- based LLINs and the persistently high burden of malaria despite aggressive scale up of LLINs in countries like Uganda, additional malaria control measures are needed. IRS is an attractive option. Historically, IRS programs were used to dramatically reduce and even eliminate malaria in many parts of the world. Thus, it is surprising that the evidence base from contemporary controlled trials on the impact of adding IRS to LLINs for vector control is limited. A recent systematic review of cluster randomized controlled trials conducted in sub- Saharan Africa since 2008, reported that adding IRS using a “pyrethroid- like” insecticide to LLINs did not provide any benefits, while adding IRS with a “non- pyrethroid- like” insecticide produced mixed results \(^{5}\) . Among the four trials comparing IRS plus LLINs with LLINs alone, three evaluated IRS with a carbamate (bendiocarb) and one
+
+<--- Page Split --->
+
+evaluated a long- lasting organophosphate, pirimiphos- methyl (Actellic 300CS®) \(^{30 - 33}\) . Only two trials (both using bendiocarb) assessed malaria incidence; one from Sudan found a \(35\%\) reduction when adding IRS to LLINs \(^{31}\) , while another from Benin found no benefit of adding IRS \(^{30}\) . All four trials assessed parasite prevalence, with an overall non- significant trend towards a lower prevalence when adding IRS to LLINs (RR=0.67, 95% CI 0.35- 1.28) \(^{5}\) . However, when the analyses were restricted to include only the two studies with LLIN usage over \(50\%\) , adding IRS reduced parasite prevalence by over \(50\%\) (RR=0.47, 95% CI 0.33- 0.67) \(^{5}\) . Of note, none of the trials that evaluated the impact of adding IRS with a “non- pyrethroid- like” insecticide assessed outcomes beyond two years. More recently, a number of observational studies have reported benefits of using IRS with pirimiphos- methyl (Actellic 300CS®). In the Mopti Region of Mali, delivery of a single round of IRS with Actellic 300CS® was associated with a \(42\%\) decrease in the peak incidence of laboratory confirmed malaria cases reported at public health facilities \(^{34}\) . In the Koulikoro Region of Mali, villages that received a single round of IRS with Actellic 300CS® combined with LLINs observed a greater than \(50\%\) decrease in the incidence of malaria compared to villages that only received LLINs \(^{35}\) . In the Northern Region of Ghana, districts that received IRS with Actellic 300CS® reported 26- 58% fewer cases of laboratory confirmed malaria cases reported at public health facilities over a two- year period, compared to districts that did not receive IRS \(^{36}\) . In Northern Zambia, implementation of IRS with Actellic 300CS® targeting only high burden areas over a three year period was associated with a \(25\%\) decline in parasite prevalence during the rainy season, but no decline during the dry season \(^{37}\) . In Western Kenya, the introduction of a single round of IRS with Actellic 300CS® was associated with a 44- 65% decrease in district level malaria case counts over a 10 month period compared to pre- IRS levels \(^{38}\) . In addition, several recent reports have documented dramatic resurgences
+
+<--- Page Split --->
+
+following the withdrawal of IRS with bendiocarb in Benin<sup>39</sup>, and the withdrawal of IRS with Actellic 300CS® in Mali and Ghana<sup>34,36</sup>.  
+
+The results from this study provides additional support for the critical role IRS can play in reducing the burden of malaria in African countries with high LLINs coverage. We analyzed a large, rigorously collected dataset, which is a strength of study. Data were collected over nearly seven years through an enhanced health facility- based surveillance system covering 14 districts in Uganda where IRS was being withdrawn, re- started, and initiated. This enhanced surveillance system facilitated laboratory testing and provided prospectively collected, individual- level data, allowing for analyses of quantitative changes in laboratory- confirmed cases of malaria over time, controlling for temporal changes in rainfall, seasonal effects, diagnostic practices, and health seeking behavior. Previous work by our group documented a marked decrease in malaria test positivity rates after four years of sustained IRS with bendiocarb in one district of Northern Uganda followed by a rapid resurgence over an 18- month period after IRS was withdrawn<sup>11</sup>. In this study we expand on these findings by including data from three districts and covering a 31- month period following the withdrawal of IRS. We were able to quantify more than a 5- fold increase in malaria cases which was sustained over the 10- 31 months following the withdrawal of IRS. This marked resurgence occurred despite the fact the first universal LLIN distribution campaign was timed to occur right after IRS was withdrawn. Given the dramatic nature of the resurgence, the Ugandan government was able to procure funding for a single round of IRS with Actellic 300CS® approximately three years after IRS was withdrawn in 10 districts of Northern Uganda. In this study, we assessed the impact of this single round in nine of these districts. This single round was associated with over a 5- fold decrease in malaria cases after 8- 12 months, with
+
+<--- Page Split --->
+
+malaria cases returning to pre- IRS levels after almost 2 years. These data suggest that IRS with longer- acting formulations such as Actellic 300CS® administered every 2 years may be a cost- effective strategy for mitigating the risk of resurgence following sustained IRS and/or enabling countries to expand coverage when resources are limited. This study also evaluated the impact of five years of sustained IRS in 5 districts of Eastern Uganda, starting first with bendiocarb and then switching to Actellic 300CS® after 18 months. Rounds of IRS were initially associated with marked decreases in malaria cases followed by peaks before subsequent rounds until the \(4^{\text{th}}\) and \(5^{\text{th}}\) years after IRS was initiated when there was a sustained decrease of almost 7- fold compared to pre- IRS level. Given the before- and- after nature of our study design, it is not clear whether the maximum sustained benefits of IRS seen after 4- 5 years were due to the cumulative effect of multiple rounds of IRS, the switch from bendiocarb to Actellic 300CS®, the second universal LLIN distribution campaign which occurred in this area in 2017, and/or other factors.  
+
+This study had several limitations. First, we used an observational study design, with measures of impact based on comparisons made before- and- after key changes in IRS policy. Although cluster randomized controlled trials are the gold standard study design for estimating the impact of IRS, it could be argued that withholding IRS would be unethical, given what is known about its impact in Uganda. Second, our estimates of impact could have been confounded by secular trends in factors not accounted for in our analyses. However, we feel that our overall conclusions are robust given the large amount of data available from multiple sites over an extended period with multiple complementary objectives providing consistent findings. Third, we could not assess the impact of IRS independent of LLIN use and did not have access to measures of IRS or LLIN coverage from our study populations. However, we were able to provide a “real world”
+
+<--- Page Split --->
+
+assessment of IRS in a setting where LLIN use is strongly supported by repeated universal distribution campaigns that are becoming increasingly common in sub- Saharan Africa. Finally, our study outcome was limited to case counts of laboratory confirmed malaria captured at health facilities. Thus, we were unable to measure the impact of IRS on other important indicators such as measures of transmission intensity, parasite prevalence, or mortality.  
+
+There is a growing body of evidence that combining LLINs with IRS using "non- pyrethroid- like" insecticides, especially the long acting organophosphate Actellic 300CS®, is highly effective at reducing the burden of malaria in Uganda, and elsewhere in Africa. Despite these encouraging findings, IRS coverage in Africa has been moving in the wrong direction. The proportion of those at risk protected by IRS in Africa peaked at just over \(10\%\) in 2010. However, the spread of pyrethroid resistance has led many control programs to switch to more expensive formulations resulting in a \(53\%\) decrease in the number of houses sprayed between years of peak coverage and 2015 across 18 countries supported by the U.S. President's Malaria Initiative<sup>40</sup> and an overall reduction in the proportion protected by IRS in Africa to less than \(5\%\) in 2018<sup>2</sup>. Given the lack of recent progress in reducing the global burden of malaria coupled with challenges in funding, renewed commitments are needed to address the "high burden to high impact" approach now being advocated by the World Health Organization<sup>2</sup>. IRS is a widely available tool that could be scaled up, however demands currently exceed the availability of resources. Additional work is needed to optimize the use of IRS, prevent further spread of insecticide resistance, and better evaluate the cost effectiveness of IRS in the context of other control interventions.  
+
+## Methods
+
+<--- Page Split --->
+
+## Study sites and vector control interventions  
+
+This study utilized data from 14 health facilities located in 14 districts in Northern and Eastern Uganda (Fig 4) which were part of a larger comprehensive malaria surveillance network called the Uganda Malaria Surveillance Program (UMSP). Between 2007 and 2009, IRS was implemented in 10 high burden districts in northern Uganda. DDT or pyrethroids were initially used but in 2010 the insecticide was changed to a carbamate (bendiocarb) due to concern regarding the spread of pyrethroid resistance. Rounds of bendiocarb were repeated approximately every 6 months until 2014 when the IRS program was discontinued, so that resources could be shifted to other high burden districts. In 2017, these 10 districts in northern Uganda received a single round of the organophosphate pirimiphos- methyl (Actellic 300CS®) following reports of malaria resurgence after IRS has been discontinued in 2014. Between 2014 and 2015, IRS with bendiocarb was implemented in 14 districts in the Northern and Eastern part of the country. Rounds of bendiocarb were repeated approximately every six months until 2016 when the formulation was changed to Actellic 300CS®, which continues to be administered once a year.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig 4. Map of Uganda showing study sites and IRS districts. </center>  
+
+Universal LLIN distribution campaigns were conducted in 2013- 14 and 2017- 18, where LLINs were distributed free- of- charge by the Uganda Ministry of Health targeting 1 LLIN for every two household residents.  
+
+## Health-facility based surveillance  
+
+Enhanced malaria surveillance was established by UMSP in 2006, as previously described 41. UMSP operates Malaria Reference Centers (MRCs) at 70 level III/IV public health facilities across Uganda. At each MRC, individual- level data from standardized registers for all patients presenting to the outpatient departments are entered into an Access database by on- site data entry officers. Variables include patient demographics, results of laboratory testing for malaria (rapid
+
+<--- Page Split --->
+
+diagnostic test [RDT] or microscopy), diagnoses given, and treatments prescribed. Emphasis is placed on ensuring that patients with suspected malaria undergo testing, by either RDT or microscopy.  
+
+This study utilized data from 14 MRCs located in districts that either previously had IRS or have ongoing IRS campaigns. We estimated the impact of withdrawing IRS using data from three sites in Northern Uganda that had at least six months of data preceding the final round of IRS administered in 2014. To estimate the impact of restarting IRS with a single round administered in 2017, we used data from nine sites in Northern Uganda. To estimate the impact of sustained IRS over five years, we used data from five sites in Eastern Uganda where IRS had been implemented since 2014- 15.  
+
+## Measures  
+
+Exposure. The exposure was specified as an indicator variable for each month since IRS was withdrawn or initiated relative to a baseline period (Fig 5 and Supplementary Fig S7). We also fit separate models with categorical exposure variables divided into distinct periods of months. To determine the impact of withdrawing IRS after at least five years of sustained use, the baseline period was defined as the final year of sustained IRS use, and the evaluation period lasted through 2016, prior to when an additional round of IRS was implemented. In order to determine the impact of restarting IRS with a single round of IRS, the baseline period was defined as one year prior to the single round of IRS and the evaluation period went through December 2019. To determine the impact of initiating and sustaining IRS, the baseline period was the year prior to IRS initiation, and the evaluation period lasted through December 2019.
+
+<--- Page Split --->
+
+Fig 5. Timeline summarizing the dates of IRS campaigns, baseline and evaluation periods. Objective 1 is to assess the impact of withdrawing IRS after five years of sustained use; Objective 2 is to assess the impact of restarting IRS with a single round; and Objective 3 is to assess the impact of initiating and sustaining IRS.  
+
+![](images/Figure_1.jpg)
+  
+
+Outcome. The primary outcome was the monthly count of laboratory- confirmed malaria cases at each MRC. The case count was corrected for testing rates by multiplying the number of individuals with suspected malaria but not tested each month by the test positivity rate (the number who tested positive divided by the total number tested) for that month and adding the result to the number of laboratory- confirmed positive cases. As a sensitivity analysis, we re- specified the models including only laboratory- confirmed case counts as the outcome.  
+
+Covariates. We adjusted for time- varying variables that impact malaria burden and malaria case detection at the health facility. These variables included average rainfall at the health facility lagged by 1 month, indicator variables for month of the year (to adjust for seasonal effects), the proportion of tests that were RDTs in that month (vs. microscopy), and the number of individuals who attended the health facility but were not suspected of having malaria in that month (to adjust for care- seeking behaviors).
+
+<--- Page Split --->
+
+## Statistical analysis  
+
+For each objective, we specified mixed effects negative binomial regression models with random intercepts for health facility. Coefficients for the exposure variable were exponentiated to represent the incidence rate ratio (IRR) comparing the incidence of malaria in the month of interest relative to the baseline period. This method assumes that the underlying population has remained constant over the study period.
+
+<--- Page Split --->
+
+386 References387 1 Bhatt, S. et al. The effect of malaria control on Plasmodium falciparum in Africa between2000 and 2015. Nature 526, 207- 211, doi:10.1038/nature15535 (2015).390 2 Organization, W. H. World Malaria Report 2019. (2019).391 3 Hemingway, J. et al. Averting a malaria disaster: will insecticide resistance derail malariacontrol? Lancet 387, 1785- 1788, doi:10.1016/S0140- 6736(15)00417- 1 (2016).392 4 Ranson, H. & Lissenden, N. Insecticide Resistance in African Anopheles Mosquitoes: AWorsening Situation that Needs Urgent Action to Maintain Malaria Control. Trends Parasitol32, 187- 196, doi:10.1016/j.pt.2015.11.010 (2016).393 5 Choi, L., Pryce, J. & Garner, P. Indoor residual spraying for preventing malaria incommunities using insecticide- treated nets. Cochrane database of systematic reviews (Online) 5,CD012688, doi:10.1002/14651858.CD012688.pub2 (2019).396 6 Sherrard- Smith, E. et al. Systematic review of indoor residual spray efficacy andeffectiveness against Plasmodium falciparum in Africa. Nat Commun 9, 4982,doi:10.1038/s41467- 018- 07357- w (2018).397 7 Uganda National Malaria Control Division (NMCD), Uganda Bureau of Statistics(UBOS) & ICF. Uganda Malaria Indicator Survey 2018- 19. (NMCD, UBOS, and ICF, Kampala,Uganda, and Rockville, Maryland, USA, 2020).398 8 Kigozi, R. et al. Indoor residual spraying of insecticide and malaria morbidity in a hightransmission intensity area of Uganda. PLoS One 7, e42857, doi:10.1371/journal.pone.0042857(2012).
+
+<--- Page Split --->
+
+9 Steinhardt, L. C. et al. The effect of indoor residual spraying on malaria and anemia in a high- transmission area of northern Uganda. Am J Trop Med Hyg 88, 855- 861, doi:10.4269/ajtmh.12- 0747 (2013).  
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+10 Okullo, A. E. et al. Malaria incidence among children less than 5 years during and after cessation of indoor residual spraying in Northern Uganda. Malar J 16, 319, doi:10.1186/s12936- 017- 1966- x (2017).  
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+11 Raouf, S. et al. Resurgence of Malaria Following Discontinuation of Indoor Residual Spraying of Insecticide in an Area of Uganda With Previously High- Transmission Intensity. Clin Infect Dis 65, 453- 460, doi:10.1093/cid/cix251 (2017).  
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+12 Uganda Bureau of Statistics (UBOS) and ICF International. Uganda Malaria Indicator Survey 2014- 15. (UBOS and ICF International, Kampala, Uganda and Rockville, Maryland, USA, 2015).  
+
+13 Organization, W. H. Framework for Implementing the Global Technical Strategy for Malaria 2016- 2030 in the African Region. (2016).  
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+14 Pryce, J., Richardson, M. & Lengeler, C. Insecticide- treated nets for preventing malaria.  
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+Cochrane database of systematic reviews (Online) 11, CD000363,  
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+15 Echodu, R. et al. High insecticide resistances levels in Anopheles gambiae s.l. in  
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+northern Uganda and its relevance for future malaria control. BMC Res Notes 13, 348,  
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+16 Lynd, A. et al. LLIN Evaluation in Uganda Project (LLINEUP): a cross- sectional survey of species diversity and insecticide resistance in 48 districts of Uganda. Parasit Vectors 12, 94, doi:10.1186/s13071- 019- 3353- 7 (2019).
+
+<--- Page Split --->
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+17 Okia, M. et al. Insecticide resistance status of the malaria mosquitoes: Anopheles 
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+gambiae and Anopheles funestus in eastern and northern Uganda. Malar J 17, 157, 
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+<http://www.who.int/malaria/amdip/amdip_afro.htm> ( 
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+20 Sougoufara, S. et al. Biting by Anopheles funestus in broad daylight after use of long-lasting insecticidal nets: a new challenge to malaria elimination. Malar J 13, 125, 
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+21 Gonahasa, S. et al. LLIN Evaluation in Uganda Project (LLINEUP): factors associated with ownership and use of long-lasting insecticidal nets in Uganda: a cross-sectional survey of 48 districts. Malar J 17, 421, doi:10.1186/s12936-018-2571-3 (2018). 
+
+22 Staedke, S. G. et al. Effect of long-lasting insecticidal nets with and without piperonyl butoxide on malaria indicators in Uganda (LLINEUP): a pragmatic, cluster-randomised trial 
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+23 Rugnao, S. et al. LLIN Evaluation in Uganda Project (LLINEUP): factors associated with childhood parasitaemia and anaemia 3 years after a national long-lasting insecticidal net distribution campaign: a cross-sectional survey. Malar J 18, 207, doi:10.1186/s12936-019-2838-3 (2019).
+
+<--- Page Split --->
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+24 WHO. Achieving and maintaining universal coverage with long-lasting insecticidal nets for malaria control. (2017). 
+
+25 Wills, A. B. et al. Physical durability of PermaNet 2.0 long-lasting insecticidal nets over three to 32 months of use in Ethiopia. Malar J 12, 242, doi:10.1186/1475-2875-12-242 (2013). 
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+27 Massue, D. J. et al. Durability of Olyset campaign nets distributed between 2009 and 2011 in eight districts of Tanzania. Malar J 15, 176, doi:10.1186/s12936-016-1225-6 (2016). 
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+28 Tan, K. R. et al. A longitudinal study of the durability of long-lasting insecticidal nets in Zambia. Malar J 15, 106, doi:10.1186/s12936-016-1154-4 (2016). 
+
+29 Randriamaherijaoana, S., Raharinjatovo, J. & Boyer, S. Durability monitoring of long-lasting insecticidal (mosquito) nets (LLINs) in Madagascar: physical integrity and insecticidal activity. Parasit Vectors 10, 564, doi:10.1186/s13071-017-2419-7 (2017). 
+
+30 Corbel, V. et al. Combination of malaria vector control interventions in pyrethroid resistance area in Benin: a cluster randomised controlled trial. Lancet Infect Dis 12, 617-626, doi:10.1016/S1473-3099(12)70081-6 (2012). 
+
+31 Kafy, H. T. et al. Impact of insecticide resistance in Anopheles arabiensis on malaria incidence and prevalence in Sudan and the costs of mitigation. Proc Natl Acad Sci U S A 114, E11267-E11275, doi:10.1073/pnas.1713814114 (2017). 
+
+32 Protopopoff, N. et al. Effectiveness of a long-lasting piperonyl butoxide-treated insecticidal net and indoor residual spray interventions, separately and together, against malaria
+
+<--- Page Split --->
+
+transmitted by pyrethroid-resistant mosquitoes: a cluster, randomised controlled, two-by-two factorial design trial. Lancet 391, 1577- 1588, doi:10.1016/S0140- 6736(18)30427- 6 (2018).  
+
+West, P. A. et al. Indoor residual spraying in combination with insecticide- treated nets compared to insecticide- treated nets alone for protection against malaria: a cluster randomised trial in Tanzania. PLoS Med 11, e1001630, doi:10.1371/journal.pmed.1001630 (2014).  
+
+Wagman, J. et al. Rapid reduction of malaria transmission following the introduction of indoor residual spraying in previously unsprayed districts: an observational analysis of Mopti Region, Mali, in 2017. Malar J 19, 340, doi:10.1186/s12936- 020- 03414- 2 (2020).  
+
+Kane, F. et al. Performance of IRS on malaria prevalence and incidence using pirimiphos- methyl in the context of pyrethroid resistance in Koulikoro region, Mali. Malar J 19, 286, doi:10.1186/s12936- 020- 03357- 8 (2020).  
+
+Gogue, C. et al. An observational analysis of the impact of indoor residual spraying in Northern, Upper East, and Upper West Regions of Ghana: 2014 through 2017. Malar J 19, 242, doi:10.1186/s12936- 020- 03318- 1 (2020).  
+
+Hast, M. A. et al. The Impact of 3 Years of Targeted Indoor Residual Spraying With Pirimiphos- Methyl on Malaria Parasite Prevalence in a High- Transmission Area of Northern Zambia. Am J Epidemiol 188, 2120- 2130, doi:10.1093/aje/kwz107 (2019).  
+
+Abong'o, B. et al. Impact of indoor residual spraying with pirimiphos- methyl (Actellic 300CS) on entomological indicators of transmission and malaria case burden in Migori County, western Kenya. Scientific reports 10, 4518, doi:10.1038/s41598- 020- 61350- 2 (2020).  
+
+Aikpon, R. Y. et al. Upsurge of malaria transmission after indoor residual spraying withdrawal in Atacora region in Benin, West Africa. Malar J 19, 3, doi:10.1186/s12936- 019- 3086- 2 (2020).
+
+<--- Page Split --->
+
+40 Oxborough, R. M. Trends in US President's Malaria Initiative- funded indoor residual spray coverage and insecticide choice in sub- Saharan Africa (2008- 2015): urgent need for affordable, long- lasting insecticides. Malar J 15, 146, doi:10.1186/s12936- 016- 1201- 1 (2016). 41 Sserwanga, A. et al. Improved malaria case management through the implementation of a health facility- based sentinel site surveillance system in Uganda. PLoS One 6, e16316, doi:10.1371/journal.pone.0016316 (2011).
+
+<--- Page Split --->
+
+## Acknowledgements  
+
+We would like to acknowledge the health workers at all 14 health facilities that contributed data for this study. We would like to thank the Ugandan Ministry of Health National Malaria Control Division, and USAID – President’s Malaria Initiative. This work was supported by the National Institutes of Health as part of the International Centers of Excellence in Malaria Research (ICMER) program (U19AI089674). AE is supported by the National Institute of Allergy and Infectious Diseases (F31AI150029). JIN is supported by the Fogarty International Center (Emerging Global Leader Award grant number K43TW010365). EA is supported by the Fogarty International Center of the National Institutes of Health under Award Number D43TW010526.  
+
+## Author Contributions  
+
+JFN, AE, GD, and IRB conceived of the study. JFN led the data collection activities with support from JIN, AM, MK, AS, JK, EA, SG, CE, SGS, CMS, and MRK. AE and IRB led the data analysis with support from GD. AE and JFN drafted the manuscript with support from GD, SGS, and IRB. All authors contributed to interpretation of the results and edited the manuscripts. All authors read and approved the final manuscript.  
+
+## Competing Interests  
+
+The authors declare no competing interests.  
+
+## Materials and Correspondence  
+
+Correspondence to Adrienne Epstein: Adrienne.Epstein@ucsf.edu
+
+<--- Page Split --->
+
+Table 1. Summary statistics from health-facility based surveillance sites where IRS was stopped after sustained use.
+
+<table><tr><td>MRC<br>(District)</td><td>Time period</td><td>Number of<br>months<br>included</td><td>Total<br>outpatient<br>visits, n</td><td>Suspected<br>malaria<br>cases, n (%<br>of total)</td><td>Tested for<br>malaria, n<br>(% of<br>suspected)</td><td>RDT<br>performed<br>(versus<br>microscopy),<br>n(% of<br>tested)</td><td>Confirmed<br>malaria<br>cases, n (% of tested)</td><td>Confirmed<br>cases<br>adjusted for testing rate, n</td><td>Mean<br>monthly<br>confirmed<br>cases adjusted for testing rate, n</td></tr><tr><td rowspan="2">Aboke HCIV<br>(Kole)</td><td>Baseline</td><td>9</td><td>14,015</td><td>3,766 (26.9)</td><td>3,735 (99.2)</td><td>2,450 (65.6)</td><td>923 (24.7)</td><td>932</td><td>104</td></tr><tr><td>Evaluation</td><td>25</td><td>46,850</td><td>21,245 (45.3)</td><td>18,185 (85.6)</td><td>17,210 (94.6)</td><td>14,200 (78.0)</td><td>16,699</td><td>668</td></tr><tr><td rowspan="2">Aduku HCIV<br>(Kwania)</td><td>Baseline</td><td>13</td><td>24,164</td><td>13,742 (56.9)</td><td>13,719 (99.8)</td><td>1,049 (7.6)</td><td>3,254 (23.7)</td><td>3,529</td><td>272</td></tr><tr><td>Evaluation</td><td>32</td><td>57,470</td><td>30,035 (52.2)</td><td>25,896 (86.2)</td><td>10,731 (41.4)</td><td>13,537 (52.3)</td><td>15,717</td><td>491</td></tr><tr><td rowspan="2">Anyeke<br>HCIV<br>(Oyam)</td><td>Baseline</td><td>8</td><td>15,859</td><td>3,514 (22.2)</td><td>2,627 (74.8)</td><td>2,604 (99.1)</td><td>680 (25.9)</td><td>918</td><td>115</td></tr><tr><td>Evaluation</td><td>25</td><td>66,501</td><td>28,755 (43.2)</td><td>20,659 (71.8)</td><td>16,147 (78.2)</td><td>13,559 (65.6)</td><td>18,774</td><td>751</td></tr></table>
+
+<--- Page Split --->
+
+
+Table 2. Summary statistics from health-facility based surveillance sites that received a single round of IRS.   
+
+<table><tr><td>MRC (District)</td><td>Time period</td><td>Number of months included</td><td>Total outpatient visits, n</td><td>Suspected malaria cases, n (% of total)</td><td>Tested for malaria, n (% of suspected)</td><td>RDT performed (versus microscopy), n (% of tested)</td><td>Confirmed malaria cases, n (% of tested)</td><td>Confirmed cases adjusted for testing rate, n</td><td>Mean monthly confirmed cases adjusted for testing rate, n</td></tr><tr><td rowspan="2">Aboke HCIV (Kole)</td><td>Baseline</td><td>14</td><td>21,186</td><td>11,752 (55.5)</td><td>9,613 (81.8)</td><td>9,079 (94.5)</td><td>7,297 (75.9)</td><td>9,006</td><td>643</td></tr><tr><td>Evaluation</td><td>34</td><td>54,826</td><td>30,973 (56.5)</td><td>30,674 (99.0)</td><td>29,064 (94.8)</td><td>22,097 (72.0)</td><td>22,308</td><td>656</td></tr><tr><td rowspan="2">Aduku HCIV (Kwania)</td><td>Baseline</td><td>17</td><td>35,017</td><td>20,645 (59.0)</td><td>17,156 (83.1)</td><td>7,938 (46.3)</td><td>9,699 (56.5)</td><td>11,465</td><td>674</td></tr><tr><td>Evaluation</td><td>31</td><td>65,379</td><td>32,260 (49.3)</td><td>31,337 (97.1)</td><td>20,385 (65.1)</td><td>15,201 (48.5)</td><td>15,534</td><td>501</td></tr><tr><td rowspan="2">Anyeke HCIV (Oyam)</td><td>Baseline</td><td>14</td><td>35,378</td><td>18,445 (52.1)</td><td>12,997 (70.5)</td><td>9,151 (70.4)</td><td>8,967 (69.0)</td><td>12,595</td><td>900</td></tr><tr><td>Evaluation</td><td>34</td><td>70,149</td><td>33,618 (47.9)</td><td>32,522 (96.7)</td><td>31,208 (96.0)</td><td>21,799 (67.0)</td><td>22,375</td><td>658</td></tr><tr><td rowspan="2">Awach HCIV (Gulu)</td><td>Baseline</td><td>17</td><td>36,923</td><td>21,920 (59.4)</td><td>17,927 (82.0)</td><td>17,736 (98.7)</td><td>13,663 (76.0)</td><td>16,749</td><td>985</td></tr><tr><td>Evaluation</td><td>30</td><td>69,375</td><td>36,760 (53.0)</td><td>35,189 (95.7)</td><td>34,070 (96.8)</td><td>21,879 (62.2)</td><td>22,851</td><td>762</td></tr><tr><td rowspan="2">Lalogi HCIV (Omoro)</td><td>Baseline</td><td>17</td><td>54,436</td><td>32,642 (60.0)</td><td>31,545 (96.6)</td><td>31,490 (99.8)</td><td>23,106 (73.2)</td><td>23,948</td><td>1,409</td></tr><tr><td>Evaluation</td><td>31</td><td>72,449</td><td>41,846 (57.8)</td><td>41,668 (99.6)</td><td>40,804 (97.9)</td><td>22,986 (55.2)</td><td>23,060</td><td>744</td></tr><tr><td rowspan="2">Patongo HCIII (Agago)</td><td>Baseline</td><td>14</td><td>24,686</td><td>15,453 (62.6)</td><td>15,122 (97.9)</td><td>14,758 (97.6)</td><td>11,313 (74.8)</td><td>11,487</td><td>821</td></tr><tr><td>Evaluation</td><td>34</td><td>54,486</td><td>34,482 (63.3)</td><td>33,797 (98.0)</td><td>32,176 (95.2)</td><td>17,231 (51.0)</td><td>17,440</td><td>513</td></tr><tr><td rowspan="2">Atiak HCIV (Amuru)</td><td>Baseline</td><td>14</td><td>38,916</td><td>25,929 (66.6)</td><td>22,418 (86.5)</td><td>22,335 (99.6)</td><td>18,978 (84.7)</td><td>21,966</td><td>1,569</td></tr><tr><td>Evaluation</td><td>34</td><td>60,750</td><td>31,650 (52.1)</td><td>30,754 (97.2)</td><td>30,541 (99.3)</td><td>19,766 (64.3)</td><td>20,325</td><td>598</td></tr><tr><td rowspan="2">Padibe HCIV (Lamwo)</td><td>Baseline</td><td>20</td><td>29,740</td><td>20,589 (69.0)</td><td>20,427 (99.2)</td><td>20,420 (99.9)</td><td>17,031 (83.4)</td><td>17,161</td><td>858</td></tr><tr><td>Evaluation</td><td>28</td><td>50,117</td><td>26,883 (53.6)</td><td>26,831 (99.8)</td><td>25,956 (96.7)</td><td>15,199 (56.6)</td><td>15,224</td><td>544</td></tr><tr><td rowspan="2">Namokora HCIV (Kitgum)</td><td>Baseline</td><td>17</td><td>27,802</td><td>22,597 (81.3)</td><td>19,990 (88.5)</td><td>18,909 (94.6)</td><td>12,294 (61.5)</td><td>14,401</td><td>847</td></tr><tr><td>Evaluation</td><td>31</td><td>56,765</td><td>40,185 (70.8)</td><td>39,966 (99.5)</td><td>38,468 (96.3)</td><td>21,958 (54.9)</td><td>22,063</td><td>712</td></tr></table>
+
+<--- Page Split --->
+
+
+Table 3. Summary statistics from health-facility based surveillance sites where IRS was initiated and sustained.   
+
+<table><tr><td>MRC (District)</td><td>Time period</td><td>Number of months included</td><td>Total outpatient visits, n</td><td>Suspected malaria cases, n (%)</td><td>Tested for malaria, n (%)</td><td>RDT performed (versus microscopy), n (% of tested)</td><td>Confirmed malaria cases, n (%)</td><td>Confirmed malaria cases adjusted for testing rate, n</td><td>Mean monthly confirmed cases adjusted for testing rate, n</td></tr><tr><td rowspan="2">Nagongera HCIV (Tororo</td><td>Baseline</td><td>13</td><td>22,859</td><td>14,676 (64.2)</td><td>14,516 (98.9)</td><td>799 (5.5)</td><td>3,682 (25.4)</td><td>3,722</td><td>286</td></tr><tr><td>Evaluation</td><td>59</td><td>97,012</td><td>36,308 (37.4)</td><td>36,069 (99.3)</td><td>13,129 (36.4)</td><td>4,984 (13.8)</td><td>5,022</td><td>85</td></tr><tr><td rowspan="2">Amolatar HCIV (Amolatar)</td><td>Baseline</td><td>12</td><td>19,552</td><td>8,547 (43.7)</td><td>6,512 (76.2)</td><td>5,923 (91.0)</td><td>3,701 (56.8)</td><td>4,845</td><td>404</td></tr><tr><td>Evaluation</td><td>59</td><td>89,779</td><td>24,889 (27.8)</td><td>21,849 (87.9)</td><td>19,459 (89.1)</td><td>4,822 (22.1)</td><td>5,854</td><td>99</td></tr><tr><td rowspan="2">Dokolo HCIV (Dokolo)</td><td>Baseline</td><td>12</td><td>25,570</td><td>12,854 (50.3)</td><td>8,875 (69.0)</td><td>8,212 (92.5)</td><td>5,211 (58.7)</td><td>7,889</td><td>657</td></tr><tr><td>Evaluation</td><td>59</td><td>129,245</td><td>46,428 (35.9)</td><td>44,972 (96.9)</td><td>42,259 (94.0)</td><td>10,210 (22.7)</td><td>10,761</td><td>183</td></tr><tr><td rowspan="2">Orum HCIV (Onuke)</td><td>Baseline</td><td>11</td><td>16,120</td><td>9,324 (57.8)</td><td>8,929 (95.8)</td><td>3,990 (44.7)</td><td>5,974 (66.9)</td><td>6,236</td><td>567</td></tr><tr><td>Evaluation</td><td>59</td><td>65,036</td><td>37,430 (57.6)</td><td>36,371 (97.2)</td><td>19,536 (53.7)</td><td>16,481 (45.3)</td><td>17,069</td><td>289</td></tr><tr><td rowspan="2">Alebong HCIV (Alebong)</td><td>Baseline</td><td>8</td><td>15,359</td><td>6,694 (43.6)</td><td>4,789 (71.5)</td><td>4,620 (96.5)</td><td>3,209 (67.0)</td><td>4,317</td><td>540</td></tr><tr><td>Evaluation</td><td>59</td><td>94,055</td><td>40,821 (43.0)</td><td>36,211 (88.7)</td><td>32,327 (89.3)</td><td>12,037 (33.2)</td><td>13,869</td><td>235</td></tr></table>
+
+<--- Page Split --->
+
+## Figures  
+
+![](images/Figure_2.jpg)
+
+<center>Figure 1 </center>  
+
+Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of withdrawing IRS after 5 years of sustained use. The blue shaded region represents the \(95\%\) confidence interval around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) confidence interval around adjusted IRR.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 2 </center>  
+
+Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of restarting IRS with a single round. The blue shaded region represents the \(95\%\) CI around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) CI around adjusted IRR.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 3 </center>  
+
+Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of initiating and sustaining IRS. The blue shaded region represents the \(95\%\) CI around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) CI around adjusted IRR.  
+
+![PLACEHOLDER_31_1]
+
+
+<--- Page Split --->
+![PLACEHOLDER_32_0]
+
+<center>Figure 4 </center>  
+
+Timeline summarizing the dates of IRS campaigns, baseline 357 and evaluation periods. Objective 1 is to assess the impact of withdrawing IRS after five years of sustained use; Objective 2 is to assess the impact of restarting IRS with a single round; and Objective 3 is to assess the impact of initiating and sustaining IRS.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- IRSprojectsupplements.pdf
+
+<--- Page Split --->

preprint/preprint__075d82fd5d37a02cde8eab26a4d85528ea15df290443dfb4d60ca9ac191d6a24/preprint__075d82fd5d37a02cde8eab26a4d85528ea15df290443dfb4d60ca9ac191d6a24_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 106, 941, 210]]<|/det|>
+# The impact of stopping and starting indoor residual spraying on malaria burden in 14 districts of Uganda  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 748, 317]]<|/det|>
+Jane Namuganga Infectious Diseases Research Collaboration Adrienne Epstein ( \(\boxed{}\) adrienne.epstein@ucsf.edu) University of California, San Francisco https://orcid.org/0000- 0002- 8253- 6102  
+
+<|ref|>text<|/ref|><|det|>[[44, 323, 435, 365]]<|/det|>
+Joaniter Nankabirwa Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 371, 435, 411]]<|/det|>
+Arthur Mpimbaza Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 417, 435, 458]]<|/det|>
+Moses Kiggundu Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 464, 435, 504]]<|/det|>
+Asadu Sserwanga Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 510, 435, 550]]<|/det|>
+James Kapisi Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 556, 435, 596]]<|/det|>
+Emmanuel Arinaitwe Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 602, 435, 642]]<|/det|>
+Samuel Gonahasa Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 648, 345, 688]]<|/det|>
+Jimmy Opigo National Malaria Control Division  
+
+<|ref|>text<|/ref|><|det|>[[44, 694, 435, 734]]<|/det|>
+Chris Ebong Infectious Diseases Research Collaboration  
+
+<|ref|>text<|/ref|><|det|>[[44, 740, 465, 781]]<|/det|>
+Sarah Staedke London School of Hygiene & Tropical Medicine  
+
+<|ref|>text<|/ref|><|det|>[[44, 787, 585, 827]]<|/det|>
+Josephat Shillul US President's Malaria Initiative - VectorLink Uganda Project  
+
+<|ref|>text<|/ref|><|det|>[[44, 833, 585, 873]]<|/det|>
+Michael Okia US President's Malaria Initiative - VectorLink Uganda Project  
+
+<|ref|>text<|/ref|><|det|>[[44, 879, 345, 920]]<|/det|>
+Damian Rutazaana National Malaria Control Division  
+
+<|ref|>text<|/ref|><|det|>[[44, 926, 294, 944]]<|/det|>
+Catherine Maiteki- Ssebuguzi
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 46, 345, 65]]<|/det|>
+National Malaria Control Division  
+
+<|ref|>text<|/ref|><|det|>[[44, 70, 395, 110]]<|/det|>
+Kassahun Belay US President's Malaria Initiative, USAID  
+
+<|ref|>text<|/ref|><|det|>[[44, 116, 228, 156]]<|/det|>
+Moses Kamya Makerere University  
+
+<|ref|>text<|/ref|><|det|>[[44, 163, 390, 204]]<|/det|>
+Grant Dorsey University of California, San Francisco  
+
+<|ref|>text<|/ref|><|det|>[[44, 210, 390, 250]]<|/det|>
+Isabel Rodriguez- Barraquer University of California, San Francisco  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 291, 102, 309]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 328, 680, 349]]<|/det|>
+Keywords: malaria, disease control, insecticide, vector control intervention  
+
+<|ref|>text<|/ref|><|det|>[[44, 367, 346, 387]]<|/det|>
+Posted Date: December 29th, 2020  
+
+<|ref|>text<|/ref|><|det|>[[44, 404, 463, 425]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 126095/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 441, 910, 485]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 520, 909, 564]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on May 11th, 2021. See the published version at https://doi.org/10.1038/s41467- 021- 22896- 5.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[137, 90, 860, 135]]<|/det|>
+# The impact of stopping and starting indoor residual spraying on malaria burden in 14 districts of Uganda  
+
+<|ref|>text<|/ref|><|det|>[[112, 193, 884, 320]]<|/det|>
+Jane F. Namuganga1\\*, Adrienne Epstein2\\*, Joaniter I. Nankabirwa1,3, Arthur Mpimbaza1,4, Moses Kiggundu1, Asadu Serwanga1, James Kapisi1, Emmanuel Arinaitwe1, Samuel Gonahasa1, Jimmy Opigo5, Chris Ebong1, Sarah G. Staedke6, Josephat Shililu7, Michael Okia7, Damian Rutazaanas, Catherine Maiteki- Ssebuguzi5, Kassahun Belay8, Moses R. Kamya1,3, Grant Dorsey9, Isabel Rodriquez- Barraquer9  
+
+<|ref|>text<|/ref|><|det|>[[112, 375, 869, 416]]<|/det|>
+1 Infectious Diseases Research Collaboration, Kampala, Uganda  
+
+<|ref|>text<|/ref|><|det|>[[112, 418, 870, 458]]<|/det|>
+2 Department of Epidemiology and Biostatistics, University of California San Francisco, San Francisco, California, United States of America  
+
+<|ref|>text<|/ref|><|det|>[[112, 464, 870, 504]]<|/det|>
+3 Department of Medicine, Makerere University, College of Health Sciences, Kampala, Uganda  
+
+<|ref|>text<|/ref|><|det|>[[112, 499, 833, 539]]<|/det|>
+4 Child Health and Development Centre, Makerere University, College of Health Sciences, Kampala, Uganda  
+
+<|ref|>text<|/ref|><|det|>[[112, 550, 710, 571]]<|/det|>
+5 National Malaria Control Division, Ministry of Health, Kampala, Uganda  
+
+<|ref|>text<|/ref|><|det|>[[112, 584, 737, 605]]<|/det|>
+6 London School of Hygiene and Tropical Medicine, London, United Kingdom  
+
+<|ref|>text<|/ref|><|det|>[[112, 618, 775, 640]]<|/det|>
+7 US President's Malaria Initiative - VectorLink Uganda Project, Kampala, Uganda  
+
+<|ref|>text<|/ref|><|det|>[[112, 653, 712, 673]]<|/det|>
+8 US President's Malaria Initiative, USAID/Uganda Senior Malaria Advisor  
+
+<|ref|>text<|/ref|><|det|>[[112, 687, 850, 726]]<|/det|>
+9 Department of Medicine, University of California San Francisco, San Francisco, California, United States of America  
+
+<|ref|>text<|/ref|><|det|>[[112, 740, 349, 759]]<|/det|>
+\*Adrienne.Epstein@ucsf.edu  
+
+<|ref|>text<|/ref|><|det|>[[112, 775, 498, 796]]<|/det|>
+\* These authors contributed equally to this work.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[66, 91, 203, 111]]<|/det|>
+## 40 Abstract  
+
+<|ref|>text<|/ref|><|det|>[[110, 128, 874, 465]]<|/det|>
+The scale- up of malaria control efforts has led to marked reductions in malaria burden over the past twenty years, but progress has slowed. Implementation of indoor residual spraying (IRS) of insecticide, a proven vector control intervention, has been limited and difficult to sustain partly because questions remain on its added impact over widely accepted interventions such as bed nets. Using data from 14 enhanced surveillance health facilities in Uganda, a country with high bet net coverage yet high malaria burden, we estimate the impact of starting and stopping IRS. We show that stopping IRS resulted in a 5- fold increase in malaria incidence within 10 months, but reinstating IRS led to an over 5- fold decrease within 8 months. In areas where IRS was initiated and sustained, malaria incidence dropped by \(85\%\) after year 4. IRS could play a critical role in achieving global malaria targets, particularly in areas where progress has stalled.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[113, 91, 243, 110]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[111, 123, 881, 712]]<|/det|>
+Over the past twenty years the scale- up of malaria control efforts has led to marked reductions in morbidity and mortality \(^{1,2}\) . However, global progress has slowed in recent years, particularly in sub- Saharan Africa, which accounted for \(93\%\) of the world's 228 million cases in \(2018^{2}\) . Longlasting insecticidal nets (LLINs) and indoor residual spraying of insecticide (IRS) are the primary vector control interventions used for the prevention of malaria. The World Health Organization recommends universal coverage of LLINs for at- risk populations in sub- Saharan Africa, where the proportion of households owning at least one LLIN is estimated to have increased from \(47\%\) in 2010 to \(72\%\) in 2018. Until recently, pyrethroids were the only class of insecticides approved for use in LLINs and, given the emergence of widespread pyrethroid resistance \(^{3,4}\) , there is concern that the effectiveness of LLINs may be diminishing. Unlike LLINs, IRS has the advantage of utilizing multiple different classes of insecticides and combing IRS with LLINs may improve malaria control and slow the spread of pyrethroid resistance. However, few controlled trials have evaluated the effect of adding IRS to communities using LLINs and the evidence is mixed, with a few studies showing benefits when IRS included 'non- pyrethroid- like' insecticides \(^{5}\) . Other barriers to IRS delivery – including cost, logistics, and community acceptance – have limited its use \(^{6}\) , such that less than \(5\%\) of the population at risk in sub- Saharan Africa was protected by IRS in 2018, a decrease from over \(10\%\) coverage in \(2010^{2}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 755, 879, 881]]<|/det|>
+Uganda is illustrative of a country where the burden of malaria remains high and progress has slowed in recent years \(^{2}\) . Malaria control efforts in Uganda have primarily focused on LLINs. In 2013- 14 it became the first country to implement a universal LLIN distribution campaign, which was repeated in 2017- 18. In 2018- 19, Uganda had the highest coverage of LLINs in the world,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 881, 352]]<|/det|>
+with \(83\%\) of households reported owning at least one LLIN<sup>7</sup>. In contrast to LLINs, the implementation of IRS in Uganda has been focal and limited. In 2006, IRS was reintroduced into Uganda for the first time since the 1960s. In 2007- 09, the IRS program was shifted to 10 high burden districts in the north, leading to large reductions in malaria burden<sup>8,9</sup>. In 2014, the IRS program was relocated from these 10 northern districts to 14 districts in the eastern part of the country, where it has been sustained. The discontinuation of IRS in the 10 northern districts was followed by a marked resurgence in malaria cases<sup>10,11</sup>, prompting the implementation of a single round of IRS in these 10 districts in 2017.  
