[{"abstract":[{"lang":"eng","text":"Neurons in the brain are wired into adaptive networks that exhibit collective dynamics as diverse as scale-specific oscillations and scale-free neuronal avalanches. Although existing models account for oscillations and avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically or intractable to infer from data rigorously. Here we propose a feedback-driven Ising-like class of neural networks that captures avalanches and oscillations simultaneously and quantitatively. In the simplest yet fully microscopic model version, we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model’s two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations to collective behaviors of extreme events and neuronal avalanches. Importantly, the inferred parameters indicate that the co-existence of scale-specific (oscillations) and scale-free (avalanches) dynamics occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations."}],"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"20","publication_status":"published","oa_version":"Published Version","page":"254-263","date_updated":"2023-08-16T12:41:53Z","status":"public","title":"Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain","file":[{"creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_name":"2023_NatureCompScience_Lombardi.pdf","file_size":4474284,"checksum":"7c63b2b2edfd68aaffe96d70ca6a865a","file_id":"14073","date_created":"2023-08-16T12:39:57Z","success":1,"date_updated":"2023-08-16T12:39:57Z"}],"external_id":{"arxiv":["2108.06686"]},"publication":"Nature Computational Science","arxiv":1,"citation":{"ama":"Lombardi F, Pepic S, Shriki O, Tkačik G, De Martino D. Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain. <i>Nature Computational Science</i>. 2023;3:254-263. doi:<a href=\"https://doi.org/10.1038/s43588-023-00410-9\">10.1038/s43588-023-00410-9</a>","short":"F. Lombardi, S. Pepic, O. Shriki, G. Tkačik, D. De Martino, Nature Computational Science 3 (2023) 254–263.","ista":"Lombardi F, Pepic S, Shriki O, Tkačik G, De Martino D. 2023. Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain. Nature Computational Science. 3, 254–263.","apa":"Lombardi, F., Pepic, S., Shriki, O., Tkačik, G., &#38; De Martino, D. (2023). Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain. <i>Nature Computational Science</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s43588-023-00410-9\">https://doi.org/10.1038/s43588-023-00410-9</a>","mla":"Lombardi, Fabrizio, et al. “Statistical Modeling of Adaptive Neural Networks Explains Co-Existence of Avalanches and Oscillations in Resting Human Brain.” <i>Nature Computational Science</i>, vol. 3, Springer Nature, 2023, pp. 254–63, doi:<a href=\"https://doi.org/10.1038/s43588-023-00410-9\">10.1038/s43588-023-00410-9</a>.","ieee":"F. Lombardi, S. Pepic, O. Shriki, G. Tkačik, and D. De Martino, “Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain,” <i>Nature Computational Science</i>, vol. 3. Springer Nature, pp. 254–263, 2023.","chicago":"Lombardi, Fabrizio, Selver Pepic, Oren Shriki, Gašper Tkačik, and Daniele De Martino. “Statistical Modeling of Adaptive Neural Networks Explains Co-Existence of Avalanches and Oscillations in Resting Human Brain.” <i>Nature Computational Science</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1038/s43588-023-00410-9\">https://doi.org/10.1038/s43588-023-00410-9</a>."},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"},{"_id":"eb943429-77a9-11ec-83b8-9f471cdf5c67","name":"Functional Advantages of Critical Brain Dynamics","grant_number":"M03318"},{"grant_number":"P34015","_id":"626c45b5-2b32-11ec-9570-e509828c1ba6","name":"Efficient coding with biophysical realism"}],"has_accepted_license":"1","scopus_import":"1","_id":"12762","oa":1,"author":[{"orcid":"0000-0003-2623-5249","id":"A057D288-3E88-11E9-986D-0CF4E5697425","last_name":"Lombardi","first_name":"Fabrizio","full_name":"Lombardi, Fabrizio"},{"full_name":"Pepic, Selver","first_name":"Selver","last_name":"Pepic","id":"F93245C4-C3CA-11E9-B4F0-C6F4E5697425"},{"last_name":"Shriki","full_name":"Shriki, Oren","first_name":"Oren"},{"orcid":"0000-0002-6699-1455","last_name":"Tkačik","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","full_name":"Tkačik, Gašper","first_name":"Gašper"},{"last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5214-4706","full_name":"De Martino, Daniele","first_name":"Daniele"}],"date_published":"2023-03-20T00:00:00Z","year":"2023","publisher":"Springer Nature","doi":"10.1038/s43588-023-00410-9","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"eissn":["2662-8457"]},"quality_controlled":"1","month":"03","article_type":"original","volume":3,"department":[{"_id":"GaTk"},{"_id":"GradSch"}],"acknowledgement":"This research was funded in whole, or in part, by the Austrian Science Fund (FWF) (grant no. PT1013M03318 to F.L. and no. P34015 to G.T.). For the purpose of open access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. The study was supported by the European Union Horizon 2020 research and innovation program under the Marie Sklodowska-Curie action (grant agreement No. 754411 to F.L.).","date_created":"2023-03-26T22:01:08Z","intvolume":"         3","file_date_updated":"2023-08-16T12:39:57Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","ddc":["570"]},{"publisher":"IOP Publishing","year":"2019","language":[{"iso":"eng"}],"doi":"10.1088/1751-8121/aaf2dd","type":"journal_article","oa":1,"_id":"6049","author":[{"full_name":"De Martino, Daniele","first_name":"Daniele","orcid":"0000-0002-5214-4706","last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87"}],"date_published":"2019-01-07T00:00:00Z","department":[{"_id":"GaTk"}],"date_created":"2019-02-24T22:59:19Z","article_number":"045002","intvolume":"        52","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (in subscription journal)","ddc":["570"],"file_date_updated":"2020-07-14T12:47:17Z","quality_controlled":"1","month":"01","volume":52,"isi":1,"date_updated":"2023-08-24T14:49:23Z","status":"public","ec_funded":1,"abstract":[{"lang":"eng","text":"In this article it is shown that large systems with many interacting units endowing multiple phases display self-oscillations in the presence of linear feedback between the control and order parameters, where an Andronov–Hopf bifurcation takes over the phase transition. This is simply illustrated through the mean field Landau theory whose feedback dynamics turn out to be described by the Van der Pol equation and it is then validated for the fully connected Ising model following heat bath dynamics. Despite its simplicity, this theory accounts potentially for a rich range of phenomena: here it is applied to describe in a stylized way (i) excess demand-price cycles due to strong herding in a simple agent-based market model; (ii) congestion waves in queuing networks triggered by user feedback to delays in overloaded conditions; and (iii) metabolic network oscillations resulting from cell growth control in a bistable phenotypic landscape."}],"oa_version":"Published Version","publication_status":"published","day":"07","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734"}],"citation":{"short":"D. De Martino, Journal of Physics A: Mathematical and Theoretical 52 (2019).","ista":"De Martino D. 2019. Feedback-induced self-oscillations in large interacting systems subjected to phase transitions. Journal of Physics A: Mathematical and Theoretical. 52(4), 045002.","mla":"De Martino, Daniele. “Feedback-Induced Self-Oscillations in Large Interacting Systems Subjected to Phase Transitions.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 52, no. 4, 045002, IOP Publishing, 2019, doi:<a href=\"https://doi.org/10.1088/1751-8121/aaf2dd\">10.1088/1751-8121/aaf2dd</a>.","apa":"De Martino, D. (2019). Feedback-induced self-oscillations in large interacting systems subjected to phase transitions. <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1751-8121/aaf2dd\">https://doi.org/10.1088/1751-8121/aaf2dd</a>","ama":"De Martino D. Feedback-induced self-oscillations in large interacting systems subjected to phase transitions. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2019;52(4). doi:<a href=\"https://doi.org/10.1088/1751-8121/aaf2dd\">10.1088/1751-8121/aaf2dd</a>","chicago":"De Martino, Daniele. “Feedback-Induced Self-Oscillations in Large Interacting Systems Subjected to Phase Transitions.” <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing, 2019. <a href=\"https://doi.org/10.1088/1751-8121/aaf2dd\">https://doi.org/10.1088/1751-8121/aaf2dd</a>.","ieee":"D. De Martino, “Feedback-induced self-oscillations in large interacting systems subjected to phase transitions,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 52, no. 4. IOP Publishing, 2019."},"has_accepted_license":"1","issue":"4","scopus_import":"1","external_id":{"isi":["000455379500001"]},"title":"Feedback-induced self-oscillations in large interacting systems subjected to phase transitions","file":[{"creator":"kschuh","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":1804557,"file_name":"2019_IOP_DeMartino.pdf","date_updated":"2020-07-14T12:47:17Z","file_id":"6344","date_created":"2019-04-19T12:18:57Z","checksum":"1112304ad363a6d8afaeccece36473cf"}],"publication":"Journal of Physics A: Mathematical and Theoretical"},{"month":"04","quality_controlled":"1","volume":4,"article_number":"e00596","date_created":"2018-12-11T11:45:44Z","department":[{"_id":"GaTk"}],"file_date_updated":"2020-07-14T12:45:59Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["530"],"intvolume":"         4","author":[{"last_name":"De Martino","full_name":"De Martino, Andrea","first_name":"Andrea"},{"full_name":"De Martino, Daniele","first_name":"Daniele","orcid":"0000-0002-5214-4706","last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87"}],"_id":"306","oa":1,"date_published":"2018-04-01T00:00:00Z","doi":"10.1016/j.heliyon.2018.e00596","language":[{"iso":"eng"}],"year":"2018","publisher":"Elsevier","type":"journal_article","publication":"Heliyon","title":"An introduction to the maximum entropy approach and its application to inference problems in biology","file":[{"date_updated":"2020-07-14T12:45:59Z","date_created":"2019-02-06T07:36:24Z","checksum":"67010cf5e3b3e0637c659371714a715a","file_id":"5929","file_size":994490,"file_name":"2018_Heliyon_DeMartino.pdf","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst"}],"citation":{"ama":"De Martino A, De Martino D. An introduction to the maximum entropy approach and its application to inference problems in biology. <i>Heliyon</i>. 