+
+<|ref|>text<|/ref|><|det|>[[111, 403, 884, 632]]<|/det|>
+In this study, we used data from a network of health facility- based malaria surveillance sites to evaluate the impact of different IRS delivery scenarios in 14 districts in Uganda. This study had three objectives: (1) to estimate the impact of withdrawing IRS after five years of sustained use on the burden of malaria in three sites in Northern Uganda; (2) to estimate the impact of restarting IRS with a single round three to four years after IRS was discontinued on the burden of malaria in nine sites in Northern Uganda; and (3) to estimate the impact of five years of sustained IRS on the burden of malaria in five sites in Northern and Eastern Uganda.  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 683, 189, 701]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 722, 510, 742]]<|/det|>
+## Impact of withdrawing IRS after sustained use  
+
+<|ref|>text<|/ref|><|det|>[[112, 755, 878, 882]]<|/det|>
+Across the three sites included in the analysis, a total of 224,859 outpatient visits were observed (Table 1). During the baseline period, average monthly cases ranged from 104- 272 and TPR ranged from \(23.7\% - 25.9\%\) . This increased to 491- 751 and \(52.3\% - 78.0\%\) respectively, during the evaluation period (Supplementary Fig S1).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 123, 884, 460]]<|/det|>
+Monthly adjusted IRRs and \(95\%\) confidence intervals (CI) for the three sites combined are presented in Fig 1 and Supplementary Table S1. These results showed an initial reduction in malaria cases after the final round of IRS relative to the baseline period until (adjusted IRR in the first month after \(\mathrm{IRS} = 0.19\) , \(95\%\) CI 0.09- 0.42) about four to five months after the final IRS campaign when malaria cases began to increase. Over the 10- 31 months after IRS was stopped, the number of malaria cases increased by over 5- fold relative to the baseline period (adjusted \(\mathrm{IRR} = 5.24\) , \(95\%\) CI 3.67- 7.50). This corresponds to predicted case counts of near zero immediately following final IRS campaign followed by an increase to about 1000 cases per month at each site (Fig 1). These results were consistent when considering only laboratory- confirmed cases unadjusted for testing rates (Supplementary Fig S2).  
+
+<|ref|>image<|/ref|><|det|>[[112, 545, 875, 765]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[112, 472, 881, 544]]<|/det|>
+<center>Fig 1. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of withdrawing IRS after 5 years of sustained use. The blue shaded region represents the \(95\%\) confidence interval around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) confidence interval around adjusted IRR. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 817, 490, 837]]<|/det|>
+## Impact of restarting IRS with a single round  
+
+<|ref|>text<|/ref|><|det|>[[111, 851, 880, 906]]<|/det|>
+A total of 858,380 outpatient visits were recorded across the analysis period for the nine sites. (Table 2). Mean monthly malaria cases ranged from 643- 1,569 and the TPR ranged from \(56.5\%\) -
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 864, 179]]<|/det|>
+84.7% during the baseline period. These ranges were 501- 762 and 48.5%- 72.0% respectively during the evaluation period. Temporal trends of laboratory- confirmed malaria cases over time for the individual health facilities are presented in Supplementary Fig S3.  
+
+<|ref|>text<|/ref|><|det|>[[111, 210, 881, 475]]<|/det|>
+Monthly adjusted IRRs and 95% CI for the nine sites combined are presented in Fig 2 and Supplementary Table S2. The single round of IRS led to a reduction in malaria cases until approximately 23 months post- IRS. Over the 8- 12 months after the single round of IRS, malaria cases decreased by over 5- fold relative to the baseline period (adjusted \(\mathrm{IRR} = 0.17\) , 95% CI 0.15- 0.20). After 23 months following the single round of IRS, malaria cases returned to a level similar to the baseline period before the single round of IRS (adjusted IRR for months \(23 - 31 = 1.06\) , 95% CI 0.92- 1.21). These results were consistent when considering only laboratory- confirmed cases unadjusted for testing rates (Supplementary Fig S4).  
+
+<|ref|>image<|/ref|><|det|>[[115, 560, 880, 787]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[112, 490, 877, 560]]<|/det|>
+<center>Fig 2. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of restarting IRS with a single round. The blue shaded region represents the 95% CI around the predicted case counts from the adjusted regression model. Vertical bars represent the 95% CI around adjusted IRR. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 819, 445, 839]]<|/det|>
+## Impact of initiating and sustaining IRS  
+
+<|ref|>text<|/ref|><|det|>[[112, 853, 850, 874]]<|/det|>
+In total, 574,587 outpatient visits were observed across the five sites included in the analysis.  
+
+<|ref|>text<|/ref|><|det|>[[112, 888, 857, 908]]<|/det|>
+(Table 3). During the baseline period, average monthly malaria cases adjusted for testing rates
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 881, 207]]<|/det|>
+ranged from 286- 657 and the TPR ranged from \(25.4\% - 67.0\%\) . This range decreased to 85- 289 for malaria cases and \(13.8\% - 45.3\%\) for the TPR during the evaluation period. Temporal trends of laboratory- confirmed malaria cases over time for the individual health facilities are presented in Supplementary Fig S5.  
+
+<|ref|>text<|/ref|><|det|>[[111, 228, 879, 528]]<|/det|>
+Monthly adjusted IRRs and \(95\%\) CI for the five sites combined are presented in Fig 3 and Supplementary Table S3. There was a modest overall reduction in malaria case counts in the first three years after IRS was initiated relative to the baseline period, with some peaks in case counts returning to near baseline levels just prior to when rounds of IRS were administered. However, after the third year of sustained use, malaria case counts dropped substantially and remained low relative to the period before IRS was initiated. In the \(4^{\text{th}}\) and \(5^{\text{th}}\) year after IRS was initiated and sustained, malaria cases dropped by \(85\%\) (adjusted \(\mathrm{IRR} = 0.15\) , \(95\%\) CI 0.12- 0.18). These results were consistent when considering only laboratory- confirmed cases unadjusted for testing rates (Supplementary Fig S6).  
+
+<|ref|>image<|/ref|><|det|>[[112, 612, 880, 840]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[112, 543, 861, 614]]<|/det|>
+<center>Fig 3. Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of initiating and sustaining IRS. The blue shaded region represents the \(95\%\) CI around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) CI around adjusted IRR. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[113, 91, 220, 111]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[111, 123, 884, 680]]<|/det|>
+Uganda has been exceptionally successful in scaling- up coverage of LLINs. Following the mass distribution campaigns to deliver free LLINs in 2013- 14 and 2017- 18, \(90\%\) and \(83\%\) of households respectively reported ownership of at least one LLIN \(^{7,12}\) . However, despite this success, the burden of malaria remains high in much of the country. Uganda had the \(3^{\text{rd}}\) highest number of malaria cases reported in 2018, with reported case incidence increasing since \(2014^{2}\) . If Uganda is to achieve the goals established by the World Health Organization’s Global Technical Strategy for malaria including reducing malaria case incidence by at least \(90\%\) by 2030 as compared with \(2015^{13}\) , additional malaria control measures will be needed. This report highlights the critical role of IRS in substantially reducing the burden of malaria in areas where transmission remains high despite deployment of LLINs. Withdrawing IRS after five years of sustained use in three districts in northern Uganda resulted in a more than 5- fold increase in malaria cases within 10 months. Re- starting IRS with a single round in nine districts in Northern Uganda approximately three years after IRS had been stopped led to a transient but important (more than a 5- fold) decrease in malaria cases within 8- 12 months, returning to pre- IRS levels after 23 months. Initiating and sustaining IRS in five districts in Eastern Uganda led to a gradual reduction in malaria cases reaching almost a 7- fold reduction after 4- 5 years.  
+
+<|ref|>text<|/ref|><|det|>[[112, 722, 884, 882]]<|/det|>
+Robust evidence supports the widespread use of LLINs for malaria control. In a systematic review of clinical trials conducted between 1987 and 2001, insecticide treated nets reduced all cause child mortality by \(17\%\) and the incidence of uncomplicated \(P\) . falciparum malaria by almost half \(^{14}\) . However, there is concern that the effectiveness of LLINs may be diminishing due to widespread resistance to pyrethroids which until recently were the only class of insecticides
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 88, 881, 494]]<|/det|>
+approved for LLINs. Similar to many other African countries, high- level resistance to pyrethroids among the principle Anopheles vectors has been reported recently throughout Uganda \(^{15 - 17}\) . In addition, behavioral changes in vector biting activity following the introduction of LLINs have been reported which could present new challenges for malaria control \(^{18 - 20}\) . Finally, the effectiveness of LLINs may be further compromised by poor adherence and waning coverage in the setting of free distribution campaigns done intermittently. In Uganda, less than \(18\%\) of households reported adequate coverage (defined as at least one LLIN per 2 residents) three years after the 2013- 14 distribution campaign \(^{21}\) and adequate coverage decreased from \(71\%\) to \(51\%\) between 6 and 18 months following the 2017- 18 distribution campaign \(^{22}\) . Although the World Health Organization recommends mass distribution campaigns every three years, mounting evidence suggests that LLINs should be distributed more frequently to sustain high coverage \(^{23 - 29}\) .  
+
+<|ref|>text<|/ref|><|det|>[[110, 541, 880, 877]]<|/det|>
+Given concerns about the current effectiveness of pyrethroid- based LLINs and the persistently high burden of malaria despite aggressive scale up of LLINs in countries like Uganda, additional malaria control measures are needed. IRS is an attractive option. Historically, IRS programs were used to dramatically reduce and even eliminate malaria in many parts of the world. Thus, it is surprising that the evidence base from contemporary controlled trials on the impact of adding IRS to LLINs for vector control is limited. A recent systematic review of cluster randomized controlled trials conducted in sub- Saharan Africa since 2008, reported that adding IRS using a “pyrethroid- like” insecticide to LLINs did not provide any benefits, while adding IRS with a “non- pyrethroid- like” insecticide produced mixed results \(^{5}\) . Among the four trials comparing IRS plus LLINs with LLINs alone, three evaluated IRS with a carbamate (bendiocarb) and one
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 88, 872, 876]]<|/det|>
+evaluated a long- lasting organophosphate, pirimiphos- methyl (Actellic 300CS®) \(^{30 - 33}\) . Only two trials (both using bendiocarb) assessed malaria incidence; one from Sudan found a \(35\%\) reduction when adding IRS to LLINs \(^{31}\) , while another from Benin found no benefit of adding IRS \(^{30}\) . All four trials assessed parasite prevalence, with an overall non- significant trend towards a lower prevalence when adding IRS to LLINs (RR=0.67, 95% CI 0.35- 1.28) \(^{5}\) . However, when the analyses were restricted to include only the two studies with LLIN usage over \(50\%\) , adding IRS reduced parasite prevalence by over \(50\%\) (RR=0.47, 95% CI 0.33- 0.67) \(^{5}\) . Of note, none of the trials that evaluated the impact of adding IRS with a “non- pyrethroid- like” insecticide assessed outcomes beyond two years. More recently, a number of observational studies have reported benefits of using IRS with pirimiphos- methyl (Actellic 300CS®). In the Mopti Region of Mali, delivery of a single round of IRS with Actellic 300CS® was associated with a \(42\%\) decrease in the peak incidence of laboratory confirmed malaria cases reported at public health facilities \(^{34}\) . In the Koulikoro Region of Mali, villages that received a single round of IRS with Actellic 300CS® combined with LLINs observed a greater than \(50\%\) decrease in the incidence of malaria compared to villages that only received LLINs \(^{35}\) . In the Northern Region of Ghana, districts that received IRS with Actellic 300CS® reported 26- 58% fewer cases of laboratory confirmed malaria cases reported at public health facilities over a two- year period, compared to districts that did not receive IRS \(^{36}\) . In Northern Zambia, implementation of IRS with Actellic 300CS® targeting only high burden areas over a three year period was associated with a \(25\%\) decline in parasite prevalence during the rainy season, but no decline during the dry season \(^{37}\) . In Western Kenya, the introduction of a single round of IRS with Actellic 300CS® was associated with a 44- 65% decrease in district level malaria case counts over a 10 month period compared to pre- IRS levels \(^{38}\) . In addition, several recent reports have documented dramatic resurgences
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 848, 144]]<|/det|>
+following the withdrawal of IRS with bendiocarb in Benin<sup>39</sup>, and the withdrawal of IRS with Actellic 300CS® in Mali and Ghana<sup>34,36</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[110, 191, 880, 880]]<|/det|>
+The results from this study provides additional support for the critical role IRS can play in reducing the burden of malaria in African countries with high LLINs coverage. We analyzed a large, rigorously collected dataset, which is a strength of study. Data were collected over nearly seven years through an enhanced health facility- based surveillance system covering 14 districts in Uganda where IRS was being withdrawn, re- started, and initiated. This enhanced surveillance system facilitated laboratory testing and provided prospectively collected, individual- level data, allowing for analyses of quantitative changes in laboratory- confirmed cases of malaria over time, controlling for temporal changes in rainfall, seasonal effects, diagnostic practices, and health seeking behavior. Previous work by our group documented a marked decrease in malaria test positivity rates after four years of sustained IRS with bendiocarb in one district of Northern Uganda followed by a rapid resurgence over an 18- month period after IRS was withdrawn<sup>11</sup>. In this study we expand on these findings by including data from three districts and covering a 31- month period following the withdrawal of IRS. We were able to quantify more than a 5- fold increase in malaria cases which was sustained over the 10- 31 months following the withdrawal of IRS. This marked resurgence occurred despite the fact the first universal LLIN distribution campaign was timed to occur right after IRS was withdrawn. Given the dramatic nature of the resurgence, the Ugandan government was able to procure funding for a single round of IRS with Actellic 300CS® approximately three years after IRS was withdrawn in 10 districts of Northern Uganda. In this study, we assessed the impact of this single round in nine of these districts. This single round was associated with over a 5- fold decrease in malaria cases after 8- 12 months, with
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 883, 494]]<|/det|>
+malaria cases returning to pre- IRS levels after almost 2 years. These data suggest that IRS with longer- acting formulations such as Actellic 300CS® administered every 2 years may be a cost- effective strategy for mitigating the risk of resurgence following sustained IRS and/or enabling countries to expand coverage when resources are limited. This study also evaluated the impact of five years of sustained IRS in 5 districts of Eastern Uganda, starting first with bendiocarb and then switching to Actellic 300CS® after 18 months. Rounds of IRS were initially associated with marked decreases in malaria cases followed by peaks before subsequent rounds until the \(4^{\text{th}}\) and \(5^{\text{th}}\) years after IRS was initiated when there was a sustained decrease of almost 7- fold compared to pre- IRS level. Given the before- and- after nature of our study design, it is not clear whether the maximum sustained benefits of IRS seen after 4- 5 years were due to the cumulative effect of multiple rounds of IRS, the switch from bendiocarb to Actellic 300CS®, the second universal LLIN distribution campaign which occurred in this area in 2017, and/or other factors.  
+
+<|ref|>text<|/ref|><|det|>[[111, 541, 879, 876]]<|/det|>
+This study had several limitations. First, we used an observational study design, with measures of impact based on comparisons made before- and- after key changes in IRS policy. Although cluster randomized controlled trials are the gold standard study design for estimating the impact of IRS, it could be argued that withholding IRS would be unethical, given what is known about its impact in Uganda. Second, our estimates of impact could have been confounded by secular trends in factors not accounted for in our analyses. However, we feel that our overall conclusions are robust given the large amount of data available from multiple sites over an extended period with multiple complementary objectives providing consistent findings. Third, we could not assess the impact of IRS independent of LLIN use and did not have access to measures of IRS or LLIN coverage from our study populations. However, we were able to provide a “real world”
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 877, 250]]<|/det|>
+assessment of IRS in a setting where LLIN use is strongly supported by repeated universal distribution campaigns that are becoming increasingly common in sub- Saharan Africa. Finally, our study outcome was limited to case counts of laboratory confirmed malaria captured at health facilities. Thus, we were unable to measure the impact of IRS on other important indicators such as measures of transmission intensity, parasite prevalence, or mortality.  
+
+<|ref|>text<|/ref|><|det|>[[111, 295, 880, 808]]<|/det|>
+There is a growing body of evidence that combining LLINs with IRS using "non- pyrethroid- like" insecticides, especially the long acting organophosphate Actellic 300CS®, is highly effective at reducing the burden of malaria in Uganda, and elsewhere in Africa. Despite these encouraging findings, IRS coverage in Africa has been moving in the wrong direction. The proportion of those at risk protected by IRS in Africa peaked at just over \(10\%\) in 2010. However, the spread of pyrethroid resistance has led many control programs to switch to more expensive formulations resulting in a \(53\%\) decrease in the number of houses sprayed between years of peak coverage and 2015 across 18 countries supported by the U.S. President's Malaria Initiative<sup>40</sup> and an overall reduction in the proportion protected by IRS in Africa to less than \(5\%\) in 2018<sup>2</sup>. Given the lack of recent progress in reducing the global burden of malaria coupled with challenges in funding, renewed commitments are needed to address the "high burden to high impact" approach now being advocated by the World Health Organization<sup>2</sup>. IRS is a widely available tool that could be scaled up, however demands currently exceed the availability of resources. Additional work is needed to optimize the use of IRS, prevent further spread of insecticide resistance, and better evaluate the cost effectiveness of IRS in the context of other control interventions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 857, 202, 876]]<|/det|>
+## Methods
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[112, 90, 482, 109]]<|/det|>
+## Study sites and vector control interventions  
+
+<|ref|>text<|/ref|><|det|>[[110, 121, 880, 597]]<|/det|>
+This study utilized data from 14 health facilities located in 14 districts in Northern and Eastern Uganda (Fig 4) which were part of a larger comprehensive malaria surveillance network called the Uganda Malaria Surveillance Program (UMSP). Between 2007 and 2009, IRS was implemented in 10 high burden districts in northern Uganda. DDT or pyrethroids were initially used but in 2010 the insecticide was changed to a carbamate (bendiocarb) due to concern regarding the spread of pyrethroid resistance. Rounds of bendiocarb were repeated approximately every 6 months until 2014 when the IRS program was discontinued, so that resources could be shifted to other high burden districts. In 2017, these 10 districts in northern Uganda received a single round of the organophosphate pirimiphos- methyl (Actellic 300CS®) following reports of malaria resurgence after IRS has been discontinued in 2014. Between 2014 and 2015, IRS with bendiocarb was implemented in 14 districts in the Northern and Eastern part of the country. Rounds of bendiocarb were repeated approximately every six months until 2016 when the formulation was changed to Actellic 300CS®, which continues to be administered once a year.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 110, 880, 530]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 91, 616, 110]]<|/det|>
+<center>Fig 4. Map of Uganda showing study sites and IRS districts. </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 575, 880, 666]]<|/det|>
+Universal LLIN distribution campaigns were conducted in 2013- 14 and 2017- 18, where LLINs were distributed free- of- charge by the Uganda Ministry of Health targeting 1 LLIN for every two household residents.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 715, 397, 733]]<|/det|>
+## Health-facility based surveillance  
+
+<|ref|>text<|/ref|><|det|>[[112, 747, 880, 910]]<|/det|>
+Enhanced malaria surveillance was established by UMSP in 2006, as previously described 41. UMSP operates Malaria Reference Centers (MRCs) at 70 level III/IV public health facilities across Uganda. At each MRC, individual- level data from standardized registers for all patients presenting to the outpatient departments are entered into an Access database by on- site data entry officers. Variables include patient demographics, results of laboratory testing for malaria (rapid
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 866, 180]]<|/det|>
+diagnostic test [RDT] or microscopy), diagnoses given, and treatments prescribed. Emphasis is placed on ensuring that patients with suspected malaria undergo testing, by either RDT or microscopy.  
+
+<|ref|>text<|/ref|><|det|>[[111, 228, 877, 459]]<|/det|>
+This study utilized data from 14 MRCs located in districts that either previously had IRS or have ongoing IRS campaigns. We estimated the impact of withdrawing IRS using data from three sites in Northern Uganda that had at least six months of data preceding the final round of IRS administered in 2014. To estimate the impact of restarting IRS with a single round administered in 2017, we used data from nine sites in Northern Uganda. To estimate the impact of sustained IRS over five years, we used data from five sites in Eastern Uganda where IRS had been implemented since 2014- 15.  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 509, 199, 526]]<|/det|>
+## Measures  
+
+<|ref|>text<|/ref|><|det|>[[111, 541, 884, 876]]<|/det|>
+Exposure. The exposure was specified as an indicator variable for each month since IRS was withdrawn or initiated relative to a baseline period (Fig 5 and Supplementary Fig S7). We also fit separate models with categorical exposure variables divided into distinct periods of months. To determine the impact of withdrawing IRS after at least five years of sustained use, the baseline period was defined as the final year of sustained IRS use, and the evaluation period lasted through 2016, prior to when an additional round of IRS was implemented. In order to determine the impact of restarting IRS with a single round of IRS, the baseline period was defined as one year prior to the single round of IRS and the evaluation period went through December 2019. To determine the impact of initiating and sustaining IRS, the baseline period was the year prior to IRS initiation, and the evaluation period lasted through December 2019.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 90, 864, 162]]<|/det|>
+Fig 5. Timeline summarizing the dates of IRS campaigns, baseline and evaluation periods. Objective 1 is to assess the impact of withdrawing IRS after five years of sustained use; Objective 2 is to assess the impact of restarting IRS with a single round; and Objective 3 is to assess the impact of initiating and sustaining IRS.  
+
+<|ref|>image<|/ref|><|det|>[[130, 200, 875, 408]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[111, 430, 880, 625]]<|/det|>
+Outcome. The primary outcome was the monthly count of laboratory- confirmed malaria cases at each MRC. The case count was corrected for testing rates by multiplying the number of individuals with suspected malaria but not tested each month by the test positivity rate (the number who tested positive divided by the total number tested) for that month and adding the result to the number of laboratory- confirmed positive cases. As a sensitivity analysis, we re- specified the models including only laboratory- confirmed case counts as the outcome.  
+
+<|ref|>text<|/ref|><|det|>[[111, 675, 884, 868]]<|/det|>
+Covariates. We adjusted for time- varying variables that impact malaria burden and malaria case detection at the health facility. These variables included average rainfall at the health facility lagged by 1 month, indicator variables for month of the year (to adjust for seasonal effects), the proportion of tests that were RDTs in that month (vs. microscopy), and the number of individuals who attended the health facility but were not suspected of having malaria in that month (to adjust for care- seeking behaviors).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[113, 135, 272, 153]]<|/det|>
+## Statistical analysis  
+
+<|ref|>text<|/ref|><|det|>[[112, 167, 880, 328]]<|/det|>
+For each objective, we specified mixed effects negative binomial regression models with random intercepts for health facility. Coefficients for the exposure variable were exponentiated to represent the incidence rate ratio (IRR) comparing the incidence of malaria in the month of interest relative to the baseline period. This method assumes that the underlying population has remained constant over the study period.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 90, 883, 811]]<|/det|>
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+West, P. A. et al. Indoor residual spraying in combination with insecticide- treated nets compared to insecticide- treated nets alone for protection against malaria: a cluster randomised trial in Tanzania. PLoS Med 11, e1001630, doi:10.1371/journal.pmed.1001630 (2014).  
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+Wagman, J. et al. Rapid reduction of malaria transmission following the introduction of indoor residual spraying in previously unsprayed districts: an observational analysis of Mopti Region, Mali, in 2017. Malar J 19, 340, doi:10.1186/s12936- 020- 03414- 2 (2020).  
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+Kane, F. et al. Performance of IRS on malaria prevalence and incidence using pirimiphos- methyl in the context of pyrethroid resistance in Koulikoro region, Mali. Malar J 19, 286, doi:10.1186/s12936- 020- 03357- 8 (2020).  
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+Gogue, C. et al. An observational analysis of the impact of indoor residual spraying in Northern, Upper East, and Upper West Regions of Ghana: 2014 through 2017. Malar J 19, 242, doi:10.1186/s12936- 020- 03318- 1 (2020).  
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+Abong'o, B. et al. Impact of indoor residual spraying with pirimiphos- methyl (Actellic 300CS) on entomological indicators of transmission and malaria case burden in Migori County, western Kenya. Scientific reports 10, 4518, doi:10.1038/s41598- 020- 61350- 2 (2020).  
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+Aikpon, R. Y. et al. Upsurge of malaria transmission after indoor residual spraying withdrawal in Atacora region in Benin, West Africa. Malar J 19, 3, doi:10.1186/s12936- 019- 3086- 2 (2020).
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+40 Oxborough, R. M. Trends in US President's Malaria Initiative- funded indoor residual spray coverage and insecticide choice in sub- Saharan Africa (2008- 2015): urgent need for affordable, long- lasting insecticides. Malar J 15, 146, doi:10.1186/s12936- 016- 1201- 1 (2016). 41 Sserwanga, A. et al. Improved malaria case management through the implementation of a health facility- based sentinel site surveillance system in Uganda. PLoS One 6, e16316, doi:10.1371/journal.pone.0016316 (2011).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 91, 280, 109]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[111, 123, 877, 395]]<|/det|>
+We would like to acknowledge the health workers at all 14 health facilities that contributed data for this study. We would like to thank the Ugandan Ministry of Health National Malaria Control Division, and USAID – President’s Malaria Initiative. This work was supported by the National Institutes of Health as part of the International Centers of Excellence in Malaria Research (ICMER) program (U19AI089674). AE is supported by the National Institute of Allergy and Infectious Diseases (F31AI150029). JIN is supported by the Fogarty International Center (Emerging Global Leader Award grant number K43TW010365). EA is supported by the Fogarty International Center of the National Institutes of Health under Award Number D43TW010526.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 440, 302, 458]]<|/det|>
+## Author Contributions  
+
+<|ref|>text<|/ref|><|det|>[[111, 471, 884, 632]]<|/det|>
+JFN, AE, GD, and IRB conceived of the study. JFN led the data collection activities with support from JIN, AM, MK, AS, JK, EA, SG, CE, SGS, CMS, and MRK. AE and IRB led the data analysis with support from GD. AE and JFN drafted the manuscript with support from GD, SGS, and IRB. All authors contributed to interpretation of the results and edited the manuscripts. All authors read and approved the final manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 682, 288, 700]]<|/det|>
+## Competing Interests  
+
+<|ref|>text<|/ref|><|det|>[[115, 733, 460, 752]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 823, 377, 841]]<|/det|>
+## Materials and Correspondence  
+
+<|ref|>text<|/ref|><|det|>[[115, 856, 638, 875]]<|/det|>
+Correspondence to Adrienne Epstein: Adrienne.Epstein@ucsf.edu
+
+<--- Page Split --->
+<|ref|>table_caption<|/ref|><|det|>[[120, 94, 688, 103]]<|/det|>
+Table 1. Summary statistics from health-facility based surveillance sites where IRS was stopped after sustained use.
+
+<|ref|>table<|/ref|><|det|>[[115, 110, 920, 290]]<|/det|>
+
+<table><tr><td>MRC<br>(District)</td><td>Time period</td><td>Number of<br>months<br>included</td><td>Total<br>outpatient<br>visits, n</td><td>Suspected<br>malaria<br>cases, n (%<br>of total)</td><td>Tested for<br>malaria, n<br>(% of<br>suspected)</td><td>RDT<br>performed<br>(versus<br>microscopy),<br>n(% of<br>tested)</td><td>Confirmed<br>malaria<br>cases, n (% of tested)</td><td>Confirmed<br>cases<br>adjusted for testing rate, n</td><td>Mean<br>monthly<br>confirmed<br>cases adjusted for testing rate, n</td></tr><tr><td rowspan="2">Aboke HCIV<br>(Kole)</td><td>Baseline</td><td>9</td><td>14,015</td><td>3,766 (26.9)</td><td>3,735 (99.2)</td><td>2,450 (65.6)</td><td>923 (24.7)</td><td>932</td><td>104</td></tr><tr><td>Evaluation</td><td>25</td><td>46,850</td><td>21,245 (45.3)</td><td>18,185 (85.6)</td><td>17,210 (94.6)</td><td>14,200 (78.0)</td><td>16,699</td><td>668</td></tr><tr><td rowspan="2">Aduku HCIV<br>(Kwania)</td><td>Baseline</td><td>13</td><td>24,164</td><td>13,742 (56.9)</td><td>13,719 (99.8)</td><td>1,049 (7.6)</td><td>3,254 (23.7)</td><td>3,529</td><td>272</td></tr><tr><td>Evaluation</td><td>32</td><td>57,470</td><td>30,035 (52.2)</td><td>25,896 (86.2)</td><td>10,731 (41.4)</td><td>13,537 (52.3)</td><td>15,717</td><td>491</td></tr><tr><td rowspan="2">Anyeke<br>HCIV<br>(Oyam)</td><td>Baseline</td><td>8</td><td>15,859</td><td>3,514 (22.2)</td><td>2,627 (74.8)</td><td>2,604 (99.1)</td><td>680 (25.9)</td><td>918</td><td>115</td></tr><tr><td>Evaluation</td><td>25</td><td>66,501</td><td>28,755 (43.2)</td><td>20,659 (71.8)</td><td>16,147 (78.2)</td><td>13,559 (65.6)</td><td>18,774</td><td>751</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[113, 110, 905, 533]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[123, 93, 649, 105]]<|/det|>
+Table 2. Summary statistics from health-facility based surveillance sites that received a single round of IRS.   
+
+<table><tr><td>MRC (District)</td><td>Time period</td><td>Number of months included</td><td>Total outpatient visits, n</td><td>Suspected malaria cases, n (% of total)</td><td>Tested for malaria, n (% of suspected)</td><td>RDT performed (versus microscopy), n (% of tested)</td><td>Confirmed malaria cases, n (% of tested)</td><td>Confirmed cases adjusted for testing rate, n</td><td>Mean monthly confirmed cases adjusted for testing rate, n</td></tr><tr><td rowspan="2">Aboke HCIV (Kole)</td><td>Baseline</td><td>14</td><td>21,186</td><td>11,752 (55.5)</td><td>9,613 (81.8)</td><td>9,079 (94.5)</td><td>7,297 (75.9)</td><td>9,006</td><td>643</td></tr><tr><td>Evaluation</td><td>34</td><td>54,826</td><td>30,973 (56.5)</td><td>30,674 (99.0)</td><td>29,064 (94.8)</td><td>22,097 (72.0)</td><td>22,308</td><td>656</td></tr><tr><td rowspan="2">Aduku HCIV (Kwania)</td><td>Baseline</td><td>17</td><td>35,017</td><td>20,645 (59.0)</td><td>17,156 (83.1)</td><td>7,938 (46.3)</td><td>9,699 (56.5)</td><td>11,465</td><td>674</td></tr><tr><td>Evaluation</td><td>31</td><td>65,379</td><td>32,260 (49.3)</td><td>31,337 (97.1)</td><td>20,385 (65.1)</td><td>15,201 (48.5)</td><td>15,534</td><td>501</td></tr><tr><td rowspan="2">Anyeke HCIV (Oyam)</td><td>Baseline</td><td>14</td><td>35,378</td><td>18,445 (52.1)</td><td>12,997 (70.5)</td><td>9,151 (70.4)</td><td>8,967 (69.0)</td><td>12,595</td><td>900</td></tr><tr><td>Evaluation</td><td>34</td><td>70,149</td><td>33,618 (47.9)</td><td>32,522 (96.7)</td><td>31,208 (96.0)</td><td>21,799 (67.0)</td><td>22,375</td><td>658</td></tr><tr><td rowspan="2">Awach HCIV (Gulu)</td><td>Baseline</td><td>17</td><td>36,923</td><td>21,920 (59.4)</td><td>17,927 (82.0)</td><td>17,736 (98.7)</td><td>13,663 (76.0)</td><td>16,749</td><td>985</td></tr><tr><td>Evaluation</td><td>30</td><td>69,375</td><td>36,760 (53.0)</td><td>35,189 (95.7)</td><td>34,070 (96.8)</td><td>21,879 (62.2)</td><td>22,851</td><td>762</td></tr><tr><td rowspan="2">Lalogi HCIV (Omoro)</td><td>Baseline</td><td>17</td><td>54,436</td><td>32,642 (60.0)</td><td>31,545 (96.6)</td><td>31,490 (99.8)</td><td>23,106 (73.2)</td><td>23,948</td><td>1,409</td></tr><tr><td>Evaluation</td><td>31</td><td>72,449</td><td>41,846 (57.8)</td><td>41,668 (99.6)</td><td>40,804 (97.9)</td><td>22,986 (55.2)</td><td>23,060</td><td>744</td></tr><tr><td rowspan="2">Patongo HCIII (Agago)</td><td>Baseline</td><td>14</td><td>24,686</td><td>15,453 (62.6)</td><td>15,122 (97.9)</td><td>14,758 (97.6)</td><td>11,313 (74.8)</td><td>11,487</td><td>821</td></tr><tr><td>Evaluation</td><td>34</td><td>54,486</td><td>34,482 (63.3)</td><td>33,797 (98.0)</td><td>32,176 (95.2)</td><td>17,231 (51.0)</td><td>17,440</td><td>513</td></tr><tr><td rowspan="2">Atiak HCIV (Amuru)</td><td>Baseline</td><td>14</td><td>38,916</td><td>25,929 (66.6)</td><td>22,418 (86.5)</td><td>22,335 (99.6)</td><td>18,978 (84.7)</td><td>21,966</td><td>1,569</td></tr><tr><td>Evaluation</td><td>34</td><td>60,750</td><td>31,650 (52.1)</td><td>30,754 (97.2)</td><td>30,541 (99.3)</td><td>19,766 (64.3)</td><td>20,325</td><td>598</td></tr><tr><td rowspan="2">Padibe HCIV (Lamwo)</td><td>Baseline</td><td>20</td><td>29,740</td><td>20,589 (69.0)</td><td>20,427 (99.2)</td><td>20,420 (99.9)</td><td>17,031 (83.4)</td><td>17,161</td><td>858</td></tr><tr><td>Evaluation</td><td>28</td><td>50,117</td><td>26,883 (53.6)</td><td>26,831 (99.8)</td><td>25,956 (96.7)</td><td>15,199 (56.6)</td><td>15,224</td><td>544</td></tr><tr><td rowspan="2">Namokora HCIV (Kitgum)</td><td>Baseline</td><td>17</td><td>27,802</td><td>22,597 (81.3)</td><td>19,990 (88.5)</td><td>18,909 (94.6)</td><td>12,294 (61.5)</td><td>14,401</td><td>847</td></tr><tr><td>Evaluation</td><td>31</td><td>56,765</td><td>40,185 (70.8)</td><td>39,966 (99.5)</td><td>38,468 (96.3)</td><td>21,958 (54.9)</td><td>22,063</td><td>712</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[113, 110, 920, 380]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[122, 95, 666, 107]]<|/det|>
+Table 3. Summary statistics from health-facility based surveillance sites where IRS was initiated and sustained.   
+
+<table><tr><td>MRC (District)</td><td>Time period</td><td>Number of months included</td><td>Total outpatient visits, n</td><td>Suspected malaria cases, n (%)</td><td>Tested for malaria, n (%)</td><td>RDT performed (versus microscopy), n (% of tested)</td><td>Confirmed malaria cases, n (%)</td><td>Confirmed malaria cases adjusted for testing rate, n</td><td>Mean monthly confirmed cases adjusted for testing rate, n</td></tr><tr><td rowspan="2">Nagongera HCIV (Tororo</td><td>Baseline</td><td>13</td><td>22,859</td><td>14,676 (64.2)</td><td>14,516 (98.9)</td><td>799 (5.5)</td><td>3,682 (25.4)</td><td>3,722</td><td>286</td></tr><tr><td>Evaluation</td><td>59</td><td>97,012</td><td>36,308 (37.4)</td><td>36,069 (99.3)</td><td>13,129 (36.4)</td><td>4,984 (13.8)</td><td>5,022</td><td>85</td></tr><tr><td rowspan="2">Amolatar HCIV (Amolatar)</td><td>Baseline</td><td>12</td><td>19,552</td><td>8,547 (43.7)</td><td>6,512 (76.2)</td><td>5,923 (91.0)</td><td>3,701 (56.8)</td><td>4,845</td><td>404</td></tr><tr><td>Evaluation</td><td>59</td><td>89,779</td><td>24,889 (27.8)</td><td>21,849 (87.9)</td><td>19,459 (89.1)</td><td>4,822 (22.1)</td><td>5,854</td><td>99</td></tr><tr><td rowspan="2">Dokolo HCIV (Dokolo)</td><td>Baseline</td><td>12</td><td>25,570</td><td>12,854 (50.3)</td><td>8,875 (69.0)</td><td>8,212 (92.5)</td><td>5,211 (58.7)</td><td>7,889</td><td>657</td></tr><tr><td>Evaluation</td><td>59</td><td>129,245</td><td>46,428 (35.9)</td><td>44,972 (96.9)</td><td>42,259 (94.0)</td><td>10,210 (22.7)</td><td>10,761</td><td>183</td></tr><tr><td rowspan="2">Orum HCIV (Onuke)</td><td>Baseline</td><td>11</td><td>16,120</td><td>9,324 (57.8)</td><td>8,929 (95.8)</td><td>3,990 (44.7)</td><td>5,974 (66.9)</td><td>6,236</td><td>567</td></tr><tr><td>Evaluation</td><td>59</td><td>65,036</td><td>37,430 (57.6)</td><td>36,371 (97.2)</td><td>19,536 (53.7)</td><td>16,481 (45.3)</td><td>17,069</td><td>289</td></tr><tr><td rowspan="2">Alebong HCIV (Alebong)</td><td>Baseline</td><td>8</td><td>15,359</td><td>6,694 (43.6)</td><td>4,789 (71.5)</td><td>4,620 (96.5)</td><td>3,209 (67.0)</td><td>4,317</td><td>540</td></tr><tr><td>Evaluation</td><td>59</td><td>94,055</td><td>40,821 (43.0)</td><td>36,211 (88.7)</td><td>32,327 (89.3)</td><td>12,037 (33.2)</td><td>13,869</td><td>235</td></tr></table>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 44, 143, 69]]<|/det|>
+## Figures  
+
+<|ref|>image<|/ref|><|det|>[[44, 90, 950, 360]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 382, 115, 401]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 423, 953, 512]]<|/det|>
+Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of withdrawing IRS after 5 years of sustained use. The blue shaded region represents the \(95\%\) confidence interval around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) confidence interval around adjusted IRR.  
+
+<|ref|>image<|/ref|><|det|>[[44, 516, 951, 783]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 803, 117, 822]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 845, 953, 910]]<|/det|>
+Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of restarting IRS with a single round. The blue shaded region represents the \(95\%\) CI around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) CI around adjusted IRR.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[45, 45, 951, 312]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 334, 117, 352]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 375, 955, 440]]<|/det|>
+Adjusted IRR and predicted case counts from multilevel negative binomial model assessing the impact of initiating and sustaining IRS. The blue shaded region represents the \(95\%\) CI around the predicted case counts from the adjusted regression model. Vertical bars represent the \(95\%\) CI around adjusted IRR.  
+
+<|ref|>image<|/ref|><|det|>[[42, 444, 955, 938]]<|/det|>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[62, 112, 944, 360]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 43, 117, 62]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 420, 952, 518]]<|/det|>
+Timeline summarizing the dates of IRS campaigns, baseline 357 and evaluation periods. Objective 1 is to assess the impact of withdrawing IRS after five years of sustained use; Objective 2 is to assess the impact of restarting IRS with a single round; and Objective 3 is to assess the impact of initiating and sustaining IRS.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 543, 311, 570]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 593, 765, 614]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[61, 632, 320, 652]]<|/det|>
+- IRSprojectsupplements.pdf
+
+<--- Page Split --->

preprint/preprint__078ee3115bb7f9caf7ff08bd41325e1b3d5bc1c68c6da418cda25d198e700819/images_list.json

@@ -0,0 +1,77 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 ONE architecture and hardware implementations. (a) Illustration of processing branches and flows in the ONE architecture to predict output spatiotemporal output physical quantities from corresponding input and solve PDEs involving single or multiple physics. Illustrations of integrated and free-space implementations of reconfigurable (b) DONN and (c) XBAR structures.",
+    "footnote": [],
+    "bbox": [
+      [
+        213,
+        90,
+        830,
+        479
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Solving Darcy flow and magnetostatic Poisson's equations. (a) Illustration of the Darcy flow equation describing a fluid flow through a porous medium. The ONE architecture learns the mapping between the permeability and pressure fields. (b) Training loss curves for input data with different resolutions. (c) Comparison of the training loss of different models at various resolutions. (d) Input permeability field, the expected ground truth of output pressure field, the predicted output pressure field, the absolute error between the expected and predicted outputs, and the relative error between the expected and predicted outputs, at 85 and 421 resolutions. (e) Illustration of the magnetostatic Poisson's equation calculating the demagnetizing field generated by the magnetization field. The ONE architecture learns the mapping between these two fields. (f) Validation loss curve for the ONE architecture solving the magnetostatic Poisson's equation and (g) corresponding input magnetization field, the expected ground truth of output demagnetizing field, the predicted output demagnetizing field, the absolute and normalized errors between the expected and predicted outputs.",
+    "footnote": [],
+    "bbox": [
+      [
+        171,
+        88,
+        784,
+        486
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Solving time-dependent Navier-Stokes and Maxwell's equations. Illustrations of (a) Navier-Stokes equation for solving the time evolution of the vorticity field in a viscous, incompressible fluid in vorticity form on the unit torus and (b) Maxwell's equations for solving the time evolution of the electric field in a dielectric metasurface. Validation loss curves for (c) solving the Navier-Stokes equation and (d) Maxwell's equations using the ONE architecture. The expected ground truth field, the predicted field, and the absolute and relative errors between these two fields for (e) the Navier-Stokes equation and (f) Maxwell's equations, respectively.",
+    "footnote": [],
+    "bbox": [
+      [
+        172,
+        88,
+        785,
+        428
+      ]
+    ],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Solving multiphysics PDEs. (a) Illustration of solving coupled PDEs in an electrical heating problem involving electric current physics and heat transfer physics. (b) Validation loss curve. (c) A few representative 2D voltage profiles in the circuit. (d) The expected ground truth temperature profile, the predicted profile, and the absolute and relative errors between these two profiles.",
+    "footnote": [],
+    "bbox": [
+      [
+        212,
+        264,
+        832,
+        590
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 Experimental demonstration. (a) Photo and schematic of a reconfigurable DONN experimental setup consisting of a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. Polarization components were used to configure SLMs in the phase modulation mode. (b) Output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture obtained from model calculations and experimental measurements. (c) Validation loss curves at different noise levels in optical XBAR structures and (d) the loss at the final epoch as a function of noise level.",
+    "footnote": [],
+    "bbox": [
+      [
+        175,
+        225,
+        770,
+        610
+      ]
+    ],
+    "page_idx": 12
+  }
+]

preprint/preprint__078ee3115bb7f9caf7ff08bd41325e1b3d5bc1c68c6da418cda25d198e700819/preprint__078ee3115bb7f9caf7ff08bd41325e1b3d5bc1c68c6da418cda25d198e700819.mmd

@@ -0,0 +1,399 @@
+
+# Optical Neural Engine for Solving Scientific Partial Differential Equations  
+
+Weilu Gao  
+
+weilu.gao@utah.edu  
+
+The University of Utah https://orcid.org/0000- 0003- 3139- 034X  
+
+Yingheng Tang  
+
+Lawrence Berkeley National Laboratory  
+
+Ruiyang Chen  
+
+The University of Utah https://orcid.org/0000- 0002- 1538- 1702  
+
+Minhan Lou  
+
+The University of Utah  
+
+Jichao Fan  
+
+The University of Utah  
+
+Cunxi Yu  
+
+University of Maryland, College Park  
+
+Andy Nonaka  
+
+Lawrence Berkeley National Laboratory  
+
+Zhi Yao  
+
+Lawrence Berkeley National Laboratory  
+
+Article  
+
+Keywords:  
+
+Posted Date: September 30th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 5061922/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: There is NO Competing Interest.
+
+<--- Page Split --->
+
+Version of Record: A version of this preprint was published at Nature Communications on May 17th, 2025. See the published version at https://doi.org/10.1038/s41467-025-59847-3.
+
+<--- Page Split --->
+
+# Optical Neural Engine for Solving Scientific Partial Differential Equations  
+
+Yingheng Tang \(^{1\ast}\) , Ruiyang Chen \(^{2\dagger}\) , Minhan Lou \(^{2}\) , Jichao Fan \(^{2}\) , Cunxi Yu \(^{3}\) , Andy Nonaka \(^{1}\) , Zhi (Jackie) Yao \(^{1*}\) , Weilu Gao \(^{2*}\)  
+
+\(^{1}\) Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. \(^{2}\) Department of Electrical and Computer Engineering, The University of Utah, Salt Lake City, UT 84112, USA. \(^{3}\) Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA.  
+
+\*Corresponding author(s). E- mail(s): ytang4@lbl.gov; jackie_zhiyao@lbl.gov; weilu.gao@utah.edu; †These authors contribute equally  
+
+## Abstract  
+
+Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data- driven machine learning (ML) approaches are emerging to accelerate time- consuming and computation- intensive numerical simulations of PDEs. Although optical systems offer high- throughput and energy- efficient ML hardware, there is no demonstration of utilizing them for solving PDEs. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time- dependent and time- independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson's equation in demagnetization, the Navier- Stokes equation in incompressible fluid, Maxwell's equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high- performance dual- space processing for outperforming traditional PDE solvers and being comparable with state- of- the- art ML models but also can be implemented using optical computing hardware with unique features of low- energy and highly parallel constant- time processing irrespective of model scales and real- time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large- scale scientific and engineering computations.
+
+<--- Page Split --->
+
+## Introduction  
+
+Partial differential equations (PDEs) derived from physical laws have been a powerful and faithful computational tool to accelerate the exploration and validation of scientific hypotheses instead of performing expensive and time- consuming real- world experiments [1]. Hence, numerically solving PDEs is essential for scientific research and development in nearly every scientific domain. For example, the interaction of electromagnetic waves with materials and engineered structures in broad applications such as communication, imaging, sensing, and quantum technologies is governed by Maxwell's equations [2]; automotive and flight aerodynamics for designing and manufacturing road vehicles and airplanes is determined by Navier- Stokes equation [3]; the Earth system including temperature, atmosphere, and ice sheets for understanding climate change and making policies is also described with a series of PDEs [4]. However, current numerical simulation methods to solve PDEs, such as finite difference/volume methods to solve Maxwell's and the Navier- Stokes equations, are costly in computing time and resources.  