2018;4(4). doi:<a href=\"https://doi.org/10.1016/j.heliyon.2018.e00596\">10.1016/j.heliyon.2018.e00596</a>","apa":"De Martino, A., &#38; De Martino, D. (2018). An introduction to the maximum entropy approach and its application to inference problems in biology. <i>Heliyon</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.heliyon.2018.e00596\">https://doi.org/10.1016/j.heliyon.2018.e00596</a>","ista":"De Martino A, De Martino D. 2018. An introduction to the maximum entropy approach and its application to inference problems in biology. Heliyon. 4(4), e00596.","short":"A. De Martino, D. De Martino, Heliyon 4 (2018).","mla":"De Martino, Andrea, and Daniele De Martino. “An Introduction to the Maximum Entropy Approach and Its Application to Inference Problems in Biology.” <i>Heliyon</i>, vol. 4, no. 4, e00596, Elsevier, 2018, doi:<a href=\"https://doi.org/10.1016/j.heliyon.2018.e00596\">10.1016/j.heliyon.2018.e00596</a>.","ieee":"A. De Martino and D. De Martino, “An introduction to the maximum entropy approach and its application to inference problems in biology,” <i>Heliyon</i>, vol. 4, no. 4. Elsevier, 2018.","chicago":"De Martino, Andrea, and Daniele De Martino. “An Introduction to the Maximum Entropy Approach and Its Application to Inference Problems in Biology.” <i>Heliyon</i>. Elsevier, 2018. <a href=\"https://doi.org/10.1016/j.heliyon.2018.e00596\">https://doi.org/10.1016/j.heliyon.2018.e00596</a>."},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7"}],"scopus_import":1,"issue":"4","has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","publication_status":"published","oa_version":"Published Version","abstract":[{"lang":"eng","text":"A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of ‘entropy’, and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data."}],"ec_funded":1,"date_updated":"2021-01-12T07:40:46Z","status":"public"},{"license":"https://creativecommons.org/publicdomain/zero/1.0/","status":"public","date_updated":"2024-02-21T13:45:39Z","abstract":[{"lang":"eng","text":"Supporting material to the article \r\nSTATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH\r\n\r\nboundscoli.dat\r\nFlux Bounds of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium. \r\n\r\npolcoli.dat\r\nMatrix enconding the polytope of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium, \r\nobtained from the soichiometric matrix by standard linear algebra  (reduced row echelon form).\r\n\r\nellis.dat\r\nApproximate Lowner-John ellipsoid rounding the polytope of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium\r\nobtained with the Lovasz method.\r\n\r\npoint0.dat\r\nCenter of the approximate Lowner-John ellipsoid rounding the polytope of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium\r\nobtained with the Lovasz method.\r\n\r\nlovasz.cpp  \r\nThis c++ code file receives in input the polytope of the feasible steady states of a metabolic network, \r\n(matrix and bounds), and it gives in output an approximate Lowner-John ellipsoid rounding the polytope\r\nwith the Lovasz method \r\nNB inputs are referred by defaults to the catabolic core of the E.Coli network iAF1260. \r\nFor further details we refer to  PLoS ONE 10.4 e0122670 (2015).\r\n\r\nsampleHRnew.cpp  \r\nThis c++ code file receives in input the polytope of the feasible steady states of a metabolic network, \r\n(matrix and bounds), the ellipsoid rounding the polytope, a point inside and  \r\nit gives in output a max entropy sampling at fixed average growth rate \r\nof the steady states by performing an Hit-and-Run Monte Carlo Markov chain.\r\nNB inputs are referred by defaults to the catabolic core of the E.Coli network iAF1260. \r\nFor further details we refer to  PLoS ONE 10.4 e0122670 (2015)."}],"ec_funded":1,"day":"21","tmp":{"legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","short":"CC0 (1.0)","name":"Creative Commons Public Domain Dedication (CC0 1.0)","image":"/images/cc_0.png"},"oa_version":"Published Version","has_accepted_license":"1","citation":{"ieee":"D. De Martino and G. Tkačik, “Supporting materials ‘STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH.’” Institute of Science and Technology Austria, 2018.","chicago":"De Martino, Daniele, and Gašper Tkačik. “Supporting Materials ‘STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH.’” Institute of Science and Technology Austria, 2018. <a href=\"https://doi.org/10.15479/AT:ISTA:62\">https://doi.org/10.15479/AT:ISTA:62</a>.","ama":"De Martino D, Tkačik G. Supporting materials “STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH.” 2018. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:62\">10.15479/AT:ISTA:62</a>","short":"D. De Martino, G. Tkačik, (2018).","mla":"De Martino, Daniele, and Gašper Tkačik. <i>Supporting Materials “STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH.”</i> Institute of Science and Technology Austria, 2018, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:62\">10.15479/AT:ISTA:62</a>.","ista":"De Martino D, Tkačik G. 2018. Supporting materials ‘STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH’, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:62\">10.15479/AT:ISTA:62</a>.","apa":"De Martino, D., &#38; Tkačik, G. (2018). Supporting materials “STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH.” Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:62\">https://doi.org/10.15479/AT:ISTA:62</a>"},"project":[{"call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"},{"_id":"254E9036-B435-11E9-9278-68D0E5697425","name":"Biophysics of information processing in gene regulation","call_identifier":"FWF","grant_number":"P28844-B27"}],"title":"Supporting materials \"STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH\"","file":[{"relation":"main_file","content_type":"application/zip","access_level":"open_access","creator":"system","date_updated":"2020-07-14T12:47:08Z","checksum":"97992e3e8cf8544ec985a48971708726","file_id":"5641","date_created":"2018-12-12T13:05:13Z","file_size":14376,"file_name":"IST-2018-111-v1+1_CODES.zip"}],"related_material":{"record":[{"relation":"research_paper","status":"public","id":"161"}]},"datarep_id":"111","type":"research_data","year":"2018","publisher":"Institute of Science and Technology Austria","doi":"10.15479/AT:ISTA:62","date_published":"2018-09-21T00:00:00Z","_id":"5587","oa":1,"author":[{"full_name":"De Martino, Daniele","first_name":"Daniele","orcid":"0000-0002-5214-4706","last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87"},{"id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","last_name":"Tkacik","orcid":"0000-0002-6699-1455","first_name":"Gasper","full_name":"Tkacik, Gasper"}],"keyword":["metabolic networks","e.coli core","maximum entropy","monte carlo markov chain sampling","ellipsoidal rounding"],"file_date_updated":"2020-07-14T12:47:08Z","ddc":["530"],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"GaTk"}],"date_created":"2018-12-12T12:31:41Z","month":"09"},{"has_accepted_license":"1","scopus_import":"1","issue":"1","citation":{"ieee":"D. De Martino, A. A. Mc, T. Bergmiller, C. C. Guet, and G. Tkačik, “Statistical mechanics for metabolic networks during steady state growth,” <i>Nature Communications</i>, vol. 9, no. 1. Springer Nature, 2018.","chicago":"De Martino, Daniele, Andersson Anna Mc, Tobias Bergmiller, Calin C Guet, and Gašper Tkačik. “Statistical Mechanics for Metabolic Networks during Steady State Growth.” <i>Nature Communications</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1038/s41467-018-05417-9\">https://doi.org/10.1038/s41467-018-05417-9</a>.","ama":"De Martino D, Mc AA, Bergmiller T, Guet CC, Tkačik G. Statistical mechanics for metabolic networks during steady state growth. <i>Nature Communications</i>. 2018;9(1). doi:<a href=\"https://doi.org/10.1038/s41467-018-05417-9\">10.1038/s41467-018-05417-9</a>","ista":"De Martino D, Mc AA, Bergmiller T, Guet CC, Tkačik G. 2018. Statistical mechanics for metabolic networks during steady state growth. Nature Communications. 9(1), 2988.","apa":"De Martino, D., Mc, A. A., Bergmiller, T., Guet, C. C., &#38; Tkačik, G. (2018). Statistical mechanics for metabolic networks during steady state growth. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-018-05417-9\">https://doi.org/10.1038/s41467-018-05417-9</a>","mla":"De Martino, Daniele, et al. “Statistical Mechanics for Metabolic Networks during Steady State Growth.” <i>Nature Communications</i>, vol. 9, no. 1, 2988, Springer Nature, 2018, doi:<a href=\"https://doi.org/10.1038/s41467-018-05417-9\">10.1038/s41467-018-05417-9</a>.","short":"D. De Martino, A.A. Mc, T. Bergmiller, C.C. Guet, G. Tkačik, Nature Communications 9 (2018)."},"project":[{"_id":"254E9036-B435-11E9-9278-68D0E5697425","name":"Biophysics of information processing in gene regulation","call_identifier":"FWF","grant_number":"P28844-B27"},{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"file":[{"file_size":1043205,"file_name":"2018_NatureComm_DeMartino.pdf","date_updated":"2020-07-14T12:45:06Z","checksum":"3ba7ab27b27723c7dcf633e8fc1f8f18","date_created":"2018-12-17T16:44:28Z","file_id":"5728","creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access"}],"title":"Statistical mechanics for metabolic networks during steady state growth","related_material":{"record":[{"status":"public","id":"5587","relation":"popular_science"}]},"external_id":{"isi":["000440149300021"]},"publication":"Nature Communications","status":"public","date_updated":"2024-02-21T13:45:39Z","abstract":[{"lang":"eng","text":"Which properties of metabolic networks can be derived solely from stoichiometry? Predictive results have been obtained by flux balance analysis (FBA), by