+
+Machine learning (ML) offers a new perspective on solving PDEs through data- driven approaches to enable fast and accurate simulations of many multiphysics and multiscale processes [5- 7]. However, the ML model deployment on electronic computing hardware requires substantial computing resources and consumes substantial energy. In the foreseeable future, the fundamental quantum mechanics limit will lead to a bottleneck of further reducing the energy consumption and simultaneously increasing the integration density of electronic circuits to catch up with the increasing scale of ML models in demand for solving complex problems [8, 9], thus urgently calling for new high- throughput and energy- efficient ML hardware accelerators. Recently, optical architectures, including photonic integrated circuits for matrix- vector multiplication (MVM) [10, 11], for neuro- inspired spiking neural networks [12, 13], and for photonic reservoir computing [14, 15], and free- space optical systems for MVM [16- 18] and diffractive optical neural networks (DONNs) [19- 22], are emerging as high- performance ML hardware accelerators by leveraging different particles - photons - to break down electronic bottleneck thanks to high parallelism and low static energy consumption of photons [23]. However, to date, there is no deployment of any optical computing systems for solving PDEs in any scientific domain.  
+
+Here, we present a fully reconfigurable and scalable optical neural engine (ONE) architecture that combines DONN systems for processing data in Fourier space and optical crossbar (XBAR) structures for processing data in real space to solve two- dimensional (2D) spatiotemporal profiles in time- independent and time- dependent PDEs. The ONE architecture not only leverages the advantages of high- performance dual- space processing [24], but also can be implemented using optical computing hardware with unique features of low- energy and highly parallel constant- time processing irrespective of model scales, and real- time reconfigurability for tackling multiple tasks with the same architecture. We numerically and experimentally demonstrate the capability of the ONE architecture in solving a broad range of PDEs in diverse disciplines, including the Darcy flow equation in fluid dynamics, the magnetostatic Poisson's equation in micromagnetics, the Navier- Stokes equation in aerodynamics, Maxwell's equations in nanophotonics, and coupled electric current and heat transfer equations in
+
+<--- Page Split --->
+
+a multiphysics electrical heating problem. The ONE architecture not only outperforms traditional PDE solvers because of its data- driven nature, but also shows comparable and better performance with other ML models while with substantial hardware advantages because of its implementation in the optical domain. The demonstrated ONE architecture is versatile and can be tailored with different combinations of DONN and XBAR structures for solving various PDEs, offering a transformative universal solution for large- scale scientific and engineering computations.  
+
+## Results  
+
+## ONE Architecture  
+
+Figure 1a illustrates the ONE architecture, which takes the spatiotemporal data of an input physical quantity \(\mathbf{U}\) , described as a function \(u(x,y,t)\) in terms of positions \(x\) and \(y\) and time \(t\) , to predict the spatiotemporal data of an output physical quantity \(\mathbf{G}\) described using a function \(g(x,y,t)\) . The input and output quantities \(\mathbf{U}\) and \(\mathbf{G}\) can be connected through either a single- physics PDE or coupled multiphysics PDEs. There are three branches inside the ONE architecture, including (i) Fourier space processing branch, (ii) real space processing branch, and (iii) physics parameter processing branch. The combination of both real and Fourier space processing has been proven fast, powerful, and efficient in solving PDEs [24], and the incorporation of additional physics parameter processing enables the fusion of multimodal data for complex tasks [25]. More importantly, most operations in these branches can be deployed on optical computing hardware in both real and Fourier space, enabling solving PDEs in high- throughput and energy- efficient manners. The details of each branch are described below.  
+
+In the first Fourier space processing branch, the core arithmetic operations are based on Fourier and inverse Fourier transformations to process input spatiotemporal data in the Fourier space. Their optical hardware implementations are mainly based on reconfigurable DONNs, which contain cascaded reconfigurable diffractive layers. Reconfigurable DONNs can be implemented in both integrated photonic chips [26, 27] and free space [19- 21]; see Fig. 1b. There are two fundamental operations in DONNs - optical diffraction and spatial light modulation. For the optical diffraction operation, an optical field right after the \(l\) - th diffractive layer, \(f_{l}\) , diffracts to the front of \((l + 1)\) - th layer, whose optical field, \(f_{\mathrm{in},l + 1}\) , is a convolution of \(f_{l}\) and the diffraction impulse function \(h(x,y)\) . Specifically, the complex- valued field at point \((x,y)\) on the input plane of \((l + 1)\) - th layer can be written as the convolution of all fields at the output plane of \(l\) - th layer as  
+
+\[f_{\mathrm{in},l + 1}(x,y,z) = \iint f_{l}(x^{\prime},y^{\prime},0)h(x - x^{\prime},y - y^{\prime})dx^{\prime}dy^{\prime},\]  
+
+where \(z\) is the distance between two diffractive layers and \(h(x,y)\) is the impulse response function of free space. By the convolution theorem, this 2D convolution can be efficiently calculated in Fourier space based on Fourier and inverse Fourier transformations. Specifically, the 2D Fourier transformation \(\mathcal{F}_{xy}\) of \(f\) and \(h\) , \(F\) and \(H\) , are
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 ONE architecture and hardware implementations. (a) Illustration of processing branches and flows in the ONE architecture to predict output spatiotemporal output physical quantities from corresponding input and solve PDEs involving single or multiple physics. Illustrations of integrated and free-space implementations of reconfigurable (b) DONN and (c) XBAR structures. </center>  
+
+connected through  
+
+\[\mathcal{F}_{xy}(f_{\mathrm{in},l + 1}(x,y,z)) = \mathcal{F}_{xy}(f_l(x,y,0))\mathcal{F}_{xy}(h(x,y)),\] \[F_{\mathrm{in},l + 1}(\alpha ,\beta ,z) = F_l(\alpha ,\beta ,0)H(\alpha ,\beta),\]  
+
+where \(\alpha ,\beta\) are spatial domain indices. After diffraction, the 2D inverse Fourier transformation \(\mathcal{F}_{xy}^{- 1}\) of \(F_{\mathrm{in},l + 1}(\alpha ,\beta ,z)\) , \(f_{\mathrm{in},l + 1}(x,y,z)\) , is then spatially modulated. Each diffraction pixel at location \((x,y)\) has a complex- valued electric field transmission coefficient \(t(x,y,S)e^{\phi (x,y,S)}\) , where \(t(x,y,S)\) \((\phi (x,y,S))\) is the amplitude (phase) response as a function of external stimuli \(S\) , such as voltages. The spatial light modulation operation is expressed as a pixel- wise multiplication  
+
+\[f_{l + 1}(x,y,z) = \mathcal{F}_{xy}^{-1}(F_{\mathrm{in},l + 1}(\alpha ,\beta ,z))t(x,y,S)e^{\phi (x,y,S)}\]
+
+<--- Page Split --->
+
+\[= f_{\mathrm{in},l + 1}(x,y,z)t(x,y,S)e^{\phi (x,y,S)},\]  
+
+where \(f_{l + 1}(x,y,z)\) is the near- field output field right after the \((l + 1)\) - th layer. More details can be found in Methods.  
+
+Before and between DONN kernels, there is a linear transformation operation based on fully connected layers to scale up the number of channels and a channel mixing operation based on matrix multiplications [24]. The core arithmetic operations are based on MVM. Their optical hardware implementations are mainly based on reconfigurable optical XBAR structures, which encode element values of vector \(\mathbf{v}\) and matrix \(\mathbf{M}\) into light intensity through electro- optic modulators, perform multiplications through cascaded modulators, and add signals at the output detector array. The signals are routed to follow mathematical calculations in MVM so that the reading from the detector array represents the output vector \(\mathbf{o} = \mathbf{M}\times \mathbf{v}\) . Reconfigurable XBAR structures can also be implemented in both integrated photonic chips [10, 11] and free space [16- 18]; see Fig. 1c. More details on the operation mechanism can be found in Methods and Supplementary Fig. 1.  
+
+The second real space processing branch contains fully connected layers, whose operations are also based on MVM and implemented with optical XBAR structures. The output from the Fourier space branch, \(\mathbf{F}(u)\) , and the output from the real space branch, \(\mathbf{R}(u)\) are added and further processed with a nonlinear operation. Note that the nonlinear operation is the only operation performed in electronic hardware in the ONE architecture. Moreover, this combination of real space, Fourier space, and nonlinear processing is scaled up, repeated four times, and cascaded in series. The third branch is to perform a linear transformation on other relevant physics parameters \(d(t)\) , which are time sequences instead of spatiotemporal data, based on fully connected layers. The obtained data \(\mathbf{T}(d)\) is multiplied and merged onto two other branches to have the final output \(g(x,y,t)\) . Hence, except nonlinear operations, all other operations can be done with DONN and optical XBAR systems. These two systems can be seamlessly assembled into a single integrated photonic chip or a single free- space optical system for all- optical operations without converting between optical and electronic hardware, fully leveraging the advantages of high throughput and high parallelism in optical computing systems. More details on the ONE architecture model are in Methods.  
+
+## Darcy flow and magnetostatic Poisson's equations  
+
+The first PDE we solved with the ONE architecture is the Darcy flow equation in fluid dynamics physics. This PDE describes a fluid flow through a porous medium as shown in Fig. 2a. Specifically, the equation is  
+
+\[-\nabla \cdot (k(x,y)\nabla u(x,y)) = f(x,y),\]  
+
+where \(k(x,y)\) is the permeability field of the medium, \(u(x,y)\) is the pressure field of the flow, and \(f(x,y)\) is the force function. The ONE architecture was trained to learn the mapping from the 2D function \(k(x,y)\) to function \(u(x,y)\) . More details about the equation dataset generation and training are in Methods. Figure 2b displays the training loss curves for inputs with different resolutions. The training loss
+
+<--- Page Split --->
+
+is generally low for all resolutions and slightly increases at the highest 421 resolution. Figure 2c shows the comparison of the training loss of our ONE architecture with other PDE solving models, including fully convolution networks (FCN) [28], principal component analysis- based neural network (PCANN) [29], reduced biased method (RBM) [30], graph neural operator (GNO) [31], low- rank kernel decomposition neural operator (LNO) [25], multipole graph neural operator (MGNO) [32], and Fourier neural operator (FNO) [24]. The performance of the ONE architecture is comparable with the state- of- the- art neural operators including GNO, LNO, MGNO, and FNO, and is better than FCN. Further, from the hardware perspective, the ONE architecture is constructed based on high- throughput optical computing hardware platforms so that all operations can be performed in parallel within a single clock cycle. In addition, the ONE architecture can be practically implemented on a large scale. For example, free- space reconfigurable DONNs [20, 21, 33] and optical MVM [17] are typically implemented using spatial light modulators (SLMs) with a scale \(>1000 \times 1000\) . Hence, the execution cost of solving PDEs with different scales and resolutions is invariant, meaning \(\mathcal{O}(1)\) , if the scale of the optical hardware in the ONE architecture is large enough. Figure 2d displays the input permeability field \(k(x, y)\) , the expected ground truth of output pressure field \(u(x, y)\) , the predicted output pressure field, the absolute error between the expected and predicted outputs, and the relative error between the expected and predicted outputs, at the lowest 85 and the highest 421 resolutions, respectively. This visualization further validates the ONE architecture in solving PDEs. More data on other resolutions are shown in Supplementary Fig. 2.  
+
+The second PDE we solved is the magnetostatic Poisson's equation of demagnetization in micromagnetics physics. This PDE calculates the demagnetizing field \(\mathbf{H}\) generated by the magnetization field \(\mathbf{M}\) as shown in Fig. 2e. Specifically, the equation is obtained from Maxwell's equation as  
+
+\[\nabla \cdot \mathbf{H} = -\nabla \cdot \mathbf{M}.\]  
+
+By defining an effective magnetic charge density \(\rho = - \nabla \cdot \mathbf{M}\) and a magnetic scalar potential \(\Phi\) assuming there is no free current, we can express the demagnetizing field \(\mathbf{H} = - \nabla \Phi\) and rewrite the previous equation as a Poisson's equation  
+
+\[\nabla^{2}\Phi = -\rho .\]  
+
+Similar to solving the Darcy flow equation, the ONE architecture was trained to learn the mapping from components of \(\mathbf{M}\) to \(\mathbf{H}\) vector fields. More details about the equation dataset generation and training are in Methods. Figure 2f shows the validation loss curve and Fig. 2g shows the input one component of \(\mathbf{M}\) field, the expected ground truth of output \(H_{x}\) component of \(\mathbf{H}\) field, the predicted output \(H_{x}\) component, the absolute error between the expected and predicted outputs, and normalized error between the expected and predicted outputs with respect to the maximum field strength in the ground truth. Both confirm a good performance of the ONE architecture in solving the magnetostatic Poisson's equation. More data on \(H_{y}\) and \(H_{z}\) components is shown in Supplementary Fig. 3.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Solving Darcy flow and magnetostatic Poisson's equations. (a) Illustration of the Darcy flow equation describing a fluid flow through a porous medium. The ONE architecture learns the mapping between the permeability and pressure fields. (b) Training loss curves for input data with different resolutions. (c) Comparison of the training loss of different models at various resolutions. (d) Input permeability field, the expected ground truth of output pressure field, the predicted output pressure field, the absolute error between the expected and predicted outputs, and the relative error between the expected and predicted outputs, at 85 and 421 resolutions. (e) Illustration of the magnetostatic Poisson's equation calculating the demagnetizing field generated by the magnetization field. The ONE architecture learns the mapping between these two fields. (f) Validation loss curve for the ONE architecture solving the magnetostatic Poisson's equation and (g) corresponding input magnetization field, the expected ground truth of output demagnetizing field, the predicted output demagnetizing field, the absolute and normalized errors between the expected and predicted outputs. </center>  
+
+## Navier-Stokes and Maxwell's equations  
+
+In addition to steady- state Darcy flow and magnetostatic Poisson's equations without time evolution, we employed the ONE architecture to solve time- dependent PDEs, including the Navier- Stokes equation in fluid dynamics and Maxwell equations in electromagnetics and optics. In particular, the real- time reconfigurability of DONN and optical XBAR structures makes the ONE architecture suitable for such a purpose.
+
+<--- Page Split --->
+
+Specifically, we solved a 2D Navier- Stokes equation for a viscous, incompressible fluid in vorticity form on the unit torus as shown in Fig. 3a. This PDE calculates the time evolution of vorticity described as  
+
+\[\partial_{t}w(x,y,t) + u(x,y,t)\cdot \nabla w(x,y,t) = v\Delta w(x,y,t) + f(x,y),\]  
+
+where \(u\) is the velocity field, \(w = \nabla \times u\) is the vorticity, \(\nu\) is the viscosity coefficient, \(f\) is the forcing function. The ONE architecture was trained to learn the mapping from \(w\) in a time range from 0 to \(t_0\) to \(w\) in a time range from \(t_0\) to \(t_1\) ( \(t_1 > t_0\) ). More details about the equation dataset generation and training are in Methods. Further, we also solved Maxwell's equations in a dielectric metasurface consisting of multiple cylindrical pillars in a unit cell of a periodic pattern as shown in Fig. 3b [34]. The general Maxwell's equations can calculate the time evolution of an electric field through the following equations  
+
+\[\nabla \cdot \mathbf{D} = \rho ,\] \[\nabla \cdot \mathbf{B} = 0,\] \[\nabla \times \mathbf{E} = -\frac{\partial\mathbf{B}}{\partial t},\] \[\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial\mathbf{D}}{\partial t},\]  
+
+where \(\mathbf{D}\) is the electric displacement field, \(\rho\) is the free charge density, \(\mathbf{B}\) is the magnetic flux density, \(\mathbf{E}\) is the electric field, \(\mathbf{H}\) is the magnetic field, and \(\mathbf{J}\) is the free current density. The ONE architecture was trained to learn the mapping from \(\mathbf{E}\) in a time range from 0 to \(t_0\) to \(\mathbf{E}\) in a time range from \(t_0\) to \(t_1\) ( \(t_1 > t_0\) ). More details about the dataset generation and training are in Methods. Figure 3c displays the validation loss curve for solving the Navier- Stokes equation with \(t_0 = 10\) and \(t_1 = 20\) . Figure 3d displays the validation loss curves for solving Maxwell's equations with \(t_0 = 10\) and \(t_1 = 20,30,40\) , respectively. Moreover, Figure 3e and 3f show the expected ground truth of \(w\) field and the \(E_x\) component of the \(\mathbf{E}\) field at \(t_1\) , the corresponding predicted fields at \(t_1\) , and the absolute and relative errors between ground truth and prediction for the Navier- Stokes equation and Maxwell's equations, respectively. All confirm a good performance in solving time- dependent PDEs using the ONE architecture.  
+
+## Multiphysics PDEs  
+
+Moreover, we employed the ONE architecture to solve coupled PDEs involving two physics. Specifically, we solved an electrical heating problem to obtain a temperature profile at an intermediate time step \(t_n\) , \(T(x,y,t_n)\) , in an electrical circuit when a time- dependent voltage signal was applied to the circuit pads, involving coupled electric current physics and heat transfer physics; see Fig. 4a. Specifically, for the electrical current physics, the corresponding PDE is  
+
+\[Q_{e} = d\sigma \nabla_{t}V(x,y,t),\]
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Solving time-dependent Navier-Stokes and Maxwell's equations. Illustrations of (a) Navier-Stokes equation for solving the time evolution of the vorticity field in a viscous, incompressible fluid in vorticity form on the unit torus and (b) Maxwell's equations for solving the time evolution of the electric field in a dielectric metasurface. Validation loss curves for (c) solving the Navier-Stokes equation and (d) Maxwell's equations using the ONE architecture. The expected ground truth field, the predicted field, and the absolute and relative errors between these two fields for (e) the Navier-Stokes equation and (f) Maxwell's equations, respectively. </center>  
+
+\[V(x_{0},y_{0},t) = \mathrm{rect}(t),\]  
+
+where \(Q_{e}\) is the heat rate per unit area from an electromagnetic heating source, \(d\) is the thickness of the heating layer, \(V(x,y,t)\) is the voltage profile in the circuit that is subjected to a voltage boundary condition defined in the pads \(V(x_{0},y_{0},t)\) , and \(V(x_{0},y_{0},t)\) is a pulse rectangular function \(\mathrm{rect}(t)\) with pulse height and width. For the heat transfer physics, the corresponding PDE is  
+
+\[\rho C_{p}\frac{\partial T}{\partial t} +\rho C_{p}\mathbf{u}\cdot \nabla T - \nabla \cdot (k\nabla T) = Q_{e},\]  
+
+where \(\rho\) is the mass density, \(C_{p}\) is the specific heat capacity, \(T\) is the absolute temperature, and \(k\) is the thermal conductivity. These two PDEs are connected through the quantity \(Q_{e}\) . The ONE architecture was trained to learn the mapping from \(V(x,y,t)\)
+
+<--- Page Split --->
+
+in a time range spanning all time steps in input pulses to \(T(x,y,t_{n})\) at an intermediate pulse time step \(t_{n}\) . In contrast to previous examples, the pulse information, including pulse height and width, was processed through the physics parameter processing branch in the ONE architecture (Fig. 1a) and multiplied with the output from cascaded real space processing and Fourier space processing branches to yield the final output. More details about the dataset generation and training are in Methods. Figure 4b displays the validation loss curve and Fig. 4c shows a few representative input 2D data \(V(x,y,t)\) at various time steps. Figure 4d shows the expected ground truth of \(T(x,y,t_{n})\) , the corresponding predicted temperature profile, and the absolute and relative errors between ground truth and prediction. All confirm a good performance in solving multiphysics PDEs using the ONE architecture.  
+
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 Solving multiphysics PDEs. (a) Illustration of solving coupled PDEs in an electrical heating problem involving electric current physics and heat transfer physics. (b) Validation loss curve. (c) A few representative 2D voltage profiles in the circuit. (d) The expected ground truth temperature profile, the predicted profile, and the absolute and relative errors between these two profiles. </center>  
+
+## Experimental demonstration  
+
+Finally, to demonstrate the experimental feasibility of the ONE architecture, we constructed a free- space reconfigurable DONN setup and evaluated the performance of
+
+<--- Page Split --->
+
+solving the Darcy flow equation under different hardware noise levels in optical XBAR structures. Figure 5a displays a photo and schematic of the reconfigurable DONN setup, which contains a laser source, a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. The reconfigurable encoder and diffractive layers were built upon SLMs, which can modulate the amplitude and phase of transmitted light when applying voltage. Multiple light polarization components, including polarizers and half- wave plates, were also employed to manipulate polarization states to achieve large phase modulation ranges. More details on the experimental setup are in Methods.  
+
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 Experimental demonstration. (a) Photo and schematic of a reconfigurable DONN experimental setup consisting of a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. Polarization components were used to configure SLMs in the phase modulation mode. (b) Output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture obtained from model calculations and experimental measurements. (c) Validation loss curves at different noise levels in optical XBAR structures and (d) the loss at the final epoch as a function of noise level. </center>
+
+<--- Page Split --->
+
+As shown in Supplementary Fig. 4, the experimentally measured amplitude and phase modulation responses of all three SLMs are not only discrete with respect to grey levels but also coupled and dependent. To leverage the gradient- based ML training algorithm, we utilized the Gumbel- softmax reparameterization technique to approximate a discrete distribution to a continuous distribution [21]. More details are described in Methods. Moreover, the values of input 2D data span both negative and positive values and were encoded as the grey level of the SLM in the reconfigurable input encoder (SLM0 in Fig. 5a). We performed the encoding through linear mapping from minimum and maximum values of input data to a grey- level range in the SLM. More details are described in Methods. In addition, we precisely aligned all SLMs with respect to each other within a range of a few pixels on the order of hundreds of \(\mu \mathrm{m}\) ; see Supplementary Fig. 5. Although the long optical path in the system makes the alignment sensitive to external variations, the system's full reconfigurability can enable fast adaptive pixel- by- pixel re- alignment. Figure 5b shows output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture (Fig. 1a) obtained from model calculations and experimental measurements, showing good agreement and experimentally validating the feasibility of the ONE architecture in solving PDEs. More data is shown in Supplementary Fig. 6. There are some speckles in the background of measured images, which probably originate from high- order diffraction interference, leading to numerical errors in the ONE architecture for performing regression tasks. This discrepancy between models and experiments can be mitigated through hardware- software co- design, such as incorporating loss functions based on experimental results for gradient calculations as demonstrated in prior works [20, 33, 35].  
+
+We also evaluated the performance of the ONE architecture under different noise levels of optical XBAR structures. Specifically, we added random Gaussian noise with zero mean and varying standard deviation (Std) to the values obtained from matrix multiplications to represent hardware noise, such as shot noise in photodetectors [36]. The corresponding MVM results and histograms of different noise standard deviation values are shown in Supplementary Fig. 7, and more details can be found in Methods. As shown in Fig. 5c and Fig. 5d, the validation loss increases with the increasing noise standard deviation value. The current hardware implementation of optical XBAR structures with advanced components and calibration algorithms [16- 18], including the structure we demonstrated before [36], can achieve quite a small noise level similar or below the noise level corresponding to 0.5 Std. Hence, the noise influence in optical XBAR structures on the performance of the ONE architecture is not substantial.  
+
+We further estimated the potential throughput and power consumption of the ONE architecture implemented using optical computing hardware for inference. The throughput is mainly determined by the SLM refresh rate and camera frame rate. Current commercial SLMs and cameras can have rates \(>1000\mathrm{Hz}\) , meaning that the inference time for one instance is \(< 1\mathrm{ms}\) . In contrast, it typically takes minutes to hours to numerically solve PDEs. Hence, the ONE architecture features \(>10^{5}\) (five orders of magnitude) acceleration compared to typical PDE solvers. This throughput is also comparable to the state- of- art ML model, such as FNO with a \(5\mathrm{ms}\) inference time [24]. Moreover, the system throughput can be substantially improved with device
+
+<--- Page Split --->
+
+innovation. For example, an electro-optic SLM based on organic molecules can achieve \(> \mathrm{GHz}\) switching speed [37], and an ultrafast camera can achieve a trillion frames per second [38]. With these devices, the ONE architecture can achieve an inference time \(< 1 \mathrm{ns}\) . The power consumption is mainly determined by the leakage current of liquid crystal cells in SLMs. Because of the dielectric nature of liquid crystals and their high leakage resistance, the leakage current is typically \(< 1 \mu \mathrm{A}\) . Hence, assuming a \(10 \mathrm{V}\) driving voltage, the static power consumption of SLMs is \(\sim 10 \mu \mathrm{W}\) , which is nearly \(10^{7}\) (seven orders of magnitude) smaller than typical GPU inference power \(\sim 100 \mathrm{W}\) .  
+
+## Discussion  
+
+We have demonstrated the ONE architecture and validated its performance in solving a broad range of PDEs in diverse scientific domains. The ONE architecture is versatile and can be modified to reduce the interface and connection between DONN and optical XBAR structures and facilitate the hardware implementation of the whole system. Further, in a whole system, active learning and noise- aware training can be incorporated to mitigate the discrepancy between models and practical systems for accurate deployment. Moreover, in addition to solving PDEs, the ONE architecture can be tailored to accelerate ML models for other regression problems.  
+
+## Methods  
+
+DONN diffraction model – The diffraction impulse function \(h(x, y)\) was described using the Fresnel equation as  
+
+\[h(x,y) = \frac{e^{ikz}}{i\lambda z} e^{\frac{ik}{2z} (x^{2} + y^{2})},\]  
+
+where \(\lambda\) is the wavelength, \(k = 2\pi /\lambda\) is the free- space wavenumber, \((x, y)\) are positions within a plane perpendicular to the wave propagation direction, \(z\) is the distance along the propagation direction, and \(i\) is the imaginary unit. The 2D Fourier transformation was directly performed on \(h(x, y)\) for model training and evaluation. To match the experimental setup as described below, \(h(x, y)\) was first discretized with respect to a defined rectangular mesh grid in the convolution calculation and then converted into the Fourier space through 2D Fourier transformation. More details can be found in our prior work [21].  
+
+The operation mechanism of optical XBAR structures – Supplementary Fig. 1a shows the detailed schematic of an integrated photonic XBAR structure. Specifically, the element values of a \(n \times 1\) input vector \(\mathbf{v}\) are represented by the intensities of light at input waveguides, \(\{I_{1}, I_{2}, I_{3}, \ldots , I_{n}\}\) , which can be implemented by modulating an equally distributed laser intensity through a \(n \times 1\) array of electro- optic modulators (red squares in Supplementary Fig. 1a) at input waveguides. The light on each row waveguide is then equally distributed to the column waveguides connected to that row waveguide and modulated through an electro- optic modulator on the coupled curved waveguide (yellow squares in Supplementary Fig. 1a). The element values of a \(m \times n\)
+
+<--- Page Split --->
+
+matrix \(\mathbf{M}\) are represented by the transmittance of modulators on curved waveguides, \(\{T_{i j}\} ,i\in [1,m],j\in [1,n]\) . At the end of each column waveguide, a photodetector collects all light intensity passing through the column waveguide. The obtained photocurrents or photovoltages of a \(m\times 1\) photodetector array represent the summation of multiplied input vector light intensity and matrix modulator transmittance, and the element values of output vector \(\mathbf{o}\) , \(O_{j} = \sum_{s = 1}^{n}T_{j s}I_{s},j\in [1,m]\) . Hence, this integrated photonic XBAR structure can implement MVM in the optical domain.  
+
+Similarly, Supplementary Fig. 1b shows the detailed schematic of a free- space optical XBAR structure. Specifically, the element values of a \(n\times 1\) input vector \(\mathbf{v}\) are represented by the intensities of light, \(\{I_{1},I_{2},I_{3},\dots,I_{n}\}\) , which is implemented through a \(n\times 1\) array of free- space vector SLM. The output light is broadcast to a \(m\times n\) array of matrix SLM through lenses so that the light distribution from vector SLM is identical at each column of matrix SLM. The element values of a \(m\times n\) matrix \(\mathbf{M}\) are represented by the transmittance of matrix SLM, \(\{T_{i j}\} ,i\in [1,m],j\in [1,n]\) . Lenses are then used to focus the output light from each modulator on the same column of matrix SLM to a photodetector. The readings from a \(m\times 1\) photodetector array represent the element values of output vector \(\mathbf{o}\) , \(O_{j} = \sum_{s = 1}^{n}T_{j s}I_{s},j\in [1,m]\) . Hence, this free- space optical XBAR structure can also implement MVM in the optical domain.  
+
+ONE architecture model – The ONE architecture model was constructed with two main modules – the DONN module processing data in the Fourier space and the optical XBAR module processing linear operations. The mathematical operations in DONN and optical XBAR structures have been described before and their accurate models have been implemented in our prior works, closely matching experimental results [21, 36]. Briefly, the DONN module was modeled by combining the Fresnel free- space diffraction with phase- only spatial light modulation in a range of \([0,2\pi ]\) in the model and coupled spatial light modulation as shown in Supplementary Fig. 4; the optical XBAR module was represented as matrix multiplication incorporating measurement noise. Both modules were implemented under the PyTorch 1.12 framework with graphics processing unit (GPU)- accelerated parallel computation and gradient backpropagation for training. The GPU used in this work was an Nvidia RTX 6000 card.  
+
+Darcy flow equation dataset and training – A 2D Darcy flow equation on the unit box was employed as described in detail in Ref. [24]. The corresponding PDE is a second- order, linear, elliptic PDE as  
+
+\[-\nabla \cdot (k(x,y)\nabla u(x,y)) = f(x,y), \qquad x\in (0,1),y\in (0,1),\] \[u(x) = 0, \qquad x\in \partial (0,1),y\in \partial (0,1)\]  
+
+with a Dirichlet boundary condition. We used the Darcy flow dataset from the existing dataset in Ref. [24] with a boundary condition \(u(x,y) = 0\) on domain edges. The coefficient \(k(x,y)\) was generated based on a specific distribution with the value 12 for positive inputs and 3 for negative inputs. The forcing term was fixed at \(f(x,y) = 1\) . The solution \(u(x,y)\) was computed using a second- order finite difference method on a \(421 \times 421\) grid, and other resolutions were obtained with downsampling. We used a \(10:1\) ratio for the numbers of data in the training set and validation set, respectively.
+
+<--- Page Split --->
+
+The model was trained with a total of 600 epochs and a batch size of 40. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+Magnetostatic Poisson's equation dataset and training – The demagnetizing field \(\mathbf{H}\) originates from the magnetization within the material itself, which can be calculated as the convolution of \(\mathbf{M}\) with the demagnetization tensor \(\mathbf{N}\) as  
+
+\[\mathbf{H}(\mathbf{r}) = \int \mathbf{N}(\mathbf{r} - \mathbf{r}^{\prime})\mathbf{M}(\mathbf{r}^{\prime})d\mathbf{r}^{\prime}.\]  
+
+This convolution was computed through Fourier space representations of fields. Specifically, to create the dataset, we utilized the MagneX solver [39] to simulate the time evolution of magnetization in a thin magnetic film with dimensions of \(500 \times 125 \times 3.125 \mathrm{~nm}\) . The modeling incorporated both demagnetization and exchange interactions. Initially, we relaxed the magnetic field into a stable S- state before subjecting the system to varying external magnetic fields in different scenarios. We uniformly sampled 8 bias \(\mathbf{H}\) fields in the \(x\) and \(y\) directions, each with a magnitude of 19872 A/m. The system evolved for 1 ns, during which we collected paired data of \(\mathbf{M}\) and \(\mathbf{H}\) fields. Each field was represented by three channels corresponding to the field components in \(x\) , \(y\) , and \(z\) directions. The dataset was divided into training and testing sets with an \(8:2\) ratio. The training was conducted over 500 epochs with a batch size of 128. The learning rate was set to 1.0 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+Navier- Stokes equation dataset and training – A 2D Navier- Stokes equation for a viscous, incompressible fluid in vorticity form on the unit torus was used to generate spatiotemporal data for training the ONE architecture. The details are described in Ref. [24]. Specifically, the PDEs are  
+
+\[\partial_{t}w(x,y,t) + u(x,y,t)\cdot \nabla w(x,y,t) = v\Delta w(x,y,t) + f(x,y),x\in (0,1),y\in (0,1),t\in (0,T]\] \[\nabla \cdot u(x,y,t) = 0,x\in (0,1),y\in (0,1),t\in (0,T]\] \[w(x,y,0) = w_{0}(x,y),x\in (0,1),y\in (0,1),\]  
+
+where \(w_{0}(x,y)\) is the initial vorticity and boundary conditions were used. We utilized the existing dataset with the viscosity coefficient \(v = 10^{- 3}\) from Ref. [24] for training and inference. The samples in the dataset were recorded with a time step of \(10^{- 4}\) s. We used 1000 data as the training set and 100 data as the validation set. We trained the ONE architecture model with the first 10 vorticity fields \((w(x,y,t))\) to predict the time evolution of the next 10 vorticity fields. The model was trained with a total of 600 epochs and a batch size of 40. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+Maxwell's equations dataset and training – We employed commercial Ansys Lumerical finite- difference- time- domain simulation software to generate an electric field dataset by solving Maxwell's equations in dielectric metasurfaces. Specifically, the dielectric metasurface had a periodic pattern and we used four silicon cylindrical rods as the unit cell and periodic boundary condition. Data were generated by randomly
+
+<--- Page Split --->
+
+selecting the radii of four cylindrical rods. The radius was chosen from \(39.5\mu \mathrm{m}\) to \(44.5\mu \mathrm{m}\) with a step of \(0.25\mu \mathrm{m}\) . The simulation time was set as 300000 fs. We generated a total of 1200 data and used 1000 as the training set and the rest 200 as the validation set. The model was trained in an auto- regressive style for the \(E_{x}\) component processing. The \(E_{x}\) field data between 300000 fs to 160000 fs was backward fed into to the model to predict the next 40000 fs \(E_{x}\) field data. The model was trained with a total of 500 epochs and a batch size of 20. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+Multiphysics dataset and training – We employed commercial COMSOL Multiphysics finite- element simulation software to generate a temperature profile dataset by solving coupled electric current and heat transfer PDEs in an electrical heating circuit. The circuit details can be found in Ref. [40]. Concisely, the circuit contained a serpentine- shaped Nichrome resistive layer with \(10\mu \mathrm{m}\) thick and \(5\mathrm{mm}\) wide on top of a glass plate. A silver contact pad with a dimension \(10\mathrm{mm}\times 10\mathrm{mm}\times 10\mu \mathrm{m}\) was attached at each end. The deposited side of the glass plate was in contact with the surrounding air at \(293.15\mathrm{K}\) and the back side was in contact with the heated fluid at \(353\mathrm{K}\) . Two coupled physics modules, electrical current in layered shells and heat transfer in layered shells, were used in COMSOL simulations. The input voltage pulse height was set from 5 to \(25\mathrm{V}\) with a step of \(1\mathrm{V}\) and the pulse width was set from 20 to \(60\mathrm{s}\) with a step of \(1\mathrm{s}\) . The simulation time range was from 0 to \(110\mathrm{s}\) . We generated a total number of 861 data and divided the data into training and testing set with the splitting ratio of \(8:2\) . The ONE architecture took the electric current layer data as the input spatiotemporal data and the input voltage pulse information was fed into the physics parameter data processing branch to predict temperature field data at \(55\mathrm{s}\) . The model was trained with a total of 100 epochs and a batch size of 40. The learning rate for the trainable parameters in DONNs was 0.1 and the learning rate for all other trainable parameters was 0.001 with the Adam optimizer.  
+
+DONN experimental setup and alignment – The photo and schematic diagram of the DONN experimental setup are displayed in Fig. 5a. The laser diode with a center wavelength \(532\mathrm{nm}\) (CPS532 from Thorlabs, Inc.) was used as a source. The distance between SLMs and between the last SLM and camera was set as \(25.4\mathrm{cm}\) . The polarizers and half- wave plates before and after each SLM were configured so that each SLM operated with a strong modulation of the transmitted electric field phase (phase mode) together with a moderate modulation of light amplitude. The experimentally measured amplitude and phase modulation responses of three SLMs are shown in Supplementary Fig. 4. All transmissive SLMs are the LC 2012 model from HOLOEYE Photonics AG with a refresh rate of \(60\mathrm{Hz}\) . The analog- to- digital converter has 8- bit precision for liquid crystal driving voltage, so that the grey level of SLMs is from 0 to 255. The pixel size of SLMs is \(36\mu \mathrm{m}\times 36\mu \mathrm{m}\) . The output data was captured on a CMOS camera with a frame rate of 34.8 frames per second (CS165MU1 from Thorlabs, Inc.).  
+
+We aligned the DONN setup by loading standard images on SLMs and comparing experimental results with simulation. Specifically, as shown in Supplementary Fig. 5a, standard Gaussian images, which were centered with a peak at 255 grey level and with a standard deviation of 6 pixels, were loaded in the input SLM and two diffractive
+
+<--- Page Split --->
+
+SLMs. Supplementary Fig. 5b displays the simulation pattern for the perfectly aligned setup. During the alignment process, loaded images were moved up, down, left, and right pixel- by- pixel to match the captured images by the camera with the simulation pattern. Supplementary Fig. 5c displays the matched experimental diffraction pattern when the optical setup was aligned, while Supplementary Fig. 5d shows misaligned patterns when there was five- pixel misalignment in vertical and horizontal directions, respectively.  
+
+DONN experimental training with reparameterization – The discrete look- up tables of device responses shown in Supplementary Fig. 4 break the gradient backpropagation in the ML training process in PyTorch. To solve this challenge, we utilized a differentiable reparameterization Gumbel- softmax technique, which was first introduced in Ref. [41] and demonstrated in our prior work [21]. Specifically, continuous noise from the Gumbel distribution was added to the discrete distribution. The argmax function was then used to find the optimized sample. The training problem after this Gumbel- argmax process is mathematically equivalent to the original training problem under one- hot representation [41]. Since the argmax function still breaks the gradient chain, it was replaced with the softmax function to enable differentiability. Hence, this Gumbel- softmax technique, which is also available in PyTorch, offers continuous and differentiable approximation to discrete distributions and the gradient can backpropagate to reduce the loss function.  
+
+DONN experimental grey- level encoding – The global minimum and maximum values in input 2D data were calculated as \(d_{\mathrm{min}}\) and \(d_{\mathrm{max}}\) . A grey level range from 130 to 255 in the input encoder SLM was selected for a relatively large amplitude modulation range to have enough contrast. Hence, any value \(d\) in the input 2D data was converted into a grey level through a linear mapping as  
+
+\[d = \operatorname {int}\left(\frac{255 - 130}{d_{\mathrm{max}} - d_{\mathrm{min}}} + 130\right),\]  
+
+where the int(·) operation rounded the expression to the nearest integer since the SLM grey level must be an integer.  
+
+Optical XBAR noise – The MVM results from an optical XBAR structure were uniformly randomly generated in a range of \(- 15\) to 15, which was the value range in the ONE architecture for solving the Darcy flow equation. The expected number \(o\) was then added with a randomly generated noise from a Gaussian distribution with a zero average and varying standard deviation. The noise- dressed number \(\bar{o}\) was used in ONE architecture calculations. Under different noise standard deviation levels, Supplementary Fig. 7a demonstrates \(\bar{o}\) with respect to \(o\) and Supplementary Fig. 7b displays histograms of \(\bar{o} - o\) .  
+
+## Data availability  
+
+Upon publication, all data that support the plots within this paper and other findings of this study will be available on a public GitHub repository.
+
+<--- Page Split --->
+
+## Code availability  
+
+Code availabilityUpon publication, all codes that support the plots within this paper and other findings of this study will be available on a public GitHub repository.  
+
+## Acknowledgements  
+
+AcknowledgementsR.C., C.Y., and W.G. acknowledge support from the National Science Foundation through Grants No. 2235276, No. 2316627, and No. 2428520. M.L., J.F., and W.G. also acknowledge support from the University of Utah start- up fund. Y.T., Z.Y., and A.N. were supported by Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE- AC02- 05CH11231. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE- AC02- 05CH11231 and under NERSC GenAI award under No. DDR- ERCAP0030541.  
+
+## Author Contributions Statement  
+
+Author Contributions StatementY.T. and W.G. conceived the idea and W.G. supervised the project. Y.T. constructed models and performed machine learning calculations with the help of M.L., J.F., and C.Y and under the support of A.N., Z.Y., and W.G. R.C constructed an optical experimental setup, performed experiments, and performed numerical calculations under the supervision of W.G. Y.T. and W.G. wrote the manuscript.  
+
+## Competing Interests Statement  
+
+The authors declare no competing interests.  
+
+## References  
+
+References[1] Azizzadenesheli, K., Kovachki, N., Li, Z., Liu- Schiaffini, M., Kossaifi, J., Anandkumar, A.: Neural operators for accelerating scientific simulations and design. Nat. Rev. Phys., 1- 9 (2024)[2] Griffiths, D.J.: Introduction to Electrodynamics. Cambridge University Press, New York (2023)[3] Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, New York (2000)[4] Goosse, H.: Climate System Dynamics and Modeling. Cambridge University Press, New York (2015)[5] Jiang, J., Chen, M., Fan, J.A.: Deep neural networks for the evaluation and design of photonic devices. Nat. Rev. Mater., 1- 22 (2020)
+
+<--- Page Split --->
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+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- SIFinal.pdf
+
+<--- Page Split --->

preprint/preprint__078ee3115bb7f9caf7ff08bd41325e1b3d5bc1c68c6da418cda25d198e700819/preprint__078ee3115bb7f9caf7ff08bd41325e1b3d5bc1c68c6da418cda25d198e700819_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 106, 910, 175]]<|/det|>
+# Optical Neural Engine for Solving Scientific Partial Differential Equations  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 135, 213]]<|/det|>
+Weilu Gao  
+
+<|ref|>text<|/ref|><|det|>[[55, 222, 256, 240]]<|/det|>
+weilu.gao@utah.edu  
+
+<|ref|>text<|/ref|><|det|>[[44, 268, 610, 288]]<|/det|>
+The University of Utah https://orcid.org/0000- 0003- 3139- 034X  
+
+<|ref|>text<|/ref|><|det|>[[44, 293, 175, 312]]<|/det|>
+Yingheng Tang  
+
+<|ref|>text<|/ref|><|det|>[[53, 315, 399, 334]]<|/det|>
+Lawrence Berkeley National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 340, 165, 358]]<|/det|>
+Ruiyang Chen  
+
+<|ref|>text<|/ref|><|det|>[[53, 362, 608, 381]]<|/det|>
+The University of Utah https://orcid.org/0000- 0002- 1538- 1702  
+
+<|ref|>text<|/ref|><|det|>[[44, 386, 147, 404]]<|/det|>
+Minhan Lou  
+
+<|ref|>text<|/ref|><|det|>[[53, 408, 250, 427]]<|/det|>
+The University of Utah  
+
+<|ref|>text<|/ref|><|det|>[[44, 433, 147, 450]]<|/det|>
+Jichao Fan  
+
+<|ref|>text<|/ref|><|det|>[[53, 455, 250, 473]]<|/det|>
+The University of Utah  
+
+<|ref|>text<|/ref|><|det|>[[44, 479, 122, 496]]<|/det|>
+Cunxi Yu  
+
+<|ref|>text<|/ref|><|det|>[[53, 500, 371, 519]]<|/det|>
+University of Maryland, College Park  
+
+<|ref|>text<|/ref|><|det|>[[44, 525, 162, 543]]<|/det|>
+Andy Nonaka  
+
+<|ref|>text<|/ref|><|det|>[[53, 547, 397, 566]]<|/det|>
+Lawrence Berkeley National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 572, 112, 589]]<|/det|>
+Zhi Yao  
+
+<|ref|>text<|/ref|><|det|>[[53, 593, 397, 612]]<|/det|>
+Lawrence Berkeley National Laboratory  
+
+<|ref|>text<|/ref|><|det|>[[44, 653, 105, 671]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 691, 136, 710]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 729, 355, 749]]<|/det|>
+Posted Date: September 30th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 767, 475, 787]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 5061922/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 804, 914, 848]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 865, 535, 886]]<|/det|>
+Additional Declarations: There is NO Competing Interest.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 911, 88]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on May 17th, 2025. See the published version at https://doi.org/10.1038/s41467-025-59847-3.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[223, 155, 732, 206]]<|/det|>
+# Optical Neural Engine for Solving Scientific Partial Differential Equations  
+
+<|ref|>text<|/ref|><|det|>[[190, 226, 768, 263]]<|/det|>
+Yingheng Tang \(^{1\ast}\) , Ruiyang Chen \(^{2\dagger}\) , Minhan Lou \(^{2}\) , Jichao Fan \(^{2}\) , Cunxi Yu \(^{3}\) , Andy Nonaka \(^{1}\) , Zhi (Jackie) Yao \(^{1*}\) , Weilu Gao \(^{2*}\)  
+
+<|ref|>text<|/ref|><|det|>[[186, 270, 771, 353]]<|/det|>
+\(^{1}\) Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. \(^{2}\) Department of Electrical and Computer Engineering, The University of Utah, Salt Lake City, UT 84112, USA. \(^{3}\) Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA.  