postulating that cells set metabolic fluxes to maximize growth rate. Here we consider a generalization of FBA to single-cell level using maximum entropy modeling, which we extend and test experimentally. Specifically, we define for Escherichia coli metabolism a flux distribution that yields the experimental growth rate: the model, containing FBA as a limit, provides a better match to measured fluxes and it makes a wide range of predictions: on flux variability, regulation, and correlations; on the relative importance of stoichiometry vs. optimization; on scaling relations for growth rate distributions. We validate the latter here with single-cell data at different sub-inhibitory antibiotic concentrations. The model quantifies growth optimization as emerging from the interplay of competitive dynamics in the population and regulation of metabolism at the level of single cells."}],"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"30","oa_version":"Published Version","publication_status":"published","intvolume":"         9","file_date_updated":"2020-07-14T12:45:06Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["570"],"article_processing_charge":"No","department":[{"_id":"GaTk"},{"_id":"CaGu"}],"date_created":"2018-12-11T11:44:57Z","article_number":"2988","volume":9,"isi":1,"publist_id":"7760","quality_controlled":"1","month":"07","type":"journal_article","year":"2018","publisher":"Springer Nature","doi":"10.1038/s41467-018-05417-9","language":[{"iso":"eng"}],"date_published":"2018-07-30T00:00:00Z","_id":"161","oa":1,"author":[{"full_name":"De Martino, Daniele","first_name":"Daniele","orcid":"0000-0002-5214-4706","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87","last_name":"De Martino"},{"full_name":"Mc, Andersson Anna","first_name":"Andersson Anna","last_name":"Mc"},{"first_name":"Tobias","full_name":"Bergmiller, Tobias","orcid":"0000-0001-5396-4346","id":"2C471CFA-F248-11E8-B48F-1D18A9856A87","last_name":"Bergmiller"},{"first_name":"Calin C","full_name":"Guet, Calin C","id":"47F8433E-F248-11E8-B48F-1D18A9856A87","last_name":"Guet","orcid":"0000-0001-6220-2052"},{"full_name":"Tkacik, Gasper","first_name":"Gasper","last_name":"Tkacik","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6699-1455"}]},{"year":"2017","publisher":"IOPscience","doi":"10.1088/1742-5468/aa85c3","language":[{"iso":"eng"}],"type":"journal_article","_id":"823","oa":1,"author":[{"last_name":"Colabrese","first_name":"Simona","full_name":"Colabrese, Simona"},{"full_name":"De Martino, Daniele","first_name":"Daniele","orcid":"0000-0002-5214-4706","last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Luca","full_name":"Leuzzi, Luca","last_name":"Leuzzi"},{"first_name":"Enzo","full_name":"Marinari, Enzo","last_name":"Marinari"}],"date_published":"2017-09-26T00:00:00Z","department":[{"_id":"GaTk"}],"date_created":"2018-12-11T11:48:41Z","article_number":"093404","intvolume":"      2017","article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"6826","publication_identifier":{"issn":["17425468"]},"quality_controlled":"1","month":"09","volume":2017,"isi":1,"date_updated":"2023-09-26T16:18:12Z","status":"public","abstract":[{"lang":"eng","text":"The resolution of a linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density c and the ratio α=N/M between number of variables N and number of constraints M. By means of ensemble calculations we show that the space of feasible solutions endows a Van-Der-Waals phase diagram in the plane (c, α). We give numerical evidence that the associated computational problems become more difficult across the critical point and in particular in the coexistence region."}],"ec_funded":1,"day":"26","publication_status":"published","oa_version":"Submitted Version","citation":{"ama":"Colabrese S, De Martino D, Leuzzi L, Marinari E. Phase transitions in integer linear problems. <i> Journal of Statistical Mechanics: Theory and Experiment</i>. 2017;2017(9). doi:<a href=\"https://doi.org/10.1088/1742-5468/aa85c3\">10.1088/1742-5468/aa85c3</a>","mla":"Colabrese, Simona, et al. “Phase Transitions in Integer Linear Problems.” <i> Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2017, no. 9, 093404, IOPscience, 2017, doi:<a href=\"https://doi.org/10.1088/1742-5468/aa85c3\">10.1088/1742-5468/aa85c3</a>.","short":"S. Colabrese, D. De Martino, L. Leuzzi, E. Marinari,  Journal of Statistical Mechanics: Theory and Experiment 2017 (2017).","ista":"Colabrese S, De Martino D, Leuzzi L, Marinari E. 2017. Phase transitions in integer linear problems.  Journal of Statistical Mechanics: Theory and Experiment. 2017(9), 093404.","apa":"Colabrese, S., De Martino, D., Leuzzi, L., &#38; Marinari, E. (2017). Phase transitions in integer linear problems. <i> Journal of Statistical Mechanics: Theory and Experiment</i>. IOPscience. <a href=\"https://doi.org/10.1088/1742-5468/aa85c3\">https://doi.org/10.1088/1742-5468/aa85c3</a>","ieee":"S. Colabrese, D. De Martino, L. Leuzzi, and E. Marinari, “Phase transitions in integer linear problems,” <i> Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2017, no. 9. IOPscience, 2017.","chicago":"Colabrese, Simona, Daniele De Martino, Luca Leuzzi, and Enzo Marinari. “Phase Transitions in Integer Linear Problems.” <i> Journal of Statistical Mechanics: Theory and Experiment</i>. IOPscience, 2017. <a href=\"https://doi.org/10.1088/1742-5468/aa85c3\">https://doi.org/10.1088/1742-5468/aa85c3</a>."},"project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"scopus_import":"1","issue":"9","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.06303"}],"title":"Phase transitions in integer linear problems","external_id":{"isi":["000411842900001"]},"publication":" Journal of Statistical Mechanics: Theory and Experiment"},{"scopus_import":"1","issue":"6","alternative_title":["Rapid Communications"],"citation":{"ieee":"D. De Martino, “Maximum entropy modeling of metabolic networks by constraining growth-rate moments predicts coexistence of phenotypes,” <i>Physical Review E</i>, vol. 96, no. 6. American Physical Society, 2017.","chicago":"De Martino, Daniele. “Maximum Entropy Modeling of Metabolic Networks by Constraining Growth-Rate Moments Predicts Coexistence of Phenotypes.” <i>Physical Review E</i>. American Physical Society, 2017. <a href=\"https://doi.org/10.1103/PhysRevE.96.060401\">https://doi.org/10.1103/PhysRevE.96.060401</a>.","ama":"De Martino D. Maximum entropy modeling of metabolic networks by constraining growth-rate moments predicts coexistence of phenotypes. <i>Physical Review E</i>. 2017;96(6). doi:<a href=\"https://doi.org/10.1103/PhysRevE.96.060401\">10.1103/PhysRevE.96.060401</a>","ista":"De Martino D. 2017. Maximum entropy modeling of metabolic networks by constraining growth-rate moments predicts coexistence of phenotypes. Physical Review E. 96(6), 060401.","mla":"De Martino, Daniele. “Maximum Entropy Modeling of Metabolic Networks by Constraining Growth-Rate Moments Predicts Coexistence of Phenotypes.” <i>Physical Review E</i>, vol. 96, no. 6, 060401, American Physical Society, 2017, doi:<a href=\"https://doi.org/10.1103/PhysRevE.96.060401\">10.1103/PhysRevE.96.060401</a>.","apa":"De Martino, D. (2017). Maximum entropy modeling of metabolic networks by constraining growth-rate moments predicts coexistence of phenotypes. <i>Physical Review E</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevE.96.060401\">https://doi.org/10.1103/PhysRevE.96.060401</a>","short":"D. De Martino, Physical Review E 96 (2017)."},"project":[{"call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"publication":"Physical Review E","title":"Maximum entropy modeling of metabolic networks by constraining growth-rate moments predicts coexistence of phenotypes","main_file_link":[{"url":"https://arxiv.org/abs/1707.00320","open_access":"1"}],"status":"public","date_updated":"2023-10-10T13:29:38Z","day":"21","oa_version":"Submitted Version","publication_status":"published","abstract":[{"lang":"eng","text":"In this work maximum entropy distributions in the space of steady states of metabolic networks are considered upon constraining the first and second moments of the growth rate. Coexistence of fast and slow phenotypes, with bimodal flux distributions, emerges upon considering control on the average growth (optimization) and its fluctuations (heterogeneity). This is applied to the carbon catabolic core of Escherichia coli where it quantifies the metabolic activity of slow growing phenotypes and it provides a quantitative map with metabolic fluxes, opening the possibility to detect coexistence from flux data. A preliminary analysis on data for E. coli cultures in standard conditions shows degeneracy for the inferred parameters that extend in the coexistence region."}],"ec_funded":1,"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        96","article_number":"060401","date_created":"2018-12-11T11:47:06Z","department":[{"_id":"GaTk"}],"volume":96,"month":"12","publist_id":"7266","publication_identifier":{"issn":["2470-0045"]},"quality_controlled":"1","type":"journal_article","doi":"10.1103/PhysRevE.96.060401","language":[{"iso":"eng"}],"year":"2017","publisher":"American Physical Society","date_published":"2017-12-21T00:00:00Z","author":[{"last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5214-4706","full_name":"De Martino, Daniele","first_name":"Daniele"}],"_id":"548","oa":1},{"scopus_import":"1","issue":"1","citation":{"apa":"De Martino, D., Capuani, F., &#38; De Martino, A. (2017). Quantifying the entropic cost of cellular growth control. <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>. American Institute of Physics. <a href=\"https://doi.org/10.1103/PhysRevE.96.010401\">https://doi.org/10.1103/PhysRevE.96.010401</a>","short":"D. De Martino, F. Capuani, A. De Martino,  Physical Review E Statistical Nonlinear and Soft Matter Physics  96 (2017).","mla":"De Martino, Daniele, et al. “Quantifying the Entropic Cost of Cellular Growth Control.” <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>, vol. 96, no. 1, 010401, American Institute of Physics, 2017, doi:<a href=\"https://doi.org/10.1103/PhysRevE.96.010401\">10.1103/PhysRevE.96.010401</a>.","ista":"De Martino D, Capuani F, De Martino A. 2017. Quantifying the entropic cost of cellular growth control.  