+
+<|ref|>text<|/ref|><|det|>[[260, 380, 694, 428]]<|/det|>
+\*Corresponding author(s). E- mail(s): ytang4@lbl.gov; jackie_zhiyao@lbl.gov; weilu.gao@utah.edu; †These authors contribute equally  
+
+<|ref|>sub_title<|/ref|><|det|>[[443, 454, 512, 467]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[205, 470, 750, 735]]<|/det|>
+Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data- driven machine learning (ML) approaches are emerging to accelerate time- consuming and computation- intensive numerical simulations of PDEs. Although optical systems offer high- throughput and energy- efficient ML hardware, there is no demonstration of utilizing them for solving PDEs. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time- dependent and time- independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson's equation in demagnetization, the Navier- Stokes equation in incompressible fluid, Maxwell's equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high- performance dual- space processing for outperforming traditional PDE solvers and being comparable with state- of- the- art ML models but also can be implemented using optical computing hardware with unique features of low- energy and highly parallel constant- time processing irrespective of model scales and real- time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large- scale scientific and engineering computations.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[207, 83, 357, 101]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[207, 111, 832, 310]]<|/det|>
+Partial differential equations (PDEs) derived from physical laws have been a powerful and faithful computational tool to accelerate the exploration and validation of scientific hypotheses instead of performing expensive and time- consuming real- world experiments [1]. Hence, numerically solving PDEs is essential for scientific research and development in nearly every scientific domain. For example, the interaction of electromagnetic waves with materials and engineered structures in broad applications such as communication, imaging, sensing, and quantum technologies is governed by Maxwell's equations [2]; automotive and flight aerodynamics for designing and manufacturing road vehicles and airplanes is determined by Navier- Stokes equation [3]; the Earth system including temperature, atmosphere, and ice sheets for understanding climate change and making policies is also described with a series of PDEs [4]. However, current numerical simulation methods to solve PDEs, such as finite difference/volume methods to solve Maxwell's and the Navier- Stokes equations, are costly in computing time and resources.  
+
+<|ref|>text<|/ref|><|det|>[[207, 311, 832, 555]]<|/det|>
+Machine learning (ML) offers a new perspective on solving PDEs through data- driven approaches to enable fast and accurate simulations of many multiphysics and multiscale processes [5- 7]. However, the ML model deployment on electronic computing hardware requires substantial computing resources and consumes substantial energy. In the foreseeable future, the fundamental quantum mechanics limit will lead to a bottleneck of further reducing the energy consumption and simultaneously increasing the integration density of electronic circuits to catch up with the increasing scale of ML models in demand for solving complex problems [8, 9], thus urgently calling for new high- throughput and energy- efficient ML hardware accelerators. Recently, optical architectures, including photonic integrated circuits for matrix- vector multiplication (MVM) [10, 11], for neuro- inspired spiking neural networks [12, 13], and for photonic reservoir computing [14, 15], and free- space optical systems for MVM [16- 18] and diffractive optical neural networks (DONNs) [19- 22], are emerging as high- performance ML hardware accelerators by leveraging different particles - photons - to break down electronic bottleneck thanks to high parallelism and low static energy consumption of photons [23]. However, to date, there is no deployment of any optical computing systems for solving PDEs in any scientific domain.  
+
+<|ref|>text<|/ref|><|det|>[[207, 555, 832, 739]]<|/det|>
+Here, we present a fully reconfigurable and scalable optical neural engine (ONE) architecture that combines DONN systems for processing data in Fourier space and optical crossbar (XBAR) structures for processing data in real space to solve two- dimensional (2D) spatiotemporal profiles in time- independent and time- dependent PDEs. The ONE architecture not only leverages the advantages of high- performance dual- space processing [24], but also can be implemented using optical computing hardware with unique features of low- energy and highly parallel constant- time processing irrespective of model scales, and real- time reconfigurability for tackling multiple tasks with the same architecture. We numerically and experimentally demonstrate the capability of the ONE architecture in solving a broad range of PDEs in diverse disciplines, including the Darcy flow equation in fluid dynamics, the magnetostatic Poisson's equation in micromagnetics, the Navier- Stokes equation in aerodynamics, Maxwell's equations in nanophotonics, and coupled electric current and heat transfer equations in
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 86, 790, 188]]<|/det|>
+a multiphysics electrical heating problem. The ONE architecture not only outperforms traditional PDE solvers because of its data- driven nature, but also shows comparable and better performance with other ML models while with substantial hardware advantages because of its implementation in the optical domain. The demonstrated ONE architecture is versatile and can be tailored with different combinations of DONN and XBAR structures for solving various PDEs, offering a transformative universal solution for large- scale scientific and engineering computations.  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 202, 254, 220]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 231, 348, 248]]<|/det|>
+## ONE Architecture  
+
+<|ref|>text<|/ref|><|det|>[[165, 254, 790, 454]]<|/det|>
+Figure 1a illustrates the ONE architecture, which takes the spatiotemporal data of an input physical quantity \(\mathbf{U}\) , described as a function \(u(x,y,t)\) in terms of positions \(x\) and \(y\) and time \(t\) , to predict the spatiotemporal data of an output physical quantity \(\mathbf{G}\) described using a function \(g(x,y,t)\) . The input and output quantities \(\mathbf{U}\) and \(\mathbf{G}\) can be connected through either a single- physics PDE or coupled multiphysics PDEs. There are three branches inside the ONE architecture, including (i) Fourier space processing branch, (ii) real space processing branch, and (iii) physics parameter processing branch. The combination of both real and Fourier space processing has been proven fast, powerful, and efficient in solving PDEs [24], and the incorporation of additional physics parameter processing enables the fusion of multimodal data for complex tasks [25]. More importantly, most operations in these branches can be deployed on optical computing hardware in both real and Fourier space, enabling solving PDEs in high- throughput and energy- efficient manners. The details of each branch are described below.  
+
+<|ref|>text<|/ref|><|det|>[[165, 454, 790, 624]]<|/det|>
+In the first Fourier space processing branch, the core arithmetic operations are based on Fourier and inverse Fourier transformations to process input spatiotemporal data in the Fourier space. Their optical hardware implementations are mainly based on reconfigurable DONNs, which contain cascaded reconfigurable diffractive layers. Reconfigurable DONNs can be implemented in both integrated photonic chips [26, 27] and free space [19- 21]; see Fig. 1b. There are two fundamental operations in DONNs - optical diffraction and spatial light modulation. For the optical diffraction operation, an optical field right after the \(l\) - th diffractive layer, \(f_{l}\) , diffracts to the front of \((l + 1)\) - th layer, whose optical field, \(f_{\mathrm{in},l + 1}\) , is a convolution of \(f_{l}\) and the diffraction impulse function \(h(x,y)\) . Specifically, the complex- valued field at point \((x,y)\) on the input plane of \((l + 1)\) - th layer can be written as the convolution of all fields at the output plane of \(l\) - th layer as  
+
+<|ref|>equation<|/ref|><|det|>[[278, 637, 675, 668]]<|/det|>
+\[f_{\mathrm{in},l + 1}(x,y,z) = \iint f_{l}(x^{\prime},y^{\prime},0)h(x - x^{\prime},y - y^{\prime})dx^{\prime}dy^{\prime},\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 679, 790, 737]]<|/det|>
+where \(z\) is the distance between two diffractive layers and \(h(x,y)\) is the impulse response function of free space. By the convolution theorem, this 2D convolution can be efficiently calculated in Fourier space based on Fourier and inverse Fourier transformations. Specifically, the 2D Fourier transformation \(\mathcal{F}_{xy}\) of \(f\) and \(h\) , \(F\) and \(H\) , are
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[213, 90, 830, 479]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[206, 485, 833, 534]]<|/det|>
+<center>Fig. 1 ONE architecture and hardware implementations. (a) Illustration of processing branches and flows in the ONE architecture to predict output spatiotemporal output physical quantities from corresponding input and solve PDEs involving single or multiple physics. Illustrations of integrated and free-space implementations of reconfigurable (b) DONN and (c) XBAR structures. </center>  
+
+<|ref|>text<|/ref|><|det|>[[207, 552, 345, 565]]<|/det|>
+connected through  
+
+<|ref|>equation<|/ref|><|det|>[[333, 577, 702, 612]]<|/det|>
+\[\mathcal{F}_{xy}(f_{\mathrm{in},l + 1}(x,y,z)) = \mathcal{F}_{xy}(f_l(x,y,0))\mathcal{F}_{xy}(h(x,y)),\] \[F_{\mathrm{in},l + 1}(\alpha ,\beta ,z) = F_l(\alpha ,\beta ,0)H(\alpha ,\beta),\]  
+
+<|ref|>text<|/ref|><|det|>[[206, 622, 832, 710]]<|/det|>
+where \(\alpha ,\beta\) are spatial domain indices. After diffraction, the 2D inverse Fourier transformation \(\mathcal{F}_{xy}^{- 1}\) of \(F_{\mathrm{in},l + 1}(\alpha ,\beta ,z)\) , \(f_{\mathrm{in},l + 1}(x,y,z)\) , is then spatially modulated. Each diffraction pixel at location \((x,y)\) has a complex- valued electric field transmission coefficient \(t(x,y,S)e^{\phi (x,y,S)}\) , where \(t(x,y,S)\) \((\phi (x,y,S))\) is the amplitude (phase) response as a function of external stimuli \(S\) , such as voltages. The spatial light modulation operation is expressed as a pixel- wise multiplication  
+
+<|ref|>equation<|/ref|><|det|>[[327, 722, 708, 739]]<|/det|>
+\[f_{l + 1}(x,y,z) = \mathcal{F}_{xy}^{-1}(F_{\mathrm{in},l + 1}(\alpha ,\beta ,z))t(x,y,S)e^{\phi (x,y,S)}\]
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[375, 86, 622, 102]]<|/det|>
+\[= f_{\mathrm{in},l + 1}(x,y,z)t(x,y,S)e^{\phi (x,y,S)},\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 114, 790, 144]]<|/det|>
+where \(f_{l + 1}(x,y,z)\) is the near- field output field right after the \((l + 1)\) - th layer. More details can be found in Methods.  
+
+<|ref|>text<|/ref|><|det|>[[165, 144, 790, 314]]<|/det|>
+Before and between DONN kernels, there is a linear transformation operation based on fully connected layers to scale up the number of channels and a channel mixing operation based on matrix multiplications [24]. The core arithmetic operations are based on MVM. Their optical hardware implementations are mainly based on reconfigurable optical XBAR structures, which encode element values of vector \(\mathbf{v}\) and matrix \(\mathbf{M}\) into light intensity through electro- optic modulators, perform multiplications through cascaded modulators, and add signals at the output detector array. The signals are routed to follow mathematical calculations in MVM so that the reading from the detector array represents the output vector \(\mathbf{o} = \mathbf{M}\times \mathbf{v}\) . Reconfigurable XBAR structures can also be implemented in both integrated photonic chips [10, 11] and free space [16- 18]; see Fig. 1c. More details on the operation mechanism can be found in Methods and Supplementary Fig. 1.  
+
+<|ref|>text<|/ref|><|det|>[[165, 314, 790, 544]]<|/det|>
+The second real space processing branch contains fully connected layers, whose operations are also based on MVM and implemented with optical XBAR structures. The output from the Fourier space branch, \(\mathbf{F}(u)\) , and the output from the real space branch, \(\mathbf{R}(u)\) are added and further processed with a nonlinear operation. Note that the nonlinear operation is the only operation performed in electronic hardware in the ONE architecture. Moreover, this combination of real space, Fourier space, and nonlinear processing is scaled up, repeated four times, and cascaded in series. The third branch is to perform a linear transformation on other relevant physics parameters \(d(t)\) , which are time sequences instead of spatiotemporal data, based on fully connected layers. The obtained data \(\mathbf{T}(d)\) is multiplied and merged onto two other branches to have the final output \(g(x,y,t)\) . Hence, except nonlinear operations, all other operations can be done with DONN and optical XBAR systems. These two systems can be seamlessly assembled into a single integrated photonic chip or a single free- space optical system for all- optical operations without converting between optical and electronic hardware, fully leveraging the advantages of high throughput and high parallelism in optical computing systems. More details on the ONE architecture model are in Methods.  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 557, 660, 574]]<|/det|>
+## Darcy flow and magnetostatic Poisson's equations  
+
+<|ref|>text<|/ref|><|det|>[[165, 580, 790, 624]]<|/det|>
+The first PDE we solved with the ONE architecture is the Darcy flow equation in fluid dynamics physics. This PDE describes a fluid flow through a porous medium as shown in Fig. 2a. Specifically, the equation is  
+
+<|ref|>equation<|/ref|><|det|>[[357, 640, 595, 654]]<|/det|>
+\[-\nabla \cdot (k(x,y)\nabla u(x,y)) = f(x,y),\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 666, 790, 739]]<|/det|>
+where \(k(x,y)\) is the permeability field of the medium, \(u(x,y)\) is the pressure field of the flow, and \(f(x,y)\) is the force function. The ONE architecture was trained to learn the mapping from the 2D function \(k(x,y)\) to function \(u(x,y)\) . More details about the equation dataset generation and training are in Methods. Figure 2b displays the training loss curves for inputs with different resolutions. The training loss
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[206, 86, 831, 400]]<|/det|>
+is generally low for all resolutions and slightly increases at the highest 421 resolution. Figure 2c shows the comparison of the training loss of our ONE architecture with other PDE solving models, including fully convolution networks (FCN) [28], principal component analysis- based neural network (PCANN) [29], reduced biased method (RBM) [30], graph neural operator (GNO) [31], low- rank kernel decomposition neural operator (LNO) [25], multipole graph neural operator (MGNO) [32], and Fourier neural operator (FNO) [24]. The performance of the ONE architecture is comparable with the state- of- the- art neural operators including GNO, LNO, MGNO, and FNO, and is better than FCN. Further, from the hardware perspective, the ONE architecture is constructed based on high- throughput optical computing hardware platforms so that all operations can be performed in parallel within a single clock cycle. In addition, the ONE architecture can be practically implemented on a large scale. For example, free- space reconfigurable DONNs [20, 21, 33] and optical MVM [17] are typically implemented using spatial light modulators (SLMs) with a scale \(>1000 \times 1000\) . Hence, the execution cost of solving PDEs with different scales and resolutions is invariant, meaning \(\mathcal{O}(1)\) , if the scale of the optical hardware in the ONE architecture is large enough. Figure 2d displays the input permeability field \(k(x, y)\) , the expected ground truth of output pressure field \(u(x, y)\) , the predicted output pressure field, the absolute error between the expected and predicted outputs, and the relative error between the expected and predicted outputs, at the lowest 85 and the highest 421 resolutions, respectively. This visualization further validates the ONE architecture in solving PDEs. More data on other resolutions are shown in Supplementary Fig. 2.  
+
+<|ref|>text<|/ref|><|det|>[[207, 400, 831, 457]]<|/det|>
+The second PDE we solved is the magnetostatic Poisson's equation of demagnetization in micromagnetics physics. This PDE calculates the demagnetizing field \(\mathbf{H}\) generated by the magnetization field \(\mathbf{M}\) as shown in Fig. 2e. Specifically, the equation is obtained from Maxwell's equation as  
+
+<|ref|>equation<|/ref|><|det|>[[455, 472, 581, 485]]<|/det|>
+\[\nabla \cdot \mathbf{H} = -\nabla \cdot \mathbf{M}.\]  
+
+<|ref|>text<|/ref|><|det|>[[206, 499, 831, 544]]<|/det|>
+By defining an effective magnetic charge density \(\rho = - \nabla \cdot \mathbf{M}\) and a magnetic scalar potential \(\Phi\) assuming there is no free current, we can express the demagnetizing field \(\mathbf{H} = - \nabla \Phi\) and rewrite the previous equation as a Poisson's equation  
+
+<|ref|>equation<|/ref|><|det|>[[475, 558, 560, 571]]<|/det|>
+\[\nabla^{2}\Phi = -\rho .\]  
+
+<|ref|>text<|/ref|><|det|>[[206, 584, 831, 728]]<|/det|>
+Similar to solving the Darcy flow equation, the ONE architecture was trained to learn the mapping from components of \(\mathbf{M}\) to \(\mathbf{H}\) vector fields. More details about the equation dataset generation and training are in Methods. Figure 2f shows the validation loss curve and Fig. 2g shows the input one component of \(\mathbf{M}\) field, the expected ground truth of output \(H_{x}\) component of \(\mathbf{H}\) field, the predicted output \(H_{x}\) component, the absolute error between the expected and predicted outputs, and normalized error between the expected and predicted outputs with respect to the maximum field strength in the ground truth. Both confirm a good performance of the ONE architecture in solving the magnetostatic Poisson's equation. More data on \(H_{y}\) and \(H_{z}\) components is shown in Supplementary Fig. 3.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[171, 88, 784, 486]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[165, 494, 791, 631]]<|/det|>
+<center>Fig. 2 Solving Darcy flow and magnetostatic Poisson's equations. (a) Illustration of the Darcy flow equation describing a fluid flow through a porous medium. The ONE architecture learns the mapping between the permeability and pressure fields. (b) Training loss curves for input data with different resolutions. (c) Comparison of the training loss of different models at various resolutions. (d) Input permeability field, the expected ground truth of output pressure field, the predicted output pressure field, the absolute error between the expected and predicted outputs, and the relative error between the expected and predicted outputs, at 85 and 421 resolutions. (e) Illustration of the magnetostatic Poisson's equation calculating the demagnetizing field generated by the magnetization field. The ONE architecture learns the mapping between these two fields. (f) Validation loss curve for the ONE architecture solving the magnetostatic Poisson's equation and (g) corresponding input magnetization field, the expected ground truth of output demagnetizing field, the predicted output demagnetizing field, the absolute and normalized errors between the expected and predicted outputs. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 646, 554, 663]]<|/det|>
+## Navier-Stokes and Maxwell's equations  
+
+<|ref|>text<|/ref|><|det|>[[165, 670, 790, 741]]<|/det|>
+In addition to steady- state Darcy flow and magnetostatic Poisson's equations without time evolution, we employed the ONE architecture to solve time- dependent PDEs, including the Navier- Stokes equation in fluid dynamics and Maxwell equations in electromagnetics and optics. In particular, the real- time reconfigurability of DONN and optical XBAR structures makes the ONE architecture suitable for such a purpose.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[206, 86, 832, 129]]<|/det|>
+Specifically, we solved a 2D Navier- Stokes equation for a viscous, incompressible fluid in vorticity form on the unit torus as shown in Fig. 3a. This PDE calculates the time evolution of vorticity described as  
+
+<|ref|>equation<|/ref|><|det|>[[300, 145, 737, 159]]<|/det|>
+\[\partial_{t}w(x,y,t) + u(x,y,t)\cdot \nabla w(x,y,t) = v\Delta w(x,y,t) + f(x,y),\]  
+
+<|ref|>text<|/ref|><|det|>[[206, 171, 832, 286]]<|/det|>
+where \(u\) is the velocity field, \(w = \nabla \times u\) is the vorticity, \(\nu\) is the viscosity coefficient, \(f\) is the forcing function. The ONE architecture was trained to learn the mapping from \(w\) in a time range from 0 to \(t_0\) to \(w\) in a time range from \(t_0\) to \(t_1\) ( \(t_1 > t_0\) ). More details about the equation dataset generation and training are in Methods. Further, we also solved Maxwell's equations in a dielectric metasurface consisting of multiple cylindrical pillars in a unit cell of a periodic pattern as shown in Fig. 3b [34]. The general Maxwell's equations can calculate the time evolution of an electric field through the following equations  
+
+<|ref|>equation<|/ref|><|det|>[[448, 300, 588, 393]]<|/det|>
+\[\nabla \cdot \mathbf{D} = \rho ,\] \[\nabla \cdot \mathbf{B} = 0,\] \[\nabla \times \mathbf{E} = -\frac{\partial\mathbf{B}}{\partial t},\] \[\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial\mathbf{D}}{\partial t},\]  
+
+<|ref|>text<|/ref|><|det|>[[206, 403, 832, 575]]<|/det|>
+where \(\mathbf{D}\) is the electric displacement field, \(\rho\) is the free charge density, \(\mathbf{B}\) is the magnetic flux density, \(\mathbf{E}\) is the electric field, \(\mathbf{H}\) is the magnetic field, and \(\mathbf{J}\) is the free current density. The ONE architecture was trained to learn the mapping from \(\mathbf{E}\) in a time range from 0 to \(t_0\) to \(\mathbf{E}\) in a time range from \(t_0\) to \(t_1\) ( \(t_1 > t_0\) ). More details about the dataset generation and training are in Methods. Figure 3c displays the validation loss curve for solving the Navier- Stokes equation with \(t_0 = 10\) and \(t_1 = 20\) . Figure 3d displays the validation loss curves for solving Maxwell's equations with \(t_0 = 10\) and \(t_1 = 20,30,40\) , respectively. Moreover, Figure 3e and 3f show the expected ground truth of \(w\) field and the \(E_x\) component of the \(\mathbf{E}\) field at \(t_1\) , the corresponding predicted fields at \(t_1\) , and the absolute and relative errors between ground truth and prediction for the Navier- Stokes equation and Maxwell's equations, respectively. All confirm a good performance in solving time- dependent PDEs using the ONE architecture.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 588, 399, 605]]<|/det|>
+## Multiphysics PDEs  
+
+<|ref|>text<|/ref|><|det|>[[207, 612, 832, 700]]<|/det|>
+Moreover, we employed the ONE architecture to solve coupled PDEs involving two physics. Specifically, we solved an electrical heating problem to obtain a temperature profile at an intermediate time step \(t_n\) , \(T(x,y,t_n)\) , in an electrical circuit when a time- dependent voltage signal was applied to the circuit pads, involving coupled electric current physics and heat transfer physics; see Fig. 4a. Specifically, for the electrical current physics, the corresponding PDE is  
+
+<|ref|>equation<|/ref|><|det|>[[471, 714, 625, 728]]<|/det|>
+\[Q_{e} = d\sigma \nabla_{t}V(x,y,t),\]
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[172, 88, 785, 428]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[164, 450, 791, 530]]<|/det|>
+<center>Fig. 3 Solving time-dependent Navier-Stokes and Maxwell's equations. Illustrations of (a) Navier-Stokes equation for solving the time evolution of the vorticity field in a viscous, incompressible fluid in vorticity form on the unit torus and (b) Maxwell's equations for solving the time evolution of the electric field in a dielectric metasurface. Validation loss curves for (c) solving the Navier-Stokes equation and (d) Maxwell's equations using the ONE architecture. The expected ground truth field, the predicted field, and the absolute and relative errors between these two fields for (e) the Navier-Stokes equation and (f) Maxwell's equations, respectively. </center>  
+
+<|ref|>equation<|/ref|><|det|>[[370, 547, 527, 561]]<|/det|>
+\[V(x_{0},y_{0},t) = \mathrm{rect}(t),\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 574, 791, 647]]<|/det|>
+where \(Q_{e}\) is the heat rate per unit area from an electromagnetic heating source, \(d\) is the thickness of the heating layer, \(V(x,y,t)\) is the voltage profile in the circuit that is subjected to a voltage boundary condition defined in the pads \(V(x_{0},y_{0},t)\) , and \(V(x_{0},y_{0},t)\) is a pulse rectangular function \(\mathrm{rect}(t)\) with pulse height and width. For the heat transfer physics, the corresponding PDE is  
+
+<|ref|>equation<|/ref|><|det|>[[328, 659, 625, 686]]<|/det|>
+\[\rho C_{p}\frac{\partial T}{\partial t} +\rho C_{p}\mathbf{u}\cdot \nabla T - \nabla \cdot (k\nabla T) = Q_{e},\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 697, 791, 740]]<|/det|>
+where \(\rho\) is the mass density, \(C_{p}\) is the specific heat capacity, \(T\) is the absolute temperature, and \(k\) is the thermal conductivity. These two PDEs are connected through the quantity \(Q_{e}\) . The ONE architecture was trained to learn the mapping from \(V(x,y,t)\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[206, 86, 832, 244]]<|/det|>
+in a time range spanning all time steps in input pulses to \(T(x,y,t_{n})\) at an intermediate pulse time step \(t_{n}\) . In contrast to previous examples, the pulse information, including pulse height and width, was processed through the physics parameter processing branch in the ONE architecture (Fig. 1a) and multiplied with the output from cascaded real space processing and Fourier space processing branches to yield the final output. More details about the dataset generation and training are in Methods. Figure 4b displays the validation loss curve and Fig. 4c shows a few representative input 2D data \(V(x,y,t)\) at various time steps. Figure 4d shows the expected ground truth of \(T(x,y,t_{n})\) , the corresponding predicted temperature profile, and the absolute and relative errors between ground truth and prediction. All confirm a good performance in solving multiphysics PDEs using the ONE architecture.  
+
+<|ref|>image<|/ref|><|det|>[[212, 264, 832, 590]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[206, 610, 832, 658]]<|/det|>
+<center>Fig. 4 Solving multiphysics PDEs. (a) Illustration of solving coupled PDEs in an electrical heating problem involving electric current physics and heat transfer physics. (b) Validation loss curve. (c) A few representative 2D voltage profiles in the circuit. (d) The expected ground truth temperature profile, the predicted profile, and the absolute and relative errors between these two profiles. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[208, 690, 490, 706]]<|/det|>
+## Experimental demonstration  
+
+<|ref|>text<|/ref|><|det|>[[206, 713, 832, 741]]<|/det|>
+Finally, to demonstrate the experimental feasibility of the ONE architecture, we constructed a free- space reconfigurable DONN setup and evaluated the performance of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 86, 791, 201]]<|/det|>
+solving the Darcy flow equation under different hardware noise levels in optical XBAR structures. Figure 5a displays a photo and schematic of the reconfigurable DONN setup, which contains a laser source, a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. The reconfigurable encoder and diffractive layers were built upon SLMs, which can modulate the amplitude and phase of transmitted light when applying voltage. Multiple light polarization components, including polarizers and half- wave plates, were also employed to manipulate polarization states to achieve large phase modulation ranges. More details on the experimental setup are in Methods.  
+
+<|ref|>image<|/ref|><|det|>[[175, 225, 770, 610]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[165, 632, 791, 712]]<|/det|>
+<center>Fig. 5 Experimental demonstration. (a) Photo and schematic of a reconfigurable DONN experimental setup consisting of a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. Polarization components were used to configure SLMs in the phase modulation mode. (b) Output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture obtained from model calculations and experimental measurements. (c) Validation loss curves at different noise levels in optical XBAR structures and (d) the loss at the final epoch as a function of noise level. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[207, 87, 831, 428]]<|/det|>
+As shown in Supplementary Fig. 4, the experimentally measured amplitude and phase modulation responses of all three SLMs are not only discrete with respect to grey levels but also coupled and dependent. To leverage the gradient- based ML training algorithm, we utilized the Gumbel- softmax reparameterization technique to approximate a discrete distribution to a continuous distribution [21]. More details are described in Methods. Moreover, the values of input 2D data span both negative and positive values and were encoded as the grey level of the SLM in the reconfigurable input encoder (SLM0 in Fig. 5a). We performed the encoding through linear mapping from minimum and maximum values of input data to a grey- level range in the SLM. More details are described in Methods. In addition, we precisely aligned all SLMs with respect to each other within a range of a few pixels on the order of hundreds of \(\mu \mathrm{m}\) ; see Supplementary Fig. 5. Although the long optical path in the system makes the alignment sensitive to external variations, the system's full reconfigurability can enable fast adaptive pixel- by- pixel re- alignment. Figure 5b shows output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture (Fig. 1a) obtained from model calculations and experimental measurements, showing good agreement and experimentally validating the feasibility of the ONE architecture in solving PDEs. More data is shown in Supplementary Fig. 6. There are some speckles in the background of measured images, which probably originate from high- order diffraction interference, leading to numerical errors in the ONE architecture for performing regression tasks. This discrepancy between models and experiments can be mitigated through hardware- software co- design, such as incorporating loss functions based on experimental results for gradient calculations as demonstrated in prior works [20, 33, 35].  
+
+<|ref|>text<|/ref|><|det|>[[207, 429, 831, 599]]<|/det|>
+We also evaluated the performance of the ONE architecture under different noise levels of optical XBAR structures. Specifically, we added random Gaussian noise with zero mean and varying standard deviation (Std) to the values obtained from matrix multiplications to represent hardware noise, such as shot noise in photodetectors [36]. The corresponding MVM results and histograms of different noise standard deviation values are shown in Supplementary Fig. 7, and more details can be found in Methods. As shown in Fig. 5c and Fig. 5d, the validation loss increases with the increasing noise standard deviation value. The current hardware implementation of optical XBAR structures with advanced components and calibration algorithms [16- 18], including the structure we demonstrated before [36], can achieve quite a small noise level similar or below the noise level corresponding to 0.5 Std. Hence, the noise influence in optical XBAR structures on the performance of the ONE architecture is not substantial.  
+
+<|ref|>text<|/ref|><|det|>[[207, 600, 831, 728]]<|/det|>
+We further estimated the potential throughput and power consumption of the ONE architecture implemented using optical computing hardware for inference. The throughput is mainly determined by the SLM refresh rate and camera frame rate. Current commercial SLMs and cameras can have rates \(>1000\mathrm{Hz}\) , meaning that the inference time for one instance is \(< 1\mathrm{ms}\) . In contrast, it typically takes minutes to hours to numerically solve PDEs. Hence, the ONE architecture features \(>10^{5}\) (five orders of magnitude) acceleration compared to typical PDE solvers. This throughput is also comparable to the state- of- art ML model, such as FNO with a \(5\mathrm{ms}\) inference time [24]. Moreover, the system throughput can be substantially improved with device
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 86, 790, 201]]<|/det|>
+innovation. For example, an electro-optic SLM based on organic molecules can achieve \(> \mathrm{GHz}\) switching speed [37], and an ultrafast camera can achieve a trillion frames per second [38]. With these devices, the ONE architecture can achieve an inference time \(< 1 \mathrm{ns}\) . The power consumption is mainly determined by the leakage current of liquid crystal cells in SLMs. Because of the dielectric nature of liquid crystals and their high leakage resistance, the leakage current is typically \(< 1 \mu \mathrm{A}\) . Hence, assuming a \(10 \mathrm{V}\) driving voltage, the static power consumption of SLMs is \(\sim 10 \mu \mathrm{W}\) , which is nearly \(10^{7}\) (seven orders of magnitude) smaller than typical GPU inference power \(\sim 100 \mathrm{W}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 216, 290, 234]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[165, 244, 790, 359]]<|/det|>
+We have demonstrated the ONE architecture and validated its performance in solving a broad range of PDEs in diverse scientific domains. The ONE architecture is versatile and can be modified to reduce the interface and connection between DONN and optical XBAR structures and facilitate the hardware implementation of the whole system. Further, in a whole system, active learning and noise- aware training can be incorporated to mitigate the discrepancy between models and practical systems for accurate deployment. Moreover, in addition to solving PDEs, the ONE architecture can be tailored to accelerate ML models for other regression problems.  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 373, 270, 392]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[165, 405, 789, 435]]<|/det|>
+DONN diffraction model – The diffraction impulse function \(h(x, y)\) was described using the Fresnel equation as  
+
+<|ref|>equation<|/ref|><|det|>[[385, 446, 567, 476]]<|/det|>
+\[h(x,y) = \frac{e^{ikz}}{i\lambda z} e^{\frac{ik}{2z} (x^{2} + y^{2})},\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 487, 790, 604]]<|/det|>
+where \(\lambda\) is the wavelength, \(k = 2\pi /\lambda\) is the free- space wavenumber, \((x, y)\) are positions within a plane perpendicular to the wave propagation direction, \(z\) is the distance along the propagation direction, and \(i\) is the imaginary unit. The 2D Fourier transformation was directly performed on \(h(x, y)\) for model training and evaluation. To match the experimental setup as described below, \(h(x, y)\) was first discretized with respect to a defined rectangular mesh grid in the convolution calculation and then converted into the Fourier space through 2D Fourier transformation. More details can be found in our prior work [21].  
+
+<|ref|>text<|/ref|><|det|>[[165, 606, 790, 736]]<|/det|>
+The operation mechanism of optical XBAR structures – Supplementary Fig. 1a shows the detailed schematic of an integrated photonic XBAR structure. Specifically, the element values of a \(n \times 1\) input vector \(\mathbf{v}\) are represented by the intensities of light at input waveguides, \(\{I_{1}, I_{2}, I_{3}, \ldots , I_{n}\}\) , which can be implemented by modulating an equally distributed laser intensity through a \(n \times 1\) array of electro- optic modulators (red squares in Supplementary Fig. 1a) at input waveguides. The light on each row waveguide is then equally distributed to the column waveguides connected to that row waveguide and modulated through an electro- optic modulator on the coupled curved waveguide (yellow squares in Supplementary Fig. 1a). The element values of a \(m \times n\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[207, 86, 832, 187]]<|/det|>
+matrix \(\mathbf{M}\) are represented by the transmittance of modulators on curved waveguides, \(\{T_{i j}\} ,i\in [1,m],j\in [1,n]\) . At the end of each column waveguide, a photodetector collects all light intensity passing through the column waveguide. The obtained photocurrents or photovoltages of a \(m\times 1\) photodetector array represent the summation of multiplied input vector light intensity and matrix modulator transmittance, and the element values of output vector \(\mathbf{o}\) , \(O_{j} = \sum_{s = 1}^{n}T_{j s}I_{s},j\in [1,m]\) . Hence, this integrated photonic XBAR structure can implement MVM in the optical domain.  
+
+<|ref|>text<|/ref|><|det|>[[207, 187, 832, 343]]<|/det|>
+Similarly, Supplementary Fig. 1b shows the detailed schematic of a free- space optical XBAR structure. Specifically, the element values of a \(n\times 1\) input vector \(\mathbf{v}\) are represented by the intensities of light, \(\{I_{1},I_{2},I_{3},\dots,I_{n}\}\) , which is implemented through a \(n\times 1\) array of free- space vector SLM. The output light is broadcast to a \(m\times n\) array of matrix SLM through lenses so that the light distribution from vector SLM is identical at each column of matrix SLM. The element values of a \(m\times n\) matrix \(\mathbf{M}\) are represented by the transmittance of matrix SLM, \(\{T_{i j}\} ,i\in [1,m],j\in [1,n]\) . Lenses are then used to focus the output light from each modulator on the same column of matrix SLM to a photodetector. The readings from a \(m\times 1\) photodetector array represent the element values of output vector \(\mathbf{o}\) , \(O_{j} = \sum_{s = 1}^{n}T_{j s}I_{s},j\in [1,m]\) . Hence, this free- space optical XBAR structure can also implement MVM in the optical domain.  
+
+<|ref|>text<|/ref|><|det|>[[207, 346, 832, 532]]<|/det|>
+ONE architecture model – The ONE architecture model was constructed with two main modules – the DONN module processing data in the Fourier space and the optical XBAR module processing linear operations. The mathematical operations in DONN and optical XBAR structures have been described before and their accurate models have been implemented in our prior works, closely matching experimental results [21, 36]. Briefly, the DONN module was modeled by combining the Fresnel free- space diffraction with phase- only spatial light modulation in a range of \([0,2\pi ]\) in the model and coupled spatial light modulation as shown in Supplementary Fig. 4; the optical XBAR module was represented as matrix multiplication incorporating measurement noise. Both modules were implemented under the PyTorch 1.12 framework with graphics processing unit (GPU)- accelerated parallel computation and gradient backpropagation for training. The GPU used in this work was an Nvidia RTX 6000 card.  
+
+<|ref|>text<|/ref|><|det|>[[207, 535, 832, 578]]<|/det|>
+Darcy flow equation dataset and training – A 2D Darcy flow equation on the unit box was employed as described in detail in Ref. [24]. The corresponding PDE is a second- order, linear, elliptic PDE as  
+
+<|ref|>equation<|/ref|><|det|>[[277, 591, 757, 627]]<|/det|>
+\[-\nabla \cdot (k(x,y)\nabla u(x,y)) = f(x,y), \qquad x\in (0,1),y\in (0,1),\] \[u(x) = 0, \qquad x\in \partial (0,1),y\in \partial (0,1)\]  
+
+<|ref|>text<|/ref|><|det|>[[207, 639, 832, 739]]<|/det|>
+with a Dirichlet boundary condition. We used the Darcy flow dataset from the existing dataset in Ref. [24] with a boundary condition \(u(x,y) = 0\) on domain edges. The coefficient \(k(x,y)\) was generated based on a specific distribution with the value 12 for positive inputs and 3 for negative inputs. The forcing term was fixed at \(f(x,y) = 1\) . The solution \(u(x,y)\) was computed using a second- order finite difference method on a \(421 \times 421\) grid, and other resolutions were obtained with downsampling. We used a \(10:1\) ratio for the numbers of data in the training set and validation set, respectively.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 86, 790, 129]]<|/det|>
+The model was trained with a total of 600 epochs and a batch size of 40. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+<|ref|>text<|/ref|><|det|>[[165, 133, 790, 176]]<|/det|>
+Magnetostatic Poisson's equation dataset and training – The demagnetizing field \(\mathbf{H}\) originates from the magnetization within the material itself, which can be calculated as the convolution of \(\mathbf{M}\) with the demagnetization tensor \(\mathbf{N}\) as  
+
+<|ref|>equation<|/ref|><|det|>[[368, 188, 586, 217]]<|/det|>
+\[\mathbf{H}(\mathbf{r}) = \int \mathbf{N}(\mathbf{r} - \mathbf{r}^{\prime})\mathbf{M}(\mathbf{r}^{\prime})d\mathbf{r}^{\prime}.\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 226, 790, 414]]<|/det|>
+This convolution was computed through Fourier space representations of fields. Specifically, to create the dataset, we utilized the MagneX solver [39] to simulate the time evolution of magnetization in a thin magnetic film with dimensions of \(500 \times 125 \times 3.125 \mathrm{~nm}\) . The modeling incorporated both demagnetization and exchange interactions. Initially, we relaxed the magnetic field into a stable S- state before subjecting the system to varying external magnetic fields in different scenarios. We uniformly sampled 8 bias \(\mathbf{H}\) fields in the \(x\) and \(y\) directions, each with a magnitude of 19872 A/m. The system evolved for 1 ns, during which we collected paired data of \(\mathbf{M}\) and \(\mathbf{H}\) fields. Each field was represented by three channels corresponding to the field components in \(x\) , \(y\) , and \(z\) directions. The dataset was divided into training and testing sets with an \(8:2\) ratio. The training was conducted over 500 epochs with a batch size of 128. The learning rate was set to 1.0 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+<|ref|>text<|/ref|><|det|>[[165, 417, 790, 475]]<|/det|>
+Navier- Stokes equation dataset and training – A 2D Navier- Stokes equation for a viscous, incompressible fluid in vorticity form on the unit torus was used to generate spatiotemporal data for training the ONE architecture. The details are described in Ref. [24]. Specifically, the PDEs are  
+
+<|ref|>equation<|/ref|><|det|>[[165, 487, 835, 542]]<|/det|>
+\[\partial_{t}w(x,y,t) + u(x,y,t)\cdot \nabla w(x,y,t) = v\Delta w(x,y,t) + f(x,y),x\in (0,1),y\in (0,1),t\in (0,T]\] \[\nabla \cdot u(x,y,t) = 0,x\in (0,1),y\in (0,1),t\in (0,T]\] \[w(x,y,0) = w_{0}(x,y),x\in (0,1),y\in (0,1),\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 551, 790, 666]]<|/det|>
+where \(w_{0}(x,y)\) is the initial vorticity and boundary conditions were used. We utilized the existing dataset with the viscosity coefficient \(v = 10^{- 3}\) from Ref. [24] for training and inference. The samples in the dataset were recorded with a time step of \(10^{- 4}\) s. We used 1000 data as the training set and 100 data as the validation set. We trained the ONE architecture model with the first 10 vorticity fields \((w(x,y,t))\) to predict the time evolution of the next 10 vorticity fields. The model was trained with a total of 600 epochs and a batch size of 40. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+<|ref|>text<|/ref|><|det|>[[165, 669, 790, 741]]<|/det|>
+Maxwell's equations dataset and training – We employed commercial Ansys Lumerical finite- difference- time- domain simulation software to generate an electric field dataset by solving Maxwell's equations in dielectric metasurfaces. Specifically, the dielectric metasurface had a periodic pattern and we used four silicon cylindrical rods as the unit cell and periodic boundary condition. Data were generated by randomly
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[207, 86, 832, 201]]<|/det|>
+selecting the radii of four cylindrical rods. The radius was chosen from \(39.5\mu \mathrm{m}\) to \(44.5\mu \mathrm{m}\) with a step of \(0.25\mu \mathrm{m}\) . The simulation time was set as 300000 fs. We generated a total of 1200 data and used 1000 as the training set and the rest 200 as the validation set. The model was trained in an auto- regressive style for the \(E_{x}\) component processing. The \(E_{x}\) field data between 300000 fs to 160000 fs was backward fed into to the model to predict the next 40000 fs \(E_{x}\) field data. The model was trained with a total of 500 epochs and a batch size of 20. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.  
+
+<|ref|>text<|/ref|><|det|>[[207, 204, 832, 475]]<|/det|>
+Multiphysics dataset and training – We employed commercial COMSOL Multiphysics finite- element simulation software to generate a temperature profile dataset by solving coupled electric current and heat transfer PDEs in an electrical heating circuit. The circuit details can be found in Ref. [40]. Concisely, the circuit contained a serpentine- shaped Nichrome resistive layer with \(10\mu \mathrm{m}\) thick and \(5\mathrm{mm}\) wide on top of a glass plate. A silver contact pad with a dimension \(10\mathrm{mm}\times 10\mathrm{mm}\times 10\mu \mathrm{m}\) was attached at each end. The deposited side of the glass plate was in contact with the surrounding air at \(293.15\mathrm{K}\) and the back side was in contact with the heated fluid at \(353\mathrm{K}\) . Two coupled physics modules, electrical current in layered shells and heat transfer in layered shells, were used in COMSOL simulations. The input voltage pulse height was set from 5 to \(25\mathrm{V}\) with a step of \(1\mathrm{V}\) and the pulse width was set from 20 to \(60\mathrm{s}\) with a step of \(1\mathrm{s}\) . The simulation time range was from 0 to \(110\mathrm{s}\) . We generated a total number of 861 data and divided the data into training and testing set with the splitting ratio of \(8:2\) . The ONE architecture took the electric current layer data as the input spatiotemporal data and the input voltage pulse information was fed into the physics parameter data processing branch to predict temperature field data at \(55\mathrm{s}\) . The model was trained with a total of 100 epochs and a batch size of 40. The learning rate for the trainable parameters in DONNs was 0.1 and the learning rate for all other trainable parameters was 0.001 with the Adam optimizer.  
+
+<|ref|>text<|/ref|><|det|>[[207, 479, 832, 678]]<|/det|>
+DONN experimental setup and alignment – The photo and schematic diagram of the DONN experimental setup are displayed in Fig. 5a. The laser diode with a center wavelength \(532\mathrm{nm}\) (CPS532 from Thorlabs, Inc.) was used as a source. The distance between SLMs and between the last SLM and camera was set as \(25.4\mathrm{cm}\) . The polarizers and half- wave plates before and after each SLM were configured so that each SLM operated with a strong modulation of the transmitted electric field phase (phase mode) together with a moderate modulation of light amplitude. The experimentally measured amplitude and phase modulation responses of three SLMs are shown in Supplementary Fig. 4. All transmissive SLMs are the LC 2012 model from HOLOEYE Photonics AG with a refresh rate of \(60\mathrm{Hz}\) . The analog- to- digital converter has 8- bit precision for liquid crystal driving voltage, so that the grey level of SLMs is from 0 to 255. The pixel size of SLMs is \(36\mu \mathrm{m}\times 36\mu \mathrm{m}\) . The output data was captured on a CMOS camera with a frame rate of 34.8 frames per second (CS165MU1 from Thorlabs, Inc.).  
+
+<|ref|>text<|/ref|><|det|>[[207, 679, 832, 735]]<|/det|>
+We aligned the DONN setup by loading standard images on SLMs and comparing experimental results with simulation. Specifically, as shown in Supplementary Fig. 5a, standard Gaussian images, which were centered with a peak at 255 grey level and with a standard deviation of 6 pixels, were loaded in the input SLM and two diffractive
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 86, 790, 187]]<|/det|>
+SLMs. Supplementary Fig. 5b displays the simulation pattern for the perfectly aligned setup. During the alignment process, loaded images were moved up, down, left, and right pixel- by- pixel to match the captured images by the camera with the simulation pattern. Supplementary Fig. 5c displays the matched experimental diffraction pattern when the optical setup was aligned, while Supplementary Fig. 5d shows misaligned patterns when there was five- pixel misalignment in vertical and horizontal directions, respectively.  
+
+<|ref|>text<|/ref|><|det|>[[165, 190, 790, 374]]<|/det|>
+DONN experimental training with reparameterization – The discrete look- up tables of device responses shown in Supplementary Fig. 4 break the gradient backpropagation in the ML training process in PyTorch. To solve this challenge, we utilized a differentiable reparameterization Gumbel- softmax technique, which was first introduced in Ref. [41] and demonstrated in our prior work [21]. Specifically, continuous noise from the Gumbel distribution was added to the discrete distribution. The argmax function was then used to find the optimized sample. The training problem after this Gumbel- argmax process is mathematically equivalent to the original training problem under one- hot representation [41]. Since the argmax function still breaks the gradient chain, it was replaced with the softmax function to enable differentiability. Hence, this Gumbel- softmax technique, which is also available in PyTorch, offers continuous and differentiable approximation to discrete distributions and the gradient can backpropagate to reduce the loss function.  