Physical Review E Statistical Nonlinear and Soft Matter Physics . 96(1), 010401.","ama":"De Martino D, Capuani F, De Martino A. Quantifying the entropic cost of cellular growth control. <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>. 2017;96(1). doi:<a href=\"https://doi.org/10.1103/PhysRevE.96.010401\">10.1103/PhysRevE.96.010401</a>","chicago":"De Martino, Daniele, Fabrizio Capuani, and Andrea De Martino. “Quantifying the Entropic Cost of Cellular Growth Control.” <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>. American Institute of Physics, 2017. <a href=\"https://doi.org/10.1103/PhysRevE.96.010401\">https://doi.org/10.1103/PhysRevE.96.010401</a>.","ieee":"D. De Martino, F. Capuani, and A. De Martino, “Quantifying the entropic cost of cellular growth control,” <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>, vol. 96, no. 1. American Institute of Physics, 2017."},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734"}],"title":"Quantifying the entropic cost of cellular growth control","external_id":{"isi":["000405194200002"]},"publication":" Physical Review E Statistical Nonlinear and Soft Matter Physics ","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.00219"}],"status":"public","date_updated":"2023-09-22T10:03:50Z","abstract":[{"text":"Viewing the ways a living cell can organize its metabolism as the phase space of a physical system, regulation can be seen as the ability to reduce the entropy of that space by selecting specific cellular configurations that are, in some sense, optimal. Here we quantify the amount of regulation required to control a cell's growth rate by a maximum-entropy approach to the space of underlying metabolic phenotypes, where a configuration corresponds to a metabolic flux pattern as described by genome-scale models. We link the mean growth rate achieved by a population of cells to the minimal amount of metabolic regulation needed to achieve it through a phase diagram that highlights how growth suppression can be as costly (in regulatory terms) as growth enhancement. Moreover, we provide an interpretation of the inverse temperature β controlling maximum-entropy distributions based on the underlying growth dynamics. Specifically, we show that the asymptotic value of β for a cell population can be expected to depend on (i) the carrying capacity of the environment, (ii) the initial size of the colony, and (iii) the probability distribution from which the inoculum was sampled. Results obtained for E. coli and human cells are found to be remarkably consistent with empirical evidence.","lang":"eng"}],"ec_funded":1,"day":"10","oa_version":"Submitted Version","publication_status":"published","intvolume":"        96","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","department":[{"_id":"GaTk"}],"date_created":"2018-12-11T11:49:21Z","article_number":"010401","volume":96,"isi":1,"publication_identifier":{"issn":["24700045"]},"publist_id":"6470","quality_controlled":"1","month":"07","type":"journal_article","year":"2017","publisher":"American Institute of Physics","doi":"10.1103/PhysRevE.96.010401","language":[{"iso":"eng"}],"date_published":"2017-07-10T00:00:00Z","_id":"947","oa":1,"author":[{"orcid":"0000-0002-5214-4706","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87","last_name":"De Martino","full_name":"De Martino, Daniele","first_name":"Daniele"},{"last_name":"Capuani","first_name":"Fabrizio","full_name":"Capuani, Fabrizio"},{"last_name":"De Martino","full_name":"De Martino, Andrea","first_name":"Andrea"}]},{"project":[{"call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"citation":{"ama":"De Martino D. Scales and multimodal flux distributions in stationary metabolic network models via thermodynamics. <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>. 2017;95(6):062419. doi:<a href=\"https://doi.org/10.1103/PhysRevE.95.062419\">10.1103/PhysRevE.95.062419</a>","apa":"De Martino, D. (2017). Scales and multimodal flux distributions in stationary metabolic network models via thermodynamics. <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>. American Institute of Physics. <a href=\"https://doi.org/10.1103/PhysRevE.95.062419\">https://doi.org/10.1103/PhysRevE.95.062419</a>","short":"D. De Martino,  Physical Review E Statistical Nonlinear and Soft Matter Physics  95 (2017) 062419.","mla":"De Martino, Daniele. “Scales and Multimodal Flux Distributions in Stationary Metabolic Network Models via Thermodynamics.” <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>, vol. 95, no. 6, American Institute of Physics, 2017, p. 062419, doi:<a href=\"https://doi.org/10.1103/PhysRevE.95.062419\">10.1103/PhysRevE.95.062419</a>.","ista":"De Martino D. 2017. Scales and multimodal flux distributions in stationary metabolic network models via thermodynamics.  Physical Review E Statistical Nonlinear and Soft Matter Physics . 