+
+<|ref|>text<|/ref|><|det|>[[165, 377, 790, 450]]<|/det|>
+DONN experimental grey- level encoding – The global minimum and maximum values in input 2D data were calculated as \(d_{\mathrm{min}}\) and \(d_{\mathrm{max}}\) . A grey level range from 130 to 255 in the input encoder SLM was selected for a relatively large amplitude modulation range to have enough contrast. Hence, any value \(d\) in the input 2D data was converted into a grey level through a linear mapping as  
+
+<|ref|>equation<|/ref|><|det|>[[364, 464, 589, 496]]<|/det|>
+\[d = \operatorname {int}\left(\frac{255 - 130}{d_{\mathrm{max}} - d_{\mathrm{min}}} + 130\right),\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 505, 790, 535]]<|/det|>
+where the int(·) operation rounded the expression to the nearest integer since the SLM grey level must be an integer.  
+
+<|ref|>text<|/ref|><|det|>[[165, 537, 790, 653]]<|/det|>
+Optical XBAR noise – The MVM results from an optical XBAR structure were uniformly randomly generated in a range of \(- 15\) to 15, which was the value range in the ONE architecture for solving the Darcy flow equation. The expected number \(o\) was then added with a randomly generated noise from a Gaussian distribution with a zero average and varying standard deviation. The noise- dressed number \(\bar{o}\) was used in ONE architecture calculations. Under different noise standard deviation levels, Supplementary Fig. 7a demonstrates \(\bar{o}\) with respect to \(o\) and Supplementary Fig. 7b displays histograms of \(\bar{o} - o\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 666, 361, 686]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[165, 695, 790, 725]]<|/det|>
+Upon publication, all data that support the plots within this paper and other findings of this study will be available on a public GitHub repository.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[207, 82, 406, 101]]<|/det|>
+## Code availability  
+
+<|ref|>text<|/ref|><|det|>[[207, 111, 831, 140]]<|/det|>
+Code availabilityUpon publication, all codes that support the plots within this paper and other findings of this study will be available on a public GitHub repository.  
+
+<|ref|>sub_title<|/ref|><|det|>[[208, 153, 433, 172]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[207, 181, 832, 325]]<|/det|>
+AcknowledgementsR.C., C.Y., and W.G. acknowledge support from the National Science Foundation through Grants No. 2235276, No. 2316627, and No. 2428520. M.L., J.F., and W.G. also acknowledge support from the University of Utah start- up fund. Y.T., Z.Y., and A.N. were supported by Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE- AC02- 05CH11231. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE- AC02- 05CH11231 and under NERSC GenAI award under No. DDR- ERCAP0030541.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 338, 597, 357]]<|/det|>
+## Author Contributions Statement  
+
+<|ref|>text<|/ref|><|det|>[[207, 366, 832, 437]]<|/det|>
+Author Contributions StatementY.T. and W.G. conceived the idea and W.G. supervised the project. Y.T. constructed models and performed machine learning calculations with the help of M.L., J.F., and C.Y and under the support of A.N., Z.Y., and W.G. R.C constructed an optical experimental setup, performed experiments, and performed numerical calculations under the supervision of W.G. Y.T. and W.G. wrote the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 450, 580, 470]]<|/det|>
+## Competing Interests Statement  
+
+<|ref|>text<|/ref|><|det|>[[207, 480, 530, 494]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 507, 335, 525]]<|/det|>
+## References  
+
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+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[206, 85, 831, 115]]<|/det|>
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+
+<--- 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, 179, 149]]<|/det|>
+- SIFinal.pdf
+
+<--- Page Split --->

preprint/preprint__07bb49d179d74a99cfca97aa544930e840ce529d98ed5ba46742687ced243ffc/images_list.json

@@ -0,0 +1,101 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. FTIR spectra (a), XRD pattern (b) of pristine PA1 (—), PA2 (—), PA3 (—) and TA (—). SEM micrographs of PA1 (c), PA2 (d), PA3 (e), and TA (f).",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Absorbance spectra of ninhydrin complexes of spermine before (—■—) and after adsorption of putrescine (—●—), spermidine (—▲—), spermine (—▼—), tryptamine (—◆—), tryptophan (—★—), followed by ninhydrin treatment, PA1 (a) and PA2 (b), PA3 (c), and TA (d). Absorbance spectra of the ninhydrin complexes of other amines are given in the supporting information (Figure S2), which also showed the same adsorption maxima. The inset images show the optical images of the ninhydrin complexes of spermine (i) before and (ii) after extractions with different PAs. PA absorbents (25 mg) were used for the extraction of amine solution at a concentration of 50 mg/L. All adsorption experiments were conducted at pH 7 and \\(22^{\\circ}\\mathrm{C}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        285,
+        880,
+        727
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Percentage removal efficiencies of putrescine (—), spermidine (—), spermine (—), tryptamine (—), tryptophan (—) of PA1 (a), PA2 (b), PA3 (c) and TA (d) polyaramides at different dosages. The extraction was done at room temperature for 300 min, and the amine concentrations were kept constant (50 mg/L). .All adsorption experiments were conducted at pH 7 and \\(22^{\\circ}C\\)",
+    "footnote": [],
+    "bbox": [
+      [
+        137,
+        81,
+        857,
+        504
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Effect of time \\((15 - 300\\mathrm{min})\\) and concentration \\((5 - 150\\mathrm{mg / L})\\) of putrescine ( \\(\\bullet\\) -), spermidine ( \\(\\bullet\\) -), spermine ( \\(\\bullet\\) -), tryptamine ( \\(\\bullet\\) -) and tryptophan ( \\(\\bullet\\) -) on removal efficiency, PA1 (a, b), PA2 (c, d), PA3 (e, f) and TA (g, h). The amount of all PAs used for the adsorption experiments was kept constant at \\(25\\mathrm{mg}\\) .",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Langmuir (a, c, e and g) and pseudo-second-order kinetics (b, d, f and h) plots for PA1 (a, b), PA2 (c, d), PA3 (e, f), TA (g, h) at neutral pH and 298 K using different concentrations (5 - 150 mg/mL) of the putrescine (- - -), spermidine (- - -), spermine (- - -), tryptamine (- - -) and tryptophan (- - -) and a fixed concentration of absorbents (25 mg). The Freundlich isotherm and pseudo-first order kinetic regressions for PAs 1 - 3 and TA, are given in the supporting information (Figure S3).",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. Removal efficiencies of PA 1 - 3 after repeated adsorption-desorption cycles (cycle 1 (■), cycle 2 (■), cycle 3 (■), cycle 4 (■), and cycle 5 (■)). The concentration of putrescine (a), spermidine (b), spermine (c), and tryptamine (d) used was \\(50 \\mathrm{mg / L}\\) , a time of \\(300 \\mathrm{min}\\) , and an adsorbent dose of \\(25 \\mathrm{mg}\\) was kept constant. The regeneration data of PA 1 - 3 after adsorption of tryptophan are given in the supporting information (Figure S6). The regeneration data for TA using all amines are given in the supporting information (Figure S7).",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        312,
+        880,
+        800
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. (a) UV-Vis spectra of the ninhydrin treated extracts obtained from fish sample kept at different time points of 6 h, 24 h, and 48 h at room temperature before (6 h (-), 24 h (-), 24 h (-)) and after (6 h (-), 24 h (-), and 48h (-)) extraction with PA 1-3 samples (25 mg). Note that the absorbance of solutions after extraction with PA was almost zero, indicating a complete removal of amines. (b) The extraction efficiencies of PAs (50 mg) for the removal of amines from solutions collected after keeping the fish samples for 6 h, 12 h, and 24 h at room temperature. The extraction time was kept at 5 h for all samples. (c) LC traces of extract collected from fish sample (2 g) after 48 h at room temperature. Optical images of fish samples (2 g) and LCMS traces of 6h and 24 h fish extracts are given in the supporting information (Figure S8).",
+    "footnote": [],
+    "bbox": [
+      [
+        60,
+        155,
+        870,
+        655
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Scheme 2. The complexation and extraction behaviour of PA with amines from solution",
+    "footnote": [],
+    "bbox": [
+      [
+        118,
+        95,
+        820,
+        380
+      ]
+    ],
+    "page_idx": 17
+  }
+]

preprint/preprint__07bb49d179d74a99cfca97aa544930e840ce529d98ed5ba46742687ced243ffc/preprint__07bb49d179d74a99cfca97aa544930e840ce529d98ed5ba46742687ced243ffc.mmd

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+
+# Engineered Polyaramides for Extraction of Bioamines from Water  
+
+Gomathi Mahadevan National University of Singapore Suresh Valiyaveettil chmsv@nus.edu.sg  
+
+National University of Singapore  
+
+## Article  
+
+Keywords: Polyaramide, biogenic amines, extraction, adsorption efficiency, LCMS, environmental matrix  
+
+Posted Date: August 11th, 2025  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 7238623/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 October 21st, 2025. See the published version at https://doi.org/10.1038/s41598- 025- 20410- 1.
+
+<--- Page Split --->
+
+# Engineered Polyaramides for Extraction of Bioamines from Water  
+
+Gomathi Mahadevan and Suresh Valiyaveettil\*  
+
+Department of Chemistry, National University of Singapore  3 Science Drive 3, Singapore 117543  Email: chmsv@nus.edu.sg  
+
+## Abstract  
+
+Biogenic amines (BAs) are prevalent in fermented foods, protein- rich meats, and brewed food additives. High concentrations of BAs can induce health issues such as headaches, high blood pressure, and palpitations. Polyaramides (PAs) prepared from the reaction of trimesoyl chloride with ethylene diamine (ED), \(p\) - xylene diamine (PXD), and \(m\) - xylene diamine (MXD) and characterized using different characterization techniques, FTIR, XRD, SEM, TGA, and DLS measurements. All PAs were used for the removal of five biogenic amines (i.e., putrescine, spermidine, spermine, tryptamine, and tryptophan) from water. All PAs showed high removal efficiencies for biogenic amines, and the data collected fit well with the Langmuir isotherm and pseudo- second- order kinetic models. Among three different polymers, PA3 showed exceptional adsorption capacities, achieving removal efficiencies of \(97.1 \pm 0.24\%\) (putrescine), \(99 \pm 0.68\%\) (spermidine), \(99.6 \pm 0.23\%\) (spermine), \(99 \pm 1.68\%\) (tryptamine), and \(97 \pm 0.08\%\) (tryptophan) at an equilibrium concentration of \(25 \mathrm{mg}\) PA and an adsorption time of 300 minutes. Furthermore, adsorbent regeneration was established via washing with an acid solution, and the removal efficiency was retained after five cycles of repeated washings and extractions. As a proof of concept, the synthesized PAs were used to extract the amines from a decaying fish sample for different periods, which showed \(99\%\) extraction and removal efficiencies. The chemical nature of the extracted BAs was identified using LCMS. Such synthetic polyaramides for removing pollutants from environmental matrices are interesting candidates for developing functional materials.  
+
+Keywords: Polyaramide, biogenic amines, extraction, adsorption efficiency, LCMS, environmental matrix.
+
+<--- Page Split --->
+
+## Introduction  
+
+The freshness of meat or fish products in the market is difficult to measure, owing to the lack of suitable fast and reliable methods. Biogenic amines (BAs) such as cadaverine, putrescine, spermidine, spermine, phenylethylamine, tyramine, and histamine are present or generated in biological samples with aging or under stress. \(^{1,2}\) The production of BAs is primarily a result of the decarboxylation of amino acids catalysed by microorganisms. \(^{3}\) Microbial species in the environment degrade the biological tissues to release small molecular metabolites, including significant amounts of BAs. \(^{4}\) A high concentration of BAs in human body fluids causes health issues, such as asthma, headaches, and irregular blood pressure. \(^{5,6}\) Many aged foods, such as fish, wine, beer, meat products, and fermented foods, contain BAs, which accumulate with time due to microbial degradation. \(^{7}\) BAs from decaying old food products or effluents from fish markets or butcheries end up in local water bodies, posing adverse health risks to living organisms. \(^{6,8}\) Furthermore, studies have demonstrated that BA accumulates in algae during summertime blooming, which results in an abrupt increase in the concentration of amines in marine or coastal locations. \(^{1,9}\) A few reports are available on the extraction and identification of BAs from decaying fish samples by using the HPLC technique. \(^{5,10}\)  
+
+New functional materials and methodologies are needed for the detection, removal, and quantification of the BAs from water. \(^{11,12}\) A few materials were used to detect the presence of biogenic amines in food and water. \(^{13 - 15}\) However, removing amines or other metabolites from different raw food materials has not been well studied due to the complexity of the matrix. Amines such as putrescine and spermine were extracted and removed from meat products using absorbents such as iron oxide and graphene, but multiple treatments were necessary to achieve high removal efficiencies. \(^{16 - 18}\)  
+
+Water pollution caused by various contaminants such as heavy metals, pesticides, biological waste, and industrial chemicals poses a significant threat to human health and the environment. \(^{4}\) In recent years, polyamides have emerged as a promising material for water purification technology. Polyamides, a class of synthetic polymers, are widely employed in various industrial applications due to their excellent mechanical properties, thermal stability, and chemical resistance. \(^{19 - 21}\) Here, we use synthetic, highly branched polyamides (PAs) for the removal of BAs from spiked water samples to develop a purification system for future applications (Scheme 1).
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+  
+
+Scheme 1. Synthetic scheme (a) of PAs 1- 3 and triamide (TA), and chemical structure (b) of amines used for the extraction.  
+
+In our design strategy, the electron- deficient amide groups, hydrophobic interactions, and the network structure of PA were employed for the extraction of organic amines from water. Our objectives include the extraction of amines from an aqueous environment and understanding the structure- property correlations of the three PAs. The synthetic strategy includes trimesoyl chloride (TMC) as a trifunctional monomer and one of the linear ethylene diamine (ED), \(p\) - xylene diamine (PXD), and bend \(m\) - xylene diamine (MXD) for the synthesis of PAs (Scheme 1a). Ethylene diamine (ED) is a flexible linear molecule, whereas aromatic amines such as \(p\) - xylene diamine (PXD) and \(m\) - xylene diamine (MXD) are rigid molecules. A
+
+<--- Page Split --->
+
+model triamide (TA) was prepared using TMC and aniline (AN) for comparison of structure and properties. All three PAs with different structural features were utilized for the removal of BAs such as putrescine (i), spermidine (ii), spermine (iii), tryptamine (iv), and tryptophan (v), from water (Scheme 1b). The amide groups inside the polymer lattice are electron-deficient moieties and interact strongly with electron-rich pollutants (e.g. amines, anions) through electrostatic interactions. Impact of experimental factors such as concentration of PAs and amines, extraction time on adsorption efficiency, isotherm and kinetic model treatments of the data, regeneration of PAs, proof- of- concept demonstration of extracting amines from decaying fish sample, comparison of PAs with other adsorbents towards amine extraction, and mechanism of extraction are discussed in this manuscript. Although many polyamides have been reported in the literature, \(^{10,13,21}\) the PAs discussed here demonstrate significant efficiency towards the extraction of biogenic amines, making them suitable for separation and purification technologies.  
+
+## Materials and Methods  
+
+1,3,5- Trimesoyl chloride (TMC), ethylenediamine (ED), \(p\) - xylenediamine (PXD), \(m\) - xylenediamine (MXD), aniline, dimethylformamide (DMF, HPLC grade), and triethylamine (TEA) were purchased from Sigma Aldrich Pte Ltd. All chemicals were used as received without any further purification. Deionized water was used throughout the experiments. A Bruker ALPHA FT- IR spectrophotometer was used to record the FTIR spectra (500 – 4000 cm\(^{- 1}\)) both before and after the extraction of amines using KBr as the matrix. The size and surface charges of the materials were measured using the Malvern Zetasizer Nano- ZS90. The thermogravimetric analyses (TGA) were done using a Discovery TGA apparatus in a nitrogen atmosphere within the 25 – 1000 °C temperature range and a heating rate of 10 °C/min. The UV- Vis spectra of every sample were recorded using a Shimadzu- 1601 spectrophotometer. The synthesized PA’s morphologies were established using a JEOL JSM- 6701F scanning electron microscope (SEM). The crystallinity of the polyaramides was investigated with the help of a Bruker D8 Advance Powder Crystal X- ray diffractometer with Cu Kα radiation (λ = 0.154 nm) operating at 40 kV and 40 mA within the 20 range of 5 - 70°.  
+
+## Synthesis and Characterisation of PAs  
+
+All polyaramides (PAs) and the control molecules were synthesized and fully characterized using the reported procedures. \(^{22}\) Full details on the synthesis and characterisation of the PAs are given in the supporting information.
+
+<--- Page Split --->
+
+## Removal of Amines Using PAs  
+
+Commercially available amines (putrescine, spermidine, spermine, tryptamine, and tryptophan) were dissolved in Milli- Q water to prepare a stock solution (50 mg/L) and used for extraction studies. The extraction was carried out at room temperature (22 °C) and a neutral pH of 7. A calibration curve was prepared after mixing the amine solution of different concentrations with an appropriate amount of ninhydrin solution. Ninhydrin reacts with the amines to form a blue adduct, whose concentration is monitored using UV- Vis spectroscopy to quantify the amount of amine in the solution. Different amounts of PA absorbent (2- 50 mg) were added to the amine solution (6 mL), and the extraction was carried out for 300 min. The solution was centrifuged, and the supernatant was mixed with dilute ninhydrin solution (0.01M) to get a blue- colored solution after 30 min at pH 8. \(^{10}\) UV- Vis spectra of the blue solutions were recorded, and the concentration of amine was determined from a calibration curve. The removal efficiency was calculated from the spectroscopic data obtained before and after extraction using equation (1). \(^{23}\)  
+
+\[\mathrm{Removal~efficiency~(\mathrm{RE})} = \frac{\mathrm{C_0 - C_e}}{\mathrm{C_0}}\cdot \mathrm{X}100\% \quad (1)\]  
+
+where \(\mathrm{C_0}\) (mg/L) is the initial concentration and \(\mathrm{C_e}\) (mg/L) is the equilibrium concentration of amines.  
+
+## Isotherm and Kinetic Model Studies  
+
+The amines were extracted using an optimized amount (25 mg) of PA absorbents from dilute solutions (6 mL) containing varying concentrations (5 - 150 mg/L). Adsorption studies were repeated three times for each concentration, and the average value was reported. The collected data were used to analyse the common adsorption models, such as the Langmuir and the Freundlich isotherm models. The Langmuir isotherm model (Equation 2) fits the data well, indicating the formation of continuous monolayers on the surface of the PAs. \(^{24}\)  
+
+\[\mathrm{Q_e} = \frac{\mathrm{Q_{max}}\mathrm{K_L}\mathrm{C_e}}{1 + \mathrm{K_L}\mathrm{C_e}} \quad (2)\]  
+
+\(\mathrm{Q_{max}}\) (mg/g) is the maximum adsorption capacity of amines, and \(\mathrm{Q_e}\) (mg/g) is the equilibrium adsorption capacity. The equilibrium concentration is represented by the letter \(\mathrm{C_e}\) , and \(\mathrm{K_L}\) is the binding energy- related constant. Multilayer adsorption on heterogeneous surfaces is treated by the Freundlich empirical equation (3). \(^{24}\)
+
+<--- Page Split --->
+
+\[\mathrm{Q}_{\mathrm{e}} = \mathrm{K}_{\mathrm{F}}\mathrm{C}_{\mathrm{e}}^{1 / \mathrm{n}} \quad (3)\]  
+
+where \(\mathrm{C}_{\mathrm{e}}\) (mg/L) is the equilibrium concentration and \(\mathrm{Q}_{\mathrm{e}}\) (mg/g) is the adsorbent's quantity of absorbed amines per unit mass at equilibrium. \(\mathrm{K}_{\mathrm{F}}\) and \(\mathrm{n}\) represent adsorption capacity and intensity, respectively. In a linear form, Equation 3 could be extended as Equation 4.25  
+
+\[\mathrm{Log} \mathrm{Q}_{\mathrm{e}} = \log \mathrm{K}_{\mathrm{F}} + \frac{1}{n} \log C_{\mathrm{e}} \quad (4)\]  
+
+The PA (25 mg) was mixed with the appropriate amine solution (50 mg/ L, 6 mL) at room temperature and shaken mechanically for different time points (15 - 300 min). The solutions were centrifuged, and the collected supernatant was filtered. The filtrate was analyzed to determine the extraction efficiency of the PA towards the amine. The adsorption experiments were repeated three times for each concentration, and the average value was used for calculations. The extraction data were shown using the pseudo- first- order (Equation 5) and pseudo- second- order (Equation 6) kinetic models.26,27  
+
+\[\begin{array}{l}{\ln (\mathrm{q}_{\mathrm{e}} - \mathrm{q}_{\mathrm{t}}) = \ln \mathrm{q}_{\mathrm{e}} - \mathrm{k}_{1}\mathrm{t}}\\ {\frac{\mathrm{t}}{\mathrm{q}_{\mathrm{t}}} = \frac{\mathrm{t}}{\mathrm{q}_{\mathrm{e}}} +\frac{1}{\mathrm{k}_{2}\mathrm{q}_{\mathrm{e}}^{2}}} \end{array} \quad (5)\]  
+
+In this equation, \(\mathrm{q}_{\mathrm{e}}\) (mg/g) represents the amount of amine extracted at equilibrium, and \(\mathrm{q}_{\mathrm{t}}\) (mg/g) represents the number of pollutants absorbed at a given time t (min). The letters \(\mathrm{k}_{1}\) and \(\mathrm{k}_{2}\) are used to denote the rate constants in the pseudo- first- order and pseudo- second- order kinetic models. The slope and intercepts of the linear curves are used to calculate the values of \(\mathrm{k}_{1}\) , \(\mathrm{k}_{2}\) , and the adsorption capacity.  
+
+## Regeneration Studies  
+
+As described above, all synthesized PAs were used to extract different amines from the solution. The PAs with amines absorbed on the surface were regenerated using a dilute HCl solution (0.3 M, 10 mL). After acid washing, the PAs were washed with water to remove traces of acid on the surface, which was checked with pH paper. The thoroughly washed PAs were collected after filtration, dried at 70 °C, and used again for extracting the amines from water. The acid washings and amine extractions were successively done five times, and no significant changes in the removal efficiencies were observed.  
+
+## Biogenic Amine Extraction from Mackerel (Scomber Japonicus) Sample
+
+<--- Page Split --->
+
+To quantify the amount of biogenic amine generation over time due to microbial degradation, fresh fish tissues (2 g) purchased from a local supermarket were kept at room temperature (22°C) for different time durations (6 h, 24 h, and 48 h). After each exposure period, the fish tissue was subjected to a homogenization process with miliQ water (2 g, 10 mL) for 2 minutes. Subsequently, the homogenate was centrifuged for 10 minutes at 4 °C (5,000 rotations per minute) to obtain the supernatant. This extraction process was repeated once, and the resulting supernatants were combined and adjusted to a volume of 25 mL. The resulting extract was stored in a 50 mL centrifuge tube at 4 °C until further treatment. The extraction experiment was carried out by using the procedure mentioned above. Ninhydrin tests were used to quantify the extraction efficiency and the amine content before and after the extraction study.  
+
+## Liquid Chromatography - Mass Spectrometry (LCMS) Analysis  
+
+The mass spectra were obtained using the TSQ Quantum Discovery triple- quadrupole tandem mass spectrometer from Thermo Electron, coupled with a Surveyor high- performance liquid chromatography system from Thermo Finnigan. The system included a thermostated autosampler and a Phenomenex Gemini® 5 μm C18 110 Å 2.0 x 100 mm column kept at 30 °C, connected to a 4 × 2 mm polar RP precolumn from Phenomenex. A 5 μL sample was separated at a flow rate of 0.2 mL/min using a solvent system composed of water (A) and acetonitrile with 0.1% formic acid (B). A linear gradient was applied, increasing the concentration of B from 0% to 45% over 35 minutes and then to 100% over 13 minutes. The mass spectrometer operated in positive electrospray ionization mode (ESI+), with a spray needle voltage of 3.5 kV and a spray current of 5 μA.  
+
+## Results and Discussion  
+
+## Characterization of PAs  
+
+All polyaramides were synthesized and fully characterized using the reported literature procedures.28,29 The design criteria involve the use of A3 (i.e., trimesoyl chloride) and B2 (i.e., diamine) monomers to create a branched polyaramide architecture. The choice of three structurally different amines provides a 3D polyaramide architecture with a significant number of electron- deficient amide groups along the polymer chain. The polyaramides are synthesized with amines with different degrees of flexibility and structural geometries – linear (i.e., EA, PX) vs bent (i.e., MX) structures. Also, the polyaramides from A3 and B2 monomers provide a branched architecture. In the FTIR spectra, all synthesized PAs showed a broad peak from
+
+<--- Page Split --->
+
+3400 - 3485 \(\mathrm{cm^{- 1}}\) corresponding to the amide groups, peaks at \(3075\mathrm{cm^{- 1}}\) (C- H, aromatic), peaks around \(2925\mathrm{cm^{- 1}}\) and \(2852\mathrm{cm^{- 1}}\) representing the stretching vibrations of aliphatic - \(\mathrm{CH_2}\) along the polymer backbone (Figure. 1a). The strong peaks observed around \(1655\mathrm{cm^{- 1}}\) and \(1545\mathrm{cm^{- 1}}\) were assigned as \(>c = 0\) stretching of the amide group (i.e. amide I and amide II peaks). \(^{30,31}\) The other peaks in the FTIR spectra were accounted as \(1420\mathrm{cm^{- 1}}\) (in- plane bending vibration of \(>CH_2\) ), and \(720\mathrm{cm^{- 1}}\) ( \(>N\) - H stretching). \(^{30,31}\) The model compound TA showed a broad peak at \(3469 - 3525\mathrm{cm^{- 1}}\) , region and \(3252\mathrm{cm^{- 1}}\) for \(>N\) - H stretching vibration, peaks observed at \(3031\mathrm{cm^{- 1}}\) (Ar- H), and the peak position observed at \(2921\) and \(2843\mathrm{cm^{- 1}}\) for aliphatic - CH- stretching vibrations (Figure. 1a). The stretching vibrations of the \(>c = 0\) bond of the amide group were observed at \(1658\) and \(1545\mathrm{cm^{- 1}}\) . The peak positions at \(1446\) , \(1320\) , and \(722\mathrm{cm^{- 1}}\) indicated \(>CH_2\) in- plane bending vibration. \(^{31}\)  
+
+![](images/Figure_2.jpg)
+
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 1. FTIR spectra (a), XRD pattern (b) of pristine PA1 (—), PA2 (—), PA3 (—) and TA (—). SEM micrographs of PA1 (c), PA2 (d), PA3 (e), and TA (f). </center>  
+
+All three polymers showed broad XRD peaks at \(24.55^{\circ}\) (3.62 Å, PA1), \(24.28^{\circ}\) (3.66 Å, PA2), and \(24.94^{\circ}\) (3.56 Å, PA3) (Figure. 1b), which correspond to a disordered amorphous lattice. The small molecule showed many sharp XRD patterns at \(20 = 6.34^{\circ}\) (13.92 Å), \(12.64^{\circ}\) (6.99 Å), \(13.90^{\circ}\) (6.36 Å), \(21.18^{\circ}\) (4.19 Å), \(22.18^{\circ}\) (4.00 Å), which implies a highly crystalline lattice. The TGA data revealed that all polyamrides (PAs 1- 3) have excellent thermal stability, degrading at \(400 - 420^{\circ}\) C (Figure S1). From the TGA traces, the observed mass loss above \(400^{\circ}\) C was calculated as \(63.18 \pm 1.23\%\) (PA1), \(70.24 \pm 1.30\%\) (PA2), \(73.40 \pm 0.54\%\) (PA3), and \(75.33 \pm 0.10\%\) (TA) due to amide bond degradation. Since the TGA was done in a nitrogen atmosphere, the remaining solid could be a highly stable carbon analogue.  
+
+PAs 1 - 3 were dispersed in water and showed zetapotentials of \((- )7.56 \pm 2.23 \mathrm{mV}\) , \((- )12.58 \pm 0.34 \mathrm{mV}\) , and \((- )18.98 \pm 1.24 \mathrm{mV}\) . Such negative values are attributed to the presence of carboxylate groups (- COO\(^{- }\)) on the surface,\(^{34,35}\) which have emerged from the acyl group of TMC. Biogenic amines are protonated in water at a neutral pH of \(6 - 7.^{36,37}\) The zetapotentials measurement of amine dissolved in water showed positive zetapotentials of \((- )6.56 \pm 0.56 \mathrm{mV}\) (putrescine), \((- )7.23 \pm 1.55 \mathrm{mV}\) (spermidine), \((- )8.82 \pm 0.78 \mathrm{mV}\) (spermine), \((- )4.87 \pm 0.66\)
+
+<--- Page Split --->
+
+mv (tryptamine), and \((+1.87 \pm 0.34\) (tryptophan). The SEM images of PA1, PA2, and PA3 revealed spherical morphology structures (Figure 1c- e). However, the SEM images of crystalline small molecule TA showed a ribbon- type structure (Figure 1f).  
+
+## Extraction of Amines from Water  
+
+The synthesized PAs were used for the extraction of biogenic amines from water using a batch process and monitored using UV- Vis spectroscopy.  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 2. Absorbance spectra of ninhydrin complexes of spermine before (—■—) and after adsorption of putrescine (—●—), spermidine (—▲—), spermine (—▼—), tryptamine (—◆—), tryptophan (—★—), followed by ninhydrin treatment, PA1 (a) and PA2 (b), PA3 (c), and TA (d). Absorbance spectra of the ninhydrin complexes of other amines are given in the supporting information (Figure S2), which also showed the same adsorption maxima. The inset images show the optical images of the ninhydrin complexes of spermine (i) before and (ii) after extractions with different PAs. PA absorbents (25 mg) were used for the extraction of amine solution at a concentration of 50 mg/L. All adsorption experiments were conducted at pH 7 and \(22^{\circ}\mathrm{C}\) . </center>
+
+<--- Page Split --->
+
+The amine molecules present in the supernatant reacted with the carbonyl group of the ninhydrin and formed a blue- colored solution. The concentration of the complex and color of the solution are proportional to the amount of amine present in the solution. \(^{38}\) The intensity values at the adsorption maximum \((\lambda_{\mathrm{max}})\) is \(563 \mathrm{nm}\) in the UV- Vis spectra of the ninhydrin complex were measured, and the removal efficiencies of all PAs were calculated (Figure 2a- c). Strong electrostatic interactions between PAs and amines present in water facilitated the adsorption and enhanced the removal efficiencies \((\sim 96 - 99\%)\) . As expected, the removal efficiencies of the model compounds, triamide TA \((73.46 \pm 2.12\%)\) , Figure 2d, is lower than other PA polymers.  
+
+## Effect of Different Dosages  
+
+In a typical procedure, an appropriate concentration of amine solution \((50 \mathrm{mg / L}, 6 \mathrm{mL})\) was added to various amounts of PAs ranging from 2 to \(50 \mathrm{mg}\) . The extractions were carried out for \(300 \mathrm{min}\) , the mixture was centrifuged, and the remaining concentration of amine in the supernatant was determined using the ninhydrin test, and the extraction efficiency was reported in Figure 3a- d for PAs 1- 3 and TA. The maximum removal efficiencies (Equation 1) were obtained when the optimum amount of PAs \((25 \mathrm{mg})\) was used. PA1 (Figure 3a) showed removal efficiencies in the range of \(93.53 \pm 1.66 - 97.22 \pm 0.38\%\) , and PA2 (Figure 3b) showed \(93.48 \pm 0.70 - 98.74 \pm 0.12\%\) for the five amines tested. PA3 (Figure 3c) showed maximum removal efficiencies in the range of \(97.11 \pm 0.24 - 99.58 \pm 0.23\%\) for amines such as putrescine, spermidine, spermine, tryptamine, and tryptophan. The removal efficiencies of PAs remained constant, with a further increase in the adsorbent dosage of \(50 \mathrm{mg}\) due to the saturation of the surface. The saturation of the adsorbent surface occurs when all available active sites for adsorption are occupied by the target pollutants. When the adsorbate concentration is fixed, increasing the adsorbent amount increases adsorption efficiency by providing more active sites for binding. Initially, efficiency rises sharply with adsorbent dose, but increasing the adsorbent dose still increases the binding sites, and adsorption reaches equilibrium. However, beyond a certain dosage \((25 \mathrm{mg})\) , the removal efficiency is maximum because the pollutant concentration is fixed at \(50 \mathrm{mg / L}\) .
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 3. Percentage removal efficiencies of putrescine (—), spermidine (—), spermine (—), tryptamine (—), tryptophan (—) of PA1 (a), PA2 (b), PA3 (c) and TA (d) polyaramides at different dosages. The extraction was done at room temperature for 300 min, and the amine concentrations were kept constant (50 mg/L). .All adsorption experiments were conducted at pH 7 and \(22^{\circ}C\) </center>  
+
+To understand the role of dimensionality of polymers in the extraction of amines from water, a structurally similar triamide small molecule (TA) was prepared from trimesoyl chloride (A3) and aniline (B1), for comparison. The adsorption experiments with small molecule TA as control at different dosages (2 to \(50\mathrm{mg}\) ) (Figure 3d) showed lower efficiencies towards the extraction of amines. At a lower dosage (2 mg) of TA, putrescine, spermidine, spermine, tryptamine, and tryptophan were removed with low efficiencies in the range of 3.97 \(\pm 0.56\%\) - \(10.43\pm 2.35\%\) (Figure 3d). The removal efficiencies of putrescine, spermidine, spermine, tryptamine, and tryptophan at high dosages of TA (25 mg) were in the range of 48 - 57%. This is much less ( \(\sim 80\%\) ) than the removal efficiency of PA3. The network- type structure of PAs 1- 3 has large numbers of electron- deficient amide groups for interacting with amines through hydrogen bonds. Such a network is absent in the case of small molecule TA.
+
+<--- Page Split --->
+
+## Effects of Time and Concentrations of Amines on the Adsorption Efficiency  
+
+The effects of different extraction time points (15 min, 30 min, 60 min, 90 min, 120 min, 180 min and 300 min) and amine concentrations (5, 10, 50, 100 and 150 mg/L) on the removal efficiency were examined. The amine solutions (6 mL) at different concentrations were shaken with fixed amounts of PAs (1- 3, and TAs 25 mg) at room temperature for 15 - 300 min intervals. Samples were analysed, and removal efficiencies were calculated (Figure 4a- h). The removal efficiencies of amines are low at short time points (15 - 90 min) for PA1 (Figure 4a), ranging from \(5.60 \pm 0.04\) to \(55.27 \pm 1.459\%\) . At a higher time duration (300 min), the removal efficiency was increased to \(70.04 - 89.60\%\) . At longer durations, higher removal efficiency was observed due to the increase in the contact time of amine and polyaramide. For amines, removal efficiencies decreased as the initial concentration increased from \(5 \mathrm{mg / L}\) to \(150 \mathrm{mg / L}\) (Figure 4b). Lower amine concentrations (5 mg/L) yielded \(61.40 - 89.74\%\) removal, whereas higher concentrations (150 mg/L) decreased efficiency due to surface saturation. This decrease is due to the saturation of adsorption sites on the surface, leading to decreased removal efficiencies. The initial adsorption rate was higher at lower concentrations, where particle uptake resistance decreased as mass transfer increased. Same way, removal efficiency of PA2 varied with different time points and amine concentrations. After 15 minutes, efficiency was in the range of \(20.84\% - 45.91\%\) , whereas the removal efficiency increased to \(75.83 - 96.44\%\) after 300 minutes for all amines tested. The PA2 showed lower removal efficiencies at high amine concentrations (150 mg/L; \(32.73 - 51.75\%\) ) and high removal efficiencies at low concentrations of PA2 (5 mg/L; \(74.49 - 95.24\%\) , (Figure 4c,d).
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Figure 4. Effect of time \((15 - 300\mathrm{min})\) and concentration \((5 - 150\mathrm{mg / L})\) of putrescine ( \(\bullet\) -), spermidine ( \(\bullet\) -), spermine ( \(\bullet\) -), tryptamine ( \(\bullet\) -) and tryptophan ( \(\bullet\) -) on removal efficiency, PA1 (a, b), PA2 (c, d), PA3 (e, f) and TA (g, h). The amount of all PAs used for the adsorption experiments was kept constant at \(25\mathrm{mg}\) . </center>  
+
+The polymer, PA3 showed different removal efficiencies of five amines in the range of \(26.39\%\) to \(54.95\%\) after \(15\mathrm{min}\) shaking on a mechanical shaker (Figure 4e). By increasing the shaking time to \(300\mathrm{min}\) , there was a significant improvement in the removal efficiencies to \(84.39 - 99.81\%\) (Figure 4e). Similarly, at low concentrations of amines at \(5\mathrm{mg / L}\) , the polymer PA3 was able to remove \(73.65 - 99.42\%\) of all amines from water (Figure 4f). However, removal efficiencies decreased to \(40.35 - 83.14\%\) at a high concentration of amines at \(150\mathrm{mg / L}\) . The network structure of PA1 - 3 enabled high removal efficiencies as compared to the small molecule TA, with equilibrium reached within \(200\mathrm{min}\) . After \(15\mathrm{minutes}\) , the removal efficiencies of TA were at \(3.93 - 17.15\%\) (Figure 4g), and increasing the extraction time to \(300\mathrm{min}\) , the removal efficiencies were improved to \(48.33 - 56.89\%\) . The low amine concentrations ( \(5\mathrm{mg / L}\) ) in water enhanced TA's efficiencies to \(54.62 - 85.16\%\) . At high concentrations ( \(150\mathrm{mg / L}\) ) of amines, the removal efficiencies are as low as \(4.34 - 11.69\%\) for TA (Figure 4h). The small size of TA contributes to lower removal efficiency compared to other PAs.  
+
+## Isotherm Model Studies  
+
+To understand the adsorption behaviour of amines on the PA surface, the data were analysed using both the Freundlich and Langmuir isotherm models (Figure 5a- h). All necessary model equations for kinetics and isotherms are given in the Materials and Methods section (equations 2 - 6).
+
+<--- Page Split --->
+
+Table 1. Regression coefficient and isotherm parameters for the adsorption of amines (putrescine, spermidine, spermine, tryptamine, and tryptophan) on the PAs.
+
+<table><tr><td rowspan="2">Amines used for<br>adsorption</td><td rowspan="2">Polyara<br>mides<br>(PAs)<br>used</td><td colspan="3">Langmuir</td><td colspan="3">Freundlich</td></tr><tr><td>\(K_{L}\) (L/mg)</td><td>\(Q_{max}\)</td><td>\(R^{2}\)</td><td>\(K_{r}\)</td><td>n</td><td>\(R^{2}\)</td></tr><tr><td rowspan="4">Putrescine</td><td>PA1</td><td>2.9791</td><td>100.200</td><td>0.9714</td><td>6.1263</td><td>1.5064</td><td>0.9260</td></tr><tr><td>PA2</td><td>0.1657</td><td>166.667</td><td>0.9667</td><td>0.9256</td><td>1.0997</td><td>0.9350</td></tr><tr><td>PA3</td><td>0.5088</td><td>243.902</td><td>0.9851</td><td>1.6801</td><td>1.5719</td><td>0.9066</td></tr><tr><td>TA</td><td>0.5676</td><td>51.813</td><td>0.9856</td><td>1.5150</td><td>1.2566</td><td>0.9678</td></tr><tr><td rowspan="4">Spermidine</td><td>PA1</td><td>0.0953</td><td>96.0799</td><td>0.9997</td><td>1.8399</td><td>8.3402</td><td>0.9172</td></tr><tr><td>PA2</td><td>0.0036</td><td>183.824</td><td>0.9814</td><td>1.0373</td><td>1.4830</td><td>0.9119</td></tr><tr><td>PA3</td><td>0.0027</td><td>334.448</td><td>0.9667</td><td>1.4728</td><td>1.1252</td><td>0.9326</td></tr><tr><td>TA</td><td>0.0099</td><td>81.300</td><td>0.9844</td><td>1.4402</td><td>1.2730</td><td>0.9767</td></tr><tr><td rowspan="4">Spermine</td><td>PA1</td><td>0.1304</td><td>138.889</td><td>0.9851</td><td>1.2770</td><td>1.6812</td><td>0.9066</td></tr><tr><td>PA2</td><td>0.0430</td><td>163.934</td><td>0.9859</td><td>1.3033</td><td>1.1265</td><td>0.9221</td></tr><tr><td>PA3</td><td>0.1925</td><td>370.372</td><td>0.9879</td><td>2.5200</td><td>1.4210</td><td>0.9178</td></tr><tr><td>TA</td><td>0.1547</td><td>119.048</td><td>0.9206</td><td>2.2839</td><td>1.0322</td><td>0.9175</td></tr><tr><td rowspan="4">Tryptamine</td><td>PA1</td><td>0.4431</td><td>102.040</td><td>0.9788</td><td>8.7317</td><td>1.6034</td><td>0.9009</td></tr><tr><td>PA2</td><td>0.3743</td><td>142.857</td><td>0.9883</td><td>9.4471</td><td>1.7085</td><td>0.9146</td></tr><tr><td>PA3</td><td>0.1302</td><td>270.170</td><td>0.998</td><td>2.9335</td><td>1.7489</td><td>0.9820</td></tr><tr><td>TA</td><td>0.6185</td><td>83.3333</td><td>0.9917</td><td>2.3344</td><td>1.7763</td><td>0.9892</td></tr><tr><td rowspan="4">Tryptophan</td><td>PA1</td><td>0.1333</td><td>81.9672</td><td>0.9638</td><td>3.6008</td><td>1.4590</td><td>0.9182</td></tr><tr><td>PA2</td><td>0.0853</td><td>119.047</td><td>0.9923</td><td>7.2627</td><td>1.5676</td><td>0.9453</td></tr><tr><td>PA3</td><td>0.0502</td><td>232.558</td><td>0.9814</td><td>6.1574</td><td>1.5829</td><td>0.9556</td></tr><tr><td>TA</td><td>0.1394</td><td>76.9230</td><td>0.9794</td><td>1.7139</td><td>1.2933</td><td>0.9554</td></tr></table>
+
+350
+
+351 After analysis of the data, the Langmuir isotherm model provided a better fit (Table 1)(Figure 5a, c, e, and g) for each of the five amines when compared to Freundlich's model(Figure S3). The adsorption of amines on the PA surface is indicated by high values of \(K_{L}\) and
+
+<--- Page Split --->
+
+n. Monolayer formation of all amines was observed on PA surfaces, as stated by the Langmuir model. This is expected due to the strong interaction between the negatively charged PA surface and positively charged amines at neutral pH. PA3 had a higher adsorption capacity \((Q_{\mathrm{max}})\) compared to PA1, PA2, and TA for putrescine, spermidine, spermine, tryptophan, and tryptamine, with respective removal amounts of \(243.9\mathrm{mg / g}\) , \(334.4\mathrm{mg / g}\) , \(370.3\mathrm{mg / g}\) , \(270.1\mathrm{mg / g}\) , and \(232.5\mathrm{mg / g}\) from water which is calculated using Langmuir model (Table 1). The corresponding values for other polymers are given in Table 1.  
+
+![](images/Figure_unknown_0.jpg)
+
+
+<--- Page Split --->
+![PLACEHOLDER_18_0]
+
+<center>Figure 5. Langmuir (a, c, e and g) and pseudo-second-order kinetics (b, d, f and h) plots for PA1 (a, b), PA2 (c, d), PA3 (e, f), TA (g, h) at neutral pH and 298 K using different concentrations (5 - 150 mg/mL) of the putrescine (- - -), spermidine (- - -), spermine (- - -), tryptamine (- - -) and tryptophan (- - -) and a fixed concentration of absorbents (25 mg). The Freundlich isotherm and pseudo-first order kinetic regressions for PAs 1 - 3 and TA, are given in the supporting information (Figure S3). </center>  
+
+## Kinetic Model Studies  
+
+To study the mechanism, adsorption of a series of amines at different adsorption times was used (Figure 5, Table 2). The data collected from the five BAs used in the experiments were fitted with pseudo- first- order and pseudo- second- order kinetic models. The methods and materials section includes all equations relevant to both kinetic models. The practical and theoretical parameters determined from the data are given in Figure 5b, d, f and h and summarised in Table 2. The pseudo- second- order kinetic models fit the adsorption data for the five amines more closely than pseudo- first- order kinetic models for all PAs (Table 2). Higher \(\mathrm{R}^2\) values (putrescine - 0.9876, spermidine - 0.9878, spermine - 0.9999, tryptamine - 0.9986,
+
+<--- Page Split --->
+
+tryptophan – 0.9980) were obtained for PA3 using the pseudo-second-order model (Table 2).
+
+Furthermore, the theoretical removal efficiencies (Qe, cal) calculated using the pseudo-second-order model for each of the five amines are in agreement with the experimental data (Qe, exp) obtained.
+
+386
+
+Table 2. Kinetic parameters for the adsorption of amines, putrescine, spermidine, spermine,
+
+tryptamine, and tryptophan on PAs 1-3 and model compound TA.
+
+<table><tr><td rowspan="3">Amines used</td><td rowspan="3">Polya<br>mide<br>used</td><td colspan="3">Pseudo-first order</td><td colspan="4">Pseudo-second order</td></tr><tr><td>\(Q_{\mathrm {e}}\)cal</td><td>\(K_{1}\)</td><td>\(R^{2}\)</td><td>\(Q_{\mathrm {e}}\)</td><td>\(Q_{\mathrm {e}}\)</td><td>\(K_{2}\)(g</td><td>\(R^{2}\)</td></tr><tr><td>(mg g-1)</td><td>(min-1)</td><td></td><td>(exp.)<br>(mg g-1)</td><td>(cal.)<br>(mgg-1)</td><td>\(mg^{-1}\)<br>min-1)</td><td></td></tr><tr><td rowspan="4">Putrescine</td><td>PA1</td><td>9.4413</td><td>0.018</td><td>0.9104</td><td>156.780</td><td>112.36</td><td>0.0220</td><td>0.9986</td></tr><tr><td>PA2</td><td>9.2470</td><td>0.024</td><td>0.9152</td><td>159.094</td><td>149.254</td><td>0.0171</td><td>0.9873</td></tr><tr><td>PA3</td><td>8.0566</td><td>0.051</td><td>0.9179</td><td>211.345</td><td>208.333</td><td>0.0052</td><td>0.9876</td></tr><tr><td>TA</td><td>6.2463</td><td>0.04</td><td>0.9478</td><td>83.342</td><td>76.9231</td><td>0.0051</td><td>0.9903</td></tr><tr><td rowspan="4">Spermidine</td><td>PA1</td><td>17.0713</td><td>0.077</td><td>0.9172</td><td>268.902</td><td>256.41</td><td>0.0011</td><td>0.9997</td></tr><tr><td>PA2</td><td>19.0963</td><td>0.0095</td><td>0.9135</td><td>290.112</td><td>270.278</td><td>0.0107</td><td>0.9999</td></tr><tr><td>PA3</td><td>20.5734</td><td>0.0122</td><td>0.9446</td><td>303.124</td><td>277.778</td><td>0.0082</td><td>0.9878</td></tr><tr><td>TA</td><td>17.4092</td><td>0.0102</td><td>0.9121</td><td>195.564</td><td>181.811</td><td>0.0024</td><td>0.9863</td></tr><tr><td rowspan="4">Spermine</td><td>PA1</td><td>24.1987</td><td>0.0059</td><td>0.9066</td><td>258.009</td><td>263.158</td><td>0.0166</td><td>0.9851</td></tr><tr><td>PA2</td><td>36.6752</td><td>0.060</td><td>0.9591</td><td>318.909</td><td>287.356</td><td>0.0095</td><td>0.9996</td></tr><tr><td>PA3</td><td>48.9598</td><td>0.093</td><td>0.9671</td><td>304.901</td><td>294.118</td><td>0.0037</td><td>0.9999</td></tr><tr><td>TA</td><td>12.9877</td><td>0.0056</td><td>0.9477</td><td>192.778</td><td>185.183</td><td>0.0044</td><td>0.9632</td></tr><tr><td rowspan="4">Tryptamine</td><td>PA1</td><td>9.64944</td><td>0.002</td><td>0.9215</td><td>112.456</td><td>99.0099</td><td>0.0351</td><td>0.9778</td></tr><tr><td>PA2</td><td>12.9902</td><td>0.032</td><td>0.9168</td><td>124.098</td><td>109.890</td><td>0.0153</td><td>0.9987</td></tr><tr><td>PA3</td><td>19.7469</td><td>0.035</td><td>0.9247</td><td>134.678</td><td>294.117</td><td>0.0672</td><td>0.9986</td></tr><tr><td>TA</td><td>6.7823</td><td>0.022</td><td>0.8312</td><td>75.785</td><td>68.0272</td><td>0.0882</td><td>0.9640</td></tr><tr><td rowspan="4">Tryptophan</td><td>PA1</td><td>8.69371</td><td>0.0046</td><td>0.9179</td><td>298.09</td><td>90.9090</td><td>0.0107</td><td>0.9998</td></tr><tr><td>PA2</td><td>11.1439</td><td>0.0034</td><td>0.8742</td><td>183.980</td><td>108.695</td><td>0.0103</td><td>0.9999</td></tr><tr><td>PA3</td><td>18.3476</td><td>0.0094</td><td>0.9820</td><td>301.333</td><td>243.902</td><td>0.0012</td><td>0.9980</td></tr><tr><td>TA</td><td>12.7738</td><td>0.0076</td><td>0.9497</td><td>94.878</td><td>83.333</td><td>0.0117</td><td>0.9700</td></tr></table>
+
+<--- Page Split --->
+
+## Analysis of PAs After Extraction of Commercial Amines from Spiked Samples  
+
+The amine adsorption on the PAs influences the surface characteristics. Changes in the zetapotential of PAs are examined before and after the adsorption of amines. Before the amines were adsorbed, the PAs showed negative zetapotential values due to the surface - COO end groups on the polymer (Table 3). The positively charged amines are adsorbed on the negatively charged PA surface. After adsorption of amine (spermine), the zetapotential of PAs in water was measured at ambient temperature and showed positive zetapotentials for PA1 (+)14.93 ± 1.23, PA2 (+15.3 ± 2.33, and PA3 (+19.93 ± 0.45. The zetapotential for the adsorption of other amines is given in the supporting information (Table S2).  
+
+Table 3. Particle size, zetapotential, and BET analysis data for PAs and TA.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Particle Size (nm)</td><td rowspan="2">Pore Size (nm)</td><td rowspan="2">Surface area (m²/g)</td><td colspan="2">ζ Potential (mV)</td></tr><tr><td>Before</td><td>After(spermine)</td></tr><tr><td>PA1</td><td>1288 ±3.09</td><td>4.191</td><td>10.843</td><td>(-)7.56±2.23</td><td>(+)14.93 ± 1.23</td></tr><tr><td>PA2</td><td>918 ± 3.26</td><td>2.978</td><td>14.048</td><td>(-)12.58±0.34</td><td>(+)15.3 ± 2.33</td></tr><tr><td>PA3</td><td>875±1.24</td><td>3.233</td><td>29.233</td><td>(-)18.98±1.24</td><td>(+)19.93 ± 0.45</td></tr><tr><td>TA</td><td>529±3.09</td><td>5.790</td><td>5.683</td><td>(-)2.52±0.68</td><td>(+)12.88 ± 1.89</td></tr></table>  
+
+The Fourier transform infrared (FTIR) spectra of all PAs, after the adsorption of amines, showed a broad peak in the range of \(3100 - 3600\mathrm{cm}^{- 1}\) , which corresponds to the N- H stretching from the amide group on the polymer backbone and amine groups after adsorption process, (Figure S4). All PAs showed adsorption peaks corresponding to the aromatic and aliphatic - CH- groups on the polymer backbone (Figure S6a- c). Amide I and amide II peaks were observed around 1660 and \(1545\mathrm{cm}^{- 1}\) , which is slightly shifted to the higher wavelength from the peaks corresponding to the polyaramides before the adsorption of amines. This is expected due to the strong interactions of amine - NH- and amide \(> \mathrm{C} = \mathrm{O}\) groups. The other common peaks were observed around 1293, 917, and \(709\mathrm{cm}^{- 1}\) for PAs before and after adsorption.  
+
+PA solids obtained after the adsorption of amines were examined using thermogravimetric analysis under a nitrogen atmosphere. The TGA analysis was conducted throughout a temperature range from \(22^{\circ}\mathrm{C}\) to \(1000^{\circ}\mathrm{C}\) , with a heating rate of \(10^{\circ}\mathrm{C}\) per minute (Figure S5). There was no specific change observed as the smaller amount of amines adsorbed onto the PAs. The ICP analysis of nitrogen content analysis indicates an increase in the
+
+<--- Page Split --->
+
+percentage of nitrogen after adsorption of amines on PAs (Table S1). Pristine PAs showed 6.48, 6.68, 6.90, and 5.67 % of nitrogen content for PAs 1 – 3 and TA, respectively. The nitrogen content after adsorption of the amines on PAs was increased in the range of 9 to 14% (Table S1). Similar to N content, the percentages of C and H also increased after adsorption of the amines on PAs. Such results are complementary to the extraction data.  
+
+## Regeneration Studies  
+
+After adsorption of the amines on PAs, regeneration, and reuse of the same PAs were also attempted.  
+
+![PLACEHOLDER_21_0]
+
+<center>Figure 6. Removal efficiencies of PA 1 - 3 after repeated adsorption-desorption cycles (cycle 1 (■), cycle 2 (■), cycle 3 (■), cycle 4 (■), and cycle 5 (■)). The concentration of putrescine (a), spermidine (b), spermine (c), and tryptamine (d) used was \(50 \mathrm{mg / L}\) , a time of \(300 \mathrm{min}\) , and an adsorbent dose of \(25 \mathrm{mg}\) was kept constant. The regeneration data of PA 1 - 3 after adsorption of tryptophan are given in the supporting information (Figure S6). The regeneration data for TA using all amines are given in the supporting information (Figure S7). </center>
+
+<--- Page Split --->
+
+PAs (25 mg) with adsorbed amines on the surface were washed with dilute HCl solution (0.5 M, \(10~\mathrm{mL}\) ) a few times. The resulting mixture was centrifuged, and the solid was washed with water to remove traces of acid and dried at \(60^{\circ}\mathrm{C}\) . The solid was then reused for the extraction of amines from water. The removal efficiencies of regenerated PAs for different amines were measured for five repeated cycles of washings and readortions of the amines. The regenerated PAs demonstrated consistent removal efficiencies of over \(90\%\) , suggesting that PAs are a very effective and reusable adsorbent (Figure 6a- d). PAs were recovered quickly from the solution through filtration after the adsorption. The regeneration process involves protonation (acid- base reaction) of the adsorbed amines (basic) by HCl (acid), converting them into water- soluble ammonium salts for desorption. The removed PAs were utilized directly in the subsequent adsorption procedure without the need for drying or grinding.  
+
+## Extraction and Identification of Biogenic Amines from Fish Sample  
+
+To explore the application of synthesized PA materials in environmental samples, common fish samples were purchased from supermarkets and kept at room temperature for natural degradation. Cleaned fish tissue (2 g) was kept at room temperature in an open environment at different time points (6 h, 24 h, and 48 h). After homogenization in water, the samples were centrifuged. The resulting supernatant fish extract was used for LCMS analysis. A fixed amount of PAs was mixed with an appropriate amount of fish extract solution and kept in a mechanical shaker. The mixture was centrifuged, and the supernatant was treated with ninhydrin reagent to convert the amines into a blue- coloured amine- ninhydrin complex. The UV spectra of the colored complex solution were recorded for solutions before and after extraction with PAs and are presented in Figure 7a. A standard calibration curve was prepared using the known solutions of commercially available amine solutions after treatment with ninhydrin solution.  
+
+The concentration of extracted unknown amines in the solution was measured from the calibration curve. The amines generated inside the fish sample left for 6 hours in open air at ambient conditions were quantified as 2.566 mg/g, which increased to 18.45 and 34.56 mg/g with an increase in time of open- air degradation of 24 h and 48 h, respectively. A known volume (i.e. \(6~\mathrm{mL}\) ) was mixed with PA3 (50 mg) and kept on a mechanical shaker for 6 h. The removal efficiencies of the PAs were calculated from the UV adsorption spectra of the ninhydrin- treated extract solutions before and after adsorption (Figure 7b). PA3 showed high removal efficiencies
+
+<--- Page Split --->
+
+466 of \(99.42 \pm 0.12 \%\) , \(97.00 \pm 1.43 \%\) , and \(95.05 \pm 0.92 \%\) for extract of fish samples after 6 h, 24 h, and 48 h, respectively.  
+
+![PLACEHOLDER_23_0]
+
+<center>Figure 7. (a) UV-Vis spectra of the ninhydrin treated extracts obtained from fish sample kept at different time points of 6 h, 24 h, and 48 h at room temperature before (6 h (-), 24 h (-), 24 h (-)) and after (6 h (-), 24 h (-), and 48h (-)) extraction with PA 1-3 samples (25 mg). Note that the absorbance of solutions after extraction with PA was almost zero, indicating a complete removal of amines. (b) The extraction efficiencies of PAs (50 mg) for the removal of amines from solutions collected after keeping the fish samples for 6 h, 12 h, and 24 h at room temperature. The extraction time was kept at 5 h for all samples. (c) LC traces of extract collected from fish sample (2 g) after 48 h at room temperature. Optical images of fish samples (2 g) and LCMS traces of 6h and 24 h fish extracts are given in the supporting information (Figure S8). </center>  
+
+LCMS traces were utilized to identify and quantify the amines present in the extracts of fish tissues (Figure 7c). A few peaks were identified by comparing the retention time and
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+mass of the commercial amine samples. The retention peak positions at 1.03 min and 1.98 min indicated the presence of putrescine and spermidine with mass (m/z) values of 88.10 and 146.20, respectively. Tryptamine, with a retention time of 8.87 min, was identified with an m/z value of 160.10. The next major peak, with a retention time of 13.66 min and a m/z value of 186.22, was identified as 1- O- alkylglycerols. Similarly, the next major peak with a retention time of 15.88 min and a m/z value of 241.28, indicates the presence of hexadecylamine. The peak with a retention time of 18.62 min and an m/z value of 256.30 is identified as palmitic acid, which is present in fish oil. The next major peak at 26.12 min with a m/z value of 248.48 corresponds to stearic acid. The corresponding mass spectrometry data of all the major peaks observed for the components in the fish extract are given in the supporting information (Figure S9). LCMS obtained from commercial BAs solutions were used for comparison and quantification (Figure S10). The mass spectra of five different commercially available BAs used in our extraction were given in the supporting information (Figure S11).  
+
+## Comparison of the Removal Efficiency of PAs with Other Absorbents  
+
+Biogenic amines are generated through fermentation and decaying of meat and fish samples. Due to relatively low levels of BAs present in water bodies, only a limited number of research have focused on their occurrence in surface and waste waters. Nevertheless, the excessive release or accumulation of organic matter (such as animal remains or discarded food) usually contaminates water and alters the taste, smell, and dissolved oxygen levels. Such deterioration of water quality induces negative consequences for aquatic life, potentially leading to reduced activity or even death of these organisms. Zhu et al. reported that the poly(ether-block- amide) removed 54 - 72 % of biogenic amines such as histamine, putrescine, cadaverine, and tyramine from water. Another group reported 82 - 100% removal efficiency for histamine, putrescine, cadaverine, spermidine, spermine, and tryramine from water using functionalized silica material. The methods of extraction and detection techniques can impact the comparison of adsorption efficiency. The choice of adsorption method plays a significant role in the results; for example, batch extraction may favour high- capacity adsorbents, while chromatography- based methods may highlight selectivity. Additionally, batch extraction is generally more scalable than chromatography- based methods.  
+
+Here, we report a polyaramide- based adsorbents for the removal of biogenic amines from water. The removal process was thoroughly analyzed using kinetic studies, TGA, SEM, and FTIR spectra to gain valuable mechanistic insights. Furthermore, Table 4 presents a comprehensive comparison of various parameters, including different absorbents, removal
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+methods, particle concentrations, and the removal efficiencies achieved through different analytical methods. Compared to the absorbent materials reported in the literature, the PAs 1 – 3 showed high removal efficiencies (i.e. \(\sim 99.96\%\) , Table 4). 
+
+Table 4. Comparison of removal efficiency of PAs with other absorbents. 
+
+<table><tr><td></td><td>Adsorbent</td><td>Experiment method</td><td>Adsorption percentage %</td><td>Removal efficiency (mg/g)</td><td>Ref.</td></tr><tr><td>1</td><td>Graphene aerogel</td><td>Batch extraction</td><td>HIS 85.19%, CAD 74.1%, and SPD 70.11%</td><td>-</td><td>49</td></tr><tr><td>2</td><td>Poly(ether-block-amide)</td><td>Batch extraction</td><td>HIS 54%, PUT 72%, CAD 68%, TYR 87%</td><td>HIS 3.46, PUT 4.58, CAD 5.09, TYR 5.86</td><td>47</td></tr><tr><td>3</td><td>Functionalized silica material</td><td>Liquid chromatograph (LC) coupled to a mass spectrometer detector</td><td>HIS 95.0%, PUT 82.0%, CAD 88.7%, SPD 100%, SPM, 100%, TYR 13.3%</td><td>-</td><td>48</td></tr><tr><td>4</td><td>Sulfamic acid functionalised blast furnace slag</td><td>Batch extraction</td><td>PUT 90%, TYR 70%, PEA 99%</td><td>PEA 80.64, PUT 12.5 and TYR 64.52</td><td>50</td></tr><tr><td>5</td><td>Crown ether-modified mesoporous silica</td><td>High-Performance Liquid Chromatograph</td><td>TRP 40%, PUT 40%, HIS 12%, TYR 20%, SPD 98%</td><td></td><td>51</td></tr><tr><td>7</td><td>PA1</td><td>Batch Extraction</td><td>PUT 94.82 ± 0.12%, SPD 95.48 ± 0.15%, SPM 97.22 ± 0.38%, TYA 95.68 ± 1.15%, TYP 93.53 ± 1.66%</td><td>PUT 100.20, SPD 96.07, SPM 138.88, TYA 102.04, TYP 81.96</td><td>This work</td></tr><tr><td>8</td><td>PA2</td><td>Batch Extraction</td><td>PUT 94.31±1.55%, SPD 97.45± 0.10%, SPM 98.64± 0.17%, TYA 98.04 ±</td><td>PUT 166.66, SPD 183.82, SPM 163.93, TYA 142.85, TYP 119.04</td><td>This work</td></tr></table>
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+0.12%, TYP 93.48± 0.70%, 
+
+<table><tr><td>9</td><td>PA3</td><td>Batch Extraction</td><td>PUT 97.56 ± 0.24%, SPD 98.97 ± 0.68%, SPM 99.58 ± 0.23%, TYA 98.97 ± 1.68%, TYP 96.96 ± 0.08 %</td><td>PUT 243.90, SPD 334.44, SPM 370.37, TYA 270.17, TYP 232.55</td><td>This work</td></tr></table>
+
+522 Abbreviation: HIS- histamine, CAD - cadaverine, SPD - spermidine, PUT - putrescine, TYR
+523 - tyramine, SPM - spermine, PEA - 2-phenylamine, TYA - tryptamine, TYP - tryptophan. 
+
+## Mechanism of Adsorption 
+
+Biogenic amines have been shown to accumulate due to microbial attacks on meat or fish products.52 53 Biogenic amines can harm aquatic life, disrupt water ecosystems, and pose health risks to humans, particularly those with histamine intolerance or certain medical conditions.54 Table 4 shows a list of the different absorbents that have been used for removing different biogenic amines from water. The current study used commercially available biological amines such as putrescine, spermine, spermidine, tryptamine, and tryptophan to understand the removal efficiencies of PAs. 
+
+The PAs 1-3 synthesized during this study showed a negative zetapotential that is ideal for extracting the positively charged amines in water at a neutral pH. At an equilibrium concentration of PAs (25 mg) and an adsorption time of 300 min, high removal efficiencies of 97.11 ± 0.24 %, 98.97 ± 0.68 %, 99.58 ± 0.23 %, 98.97 ± 1.68 %, 96.96 ± 0.08 % for putrescine, spermidine, spermine, tryptamine, and tryptophan, respectively, were observed. The polyaramide (PA3) showed higher removal efficiency (~ 99%) than other polymers. PA3 has a greater surface area (29.23 m²/g) due to the incorporation of the nonlinear m-xylene diamine in the structure.
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+<center>Scheme 2. The complexation and extraction behaviour of PA with amines from solution </center>  
+
+Also, the zetapotentials of amine solutions in water were measured at ambient temperature and neutral pH (7.0). The respective values obtained for putrescine, spermidine, spermine, tryptamine, and tryptophan were \((+6.56 \pm 0.56 \text{mV}, (+7.23 \pm 1.55 \text{mV}, (+8.82 \pm 0.78 \text{mV}, (+4.87 \pm 0.66 \text{mV}, and (+1.87 \pm 0.34 \text{mV. All synthesized PAs showed a negative zetapotential for the adsorption of positively charged amines. After the amine adsorption, the zetapotential of the PA surface changed from negative to positive values (Table 3). The negatively charged polyaramides (PAs) attract the protonated amine molecules on the surface via electrostatic forces and H- bonding. The zetapotential of the PA surface changed from negative to positive values after extracting the amines from the solution (Table 3, Scheme 2). In addition to electrostatic interaction, hydrogen bonds also play an important role towards the removal of amines from water. PA3 showed a higher adsorption capacity (Qmax) of amine 243.9 mg/g for putrescine, 334.4 mg/g spermidine, 370.3 mg/g for spermine, 270.1 mg/g for tryptamine, and 232.5 mg/g for tryptophan. Elemental analysis indicates an increase in nitrogen content for all PAs after adsorption of biogenic amines (Table S1). PAs absorbed with spermine have a higher percentage of nitrogen content, 6.89 - 14.43 %, compared to other biogenic amines due to higher adsorption efficiency. The order of removal efficiencies of biogenic amines is spermine > spermidine > putrescine > tryptamine > tryptophan. To understand and compare the removal efficiencies of PAs, other monoamines such as hexylamine, and phenyl ethylene amine were also used for the extraction studies. PA3 exhibited removal efficiencies of 87.61 ± 2.43 and 87.30 ± 1.02 % for hexyl amine (HA) and phenylene ethylene amine (PEA),
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+respectively. Similarly, both PA2 and PA1 showed lower removal efficiencies of \(80 - 77\%\) for HA and \(70 - 50\%\) for PEA under same experimental conditions (Figure S12). Similarly, the small molecules (TA) showed \(57.70 - 73.46\%\) removal efficiencies, which are lower than that observed for PAs 1- 3. The synthesized PAs were used to extract amines and other degraded molecules in the decaying fish samples kept at room temperature for periods of \(6\mathrm{h}\) , \(24\mathrm{h}\) , and \(48\mathrm{h}\) . LCM technique and commercially available standard amine samples were used to determine the chemical identity of the compounds present in the fish extract. All three polyaramides have a new work structure, in particular, PA3 is expected to have a 3D architecture due to the bent structure of the diamine, MX. The network structure and negative zetapotential of PAs help to trap the positively charged amine molecules inside the solid lattice, which then enhances the adsorption capacities (Scheme 2).  
+
+## Conclusion  
+
+The amide- based porous network polymers effectively removed biogenic amines such as putrescin, spermidine, spermine, tryptamine, and tryptophan. The prepared PAs removed biogenic amines (BAs) from water with around \(99\%\) efficiency. All the PAs were characterized before and after adsorption of the amines. PA3 showed the highest adsorption efficiencies \((Q_{\mathrm{max}})\) as compared to the other three PAs ( \(244\mathrm{mg / g}\) putrescin, \(334\mathrm{mg / g}\) spermidine, \(370\mathrm{mg / g}\) spermine, \(270\mathrm{mg / g}\) tryptamine, and \(232\mathrm{mg / g}\) tryptophan). Absorbents (PA1- 3) and model compound TA were characterized using FTIR spectra, TGA, and SEM. The extraction data for the amines were analyzed using the Langmuir and Freundlich isotherm models and different kinetic models. The absorbents were regenerated and reused to extract amines from water. After five cycles, the PAs showed similar removal efficiencies, and there was no appreciable efficiency loss due to polymer degradation. Compared to triamide (TA), the PAs 1- 3 showed higher removal efficiencies towards various amines tested. The synthesised PAs were also used to extract amines generated by decaying natural fish tissues for \(6\mathrm{h}\) to \(48\mathrm{h}\) . The amounts of amines extracted from such fish tissues were in the range of \(2 - 35\mathrm{mg / g}\) which increased with an increase in time. Such easily accessible synthetic polymers are a great candidate for environmental remediation in the future.  
+
+## Supporting Information  
+
+Full synthetic details of polyaramides; PA1- 3 and small molecule TA; TGA (b) of PA1 (—), PA2 (—), PA3 (—) and SA1 (—) before adsorption; Absorbance spectra of ninhydrin complex of putrescin (—), spermidine (—), tryptamine (—), and tryptophan (—) at a concentration of \(50\mathrm{mg / L}\) ; Freundlich (a, c, e, g) and pseudo- first- order kinetics (b, d, f and h)
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+plots for PA1 (a and b), PA2 (and d), PA3(e and f) and SA1 (g and h) at 298 K using different concentrations (5 - 150 mg/mL) of the putrescine (--), spermidine (--), spermine (--), tryptamine (--) and tryptophan (--). A fixed concentration (25 mg in 6 mL) of PAs and SA1 are used for all studies; FTIR spectra of PA1 (a), PA2 (b), PA3 (c) and SA1 (d) after adsorption of putrescine (--), spermidine (--), spermine (--), tryptamine (--) and tryptophan (--). KBr matrix was used for recording the spectra; TGA of PA1 (a), PA2 (b), PA3 (c), and SA1 (d) after adsorption of putrescine (--), spermidine (--), spermine (--), tryptamine (--), and tryptophan (--); Removal & regeneration efficiencies of PA 1 - 3 after repeated absorption-desorption cycles 1 (--), 2 (--), 3 (--), 4 (--), and 5 (--) using tryptophan as a model amine. The tryptophan concentration was 50 mg/L, extraction time of 300 min, and an adsorbent dose of 25 mg was kept constant; Removal efficiency of SA1 after repeated adsorption-desorption cycles (cycle 1 (--), cycle 2 (--), cycle 3 (--), cycle 4 (--), and cycle 5 (--). The concentration of Putrescine (a), Spermidine(b), Spermine(c), Tryptamine(d), and tryptophan(e) (50 mg/L), time (300 min), and adsorbent dose (25 mg) were kept constant. PUT-Putrescine, SPD-Spermidine, SPM-Spermine, TYA- Tryptamine, and TYP-Tryptophan; Optical images of fish samples at different time points of 6h (a), 24 h (b), and 48 h (c). LCMS traces of crude extracts collected from fish samples kept at 6h (d) and 24 h using a C-18 reverse phase column; The mass spectra of eluents with a retention time of 1.03 min (a),1.98 min (b), 8.87 min (c), 10.33 min (d),13.88 min (e),15.88 min (f), 18.62 min (g), 26.12 min (h) observed for the fish extract collected from 48h; LCMS of standard commercial amines, putrescine (1), spermidine (2), spermine (3), tryptamine (4) and tryptophan (5). The inset represents the enlarged view of putrescine (1) and spermidine (2) peaks; The mass spectra of commercially available standard samples of putrescine (1), spermidine (2), spermine (3), tryptamine (4) and tryptophan (5); Removal efficiencies of hexylamine (a)and phenylethylamine (b) at different concentrations (5 - 100 mg) of polyaramides PA1 (--), PA2 (--) and PA3 (--). The concentration of all PAs was kept constant at 25 mg.  
+
+## Author contribution statement  
+
+GM: Experimentation, collection of data, formal analyses, writing of the paper draft. SV: Resources, ideation, methodology, and revision of the manuscript.  
+
+## Declaration of the competing interests  
+
+The authors declare no known competing financial or personal relationships that could have influenced the work reported in this paper.  
+
+## Funding  
+
+The authors acknowledge the funding support from the National Research Foundation grant A- 0004151- 00- 00 and technical support from the Department of Chemistry at the National University of Singapore.  
+
+## Data Availability
+
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+
+The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information file. All data that support the findings of this study are available from the corresponding author upon reasonable request.  
+
+## References  
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+785 (45) Jančová, P.; Pachlová, V.; Čechová, E.; Cedidlová, K.; Šerá, J.; Pištěková, H.; Buňka, F.; Buňková, L. 786 Occurrence of Biogenic Amines Producers in the Wastewater of the Dairy Industry. Molecules 787 2020, 25 (21), 5143- 5155. https://doi.org/10.3390/molecules25215143. 788 (46) Kim, S.- H.; Wei, C.- I.; Clemens, R. A.; An, H. Review: Histamine Accumulation in Seafoods and Its 789 Control to Prevent Outbreaks of Scombroid Poisoning. J. Aquat. Food Prod. Technol. 2005, 13 790 (4), 81- 100. https://doi.org/10.1300/J030v13n04_07. 791 (47) Zhu, J.; Wang, X.; Mao, L.; Chen, X.; Han, J.; Li, X.; Xia, S.; Wang, H. Electrospun Nanofibrous 792 Poly(Ether-Block-Amide) Membrane for Removing Biogenic Amines in Acidic Wastewater from 793 the Yellow Rice Wine Factory. Sci. Total Environ. 2023, 862, 160720- 160731. 794 https://doi.org/10.1016/j.scitotenv.2022.160720. 795 (48) Rodríguez- Bencomo, J. J.; Mehdi, A. Removal of Biogenic Amines from Hydroalcoholic Solutions 796 by Functionalized Silica. Food Chem. 2019, 297, 125027- 125035. 797 https://doi.org/10.1016/j.foodchem.2019.125027. 798 (49) Bajpai, V. K.; Shukla, S.; Khan, I.; Kang, S.- M.; Haldorai, Y.; Tripathi, K. M.; Jung, S.; Chen, L.; Kim, 799 T.; Huh, Y. S.; Han, Y.- K. A Sustainable Graphene Aerogel Capable of the Adsorptive Elimination 800 of Biogenic Amines and Bacteria from Soy Sauce and Highly Efficient Cell Proliferation. ACS 801 Appl. Mater. Interfaces 2019, 11 (47), 43949- 43963. https://doi.org/10.1021/acsami.9b16989. 802 (50) Dauda, M.; Al- Malack, M. H.; Basheer, C. Adsorption of Biogenic Amines from Synthetic and 803 Real Wastewater Using a Zwitterion- Functionalized Blast Furnace Slag. CLEAN - Soil Air Water 804 2021, 49 (7), 2100158- 2100170. https://doi.org/10.1002/clen.202100158. 805 (51) Saaid, M.; Saad, B.; Rahman, I. A.; Ali, A. S. M.; Saleh, M. I. Extraction of Biogenic Amines Using 806 Sorbent Materials Containing Immobilized Crown Ethers. Talanta 2010, 80 (3), 1183- 1190. 807 https://doi.org/10.1016/j.talanta.2009.09.006. 808 (52) Xia, X.; Luo, Y.; Zhang, Q.; Huang, Y.; Zhang, B. Mixed Starter Culture Regulates Biogenic Amines 809 Formation via Decarboxylation and Transamination during Chinese Rice Wine Fermentation. J. 810 Agric. Food Chem. 2018, 66 (25), 6348- 6356. https://doi.org/10.1021/acs.jafc.8b01134. 811 (53) Diaz, M.; Ladero, V.; Del Rio, B.; Redruello, B.; Fernández, M.; Martin, M. C.; Alvarez, M. A. 812 Biofilm- Forming Capacity in Biogenic Amine- Producing Bacteria Isolated from Dairy Products. 813 Front. Microbiol. 2016, 7, 591- 601. https://doi.org/10.3389/fmicb.2016.00591. 814 (54) Ding, T.; Li, Y. Biogenic Amines Are Important Indices for Characterizing the Freshness and 815 Hygienic Quality of Aquatic Products: A Review. LWT 2024, 194, 115793- 115813. 816 https://doi.org/10.1016/j.lwt.2024.115793.
+
+<--- Page Split --->
+
+# Engineered Polyamides for Extraction of Bioamines from Water  
+
+Gomathi Mahadevan and Suresh Valiyaveettil\*  Department of Chemistry, National University of Singapore  3 Science Drive 3, Singapore 117543  Email: chmsv@nus.edu.sg  
+
+![PLACEHOLDER_34_0]
+
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+Supportinginformation.docx
+
+<--- Page Split --->

preprint/preprint__07bb49d179d74a99cfca97aa544930e840ce529d98ed5ba46742687ced243ffc/preprint__07bb49d179d74a99cfca97aa544930e840ce529d98ed5ba46742687ced243ffc_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 107, 780, 174]]<|/det|>
+# Engineered Polyaramides for Extraction of Bioamines from Water  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 339, 288]]<|/det|>
+Gomathi Mahadevan National University of Singapore Suresh Valiyaveettil chmsv@nus.edu.sg  
+
+<|ref|>text<|/ref|><|det|>[[55, 315, 339, 333]]<|/det|>
+National University of Singapore  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 375, 103, 393]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 413, 936, 433]]<|/det|>
+Keywords: Polyaramide, biogenic amines, extraction, adsorption efficiency, LCMS, environmental matrix  
+
+<|ref|>text<|/ref|><|det|>[[44, 451, 322, 470]]<|/det|>
+Posted Date: August 11th, 2025  
+
+<|ref|>text<|/ref|><|det|>[[44, 489, 475, 508]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 7238623/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 526, 916, 570]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 588, 545, 607]]<|/det|>
+Additional Declarations: No competing interests reported.  
+
+<|ref|>text<|/ref|><|det|>[[42, 643, 935, 686]]<|/det|>
+Version of Record: A version of this preprint was published at Scientific Reports on October 21st, 2025. See the published version at https://doi.org/10.1038/s41598- 025- 20410- 1.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[75, 87, 876, 157]]<|/det|>
+# Engineered Polyaramides for Extraction of Bioamines from Water  
+
+<|ref|>text<|/ref|><|det|>[[292, 169, 701, 186]]<|/det|>
+Gomathi Mahadevan and Suresh Valiyaveettil\*  
+
+<|ref|>text<|/ref|><|det|>[[255, 204, 740, 252]]<|/det|>
+Department of Chemistry, National University of Singapore  3 Science Drive 3, Singapore 117543  Email: chmsv@nus.edu.sg  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 289, 221, 309]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[112, 320, 882, 781]]<|/det|>
+Biogenic amines (BAs) are prevalent in fermented foods, protein- rich meats, and brewed food additives. High concentrations of BAs can induce health issues such as headaches, high blood pressure, and palpitations. Polyaramides (PAs) prepared from the reaction of trimesoyl chloride with ethylene diamine (ED), \(p\) - xylene diamine (PXD), and \(m\) - xylene diamine (MXD) and characterized using different characterization techniques, FTIR, XRD, SEM, TGA, and DLS measurements. All PAs were used for the removal of five biogenic amines (i.e., putrescine, spermidine, spermine, tryptamine, and tryptophan) from water. All PAs showed high removal efficiencies for biogenic amines, and the data collected fit well with the Langmuir isotherm and pseudo- second- order kinetic models. Among three different polymers, PA3 showed exceptional adsorption capacities, achieving removal efficiencies of \(97.1 \pm 0.24\%\) (putrescine), \(99 \pm 0.68\%\) (spermidine), \(99.6 \pm 0.23\%\) (spermine), \(99 \pm 1.68\%\) (tryptamine), and \(97 \pm 0.08\%\) (tryptophan) at an equilibrium concentration of \(25 \mathrm{mg}\) PA and an adsorption time of 300 minutes. Furthermore, adsorbent regeneration was established via washing with an acid solution, and the removal efficiency was retained after five cycles of repeated washings and extractions. As a proof of concept, the synthesized PAs were used to extract the amines from a decaying fish sample for different periods, which showed \(99\%\) extraction and removal efficiencies. The chemical nature of the extracted BAs was identified using LCMS. Such synthetic polyaramides for removing pollutants from environmental matrices are interesting candidates for developing functional materials.  
+
+<|ref|>text<|/ref|><|det|>[[115, 795, 880, 838]]<|/det|>
+Keywords: Polyaramide, biogenic amines, extraction, adsorption efficiency, LCMS, environmental matrix.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 86, 266, 107]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[115, 116, 883, 504]]<|/det|>
+The freshness of meat or fish products in the market is difficult to measure, owing to the lack of suitable fast and reliable methods. Biogenic amines (BAs) such as cadaverine, putrescine, spermidine, spermine, phenylethylamine, tyramine, and histamine are present or generated in biological samples with aging or under stress. \(^{1,2}\) The production of BAs is primarily a result of the decarboxylation of amino acids catalysed by microorganisms. \(^{3}\) Microbial species in the environment degrade the biological tissues to release small molecular metabolites, including significant amounts of BAs. \(^{4}\) A high concentration of BAs in human body fluids causes health issues, such as asthma, headaches, and irregular blood pressure. \(^{5,6}\) Many aged foods, such as fish, wine, beer, meat products, and fermented foods, contain BAs, which accumulate with time due to microbial degradation. \(^{7}\) BAs from decaying old food products or effluents from fish markets or butcheries end up in local water bodies, posing adverse health risks to living organisms. \(^{6,8}\) Furthermore, studies have demonstrated that BA accumulates in algae during summertime blooming, which results in an abrupt increase in the concentration of amines in marine or coastal locations. \(^{1,9}\) A few reports are available on the extraction and identification of BAs from decaying fish samples by using the HPLC technique. \(^{5,10}\)  
+
+<|ref|>text<|/ref|><|det|>[[115, 519, 883, 686]]<|/det|>
+New functional materials and methodologies are needed for the detection, removal, and quantification of the BAs from water. \(^{11,12}\) A few materials were used to detect the presence of biogenic amines in food and water. \(^{13 - 15}\) However, removing amines or other metabolites from different raw food materials has not been well studied due to the complexity of the matrix. Amines such as putrescine and spermine were extracted and removed from meat products using absorbents such as iron oxide and graphene, but multiple treatments were necessary to achieve high removal efficiencies. \(^{16 - 18}\)  
+
+<|ref|>text<|/ref|><|det|>[[115, 700, 883, 892]]<|/det|>
+Water pollution caused by various contaminants such as heavy metals, pesticides, biological waste, and industrial chemicals poses a significant threat to human health and the environment. \(^{4}\) In recent years, polyamides have emerged as a promising material for water purification technology. Polyamides, a class of synthetic polymers, are widely employed in various industrial applications due to their excellent mechanical properties, thermal stability, and chemical resistance. \(^{19 - 21}\) Here, we use synthetic, highly branched polyamides (PAs) for the removal of BAs from spiked water samples to develop a purification system for future applications (Scheme 1).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[170, 85, 860, 655]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[115, 664, 880, 701]]<|/det|>
+Scheme 1. Synthetic scheme (a) of PAs 1- 3 and triamide (TA), and chemical structure (b) of amines used for the extraction.  
+
+<|ref|>text<|/ref|><|det|>[[115, 710, 881, 900]]<|/det|>
+In our design strategy, the electron- deficient amide groups, hydrophobic interactions, and the network structure of PA were employed for the extraction of organic amines from water. Our objectives include the extraction of amines from an aqueous environment and understanding the structure- property correlations of the three PAs. The synthetic strategy includes trimesoyl chloride (TMC) as a trifunctional monomer and one of the linear ethylene diamine (ED), \(p\) - xylene diamine (PXD), and bend \(m\) - xylene diamine (MXD) for the synthesis of PAs (Scheme 1a). Ethylene diamine (ED) is a flexible linear molecule, whereas aromatic amines such as \(p\) - xylene diamine (PXD) and \(m\) - xylene diamine (MXD) are rigid molecules. A
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 883, 398]]<|/det|>
+model triamide (TA) was prepared using TMC and aniline (AN) for comparison of structure and properties. All three PAs with different structural features were utilized for the removal of BAs such as putrescine (i), spermidine (ii), spermine (iii), tryptamine (iv), and tryptophan (v), from water (Scheme 1b). The amide groups inside the polymer lattice are electron-deficient moieties and interact strongly with electron-rich pollutants (e.g. amines, anions) through electrostatic interactions. Impact of experimental factors such as concentration of PAs and amines, extraction time on adsorption efficiency, isotherm and kinetic model treatments of the data, regeneration of PAs, proof- of- concept demonstration of extracting amines from decaying fish sample, comparison of PAs with other adsorbents towards amine extraction, and mechanism of extraction are discussed in this manuscript. Although many polyamides have been reported in the literature, \(^{10,13,21}\) the PAs discussed here demonstrate significant efficiency towards the extraction of biogenic amines, making them suitable for separation and purification technologies.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 413, 355, 432]]<|/det|>
+## Materials and Methods  
+
+<|ref|>text<|/ref|><|det|>[[115, 442, 883, 781]]<|/det|>
+1,3,5- Trimesoyl chloride (TMC), ethylenediamine (ED), \(p\) - xylenediamine (PXD), \(m\) - xylenediamine (MXD), aniline, dimethylformamide (DMF, HPLC grade), and triethylamine (TEA) were purchased from Sigma Aldrich Pte Ltd. All chemicals were used as received without any further purification. Deionized water was used throughout the experiments. A Bruker ALPHA FT- IR spectrophotometer was used to record the FTIR spectra (500 – 4000 cm\(^{- 1}\)) both before and after the extraction of amines using KBr as the matrix. The size and surface charges of the materials were measured using the Malvern Zetasizer Nano- ZS90. The thermogravimetric analyses (TGA) were done using a Discovery TGA apparatus in a nitrogen atmosphere within the 25 – 1000 °C temperature range and a heating rate of 10 °C/min. The UV- Vis spectra of every sample were recorded using a Shimadzu- 1601 spectrophotometer. The synthesized PA’s morphologies were established using a JEOL JSM- 6701F scanning electron microscope (SEM). The crystallinity of the polyaramides was investigated with the help of a Bruker D8 Advance Powder Crystal X- ray diffractometer with Cu Kα radiation (λ = 0.154 nm) operating at 40 kV and 40 mA within the 20 range of 5 - 70°.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 797, 505, 817]]<|/det|>
+## Synthesis and Characterisation of PAs  
+
+<|ref|>text<|/ref|><|det|>[[115, 825, 881, 893]]<|/det|>
+All polyaramides (PAs) and the control molecules were synthesized and fully characterized using the reported procedures. \(^{22}\) Full details on the synthesis and characterisation of the PAs are given in the supporting information.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[118, 108, 425, 129]]<|/det|>
+## Removal of Amines Using PAs  
+
+<|ref|>text<|/ref|><|det|>[[115, 137, 883, 450]]<|/det|>
+Commercially available amines (putrescine, spermidine, spermine, tryptamine, and tryptophan) were dissolved in Milli- Q water to prepare a stock solution (50 mg/L) and used for extraction studies. The extraction was carried out at room temperature (22 °C) and a neutral pH of 7. A calibration curve was prepared after mixing the amine solution of different concentrations with an appropriate amount of ninhydrin solution. Ninhydrin reacts with the amines to form a blue adduct, whose concentration is monitored using UV- Vis spectroscopy to quantify the amount of amine in the solution. Different amounts of PA absorbent (2- 50 mg) were added to the amine solution (6 mL), and the extraction was carried out for 300 min. The solution was centrifuged, and the supernatant was mixed with dilute ninhydrin solution (0.01M) to get a blue- colored solution after 30 min at pH 8. \(^{10}\) UV- Vis spectra of the blue solutions were recorded, and the concentration of amine was determined from a calibration curve. The removal efficiency was calculated from the spectroscopic data obtained before and after extraction using equation (1). \(^{23}\)  
+
+<|ref|>equation<|/ref|><|det|>[[175, 464, 720, 500]]<|/det|>
+\[\mathrm{Removal~efficiency~(\mathrm{RE})} = \frac{\mathrm{C_0 - C_e}}{\mathrm{C_0}}\cdot \mathrm{X}100\% \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[117, 515, 881, 559]]<|/det|>
+where \(\mathrm{C_0}\) (mg/L) is the initial concentration and \(\mathrm{C_e}\) (mg/L) is the equilibrium concentration of amines.  
+
+<|ref|>sub_title<|/ref|><|det|>[[117, 576, 485, 596]]<|/det|>
+## Isotherm and Kinetic Model Studies  
+
+<|ref|>text<|/ref|><|det|>[[115, 603, 882, 746]]<|/det|>
+The amines were extracted using an optimized amount (25 mg) of PA absorbents from dilute solutions (6 mL) containing varying concentrations (5 - 150 mg/L). Adsorption studies were repeated three times for each concentration, and the average value was reported. The collected data were used to analyse the common adsorption models, such as the Langmuir and the Freundlich isotherm models. The Langmuir isotherm model (Equation 2) fits the data well, indicating the formation of continuous monolayers on the surface of the PAs. \(^{24}\)  
+
+<|ref|>equation<|/ref|><|det|>[[175, 750, 716, 789]]<|/det|>
+\[\mathrm{Q_e} = \frac{\mathrm{Q_{max}}\mathrm{K_L}\mathrm{C_e}}{1 + \mathrm{K_L}\mathrm{C_e}} \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 797, 881, 890]]<|/det|>
+\(\mathrm{Q_{max}}\) (mg/g) is the maximum adsorption capacity of amines, and \(\mathrm{Q_e}\) (mg/g) is the equilibrium adsorption capacity. The equilibrium concentration is represented by the letter \(\mathrm{C_e}\) , and \(\mathrm{K_L}\) is the binding energy- related constant. Multilayer adsorption on heterogeneous surfaces is treated by the Freundlich empirical equation (3). \(^{24}\)
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[177, 84, 721, 110]]<|/det|>
+\[\mathrm{Q}_{\mathrm{e}} = \mathrm{K}_{\mathrm{F}}\mathrm{C}_{\mathrm{e}}^{1 / \mathrm{n}} \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[115, 116, 882, 185]]<|/det|>
+where \(\mathrm{C}_{\mathrm{e}}\) (mg/L) is the equilibrium concentration and \(\mathrm{Q}_{\mathrm{e}}\) (mg/g) is the adsorbent's quantity of absorbed amines per unit mass at equilibrium. \(\mathrm{K}_{\mathrm{F}}\) and \(\mathrm{n}\) represent adsorption capacity and intensity, respectively. In a linear form, Equation 3 could be extended as Equation 4.25  
+
+<|ref|>equation<|/ref|><|det|>[[175, 189, 716, 222]]<|/det|>
+\[\mathrm{Log} \mathrm{Q}_{\mathrm{e}} = \log \mathrm{K}_{\mathrm{F}} + \frac{1}{n} \log C_{\mathrm{e}} \quad (4)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 228, 882, 395]]<|/det|>
+The PA (25 mg) was mixed with the appropriate amine solution (50 mg/ L, 6 mL) at room temperature and shaken mechanically for different time points (15 - 300 min). The solutions were centrifuged, and the collected supernatant was filtered. The filtrate was analyzed to determine the extraction efficiency of the PA towards the amine. The adsorption experiments were repeated three times for each concentration, and the average value was used for calculations. The extraction data were shown using the pseudo- first- order (Equation 5) and pseudo- second- order (Equation 6) kinetic models.26,27  
+
+<|ref|>equation<|/ref|><|det|>[[175, 400, 716, 470]]<|/det|>
+\[\begin{array}{l}{\ln (\mathrm{q}_{\mathrm{e}} - \mathrm{q}_{\mathrm{t}}) = \ln \mathrm{q}_{\mathrm{e}} - \mathrm{k}_{1}\mathrm{t}}\\ {\frac{\mathrm{t}}{\mathrm{q}_{\mathrm{t}}} = \frac{\mathrm{t}}{\mathrm{q}_{\mathrm{e}}} +\frac{1}{\mathrm{k}_{2}\mathrm{q}_{\mathrm{e}}^{2}}} \end{array} \quad (5)\]  
+
+<|ref|>text<|/ref|><|det|>[[114, 500, 882, 620]]<|/det|>
+In this equation, \(\mathrm{q}_{\mathrm{e}}\) (mg/g) represents the amount of amine extracted at equilibrium, and \(\mathrm{q}_{\mathrm{t}}\) (mg/g) represents the number of pollutants absorbed at a given time t (min). The letters \(\mathrm{k}_{1}\) and \(\mathrm{k}_{2}\) are used to denote the rate constants in the pseudo- first- order and pseudo- second- order kinetic models. The slope and intercepts of the linear curves are used to calculate the values of \(\mathrm{k}_{1}\) , \(\mathrm{k}_{2}\) , and the adsorption capacity.  
+
+<|ref|>sub_title<|/ref|><|det|>[[117, 650, 336, 670]]<|/det|>
+## Regeneration Studies  
+
+<|ref|>text<|/ref|><|det|>[[115, 677, 882, 844]]<|/det|>
+As described above, all synthesized PAs were used to extract different amines from the solution. The PAs with amines absorbed on the surface were regenerated using a dilute HCl solution (0.3 M, 10 mL). After acid washing, the PAs were washed with water to remove traces of acid on the surface, which was checked with pH paper. The thoroughly washed PAs were collected after filtration, dried at 70 °C, and used again for extracting the amines from water. The acid washings and amine extractions were successively done five times, and no significant changes in the removal efficiencies were observed.  
+
+<|ref|>sub_title<|/ref|><|det|>[[112, 874, 842, 895]]<|/det|>
+## Biogenic Amine Extraction from Mackerel (Scomber Japonicus) Sample
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 882, 349]]<|/det|>
+To quantify the amount of biogenic amine generation over time due to microbial degradation, fresh fish tissues (2 g) purchased from a local supermarket were kept at room temperature (22°C) for different time durations (6 h, 24 h, and 48 h). After each exposure period, the fish tissue was subjected to a homogenization process with miliQ water (2 g, 10 mL) for 2 minutes. Subsequently, the homogenate was centrifuged for 10 minutes at 4 °C (5,000 rotations per minute) to obtain the supernatant. This extraction process was repeated once, and the resulting supernatants were combined and adjusted to a volume of 25 mL. The resulting extract was stored in a 50 mL centrifuge tube at 4 °C until further treatment. The extraction experiment was carried out by using the procedure mentioned above. Ninhydrin tests were used to quantify the extraction efficiency and the amine content before and after the extraction study.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 364, 769, 386]]<|/det|>
+## Liquid Chromatography - Mass Spectrometry (LCMS) Analysis  
+
+<|ref|>text<|/ref|><|det|>[[115, 393, 882, 634]]<|/det|>
+The mass spectra were obtained using the TSQ Quantum Discovery triple- quadrupole tandem mass spectrometer from Thermo Electron, coupled with a Surveyor high- performance liquid chromatography system from Thermo Finnigan. The system included a thermostated autosampler and a Phenomenex Gemini® 5 μm C18 110 Å 2.0 x 100 mm column kept at 30 °C, connected to a 4 × 2 mm polar RP precolumn from Phenomenex. A 5 μL sample was separated at a flow rate of 0.2 mL/min using a solvent system composed of water (A) and acetonitrile with 0.1% formic acid (B). A linear gradient was applied, increasing the concentration of B from 0% to 45% over 35 minutes and then to 100% over 13 minutes. The mass spectrometer operated in positive electrospray ionization mode (ESI+), with a spray needle voltage of 3.5 kV and a spray current of 5 μA.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 650, 382, 671]]<|/det|>
+## Results and Discussion  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 680, 364, 700]]<|/det|>
+## Characterization of PAs  
+
+<|ref|>text<|/ref|><|det|>[[115, 708, 882, 899]]<|/det|>
+All polyaramides were synthesized and fully characterized using the reported literature procedures.28,29 The design criteria involve the use of A3 (i.e., trimesoyl chloride) and B2 (i.e., diamine) monomers to create a branched polyaramide architecture. The choice of three structurally different amines provides a 3D polyaramide architecture with a significant number of electron- deficient amide groups along the polymer chain. The polyaramides are synthesized with amines with different degrees of flexibility and structural geometries – linear (i.e., EA, PX) vs bent (i.e., MX) structures. Also, the polyaramides from A3 and B2 monomers provide a branched architecture. In the FTIR spectra, all synthesized PAs showed a broad peak from
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 82, 882, 348]]<|/det|>
+3400 - 3485 \(\mathrm{cm^{- 1}}\) corresponding to the amide groups, peaks at \(3075\mathrm{cm^{- 1}}\) (C- H, aromatic), peaks around \(2925\mathrm{cm^{- 1}}\) and \(2852\mathrm{cm^{- 1}}\) representing the stretching vibrations of aliphatic - \(\mathrm{CH_2}\) along the polymer backbone (Figure. 1a). The strong peaks observed around \(1655\mathrm{cm^{- 1}}\) and \(1545\mathrm{cm^{- 1}}\) were assigned as \(>c = 0\) stretching of the amide group (i.e. amide I and amide II peaks). \(^{30,31}\) The other peaks in the FTIR spectra were accounted as \(1420\mathrm{cm^{- 1}}\) (in- plane bending vibration of \(>CH_2\) ), and \(720\mathrm{cm^{- 1}}\) ( \(>N\) - H stretching). \(^{30,31}\) The model compound TA showed a broad peak at \(3469 - 3525\mathrm{cm^{- 1}}\) , region and \(3252\mathrm{cm^{- 1}}\) for \(>N\) - H stretching vibration, peaks observed at \(3031\mathrm{cm^{- 1}}\) (Ar- H), and the peak position observed at \(2921\) and \(2843\mathrm{cm^{- 1}}\) for aliphatic - CH- stretching vibrations (Figure. 1a). The stretching vibrations of the \(>c = 0\) bond of the amide group were observed at \(1658\) and \(1545\mathrm{cm^{- 1}}\) . The peak positions at \(1446\) , \(1320\) , and \(722\mathrm{cm^{- 1}}\) indicated \(>CH_2\) in- plane bending vibration. \(^{31}\)  
+
+<|ref|>image<|/ref|><|det|>[[150, 355, 842, 570]]<|/det|>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[150, 84, 843, 488]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 500, 869, 536]]<|/det|>
+<center>Figure 1. FTIR spectra (a), XRD pattern (b) of pristine PA1 (—), PA2 (—), PA3 (—) and TA (—). SEM micrographs of PA1 (c), PA2 (d), PA3 (e), and TA (f). </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 544, 882, 759]]<|/det|>
+All three polymers showed broad XRD peaks at \(24.55^{\circ}\) (3.62 Å, PA1), \(24.28^{\circ}\) (3.66 Å, PA2), and \(24.94^{\circ}\) (3.56 Å, PA3) (Figure. 1b), which correspond to a disordered amorphous lattice. The small molecule showed many sharp XRD patterns at \(20 = 6.34^{\circ}\) (13.92 Å), \(12.64^{\circ}\) (6.99 Å), \(13.90^{\circ}\) (6.36 Å), \(21.18^{\circ}\) (4.19 Å), \(22.18^{\circ}\) (4.00 Å), which implies a highly crystalline lattice. The TGA data revealed that all polyamrides (PAs 1- 3) have excellent thermal stability, degrading at \(400 - 420^{\circ}\) C (Figure S1). From the TGA traces, the observed mass loss above \(400^{\circ}\) C was calculated as \(63.18 \pm 1.23\%\) (PA1), \(70.24 \pm 1.30\%\) (PA2), \(73.40 \pm 0.54\%\) (PA3), and \(75.33 \pm 0.10\%\) (TA) due to amide bond degradation. Since the TGA was done in a nitrogen atmosphere, the remaining solid could be a highly stable carbon analogue.  
+
+<|ref|>text<|/ref|><|det|>[[115, 765, 882, 907]]<|/det|>
+PAs 1 - 3 were dispersed in water and showed zetapotentials of \((- )7.56 \pm 2.23 \mathrm{mV}\) , \((- )12.58 \pm 0.34 \mathrm{mV}\) , and \((- )18.98 \pm 1.24 \mathrm{mV}\) . Such negative values are attributed to the presence of carboxylate groups (- COO\(^{- }\)) on the surface,\(^{34,35}\) which have emerged from the acyl group of TMC. Biogenic amines are protonated in water at a neutral pH of \(6 - 7.^{36,37}\) The zetapotentials measurement of amine dissolved in water showed positive zetapotentials of \((- )6.56 \pm 0.56 \mathrm{mV}\) (putrescine), \((- )7.23 \pm 1.55 \mathrm{mV}\) (spermidine), \((- )8.82 \pm 0.78 \mathrm{mV}\) (spermine), \((- )4.87 \pm 0.66\)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 84, 881, 151]]<|/det|>
+mv (tryptamine), and \((+1.87 \pm 0.34\) (tryptophan). The SEM images of PA1, PA2, and PA3 revealed spherical morphology structures (Figure 1c- e). However, the SEM images of crystalline small molecule TA showed a ribbon- type structure (Figure 1f).  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 184, 457, 203]]<|/det|>
+## Extraction of Amines from Water  
+
+<|ref|>text<|/ref|><|det|>[[115, 213, 880, 255]]<|/det|>
+The synthesized PAs were used for the extraction of biogenic amines from water using a batch process and monitored using UV- Vis spectroscopy.  
+
+<|ref|>image<|/ref|><|det|>[[115, 285, 880, 727]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 730, 880, 890]]<|/det|>
+<center>Figure 2. Absorbance spectra of ninhydrin complexes of spermine before (—■—) and after adsorption of putrescine (—●—), spermidine (—▲—), spermine (—▼—), tryptamine (—◆—), tryptophan (—★—), followed by ninhydrin treatment, PA1 (a) and PA2 (b), PA3 (c), and TA (d). Absorbance spectra of the ninhydrin complexes of other amines are given in the supporting information (Figure S2), which also showed the same adsorption maxima. The inset images show the optical images of the ninhydrin complexes of spermine (i) before and (ii) after extractions with different PAs. PA absorbents (25 mg) were used for the extraction of amine solution at a concentration of 50 mg/L. All adsorption experiments were conducted at pH 7 and \(22^{\circ}\mathrm{C}\) . </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 883, 301]]<|/det|>
+The amine molecules present in the supernatant reacted with the carbonyl group of the ninhydrin and formed a blue- colored solution. The concentration of the complex and color of the solution are proportional to the amount of amine present in the solution. \(^{38}\) The intensity values at the adsorption maximum \((\lambda_{\mathrm{max}})\) is \(563 \mathrm{nm}\) in the UV- Vis spectra of the ninhydrin complex were measured, and the removal efficiencies of all PAs were calculated (Figure 2a- c). Strong electrostatic interactions between PAs and amines present in water facilitated the adsorption and enhanced the removal efficiencies \((\sim 96 - 99\%)\) . As expected, the removal efficiencies of the model compounds, triamide TA \((73.46 \pm 2.12\%)\) , Figure 2d, is lower than other PA polymers.  
+
+<|ref|>sub_title<|/ref|><|det|>[[120, 317, 390, 337]]<|/det|>
+## Effect of Different Dosages  
+
+<|ref|>text<|/ref|><|det|>[[115, 345, 883, 784]]<|/det|>
+In a typical procedure, an appropriate concentration of amine solution \((50 \mathrm{mg / L}, 6 \mathrm{mL})\) was added to various amounts of PAs ranging from 2 to \(50 \mathrm{mg}\) . The extractions were carried out for \(300 \mathrm{min}\) , the mixture was centrifuged, and the remaining concentration of amine in the supernatant was determined using the ninhydrin test, and the extraction efficiency was reported in Figure 3a- d for PAs 1- 3 and TA. The maximum removal efficiencies (Equation 1) were obtained when the optimum amount of PAs \((25 \mathrm{mg})\) was used. PA1 (Figure 3a) showed removal efficiencies in the range of \(93.53 \pm 1.66 - 97.22 \pm 0.38\%\) , and PA2 (Figure 3b) showed \(93.48 \pm 0.70 - 98.74 \pm 0.12\%\) for the five amines tested. PA3 (Figure 3c) showed maximum removal efficiencies in the range of \(97.11 \pm 0.24 - 99.58 \pm 0.23\%\) for amines such as putrescine, spermidine, spermine, tryptamine, and tryptophan. The removal efficiencies of PAs remained constant, with a further increase in the adsorbent dosage of \(50 \mathrm{mg}\) due to the saturation of the surface. The saturation of the adsorbent surface occurs when all available active sites for adsorption are occupied by the target pollutants. When the adsorbate concentration is fixed, increasing the adsorbent amount increases adsorption efficiency by providing more active sites for binding. Initially, efficiency rises sharply with adsorbent dose, but increasing the adsorbent dose still increases the binding sites, and adsorption reaches equilibrium. However, beyond a certain dosage \((25 \mathrm{mg})\) , the removal efficiency is maximum because the pollutant concentration is fixed at \(50 \mathrm{mg / L}\) .
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[137, 81, 857, 504]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 514, 880, 598]]<|/det|>
+<center>Figure 3. Percentage removal efficiencies of putrescine (—), spermidine (—), spermine (—), tryptamine (—), tryptophan (—) of PA1 (a), PA2 (b), PA3 (c) and TA (d) polyaramides at different dosages. The extraction was done at room temperature for 300 min, and the amine concentrations were kept constant (50 mg/L). .All adsorption experiments were conducted at pH 7 and \(22^{\circ}C\) </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 604, 881, 870]]<|/det|>
+To understand the role of dimensionality of polymers in the extraction of amines from water, a structurally similar triamide small molecule (TA) was prepared from trimesoyl chloride (A3) and aniline (B1), for comparison. The adsorption experiments with small molecule TA as control at different dosages (2 to \(50\mathrm{mg}\) ) (Figure 3d) showed lower efficiencies towards the extraction of amines. At a lower dosage (2 mg) of TA, putrescine, spermidine, spermine, tryptamine, and tryptophan were removed with low efficiencies in the range of 3.97 \(\pm 0.56\%\) - \(10.43\pm 2.35\%\) (Figure 3d). The removal efficiencies of putrescine, spermidine, spermine, tryptamine, and tryptophan at high dosages of TA (25 mg) were in the range of 48 - 57%. This is much less ( \(\sim 80\%\) ) than the removal efficiency of PA3. The network- type structure of PAs 1- 3 has large numbers of electron- deficient amide groups for interacting with amines through hydrogen bonds. Such a network is absent in the case of small molecule TA.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 84, 875, 105]]<|/det|>
+## Effects of Time and Concentrations of Amines on the Adsorption Efficiency  
+
+<|ref|>text<|/ref|><|det|>[[115, 112, 883, 613]]<|/det|>
+The effects of different extraction time points (15 min, 30 min, 60 min, 90 min, 120 min, 180 min and 300 min) and amine concentrations (5, 10, 50, 100 and 150 mg/L) on the removal efficiency were examined. The amine solutions (6 mL) at different concentrations were shaken with fixed amounts of PAs (1- 3, and TAs 25 mg) at room temperature for 15 - 300 min intervals. Samples were analysed, and removal efficiencies were calculated (Figure 4a- h). The removal efficiencies of amines are low at short time points (15 - 90 min) for PA1 (Figure 4a), ranging from \(5.60 \pm 0.04\) to \(55.27 \pm 1.459\%\) . At a higher time duration (300 min), the removal efficiency was increased to \(70.04 - 89.60\%\) . At longer durations, higher removal efficiency was observed due to the increase in the contact time of amine and polyaramide. For amines, removal efficiencies decreased as the initial concentration increased from \(5 \mathrm{mg / L}\) to \(150 \mathrm{mg / L}\) (Figure 4b). Lower amine concentrations (5 mg/L) yielded \(61.40 - 89.74\%\) removal, whereas higher concentrations (150 mg/L) decreased efficiency due to surface saturation. This decrease is due to the saturation of adsorption sites on the surface, leading to decreased removal efficiencies. The initial adsorption rate was higher at lower concentrations, where particle uptake resistance decreased as mass transfer increased. Same way, removal efficiency of PA2 varied with different time points and amine concentrations. After 15 minutes, efficiency was in the range of \(20.84\% - 45.91\%\) , whereas the removal efficiency increased to \(75.83 - 96.44\%\) after 300 minutes for all amines tested. The PA2 showed lower removal efficiencies at high amine concentrations (150 mg/L; \(32.73 - 51.75\%\) ) and high removal efficiencies at low concentrations of PA2 (5 mg/L; \(74.49 - 95.24\%\) , (Figure 4c,d).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 80, 825, 757]]<|/det|>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[118, 82, 864, 310]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 340, 880, 414]]<|/det|>
+<center>Figure 4. Effect of time \((15 - 300\mathrm{min})\) and concentration \((5 - 150\mathrm{mg / L})\) of putrescine ( \(\bullet\) -), spermidine ( \(\bullet\) -), spermine ( \(\bullet\) -), tryptamine ( \(\bullet\) -) and tryptophan ( \(\bullet\) -) on removal efficiency, PA1 (a, b), PA2 (c, d), PA3 (e, f) and TA (g, h). The amount of all PAs used for the adsorption experiments was kept constant at \(25\mathrm{mg}\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 420, 882, 758]]<|/det|>
+The polymer, PA3 showed different removal efficiencies of five amines in the range of \(26.39\%\) to \(54.95\%\) after \(15\mathrm{min}\) shaking on a mechanical shaker (Figure 4e). By increasing the shaking time to \(300\mathrm{min}\) , there was a significant improvement in the removal efficiencies to \(84.39 - 99.81\%\) (Figure 4e). Similarly, at low concentrations of amines at \(5\mathrm{mg / L}\) , the polymer PA3 was able to remove \(73.65 - 99.42\%\) of all amines from water (Figure 4f). However, removal efficiencies decreased to \(40.35 - 83.14\%\) at a high concentration of amines at \(150\mathrm{mg / L}\) . The network structure of PA1 - 3 enabled high removal efficiencies as compared to the small molecule TA, with equilibrium reached within \(200\mathrm{min}\) . After \(15\mathrm{minutes}\) , the removal efficiencies of TA were at \(3.93 - 17.15\%\) (Figure 4g), and increasing the extraction time to \(300\mathrm{min}\) , the removal efficiencies were improved to \(48.33 - 56.89\%\) . The low amine concentrations ( \(5\mathrm{mg / L}\) ) in water enhanced TA's efficiencies to \(54.62 - 85.16\%\) . At high concentrations ( \(150\mathrm{mg / L}\) ) of amines, the removal efficiencies are as low as \(4.34 - 11.69\%\) for TA (Figure 4h). The small size of TA contributes to lower removal efficiency compared to other PAs.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 775, 362, 794]]<|/det|>
+## Isotherm Model Studies  
+
+<|ref|>text<|/ref|><|det|>[[115, 803, 880, 894]]<|/det|>
+To understand the adsorption behaviour of amines on the PA surface, the data were analysed using both the Freundlich and Langmuir isotherm models (Figure 5a- h). All necessary model equations for kinetics and isotherms are given in the Materials and Methods section (equations 2 - 6).
+
+<--- Page Split --->
+<|ref|>table_caption<|/ref|><|det|>[[67, 120, 880, 161]]<|/det|>
+Table 1. Regression coefficient and isotherm parameters for the adsorption of amines (putrescine, spermidine, spermine, tryptamine, and tryptophan) on the PAs.
+
+<|ref|>table<|/ref|><|det|>[[117, 175, 855, 812]]<|/det|>
+
+<table><tr><td rowspan="2">Amines used for<br>adsorption</td><td rowspan="2">Polyara<br>mides<br>(PAs)<br>used</td><td colspan="3">Langmuir</td><td colspan="3">Freundlich</td></tr><tr><td>\(K_{L}\) (L/mg)</td><td>\(Q_{max}\)</td><td>\(R^{2}\)</td><td>\(K_{r}\)</td><td>n</td><td>\(R^{2}\)</td></tr><tr><td rowspan="4">Putrescine</td><td>PA1</td><td>2.9791</td><td>100.200</td><td>0.9714</td><td>6.1263</td><td>1.5064</td><td>0.9260</td></tr><tr><td>PA2</td><td>0.1657</td><td>166.667</td><td>0.9667</td><td>0.9256</td><td>1.0997</td><td>0.9350</td></tr><tr><td>PA3</td><td>0.5088</td><td>243.902</td><td>0.9851</td><td>1.6801</td><td>1.5719</td><td>0.9066</td></tr><tr><td>TA</td><td>0.5676</td><td>51.813</td><td>0.9856</td><td>1.5150</td><td>1.2566</td><td>0.9678</td></tr><tr><td rowspan="4">Spermidine</td><td>PA1</td><td>0.0953</td><td>96.0799</td><td>0.9997</td><td>1.8399</td><td>8.3402</td><td>0.9172</td></tr><tr><td>PA2</td><td>0.0036</td><td>183.824</td><td>0.9814</td><td>1.0373</td><td>1.4830</td><td>0.9119</td></tr><tr><td>PA3</td><td>0.0027</td><td>334.448</td><td>0.9667</td><td>1.4728</td><td>1.1252</td><td>0.9326</td></tr><tr><td>TA</td><td>0.0099</td><td>81.300</td><td>0.9844</td><td>1.4402</td><td>1.2730</td><td>0.9767</td></tr><tr><td rowspan="4">Spermine</td><td>PA1</td><td>0.1304</td><td>138.889</td><td>0.9851</td><td>1.2770</td><td>1.6812</td><td>0.9066</td></tr><tr><td>PA2</td><td>0.0430</td><td>163.934</td><td>0.9859</td><td>1.3033</td><td>1.1265</td><td>0.9221</td></tr><tr><td>PA3</td><td>0.1925</td><td>370.372</td><td>0.9879</td><td>2.5200</td><td>1.4210</td><td>0.9178</td></tr><tr><td>TA</td><td>0.1547</td><td>119.048</td><td>0.9206</td><td>2.2839</td><td>1.0322</td><td>0.9175</td></tr><tr><td rowspan="4">Tryptamine</td><td>PA1</td><td>0.4431</td><td>102.040</td><td>0.9788</td><td>8.7317</td><td>1.6034</td><td>0.9009</td></tr><tr><td>PA2</td><td>0.3743</td><td>142.857</td><td>0.9883</td><td>9.4471</td><td>1.7085</td><td>0.9146</td></tr><tr><td>PA3</td><td>0.1302</td><td>270.170</td><td>0.998</td><td>2.9335</td><td>1.7489</td><td>0.9820</td></tr><tr><td>TA</td><td>0.6185</td><td>83.3333</td><td>0.9917</td><td>2.3344</td><td>1.7763</td><td>0.9892</td></tr><tr><td rowspan="4">Tryptophan</td><td>PA1</td><td>0.1333</td><td>81.9672</td><td>0.9638</td><td>3.6008</td><td>1.4590</td><td>0.9182</td></tr><tr><td>PA2</td><td>0.0853</td><td>119.047</td><td>0.9923</td><td>7.2627</td><td>1.5676</td><td>0.9453</td></tr><tr><td>PA3</td><td>0.0502</td><td>232.558</td><td>0.9814</td><td>6.1574</td><td>1.5829</td><td>0.9556</td></tr><tr><td>TA</td><td>0.1394</td><td>76.9230</td><td>0.9794</td><td>1.7139</td><td>1.2933</td><td>0.9554</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[67, 815, 95, 826]]<|/det|>
+350
+
+<|ref|>text<|/ref|><|det|>[[67, 850, 880, 912]]<|/det|>
+351 After analysis of the data, the Langmuir isotherm model provided a better fit (Table 1)(Figure 5a, c, e, and g) for each of the five amines when compared to Freundlich's model(Figure S3). The adsorption of amines on the PA surface is indicated by high values of \(K_{L}\) and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 250]]<|/det|>
+n. Monolayer formation of all amines was observed on PA surfaces, as stated by the Langmuir model. This is expected due to the strong interaction between the negatively charged PA surface and positively charged amines at neutral pH. PA3 had a higher adsorption capacity \((Q_{\mathrm{max}})\) compared to PA1, PA2, and TA for putrescine, spermidine, spermine, tryptophan, and tryptamine, with respective removal amounts of \(243.9\mathrm{mg / g}\) , \(334.4\mathrm{mg / g}\) , \(370.3\mathrm{mg / g}\) , \(270.1\mathrm{mg / g}\) , and \(232.5\mathrm{mg / g}\) from water which is calculated using Langmuir model (Table 1). The corresponding values for other polymers are given in Table 1.  
+
+<|ref|>image<|/ref|><|det|>[[117, 300, 864, 768]]<|/det|>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 84, 864, 528]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 539, 881, 644]]<|/det|>
+<center>Figure 5. Langmuir (a, c, e and g) and pseudo-second-order kinetics (b, d, f and h) plots for PA1 (a, b), PA2 (c, d), PA3 (e, f), TA (g, h) at neutral pH and 298 K using different concentrations (5 - 150 mg/mL) of the putrescine (- - -), spermidine (- - -), spermine (- - -), tryptamine (- - -) and tryptophan (- - -) and a fixed concentration of absorbents (25 mg). The Freundlich isotherm and pseudo-first order kinetic regressions for PAs 1 - 3 and TA, are given in the supporting information (Figure S3). </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 677, 344, 696]]<|/det|>
+## Kinetic Model Studies  
+
+<|ref|>text<|/ref|><|det|>[[115, 707, 881, 896]]<|/det|>
+To study the mechanism, adsorption of a series of amines at different adsorption times was used (Figure 5, Table 2). The data collected from the five BAs used in the experiments were fitted with pseudo- first- order and pseudo- second- order kinetic models. The methods and materials section includes all equations relevant to both kinetic models. The practical and theoretical parameters determined from the data are given in Figure 5b, d, f and h and summarised in Table 2. The pseudo- second- order kinetic models fit the adsorption data for the five amines more closely than pseudo- first- order kinetic models for all PAs (Table 2). Higher \(\mathrm{R}^2\) values (putrescine - 0.9876, spermidine - 0.9878, spermine - 0.9999, tryptamine - 0.9986,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[60, 85, 880, 101]]<|/det|>
+tryptophan – 0.9980) were obtained for PA3 using the pseudo-second-order model (Table 2).
+
+<|ref|>text<|/ref|><|det|>[[60, 111, 880, 172]]<|/det|>
+Furthermore, the theoretical removal efficiencies (Qe, cal) calculated using the pseudo-second-order model for each of the five amines are in agreement with the experimental data (Qe, exp) obtained.
+
+<|ref|>text<|/ref|><|det|>[[60, 187, 92, 198]]<|/det|>
+386
+
+<|ref|>text<|/ref|><|det|>[[60, 220, 880, 235]]<|/det|>
+Table 2. Kinetic parameters for the adsorption of amines, putrescine, spermidine, spermine,
+
+<|ref|>text<|/ref|><|det|>[[60, 245, 661, 260]]<|/det|>
+tryptamine, and tryptophan on PAs 1-3 and model compound TA.
+
+<|ref|>table<|/ref|><|det|>[[117, 273, 870, 863]]<|/det|>
+
+<table><tr><td rowspan="3">Amines used</td><td rowspan="3">Polya<br>mide<br>used</td><td colspan="3">Pseudo-first order</td><td colspan="4">Pseudo-second order</td></tr><tr><td>\(Q_{\mathrm {e}}\)cal</td><td>\(K_{1}\)</td><td>\(R^{2}\)</td><td>\(Q_{\mathrm {e}}\)</td><td>\(Q_{\mathrm {e}}\)</td><td>\(K_{2}\)(g</td><td>\(R^{2}\)</td></tr><tr><td>(mg g-1)</td><td>(min-1)</td><td></td><td>(exp.)<br>(mg g-1)</td><td>(cal.)<br>(mgg-1)</td><td>\(mg^{-1}\)<br>min-1)</td><td></td></tr><tr><td rowspan="4">Putrescine</td><td>PA1</td><td>9.4413</td><td>0.018</td><td>0.9104</td><td>156.780</td><td>112.36</td><td>0.0220</td><td>0.9986</td></tr><tr><td>PA2</td><td>9.2470</td><td>0.024</td><td>0.9152</td><td>159.094</td><td>149.254</td><td>0.0171</td><td>0.9873</td></tr><tr><td>PA3</td><td>8.0566</td><td>0.051</td><td>0.9179</td><td>211.345</td><td>208.333</td><td>0.0052</td><td>0.9876</td></tr><tr><td>TA</td><td>6.2463</td><td>0.04</td><td>0.9478</td><td>83.342</td><td>76.9231</td><td>0.0051</td><td>0.9903</td></tr><tr><td rowspan="4">Spermidine</td><td>PA1</td><td>17.0713</td><td>0.077</td><td>0.9172</td><td>268.902</td><td>256.41</td><td>0.0011</td><td>0.9997</td></tr><tr><td>PA2</td><td>19.0963</td><td>0.0095</td><td>0.9135</td><td>290.112</td><td>270.278</td><td>0.0107</td><td>0.9999</td></tr><tr><td>PA3</td><td>20.5734</td><td>0.0122</td><td>0.9446</td><td>303.124</td><td>277.778</td><td>0.0082</td><td>0.9878</td></tr><tr><td>TA</td><td>17.4092</td><td>0.0102</td><td>0.9121</td><td>195.564</td><td>181.811</td><td>0.0024</td><td>0.9863</td></tr><tr><td rowspan="4">Spermine</td><td>PA1</td><td>24.1987</td><td>0.0059</td><td>0.9066</td><td>258.009</td><td>263.158</td><td>0.0166</td><td>0.9851</td></tr><tr><td>PA2</td><td>36.6752</td><td>0.060</td><td>0.9591</td><td>318.909</td><td>287.356</td><td>0.0095</td><td>0.9996</td></tr><tr><td>PA3</td><td>48.9598</td><td>0.093</td><td>0.9671</td><td>304.901</td><td>294.118</td><td>0.0037</td><td>0.9999</td></tr><tr><td>TA</td><td>12.9877</td><td>0.0056</td><td>0.9477</td><td>192.778</td><td>185.183</td><td>0.0044</td><td>0.9632</td></tr><tr><td rowspan="4">Tryptamine</td><td>PA1</td><td>9.64944</td><td>0.002</td><td>0.9215</td><td>112.456</td><td>99.0099</td><td>0.0351</td><td>0.9778</td></tr><tr><td>PA2</td><td>12.9902</td><td>0.032</td><td>0.9168</td><td>124.098</td><td>109.890</td><td>0.0153</td><td>0.9987</td></tr><tr><td>PA3</td><td>19.7469</td><td>0.035</td><td>0.9247</td><td>134.678</td><td>294.117</td><td>0.0672</td><td>0.9986</td></tr><tr><td>TA</td><td>6.7823</td><td>0.022</td><td>0.8312</td><td>75.785</td><td>68.0272</td><td>0.0882</td><td>0.9640</td></tr><tr><td rowspan="4">Tryptophan</td><td>PA1</td><td>8.69371</td><td>0.0046</td><td>0.9179</td><td>298.09</td><td>90.9090</td><td>0.0107</td><td>0.9998</td></tr><tr><td>PA2</td><td>11.1439</td><td>0.0034</td><td>0.8742</td><td>183.980</td><td>108.695</td><td>0.0103</td><td>0.9999</td></tr><tr><td>PA3</td><td>18.3476</td><td>0.0094</td><td>0.9820</td><td>301.333</td><td>243.902</td><td>0.0012</td><td>0.9980</td></tr><tr><td>TA</td><td>12.7738</td><td>0.0076</td><td>0.9497</td><td>94.878</td><td>83.333</td><td>0.0117</td><td>0.9700</td></tr></table>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[117, 84, 812, 126]]<|/det|>
+## Analysis of PAs After Extraction of Commercial Amines from Spiked Samples  
+
+<|ref|>text<|/ref|><|det|>[[116, 134, 883, 326]]<|/det|>
+The amine adsorption on the PAs influences the surface characteristics. Changes in the zetapotential of PAs are examined before and after the adsorption of amines. Before the amines were adsorbed, the PAs showed negative zetapotential values due to the surface - COO end groups on the polymer (Table 3). The positively charged amines are adsorbed on the negatively charged PA surface. After adsorption of amine (spermine), the zetapotential of PAs in water was measured at ambient temperature and showed positive zetapotentials for PA1 (+)14.93 ± 1.23, PA2 (+15.3 ± 2.33, and PA3 (+19.93 ± 0.45. The zetapotential for the adsorption of other amines is given in the supporting information (Table S2).  
+
+<|ref|>table<|/ref|><|det|>[[139, 372, 850, 528]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[115, 341, 725, 360]]<|/det|>
+Table 3. Particle size, zetapotential, and BET analysis data for PAs and TA.   
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Particle Size (nm)</td><td rowspan="2">Pore Size (nm)</td><td rowspan="2">Surface area (m²/g)</td><td colspan="2">ζ Potential (mV)</td></tr><tr><td>Before</td><td>After(spermine)</td></tr><tr><td>PA1</td><td>1288 ±3.09</td><td>4.191</td><td>10.843</td><td>(-)7.56±2.23</td><td>(+)14.93 ± 1.23</td></tr><tr><td>PA2</td><td>918 ± 3.26</td><td>2.978</td><td>14.048</td><td>(-)12.58±0.34</td><td>(+)15.3 ± 2.33</td></tr><tr><td>PA3</td><td>875±1.24</td><td>3.233</td><td>29.233</td><td>(-)18.98±1.24</td><td>(+)19.93 ± 0.45</td></tr><tr><td>TA</td><td>529±3.09</td><td>5.790</td><td>5.683</td><td>(-)2.52±0.68</td><td>(+)12.88 ± 1.89</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[115, 558, 883, 774]]<|/det|>
+The Fourier transform infrared (FTIR) spectra of all PAs, after the adsorption of amines, showed a broad peak in the range of \(3100 - 3600\mathrm{cm}^{- 1}\) , which corresponds to the N- H stretching from the amide group on the polymer backbone and amine groups after adsorption process, (Figure S4). All PAs showed adsorption peaks corresponding to the aromatic and aliphatic - CH- groups on the polymer backbone (Figure S6a- c). Amide I and amide II peaks were observed around 1660 and \(1545\mathrm{cm}^{- 1}\) , which is slightly shifted to the higher wavelength from the peaks corresponding to the polyaramides before the adsorption of amines. This is expected due to the strong interactions of amine - NH- and amide \(> \mathrm{C} = \mathrm{O}\) groups. The other common peaks were observed around 1293, 917, and \(709\mathrm{cm}^{- 1}\) for PAs before and after adsorption.  
+
+<|ref|>text<|/ref|><|det|>[[115, 789, 881, 907]]<|/det|>
+PA solids obtained after the adsorption of amines were examined using thermogravimetric analysis under a nitrogen atmosphere. The TGA analysis was conducted throughout a temperature range from \(22^{\circ}\mathrm{C}\) to \(1000^{\circ}\mathrm{C}\) , with a heating rate of \(10^{\circ}\mathrm{C}\) per minute (Figure S5). There was no specific change observed as the smaller amount of amines adsorbed onto the PAs. The ICP analysis of nitrogen content analysis indicates an increase in the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 881, 200]]<|/det|>
+percentage of nitrogen after adsorption of amines on PAs (Table S1). Pristine PAs showed 6.48, 6.68, 6.90, and 5.67 % of nitrogen content for PAs 1 – 3 and TA, respectively. The nitrogen content after adsorption of the amines on PAs was increased in the range of 9 to 14% (Table S1). Similar to N content, the percentages of C and H also increased after adsorption of the amines on PAs. Such results are complementary to the extraction data.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 216, 335, 236]]<|/det|>
+## Regeneration Studies  
+
+<|ref|>text<|/ref|><|det|>[[115, 254, 880, 297]]<|/det|>
+After adsorption of the amines on PAs, regeneration, and reuse of the same PAs were also attempted.  
+
+<|ref|>image<|/ref|><|det|>[[115, 312, 880, 800]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 808, 881, 908]]<|/det|>
+<center>Figure 6. Removal efficiencies of PA 1 - 3 after repeated adsorption-desorption cycles (cycle 1 (■), cycle 2 (■), cycle 3 (■), cycle 4 (■), and cycle 5 (■)). The concentration of putrescine (a), spermidine (b), spermine (c), and tryptamine (d) used was \(50 \mathrm{mg / L}\) , a time of \(300 \mathrm{min}\) , and an adsorbent dose of \(25 \mathrm{mg}\) was kept constant. The regeneration data of PA 1 - 3 after adsorption of tryptophan are given in the supporting information (Figure S6). The regeneration data for TA using all amines are given in the supporting information (Figure S7). </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 882, 349]]<|/det|>
+PAs (25 mg) with adsorbed amines on the surface were washed with dilute HCl solution (0.5 M, \(10~\mathrm{mL}\) ) a few times. The resulting mixture was centrifuged, and the solid was washed with water to remove traces of acid and dried at \(60^{\circ}\mathrm{C}\) . The solid was then reused for the extraction of amines from water. The removal efficiencies of regenerated PAs for different amines were measured for five repeated cycles of washings and readortions of the amines. The regenerated PAs demonstrated consistent removal efficiencies of over \(90\%\) , suggesting that PAs are a very effective and reusable adsorbent (Figure 6a- d). PAs were recovered quickly from the solution through filtration after the adsorption. The regeneration process involves protonation (acid- base reaction) of the adsorbed amines (basic) by HCl (acid), converting them into water- soluble ammonium salts for desorption. The removed PAs were utilized directly in the subsequent adsorption procedure without the need for drying or grinding.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 365, 796, 386]]<|/det|>
+## Extraction and Identification of Biogenic Amines from Fish Sample  
+
+<|ref|>text<|/ref|><|det|>[[115, 402, 882, 690]]<|/det|>
+To explore the application of synthesized PA materials in environmental samples, common fish samples were purchased from supermarkets and kept at room temperature for natural degradation. Cleaned fish tissue (2 g) was kept at room temperature in an open environment at different time points (6 h, 24 h, and 48 h). After homogenization in water, the samples were centrifuged. The resulting supernatant fish extract was used for LCMS analysis. A fixed amount of PAs was mixed with an appropriate amount of fish extract solution and kept in a mechanical shaker. The mixture was centrifuged, and the supernatant was treated with ninhydrin reagent to convert the amines into a blue- coloured amine- ninhydrin complex. The UV spectra of the colored complex solution were recorded for solutions before and after extraction with PAs and are presented in Figure 7a. A standard calibration curve was prepared using the known solutions of commercially available amine solutions after treatment with ninhydrin solution.  
+
+<|ref|>text<|/ref|><|det|>[[115, 707, 882, 873]]<|/det|>
+The concentration of extracted unknown amines in the solution was measured from the calibration curve. The amines generated inside the fish sample left for 6 hours in open air at ambient conditions were quantified as 2.566 mg/g, which increased to 18.45 and 34.56 mg/g with an increase in time of open- air degradation of 24 h and 48 h, respectively. A known volume (i.e. \(6~\mathrm{mL}\) ) was mixed with PA3 (50 mg) and kept on a mechanical shaker for 6 h. The removal efficiencies of the PAs were calculated from the UV adsorption spectra of the ninhydrin- treated extract solutions before and after adsorption (Figure 7b). PA3 showed high removal efficiencies
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[60, 84, 880, 128]]<|/det|>
+466 of \(99.42 \pm 0.12 \%\) , \(97.00 \pm 1.43 \%\) , and \(95.05 \pm 0.92 \%\) for extract of fish samples after 6 h, 24 h, and 48 h, respectively.  
+
+<|ref|>image<|/ref|><|det|>[[60, 155, 870, 655]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 669, 881, 837]]<|/det|>
+<center>Figure 7. (a) UV-Vis spectra of the ninhydrin treated extracts obtained from fish sample kept at different time points of 6 h, 24 h, and 48 h at room temperature before (6 h (-), 24 h (-), 24 h (-)) and after (6 h (-), 24 h (-), and 48h (-)) extraction with PA 1-3 samples (25 mg). Note that the absorbance of solutions after extraction with PA was almost zero, indicating a complete removal of amines. (b) The extraction efficiencies of PAs (50 mg) for the removal of amines from solutions collected after keeping the fish samples for 6 h, 12 h, and 24 h at room temperature. The extraction time was kept at 5 h for all samples. (c) LC traces of extract collected from fish sample (2 g) after 48 h at room temperature. Optical images of fish samples (2 g) and LCMS traces of 6h and 24 h fish extracts are given in the supporting information (Figure S8). </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 870, 880, 914]]<|/det|>
+LCMS traces were utilized to identify and quantify the amines present in the extracts of fish tissues (Figure 7c). A few peaks were identified by comparing the retention time and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 83, 883, 399]]<|/det|>
+mass of the commercial amine samples. The retention peak positions at 1.03 min and 1.98 min indicated the presence of putrescine and spermidine with mass (m/z) values of 88.10 and 146.20, respectively. Tryptamine, with a retention time of 8.87 min, was identified with an m/z value of 160.10. The next major peak, with a retention time of 13.66 min and a m/z value of 186.22, was identified as 1- O- alkylglycerols. Similarly, the next major peak with a retention time of 15.88 min and a m/z value of 241.28, indicates the presence of hexadecylamine. The peak with a retention time of 18.62 min and an m/z value of 256.30 is identified as palmitic acid, which is present in fish oil. The next major peak at 26.12 min with a m/z value of 248.48 corresponds to stearic acid. The corresponding mass spectrometry data of all the major peaks observed for the components in the fish extract are given in the supporting information (Figure S9). LCMS obtained from commercial BAs solutions were used for comparison and quantification (Figure S10). The mass spectra of five different commercially available BAs used in our extraction were given in the supporting information (Figure S11).  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 413, 815, 435]]<|/det|>
+## Comparison of the Removal Efficiency of PAs with Other Absorbents  
+
+<|ref|>text<|/ref|><|det|>[[115, 441, 883, 808]]<|/det|>
+Biogenic amines are generated through fermentation and decaying of meat and fish samples. Due to relatively low levels of BAs present in water bodies, only a limited number of research have focused on their occurrence in surface and waste waters. Nevertheless, the excessive release or accumulation of organic matter (such as animal remains or discarded food) usually contaminates water and alters the taste, smell, and dissolved oxygen levels. Such deterioration of water quality induces negative consequences for aquatic life, potentially leading to reduced activity or even death of these organisms. Zhu et al. reported that the poly(ether-block- amide) removed 54 - 72 % of biogenic amines such as histamine, putrescine, cadaverine, and tyramine from water. Another group reported 82 - 100% removal efficiency for histamine, putrescine, cadaverine, spermidine, spermine, and tryramine from water using functionalized silica material. The methods of extraction and detection techniques can impact the comparison of adsorption efficiency. The choice of adsorption method plays a significant role in the results; for example, batch extraction may favour high- capacity adsorbents, while chromatography- based methods may highlight selectivity. Additionally, batch extraction is generally more scalable than chromatography- based methods.  
+
+<|ref|>text<|/ref|><|det|>[[115, 814, 881, 907]]<|/det|>
+Here, we report a polyaramide- based adsorbents for the removal of biogenic amines from water. The removal process was thoroughly analyzed using kinetic studies, TGA, SEM, and FTIR spectra to gain valuable mechanistic insights. Furthermore, Table 4 presents a comprehensive comparison of various parameters, including different absorbents, removal
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 85, 880, 150]]<|/det|>
+methods, particle concentrations, and the removal efficiencies achieved through different analytical methods. Compared to the absorbent materials reported in the literature, the PAs 1 – 3 showed high removal efficiencies (i.e. \(\sim 99.96\%\) , Table 4). 
+
+<|ref|>table_caption<|/ref|><|det|>[[115, 185, 712, 201]]<|/det|>
+Table 4. Comparison of removal efficiency of PAs with other absorbents. 
+
+<|ref|>table<|/ref|><|det|>[[115, 214, 880, 900]]<|/det|>
+<table><tr><td></td><td>Adsorbent</td><td>Experiment method</td><td>Adsorption percentage %</td><td>Removal efficiency (mg/g)</td><td>Ref.</td></tr><tr><td>1</td><td>Graphene aerogel</td><td>Batch extraction</td><td>HIS 85.19%, CAD 74.1%, and SPD 70.11%</td><td>-</td><td>49</td></tr><tr><td>2</td><td>Poly(ether-block-amide)</td><td>Batch extraction</td><td>HIS 54%, PUT 72%, CAD 68%, TYR 87%</td><td>HIS 3.46, PUT 4.58, CAD 5.09, TYR 5.86</td><td>47</td></tr><tr><td>3</td><td>Functionalized silica material</td><td>Liquid chromatograph (LC) coupled to a mass spectrometer detector</td><td>HIS 95.0%, PUT 82.0%, CAD 88.7%, SPD 100%, SPM, 100%, TYR 13.3%</td><td>-</td><td>48</td></tr><tr><td>4</td><td>Sulfamic acid functionalised blast furnace slag</td><td>Batch extraction</td><td>PUT 90%, TYR 70%, PEA 99%</td><td>PEA 80.64, PUT 12.5 and TYR 64.52</td><td>50</td></tr><tr><td>5</td><td>Crown ether-modified mesoporous silica</td><td>High-Performance Liquid Chromatograph</td><td>TRP 40%, PUT 40%, HIS 12%, TYR 20%, SPD 98%</td><td></td><td>51</td></tr><tr><td>7</td><td>PA1</td><td>Batch Extraction</td><td>PUT 94.82 ± 0.12%, SPD 95.48 ± 0.15%, SPM 97.22 ± 0.38%, TYA 95.68 ± 1.15%, TYP 93.53 ± 1.66%</td><td>PUT 100.20, SPD 96.07, SPM 138.88, TYA 102.04, TYP 81.96</td><td>This work</td></tr><tr><td>8</td><td>PA2</td><td>Batch Extraction</td><td>PUT 94.31±1.55%, SPD 97.45± 0.10%, SPM 98.64± 0.17%, TYA 98.04 ±</td><td>PUT 166.66, SPD 183.82, SPM 163.93, TYA 142.85, TYP 119.04</td><td>This work</td></tr></table>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[457, 83, 580, 116]]<|/det|>
+0.12%, TYP 93.48± 0.70%, 
+
+<|ref|>table<|/ref|><|det|>[[120, 131, 870, 266]]<|/det|>
+<table><tr><td>9</td><td>PA3</td><td>Batch Extraction</td><td>PUT 97.56 ± 0.24%, SPD 98.97 ± 0.68%, SPM 99.58 ± 0.23%, TYA 98.97 ± 1.68%, TYP 96.96 ± 0.08 %</td><td>PUT 243.90, SPD 334.44, SPM 370.37, TYA 270.17, TYP 232.55</td><td>This work</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[67, 283, 870, 319]]<|/det|>
+522 Abbreviation: HIS- histamine, CAD - cadaverine, SPD - spermidine, PUT - putrescine, TYR
+523 - tyramine, SPM - spermine, PEA - 2-phenylamine, TYA - tryptamine, TYP - tryptophan. 
+
+<|ref|>sub_title<|/ref|><|det|>[[117, 355, 383, 374]]<|/det|>
+## Mechanism of Adsorption 
+
+<|ref|>text<|/ref|><|det|>[[117, 385, 881, 550]]<|/det|>
+Biogenic amines have been shown to accumulate due to microbial attacks on meat or fish products.52 53 Biogenic amines can harm aquatic life, disrupt water ecosystems, and pose health risks to humans, particularly those with histamine intolerance or certain medical conditions.54 Table 4 shows a list of the different absorbents that have been used for removing different biogenic amines from water. The current study used commercially available biological amines such as putrescine, spermine, spermidine, tryptamine, and tryptophan to understand the removal efficiencies of PAs. 
+
+<|ref|>text<|/ref|><|det|>[[117, 567, 881, 755]]<|/det|>
+The PAs 1-3 synthesized during this study showed a negative zetapotential that is ideal for extracting the positively charged amines in water at a neutral pH. At an equilibrium concentration of PAs (25 mg) and an adsorption time of 300 min, high removal efficiencies of 97.11 ± 0.24 %, 98.97 ± 0.68 %, 99.58 ± 0.23 %, 98.97 ± 1.68 %, 96.96 ± 0.08 % for putrescine, spermidine, spermine, tryptamine, and tryptophan, respectively, were observed. The polyaramide (PA3) showed higher removal efficiency (~ 99%) than other polymers. PA3 has a greater surface area (29.23 m²/g) due to the incorporation of the nonlinear m-xylene diamine in the structure.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[118, 95, 820, 380]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[117, 394, 829, 413]]<|/det|>
+<center>Scheme 2. The complexation and extraction behaviour of PA with amines from solution </center>  
+
+<|ref|>text<|/ref|><|det|>[[115, 428, 883, 915]]<|/det|>
+Also, the zetapotentials of amine solutions in water were measured at ambient temperature and neutral pH (7.0). The respective values obtained for putrescine, spermidine, spermine, tryptamine, and tryptophan were \((+6.56 \pm 0.56 \text{mV}, (+7.23 \pm 1.55 \text{mV}, (+8.82 \pm 0.78 \text{mV}, (+4.87 \pm 0.66 \text{mV}, and (+1.87 \pm 0.34 \text{mV. All synthesized PAs showed a negative zetapotential for the adsorption of positively charged amines. After the amine adsorption, the zetapotential of the PA surface changed from negative to positive values (Table 3). The negatively charged polyaramides (PAs) attract the protonated amine molecules on the surface via electrostatic forces and H- bonding. The zetapotential of the PA surface changed from negative to positive values after extracting the amines from the solution (Table 3, Scheme 2). In addition to electrostatic interaction, hydrogen bonds also play an important role towards the removal of amines from water. PA3 showed a higher adsorption capacity (Qmax) of amine 243.9 mg/g for putrescine, 334.4 mg/g spermidine, 370.3 mg/g for spermine, 270.1 mg/g for tryptamine, and 232.5 mg/g for tryptophan. Elemental analysis indicates an increase in nitrogen content for all PAs after adsorption of biogenic amines (Table S1). PAs absorbed with spermine have a higher percentage of nitrogen content, 6.89 - 14.43 %, compared to other biogenic amines due to higher adsorption efficiency. The order of removal efficiencies of biogenic amines is spermine > spermidine > putrescine > tryptamine > tryptophan. To understand and compare the removal efficiencies of PAs, other monoamines such as hexylamine, and phenyl ethylene amine were also used for the extraction studies. PA3 exhibited removal efficiencies of 87.61 ± 2.43 and 87.30 ± 1.02 % for hexyl amine (HA) and phenylene ethylene amine (PEA),
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 82, 881, 349]]<|/det|>
+respectively. Similarly, both PA2 and PA1 showed lower removal efficiencies of \(80 - 77\%\) for HA and \(70 - 50\%\) for PEA under same experimental conditions (Figure S12). Similarly, the small molecules (TA) showed \(57.70 - 73.46\%\) removal efficiencies, which are lower than that observed for PAs 1- 3. The synthesized PAs were used to extract amines and other degraded molecules in the decaying fish samples kept at room temperature for periods of \(6\mathrm{h}\) , \(24\mathrm{h}\) , and \(48\mathrm{h}\) . LCM technique and commercially available standard amine samples were used to determine the chemical identity of the compounds present in the fish extract. All three polyaramides have a new work structure, in particular, PA3 is expected to have a 3D architecture due to the bent structure of the diamine, MX. The network structure and negative zetapotential of PAs help to trap the positively charged amine molecules inside the solid lattice, which then enhances the adsorption capacities (Scheme 2).  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 366, 234, 384]]<|/det|>
+## Conclusion  
+
+<|ref|>text<|/ref|><|det|>[[115, 393, 882, 782]]<|/det|>
+The amide- based porous network polymers effectively removed biogenic amines such as putrescin, spermidine, spermine, tryptamine, and tryptophan. The prepared PAs removed biogenic amines (BAs) from water with around \(99\%\) efficiency. All the PAs were characterized before and after adsorption of the amines. PA3 showed the highest adsorption efficiencies \((Q_{\mathrm{max}})\) as compared to the other three PAs ( \(244\mathrm{mg / g}\) putrescin, \(334\mathrm{mg / g}\) spermidine, \(370\mathrm{mg / g}\) spermine, \(270\mathrm{mg / g}\) tryptamine, and \(232\mathrm{mg / g}\) tryptophan). Absorbents (PA1- 3) and model compound TA were characterized using FTIR spectra, TGA, and SEM. The extraction data for the amines were analyzed using the Langmuir and Freundlich isotherm models and different kinetic models. The absorbents were regenerated and reused to extract amines from water. After five cycles, the PAs showed similar removal efficiencies, and there was no appreciable efficiency loss due to polymer degradation. Compared to triamide (TA), the PAs 1- 3 showed higher removal efficiencies towards various amines tested. The synthesised PAs were also used to extract amines generated by decaying natural fish tissues for \(6\mathrm{h}\) to \(48\mathrm{h}\) . The amounts of amines extracted from such fish tissues were in the range of \(2 - 35\mathrm{mg / g}\) which increased with an increase in time. Such easily accessible synthetic polymers are a great candidate for environmental remediation in the future.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 798, 363, 818]]<|/det|>
+## Supporting Information  
+
+<|ref|>text<|/ref|><|det|>[[117, 834, 881, 907]]<|/det|>
+Full synthetic details of polyaramides; PA1- 3 and small molecule TA; TGA (b) of PA1 (—), PA2 (—), PA3 (—) and SA1 (—) before adsorption; Absorbance spectra of ninhydrin complex of putrescin (—), spermidine (—), tryptamine (—), and tryptophan (—) at a concentration of \(50\mathrm{mg / L}\) ; Freundlich (a, c, e, g) and pseudo- first- order kinetics (b, d, f and h)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 84, 880, 549]]<|/det|>
+plots for PA1 (a and b), PA2 (and d), PA3(e and f) and SA1 (g and h) at 298 K using different concentrations (5 - 150 mg/mL) of the putrescine (--), spermidine (--), spermine (--), tryptamine (--) and tryptophan (--). A fixed concentration (25 mg in 6 mL) of PAs and SA1 are used for all studies; FTIR spectra of PA1 (a), PA2 (b), PA3 (c) and SA1 (d) after adsorption of putrescine (--), spermidine (--), spermine (--), tryptamine (--) and tryptophan (--). KBr matrix was used for recording the spectra; TGA of PA1 (a), PA2 (b), PA3 (c), and SA1 (d) after adsorption of putrescine (--), spermidine (--), spermine (--), tryptamine (--), and tryptophan (--); Removal & regeneration efficiencies of PA 1 - 3 after repeated absorption-desorption cycles 1 (--), 2 (--), 3 (--), 4 (--), and 5 (--) using tryptophan as a model amine. The tryptophan concentration was 50 mg/L, extraction time of 300 min, and an adsorbent dose of 25 mg was kept constant; Removal efficiency of SA1 after repeated adsorption-desorption cycles (cycle 1 (--), cycle 2 (--), cycle 3 (--), cycle 4 (--), and cycle 5 (--). The concentration of Putrescine (a), Spermidine(b), Spermine(c), Tryptamine(d), and tryptophan(e) (50 mg/L), time (300 min), and adsorbent dose (25 mg) were kept constant. PUT-Putrescine, SPD-Spermidine, SPM-Spermine, TYA- Tryptamine, and TYP-Tryptophan; Optical images of fish samples at different time points of 6h (a), 24 h (b), and 48 h (c). LCMS traces of crude extracts collected from fish samples kept at 6h (d) and 24 h using a C-18 reverse phase column; The mass spectra of eluents with a retention time of 1.03 min (a),1.98 min (b), 8.87 min (c), 10.33 min (d),13.88 min (e),15.88 min (f), 18.62 min (g), 26.12 min (h) observed for the fish extract collected from 48h; LCMS of standard commercial amines, putrescine (1), spermidine (2), spermine (3), tryptamine (4) and tryptophan (5). The inset represents the enlarged view of putrescine (1) and spermidine (2) peaks; The mass spectra of commercially available standard samples of putrescine (1), spermidine (2), spermine (3), tryptamine (4) and tryptophan (5); Removal efficiencies of hexylamine (a)and phenylethylamine (b) at different concentrations (5 - 100 mg) of polyaramides PA1 (--), PA2 (--) and PA3 (--). The concentration of all PAs was kept constant at 25 mg.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 588, 429, 606]]<|/det|>
+## Author contribution statement  
+
+<|ref|>text<|/ref|><|det|>[[118, 624, 802, 658]]<|/det|>
+GM: Experimentation, collection of data, formal analyses, writing of the paper draft. SV: Resources, ideation, methodology, and revision of the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 668, 500, 687]]<|/det|>
+## Declaration of the competing interests  
+
+<|ref|>text<|/ref|><|det|>[[118, 705, 880, 740]]<|/det|>
+The authors declare no known competing financial or personal relationships that could have influenced the work reported in this paper.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 749, 207, 768]]<|/det|>
+## Funding  
+
+<|ref|>text<|/ref|><|det|>[[118, 778, 863, 830]]<|/det|>
+The authors acknowledge the funding support from the National Research Foundation grant A- 0004151- 00- 00 and technical support from the Department of Chemistry at the National University of Singapore.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 841, 289, 859]]<|/det|>
+## Data Availability
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[66, 85, 874, 138]]<|/det|>
+The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information file. All data that support the findings of this study are available from the corresponding author upon reasonable request.  
+
+<|ref|>sub_title<|/ref|><|det|>[[67, 148, 230, 167]]<|/det|>
+## References  
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+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[130, 140, 866, 191]]<|/det|>
+# Engineered Polyamides for Extraction of Bioamines from Water  
+
+<|ref|>text<|/ref|><|det|>[[275, 203, 720, 268]]<|/det|>
+Gomathi Mahadevan and Suresh Valiyaveettil\*  Department of Chemistry, National University of Singapore  3 Science Drive 3, Singapore 117543  Email: chmsv@nus.edu.sg  
+
+<|ref|>image<|/ref|><|det|>[[140, 345, 870, 696]]<|/det|>
+
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+## 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, 330, 150]]<|/det|>
+Supportinginformation.docx
+
+<--- Page Split --->

preprint/preprint__07ca7119489ce742f39828987bc35bcbb114b2fcae1faac252a175d7615d08d8/images_list.json

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+    "caption": "Figure 2: Measured radial profiles of a) electron density \\(n_{e}\\) b) electron temperature \\(T_{e}\\) c) ion temperature \\(T_{i}\\) , averaged over a 100 ms time window, in the case with (red) and without (blue) B powder injection. Polynomial fits of the profiles are shown with solid lines. d) \\(T_{e}\\) from EMC3-EIRENE simulations for one case (#167234), together with a B powder grain trajectories (black) computed by the DUSTT code, with the resulting B neutral atom source(dots). e) B neutral source remapped on the normalized radial coordinate \\(r_{eff} / a_{99}\\) .",
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+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3: Time evolution of difference of normalized gradient between a powder injection shot (#166256) and its reference (#166254) for electron density (a) and temperature (b). c) Peak value of divertor density measured by Langmuir probes (black) and \\(H_{\\alpha}\\) radiation (red). d) Evolution of spectroscopic lines CVI (red), FeXVI (blue) and BV (black). e) Average value of the density fluctuation amplitude measured by PCI. Solid lines are for the powder injection shot #166256, and dotted lines for the reference #166254. Periodic oscillations at 3.33 Hz are due to the pulsed operation of diagnostic NB.",
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+    "caption": "Figure 4: Radial profiles of a) turbulent fluctuation amplitude and b) their perpendicular velocity for a powder injection shot (#166256, red) and its reference (#166254, blue), at \\(t = 5.2 \\mathrm{s}\\) (before injection, dashed lines) and \\(t = 8.5 \\mathrm{s}\\) (during injection, solid lines). Radially resolved power spectral density in terms of wave number for #166256 before (c) and during (d) powder injection, and their ratio (e).",
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+    "caption": "Figure 5: Spectrogram of the line integrated PCI signal for #166256 (a) and #167234 (b). The white dashed line indicates the approximate time of the boron powder entering the plasma. c,d) Comparison of time averaged turbulence spectrum for the B injection shot (red) and their reference shot (blue), at time before (dashed lines) and during (solid lines) powder injection.",
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+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6: Radial profiles of heat conductivities for ions (a) and electrons (b), comparing a discharge with powder injection (red) with a reference discharge (blue). c) Measured energy confinement time \\(\\tau_{E}\\) during B powder injection (red squares), and for the reference shots at the same time (blue diamonds). The experimental \\(\\tau_{E}\\) is plotted against the predicted energy confinement time from the international stellarator scaling [28].",
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preprint/preprint__07ca7119489ce742f39828987bc35bcbb114b2fcae1faac252a175d7615d08d8/preprint__07ca7119489ce742f39828987bc35bcbb114b2fcae1faac252a175d7615d08d8.mmd

@@ -0,0 +1,290 @@
+
+# Observation of a novel reduced-turbulence regime with boron powder injection in a stellarator  
+
+Federico Nespoli ( \(\boxed{\pi}\) fnespoli@pppl.gov) Princeton Plasma Physics Laboratory https://orcid.org/0000- 0001- 7644- 751X  
+
+Suguru Masuzaki National Institute for Fusion Science https://orcid.org/0000- 0003- 0161- 0938  
+
+Kenji Tanaka National Institute for Fusion Science  
+
+Naoko Ashikawa National Institute for Fusion Science  
+
+Mamoru Shoji National Institute for Fusion Science  
+
+Erik Gilson Princeton Plasma Physics Laboratory  
+
+Robert Lunsford Princeton Plasma Physics Laboratory  
+
+Tetsutaro Oishi National Institute for Fusion Science  
+
+Katsumi Ida National Institute for Fusion Science  
+
+Mikirou Yoshinuma National Institute for Fusion Science  
+
+Yuki Takemura National Institute for Fusion Science  
+
+Toshiki Kinoshita Kyushu University https://orcid.org/0000- 0003- 3930- 4434  
+
+Gen Motojima National Institute for Fusion Science  
+
+Naoki Kenmochi National Institute for Fusion Science  
+
+Gakushi Kawamura National Institute for Fusion Science  
+
+Chihiro Suzuki National Institute for Fusion Science  
+
+Alex Nagy
+
+<--- Page Split --->
+
+Princeton Plasma Physics Laboratory  
+
+Alessandro Bortolon Princeton Plasma Physics Laboratory  
+
+Novimir Pablant Princeton Plasma Physics Laboratory  
+
+Albert Mollen Princeton Plasma Physics Laboratory  
+
+Naoki Tamura National Institute for Fusion Science  
+
+David Gates Princeton University https://orcid.org/0000- 0001- 5679- 3124  
+
+Tomohiro Morisaki National Institute for Fusion Science  
+
+## Article  
+
+Keywords: Confinement Regime, Turbulent Fluctuations, Line Averaged Electron Density, Resonant Radio Frequency, Hydrogen and Deuterium Plasmas  
+
+Posted Date: June 30th, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 614131/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 Physics on January 10th, 2022. See the published version at https://doi.org/10.1038/s41567- 021- 01460- 4.
+
+<--- Page Split --->
+
+# Observation of a novel reduced-turbulence regime with boron powder injection in a stellarator  
+
+F. Nespoli\*,1, 
+S. Masuzaki2,3, 
+K. Tanaka2,4, 
+N. Ashikawa2,3, 
+M. Shoji2, 
+E.P. Gilson1, 
+R. Lunsford1, 
+T. Oishi2,3, 
+K. Ida2,3, 
+M. Yoshinuma2,3, 
+Y. Takemura2,3, 
+T. Kinoshita4, 
+G. Motojima2,3, 
+N. Kenmochi2,3, 
+G. Kawamura2,3, 
+C. Suzuki2, 
+A. Nagy1, 
+A. Bortolon1, 
+N.A. Pablant1, 
+A. Mollen1, 
+N. Tamura2, 
+D.A. Gates1, 
+T. Morisaki2,3  
+
+1 Princeton Plasma Physics Laboratory, 100 Stellarator Road, Princeton, NJ 08540, United States of America 2 National Institute for Fusion Science, 322- 6 Oroshi- cho Toki, Gifu 509- 5292, Japan 3 The Graduate University for Advanced Studies, SOKENDAI, 322- 6 Oroshi- cho Toki, Gifu 509- 5292, Japan 4 Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka, 816- 8580, Japan \* Corresponding author. Email: fnespoli@pppl.gov  
+
+## Abstract  
+
+We report the first observation of a novel confinement regime in a stellarator plasma, characterized by increased confinement and reduced turbulent fluctuations. The transition to this new regime is driven by the injection of sub- millimetric boron powder grains into the plasma. With the line averaged electron density being kept constant, substantial increase of stored energy, electron and ion temperature have been observed. At the same time, the amplitude of the plasma turbulent fluctuations is halved. While lower frequency fluctuations are damped, higher frequency modes in the range \(100 \leq f[kHz] \leq 200\) are excited. The access to this regime has been observed for different heating schemes, namely with both electron and ion cyclotron resonant radio frequency, and neutral beams, for both directions of the magnetic field, and for both hydrogen and deuterium plasmas.  
+
+## 1 Introduction  
+
+Stellarators are one of the most promising concepts for magnetic confined nuclear fusion, which could provide a clean alternative to fossil fuels and nuclear fission for mass energy production. Unlike tokamaks, their 3D magnetic filed is provided entirely by external coils, removing the need for a current to flow into the plasma, which makes it prone to instabilities and violent disruptions. This also allows the magnetic field to be tailored to minimize neoclassical transport and improve confinement. At present, the biggest degradation of confinement is given by plasma turbulence, resulting in an increased "anomalous" transport. While in principle possible, optimizing the stellarator magnetic field to reduce turbulent transport is extremely challenging due to the huge computational cost of 3D turbulence simulations. It is therefore fundamental to reduce turbulence in order to maximise the plasma confinement, finally determining the amount of fusion reactions.  
+
+In this article, we report the observation of a novel confinement regime in the Large Helical Device (LHD) stellarator [1], characterized by widespread reduction of turbulence across the plasma cross- section. In this regime, the line- averaged density remains unvaried, and both ion and electron temperature increase remarkably, without ELM- like bursts typical of H- mode [2]. The transition to this new regime, observed at constant heating power and for different heating sources, is triggered by the injection of sub- millimetric boron (B) powder into the plasma.
+
+<--- Page Split --->
+
+## 2 Motivation  
+
+The impurity powder dropper (IPD) is a device for injecting controlled amounts of sub- millimeter powder grains into the plasma under the action of gravity [3]. Its main applications is to perform a real- time boronization by injecting B powder (and B composites such as BN and \(\mathrm{B_4C}\) ) into the plasma. The powder, penetrating into the hot plasma, evaporates, and the resulting B ions are eventually deposited on the plasma facing surfaces creating a thin boron layer. Advantages over the standard glow discharge boronization include no need for the toxic diborane gas \(B_{2}H_{6}\) , and to interrupt the plasma operation. This technique has been shown to improve wall conditioning already in tokamaks [4, 5, 6, 7], reducing wall recycling and impurity content, and in general increasing the plasma performances by accessing lower plasma collisionalities. Furthermore, the IPD has revealed itself an effective tool for ELMs suppression, allowing the access ELM- free H- mode [8]. A similar powder injection technique has been recently employed on the W7- X stellarator, showing an improvement of confinement [9], most likely induced by the modification of the plasma profiles and in a change of the radial electric field.  
+
+The IPD has recently been installed on LHD, with the final goals of improving the plasma performances, and assessing the viability of the real time boronization technique in steady- state operation. Indeed, LHD is capable of extremely long discharges, up to one hour. The installation of the IPD on LHD has been guided by predictive simulations with the coupled EMC3- EIRENE and DUSTT codes [10], maximising the penetration of the powder into the plasma. The successful injection of B and BN powder in the unique LHD plasma configuration, featuring a double- null like cross section with predominantly poloidal magnetic field in the divertor, coupled to the confined plasma by a thick ergodic layer, has been demonstrated in 4- seconds- long plasmas [11], for a wide range of mass injection rates, plasma density, and heating power.  
+
+## 3 Results  
+
+A new set of powder injection experiments has been performed on LHD, featuring longer plasma duration, in the "inward shifted" magnetic configuration (position of the magnetic axis \(R_{ax} = 3.6\) m). B powder grains with diameter \(d = 150 \mu \mathrm{m}\) have been injected for a duration \(t_{d} \geq 5 \mathrm{s}\) in plasmas with different heating sources. A few seconds into powder injection, the plasma performance is observed to improve, with marked increase of both electron and ion temperature ( \(T_{e}\) , \(T_{i}\) ) and plasma stored energy \(W_{p}\) . Four different examples are shown in Fig. 1, corresponding to different heating schemes: both electron and ion cyclotron resonant heating (ECH, ICH) for subplot a, ECH only in b (but with perpendicular diagnostic neutral beam (pNB) for charge exchange spectroscopy (CXS)), \(\sim 3.5 \mathrm{MW}\) of NB in c, and \(\sim 6 \mathrm{MW}\) of NB in d. The magnetic field direction for case d is reversed with respect to cases a- c. The main plasma ion is deuterium (D) in cases a and b, while it is hydrogen (H) in cases c and d. For all cases, the line averaged density is comprised in the range \(2.7 \leq n_{e,av}[10^{19} m^{- 3}] \leq 3.7\) . The relative increase of \(T_{e}\) , \(T_{i}\) and \(W_{p}\) in between before and during B powder injection is, on average, \(\langle \Delta T_{e} / T_{e} \rangle = 27\%\) , \(\langle \Delta T_{i} / T_{i} \rangle = 25\%\) , \(\langle \Delta W_{p} / W_{p} \rangle = 17\%\) .  
+
+For all cases, a discharge with B powder injection (red) is compared with a reference discharge without powder (blue). We remark how in cases b- d, the pulsed operation of the diagnostic beam results in periodic variations on most considered quantities. In case c, huge variations in the plasma at \(t \sim 5.3 \mathrm{s}\) and \(t \sim 7.2 \mathrm{s}\) are due to the change of NB, varying from counter- current direction to co- current and vice- versa.  
+
+The effect of B powder on the plasma can be better appreciated in case a, where the gas puff is provided in feed- forward. The powder is dropped at \(t \sim 22 \mathrm{s}\) , and approximately after 1 s of free fall
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1: Time traces of, from top to bottom: line averaged density; input power; electron (solid) and ion (dotted) temperature; stored energy; injected boron mass rate (dotted, left axis) and BV spectroscopic line (solid, right axis). Red color for shots with B powder injection with IPD, blue for reference shots (no IPD). Main plasma ion is deuterium for cases a,b and hydrogen for c,d. The magnetic field direction for d is reversed with respect to a-c. </center>  
+
+it enters the plasma, where it is heated and evaporates. The effective injection and vaporization of the powder is confirmed by the sharp increase in the BV line measured by ultraviolet spectroscopy [12]. Due to the extra electron source, the line- averaged electron density \(n_{e,av}\) starts to increase. After a few seconds though, \(n_{e,av}\) decreases below the reference level: this is an effect of the real- time wall conditioning provided by the deposited boron, effectively reducing the recycling at the wall. In the other cases (b- d) the gas puff is operated with a feedback to keep the line averaged density constant, and this effect is masked.  
+
+Even though \(n_{e,av}\) remains unvaried, the powder injection changes the shape of the electron density \(n_{e}\) profile, as it is shown for one of the previously discussed shots in Fig. 2. During powder injection, \(n_{e}\) is increased in the edge region \(0.7 < r_{eff} / a_{99} < 1\) , while \(n_{e}\) is slightly decreased for \(r_{eff} / a_{99} < 0.7\) , rendering the profile more hollow. Here, \(r_{eff}\) the effective minor radius, and \(a_{99}\) the minor radius of the flux surface enclosing \(99\%\) of the stored energy. Correspondingly, the slope of the electron temperature profile \(T_{e}\) is more strongly increased in the edge region. A similar change is observed for the profiles of ion temperature \(T_{i}\) as well. The increase of \(n_{e}\) in the edge region is consistent with the powder being vaporized around the LCFS, as it results from coupled EMC3- EIRENE [13] and DUSTT [14] simulations (Fig. 2d). Indeed the powder particles, initially dropped vertically, are deflected by the plasma flow in the divertor leg; nevertheless, they reach the main plasma where they are completely evaporated, depositing neutral B atoms in the range \(1 \leq r_{eff} / a_{99} \leq 1.06\) , as shown in Fig. 2e, where the B neutral source is remapped on the normalized radial coordinate \(r_{eff} / a_{99}\) for all the discussed cases. In addition to the extra electron
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2: Measured radial profiles of a) electron density \(n_{e}\) b) electron temperature \(T_{e}\) c) ion temperature \(T_{i}\) , averaged over a 100 ms time window, in the case with (red) and without (blue) B powder injection. Polynomial fits of the profiles are shown with solid lines. d) \(T_{e}\) from EMC3-EIRENE simulations for one case (#167234), together with a B powder grain trajectories (black) computed by the DUSTT code, with the resulting B neutral atom source(dots). e) B neutral source remapped on the normalized radial coordinate \(r_{eff} / a_{99}\) . </center>  
+
+source provided by the powder, the created B ions are deposited on the plasma facing surfaces, reducing hydrogen recycling and impurity influx. This results in a two- fold reduction of \(n_{e}\) in the divertor, as measured by embedded Langmuir probe arrays. The time evolution of the peak value of \(n_{e}\) at the strike point is plotted in black in Fig. 3c for a shot with powder injection (solid line) and for the reference discharge (dotted line). \(H_{\alpha}\) radiation is also decreased (red traces), suggesting a reduction of recycling. Another indication of the effective real- time boronization is the reduction of impurity influx from the plasma facing components (Fig. 3d), as suggested from the decrease in CVI (red) and FeXVI (blue) radiation lines. The decrease in C concentration is also confirmed by CXS measurements. The above mentioned increase of \(n_{e}\) close to the LCFS due to the powder injection, combined with the decrease of \(n_{e}\) at the divertor, causes the density profile to steepen in the plasma edge, as shown in Fig. 3a, where the difference in normalized gradient \((dn_{e} / d\rho) / n_{e}\) in between the powder injection shot and the no- powder reference is plotted, with \(\rho = r_{eff} / a_{99}\) . The steepening of the gradient appears to originate around \(r_{eff} / a_{99} \geq 1\) and propagate inwards, together with an increase of the electron temperature gradient (Fig. 3b).  
+
+Simultaneously, the turbulent fluctuation level in the confined plasma is observed to be reduced to approximately half its value before powder injection, as it is shown in Fig. 3e, displaying the amplitude of the the density fluctuations measured by 2D phase contrast imaging (PCI) [15, 16], averaged over the whole plasma cross section.  
+
+The radially resolved profiles of the density fluctuation amplitude and their velocity in the direction perpendicular to the field line \(v_{\perp}\) are plotted in Fig. 4a,b, before (dashed lines) and during B powder injection (solid lines). A discharge with B powder injection (red) is compared with a
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3: Time evolution of difference of normalized gradient between a powder injection shot (#166256) and its reference (#166254) for electron density (a) and temperature (b). c) Peak value of divertor density measured by Langmuir probes (black) and \(H_{\alpha}\) radiation (red). d) Evolution of spectroscopic lines CVI (red), FeXVI (blue) and BV (black). e) Average value of the density fluctuation amplitude measured by PCI. Solid lines are for the powder injection shot #166256, and dotted lines for the reference #166254. Periodic oscillations at 3.33 Hz are due to the pulsed operation of diagnostic NB. </center>  
+
+reference shot (blue). The shaded area accounts for the variation in time over a time window of 0.4 s, to avoid instantaneous variations caused by the pulsed diagnostic NB. As the turbulent fluctuation amplitude is substantially reduced across the whole cross section (no measurements are available for \(|r_{eff} / a_{99}| < 0.37\) ), their velocity \(v_{\perp}\) is doubled in the edge of the plasma ( \(v_{\perp}\) is directed in the e- diamagnetic direction, resulting in positive/negative values in the lab frame when measured at the bottom/top of the plasma \(r_{eff} / a_{99} \lesssim 0\) ). Radially resolved power spectral density in terms of perpendicular wave number \(k_{\perp}\) are shown in Fig. 4c,d before and during B powder injection respectively. Before the powder injection, the PSD peaks for wave- numbers in the range \(0.2 \leq k_{\perp} [mm^{- 1}] \leq 0.4\) , consistent with ion temperature gradient (ITG) driven instabilities. In Refs. [17, 18], similar PCI measurements were compared with gyrokinetic simulations, determining that the observed fluctuations are indeed due to ITG turbulence. Dedicated gyrokinetic simulations are needed to confirm this result for the cases exposed here, and are foreseen for future works. During B powder injection, these ITG- like fluctuations are substantially suppressed in the confined plasma \(r_{eff} / a_{99} < 1\) , and in general across the whole spectrum. Conversely, turbulence is slightly enhanced
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4: Radial profiles of a) turbulent fluctuation amplitude and b) their perpendicular velocity for a powder injection shot (#166256, red) and its reference (#166254, blue), at \(t = 5.2 \mathrm{s}\) (before injection, dashed lines) and \(t = 8.5 \mathrm{s}\) (during injection, solid lines). Radially resolved power spectral density in terms of wave number for #166256 before (c) and during (d) powder injection, and their ratio (e). </center>  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5: Spectrogram of the line integrated PCI signal for #166256 (a) and #167234 (b). The white dashed line indicates the approximate time of the boron powder entering the plasma. c,d) Comparison of time averaged turbulence spectrum for the B injection shot (red) and their reference shot (blue), at time before (dashed lines) and during (solid lines) powder injection. </center>
+
+<--- Page Split --->
+
+around the LCFS \(r_{e f f} / a_{9 9}\sim 1\) , as it emerges from Fig. 4e, displaying the logarithm of the ratio of the PSD during ( \(t = t_{2} = 8.5\pm 0.2\) s) and before ( \(t = t_{1} = 5.2\pm 0.2\) s) B powder injection,  
+
+\[C = \log_{10}\frac{PSD(t = t_{2})}{PSD(t = t_{1})} \quad (1)\]  
+
+so that \(C< 0\) and \(C > 0\) means reduction and increase of turbulence, respectively. Turbulence is therefore reduced on most of the plasma cross section, practically suppressed in correspondence of the peaks before injection ( \(k_{\perp}\sim 0.3 m m^{- 1}\) ), and slightly enhanced around the LCFS ( \(r_{e f f} / a_{9 9}\sim 1\) ). The additional enhancement for \(k_{\perp}\leq 0.1 m m^{- 1}\) close to the plasma core \(r_{e f f} / a_{9 9}\leq 0.5\) could be an artifact due to insufficient diagnostic resolution for small \(k\) values.  
+
+This change is reflected in the time evolution of the power spectrum of the line integrated PCI signal (probing all \(r_{e f f} / a_{9 9} > 0.4\) ), shown in Fig. 5a,b for shot #166256 (D, ECH+pNB heated) and #167234 (H, NB- heated). As powder is injected (white dashed line), the dominant low- frequency fluctuations are suppressed, and a new mode emerges in the range \(100\leq f[kHz]\leq 200\) . Time averaged spectra over a window of 0.4 s, in order to attenuate the variations due to the pulsed diagnostic NB, are plotted in Fig. 5c,d for the same shots as in a,b (red) and compared to their reference shot (blue), at times before (dashed lines) and during (solid lines) powder injection. Once again, fluctuations in the range \(10\leq f[kHz]\leq 100\) are damped, while a new peak emerges in the spectrum for \(f\sim 100 - 200\mathrm{kHz}\) . In Ref. [26], a similar difference in PCI spectra has been observed in between isotope mixing and non- mixing discharges. In the first case, the spectrum peaks at \(\sim 20\) kHz, identified with ITG turbulence. At lower collisionalities, ITG turbulence is stabilized and trapped electron modes (TEM) are destabilized instead at the edge of the plasma, where gradients are steeper, resulting in a peak at \(\sim 80\mathrm{kHz}\) in the PCI spectrum.  
+
+The decrease in turbulence is observed on the whole cross section, except close to the LCFS region \(r_{e f f} / a_{9 9}\sim 1\) . Conversely to the case of a H- mode, where turbulence is suppressed in the vicinity  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6: Radial profiles of heat conductivities for ions (a) and electrons (b), comparing a discharge with powder injection (red) with a reference discharge (blue). c) Measured energy confinement time \(\tau_{E}\) during B powder injection (red squares), and for the reference shots at the same time (blue diamonds). The experimental \(\tau_{E}\) is plotted against the predicted energy confinement time from the international stellarator scaling [28]. </center>
+
+<--- Page Split --->
+
+of the LCFS only, due to a increased shear in poloidal velocity and therefore in the radial electric field \(E_{r}\) , since the poloidal velocity is mainly given by the \(\mathbf{E} \times \mathbf{B}\) drift. In Ref. [9], confinement improvement has been observed in W7- X during \(\mathrm{B}_{4} \mathrm{C}\) powder injection, which has been judged to be consistent with a change in \(E_{r}\) . In our case, no significant change in radial electric field is expected in the phase where the powder is injected into the plasma. The ambipolar radial electric field has been computed using the neoclassical transport code SFINCS [19], for all cases (except #164645 where no \(T_{i}\) measurement is available), comparing plasma with and without powder injection. In all cases, no change in \(E_{r}\) that could result in an improvement of confinement emerges from the simulation results. The increase in \(T_{e}\) , \(T_{i}\) , \(W_{p}\) observed during powder injection is associated with a reduced energy transport in the edge of the plasma, and an increase in energy confinement time. The heat conductivities for ions and electrons, \(\chi_{i}\) and \(\chi_{e}\) respectively, are computed using the DYTRANS module of TASK3D- a [27], performing a dynamics transport analysis. As a result (shown in Fig. 6 for a NBI heated case), both \(\chi_{i}\) and \(\chi_{e}\) are reduced in the plasma edge during powder injection. \(\chi_{i}\) is reduced by up to \(40\%\) for \(r_{eff} / a_{99} > 0.4\) , while \(\chi_{e}\) is reduced by up to \(50\%\) for \(r_{eff} / a_{99} > 0.5\) . The DYTRANS results are consistent with the reduction of turbulent transport in the edge of the plasma during B powder injection. The measured energy confinement time \(\tau_{E}\) (red squares in Fig. 6, plotted against the value predicted from the international stellarator scaling \(\tau_{E,IS04}\) [28]), is also increased during B powder injection, the improvement being in between \(17\%\) and \(25\%\) when compared to the reference shot at the same time (blue diamonds).  
+
+## 4 Conclusions  
+
+The Impurity Powder Dropper has been used to inject sub- millimetric boron (B) powder into the LHD plasma. During powder injection, the electron and ion temperature \(T_{e}\) , \(T_{i}\) and the plasma stored energy \(W_{p}\) have been observed to increase by approximately \(27\%\) , \(25\%\) and \(17\%\) respectively. The improvement has been observed for different heating schemes (ECH+ICH, ECH+pNB, NBH), for both directions of the magnetic field, and for both H and D plasmas. At the same time, the turbulent fluctuation amplitude measured by PCI, most possibly due to ITG type of turbulence, is observed to decrease up to a factor 2, and a secondary peak in the power spectrum of the line integrated signal has been observed to emerge at higher frequencies \(f > 100 \mathrm{kHz}\) . When powder is injected, the density profile is steepened in the edge region and made more hollow in the center, due to an additional electron source for \(r_{eff} / a_{99} \geq 1\) provided by the vaporization of the powder itself, as determined by EMC3- EIRENE and DUSTT simulations. Simultaneously, the B ions deposit on the plasma facing components, changing the wall conditions in real time: the impurity influx from the wall is reduced, together with the recycling at the divertor plates. The latter results in lower plasma density in the divertor region, contributing to increase the density gradient. The modification of the \(n_{e}\) profile at the edge is followed by the steepening of \(T_{e}\) and \(T_{i}\) in the same region, resulting finally in an increase in their value on axis. Accordingly, the analysis of dynamic transport exhibits a reduction of the heat conductivities for electrons and ions \(\chi_{e}\) and \(\chi_{i}\) in the plasma edge. The measured energy confinement time \(\tau_{E}\) is also observed to increase. As the \(n_{e}\) , \(T_{e}\) and \(T_{i}\) profiles are changed, the ambipolar radial electric field computed by the SFINCS code remains mainly unvaried. This, together with reduction of the turbulent fluctuations across the whole plasma cross section, are in contrast with an H- mode type increase of confinement, where the turbulent fluctuations are reduced in the vicinity of the separatrix due to an increased \(\mathbf{E} \times \mathbf{B}\) shear, and suggest a different underlying mechanism.  
+
+While the reason of the observed improvement of confinement is not yet clear, we suspect it to be due to the suppression of ITG turbulence. This might be an effect of the change in the profiles of the
+
+<--- Page Split --->
+
+plasma quantities, in particular of the peaking of \(n_{e}\) in the edge, resulting in a more hollow profile in the center of the plasma. Hollow density profiles have been reported to increase ITG stability, reducing turbulence fluctuations [18, 21]. Another possibility is turbulence being reduced by the increased effective charge \(Z_{eff}\) due to B injection, also referred to as plasma dilution. Indeed, an increase \(Z_{eff}\) has also been reported to have a stabilizing effect on ITG turbulence [22, 23, 24]. More likely, the combination of the two above mentioned effects might occur in our case, similarly to what reported in Ref. [25]. Dedicated gyrokinetic simulations will be necessary to verify those hypotheses, and are planned for future works.  
+
+Furthermore, additional experiments are foreseen on LHD, with the aim of better defining the parameter space where this new regime is observed, and to assess whether it is compatible with conditions relevant to future fusion reactors, i.e. with higher power and density plasmas.  
+
+## 5 Methods  
+
+Evaluation of plasma quantities and profiles  
+
+Throughout the paper, the line averaged electron density \(n_{e,av}\) is measured by means of far infrared interferometry (FIR). Radially resolved profiles of electron density and temperature \(n_{e}\) , \(T_{e}\) are measured by Thomson scattering (TS). Radially resolved profiles of ion temperature \(T_{i}\) are measured by charge exchange spectroscopy (CXS). Using magnetic reconstruction from the VMEC code, all profiles are remapped onto the normalized coordinate \(\rho = r_{eff} / a_{99}\) , with \(r_{eff}\) the effective minor radius, and \(a_{99}\) the minor radius of the flux surface enclosing 99% of the stored energy. For each time step, the \(n_{e}\) , \(T_{e}\) , \(T_{i}\) profiles are fitted with polynomials including only even power terms, ensuring zero derivative at \(r_{eff} / a_{99} = 0\) . This provides smooth spatial profiles and gradients. The values of temperatures on axis (Fig. 1) correspond to the fitted profiles evaluated at \(r_{eff} / a_{99} = 0\) . For discharges #164644 and #164645 in Fig. 1A, the diagnostic neutral beam was not operated and no \(T_{i}\) measurement from CXS is available.  
+
+Powder injection and evaluation of mass rate  
+
+The impurity powder dropper features four independent feeders, composed of a powder reservoir and a vibrating tray. The latter is vibrated by piezoelectric blades through a driving voltage, allowing to control the amplitude of the vibrations and finally the amount of powder delivered to the plasma. Each independent feeder includes an accelerometer, measuring the vibration of the tray actuated by piezoelectric blades, finally determining the injection rate of the powder into the plasma. Calibration curves have been acquired in the laboratory, allowing to convert the amplitude of the accelerometer signal into injected mass rates.  
+
+Simulations with EMC3- EIRENE and DUSTT  
+
+Interpretative simulations are performed with the coupled EMC3- EIRENE [13] and DUSTT [14] codes, after Ref. [10]. EMC3 is a fully 3D Monte Carlo code modelling the plasma transport in the edge and scrape- off layer, and it is coupled to EIRENE, describing the neutrals dynamics. The diffusion and thermal conductivities coefficients are set by matching the experimental profiles of plasma density and ion and electron temperatures. Electron density and temperature are measured by Thomson scattering, while the ion temperature is measured by charge exchange spectroscopy. The 3D plasma solutions from the EMC3- EIRENE simulations are then used as the background for the DUSTT simulations, computing the trajectory of a powder grain injected into the plasma. For those simulations, the powder grains are injected vertically at the actual IPD location with an initial velocity of 5 m/s directed downwards, consistent with the free fall of the powder grains prior
+
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+to entering the plasma. The powder material is B, and the size of the modelled powder grain is 150 \(\mu \mathrm{m}\) , matching the ones used in the experiments. As the powder grains enter the plasma, they are progressively heated up to evaporating temperature, providing a localized source of neutral B atoms.  
+
+Measurement of turbulent fluctuations  
+
+In this work, the turbulent fluctuations characteristics are measured by means of two- dimensional Phase Contrast Imaging (PCI). The diagnostic system and the spectral analysis technique are detailed in Refs. [15, 16]. The amplitude of the density fluctuation is computed from the power spectrum integrated over \(\omega\) and \(k\) as \(\sqrt{\bar{n}^{2}}\) . The cutoff wave- number of the PCI system has been investigated in detail in Ref. [29], showing how fluctuations with wave- number in the range \(0.1 \leq k [mm^{- 1}] \leq 0.8\) are measured, with an attenuated contributions to the final spectrum for \(k < 0.2mm^{- 1}\) .  
+
+Energy confinement time  
+
+The confinement time is computed from the time trace of the plasma stored energy \(W_{p}\) , smoothed in time to average over the variations provided by the perpendicular NBI. For ECH, all port- through power is assumed to be absorbed by the plasma. For ICH, it is assumed that \(75\%\) of the input power is absorbed. For NBIs, the absorbed power is assumed to be \(P_{ab} = P_{in}[1 - \exp \left(- \sigma n_{e,av}l\right)]\) , where \(\sigma = 0.43\) for H plasmas and \(l = 1.86 \mathrm{m}\) [30].  
+
+## Acknowledgments  
+
+The authors wish to thank the LHD experiment group for the excellent support of this work, and Drs. R. Seki and M. Yokoyama (NIFS) for executing TASK3D- a suite, allowing to conduct transport analyses. This work was conducted within the framework of the NIFS/PPPL International Collaboration, and it is supported by the U.S. DOE under Contract No. DE- AC02- 09CH11466 with Princeton University.  
+
+## Author Contributions  
+
+N.A., E.P.G, R.L., S.M., M.S, F.N., A.N. set up and performed the experiments. T.O., K.I., M.Y., Y.T., K.T., T.K., C.S. set up and operated the diagnostics used in the experiments and ran preliminary analysis. F.N., M.S., G.K., G.M., N.K., N.A.P, A.M. performed numerical modeling of the experiments. F.N., S.M., K.T., K.I, A.B., D.A.G further analyzed and interpreted the data. F.N. prepared the figures and wrote the manuscript. D.A.G. and T.M. supervised the project. All authors reviewed the manuscript and contributed to discussions.  
+
+## References  
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