95(6), 062419.","ieee":"D. De Martino, “Scales and multimodal flux distributions in stationary metabolic network models via thermodynamics,” <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>, vol. 95, no. 6. American Institute of Physics, p. 062419, 2017.","chicago":"De Martino, Daniele. “Scales and Multimodal Flux Distributions in Stationary Metabolic Network Models via Thermodynamics.” <i> Physical Review E Statistical Nonlinear and Soft Matter Physics </i>. American Institute of Physics, 2017. <a href=\"https://doi.org/10.1103/PhysRevE.95.062419\">https://doi.org/10.1103/PhysRevE.95.062419</a>."},"issue":"6","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/pdf/1703.00853.pdf","open_access":"1"}],"publication":" Physical Review E Statistical Nonlinear and Soft Matter Physics ","external_id":{"isi":["000404546400004"]},"title":"Scales and multimodal flux distributions in stationary metabolic network models via thermodynamics","date_updated":"2023-09-22T09:59:01Z","status":"public","publication_status":"published","page":"062419","oa_version":"Submitted Version","day":"28","ec_funded":1,"abstract":[{"lang":"eng","text":"In this work it is shown that scale-free tails in metabolic flux distributions inferred in stationary models are an artifact due to reactions involved in thermodynamically unfeasible cycles, unbounded by physical constraints and in principle able to perform work without expenditure of free energy. After implementing thermodynamic constraints by removing such loops, metabolic flux distributions scale meaningfully with the physical limiting factors, acquiring in turn a richer multimodal structure potentially leading to symmetry breaking while optimizing for objective functions."}],"date_created":"2018-12-11T11:49:25Z","department":[{"_id":"GaTk"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":"        95","month":"06","quality_controlled":"1","publication_identifier":{"issn":["24700045"]},"publist_id":"6446","isi":1,"volume":95,"language":[{"iso":"eng"}],"doi":"10.1103/PhysRevE.95.062419","publisher":"American Institute of Physics","year":"2017","type":"journal_article","author":[{"first_name":"Daniele","full_name":"De Martino, Daniele","orcid":"0000-0002-5214-4706","last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87"}],"oa":1,"_id":"959","date_published":"2017-06-28T00:00:00Z"},{"main_file_link":[{"url":"http://arxiv.org/abs/1505.04613","open_access":"1"}],"title":"Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis","publication":"Physical Biology","project":[{"call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"citation":{"ieee":"D. De Martino, “Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis,” <i>Physical Biology</i>, vol. 13, no. 1. IOP Publishing Ltd., 2016.","chicago":"De Martino, Daniele. “Genome-Scale Estimate of the Metabolic Turnover of E. Coli from the Energy Balance Analysis.” <i>Physical Biology</i>. IOP Publishing Ltd., 2016. <a href=\"https://doi.org/10.1088/1478-3975/13/1/016003\">https://doi.org/10.1088/1478-3975/13/1/016003</a>.","ama":"De Martino D. Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis. <i>Physical Biology</i>. 2016;13(1). doi:<a href=\"https://doi.org/10.1088/1478-3975/13/1/016003\">10.1088/1478-3975/13/1/016003</a>","mla":"De Martino, Daniele. “Genome-Scale Estimate of the Metabolic Turnover of E. Coli from the Energy Balance Analysis.” <i>Physical Biology</i>, vol. 13, no. 1, 016003, IOP Publishing Ltd., 2016, doi:<a href=\"https://doi.org/10.1088/1478-3975/13/1/016003\">10.1088/1478-3975/13/1/016003</a>.","apa":"De Martino, D. (2016). Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis. <i>Physical Biology</i>. IOP Publishing Ltd. <a href=\"https://doi.org/10.1088/1478-3975/13/1/016003\">https://doi.org/10.1088/1478-3975/13/1/016003</a>","short":"D. De Martino, Physical Biology 13 (2016).","ista":"De Martino D. 2016. Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis. Physical Biology. 13(1), 016003."},"issue":"1","scopus_import":1,"ec_funded":1,"abstract":[{"text":"In this article the notion of metabolic turnover is revisited in the light of recent results of out-of-equilibrium thermodynamics. By means of Monte Carlo methods we perform an exact sampling of the enzymatic fluxes in a genome scale metabolic network of E. Coli in stationary growth conditions from which we infer the metabolites turnover times. However the latter are inferred from net fluxes, and we argue that this approximation is not valid for enzymes working nearby thermodynamic equilibrium. We recalculate turnover times from total fluxes by performing an energy balance analysis of the network and recurring to the fluctuation theorem. We find in many cases values one of order of magnitude lower, implying a faster picture of intermediate metabolism.","lang":"eng"}],"publication_status":"published","oa_version":"Preprint","day":"29","date_updated":"2021-01-12T06:51:04Z","status":"public","quality_controlled":"1","publist_id":"5702","month":"01","volume":13,"department":[{"_id":"GaTk"}],"article_number":"016003","date_created":"2018-12-11T11:52:18Z","intvolume":"        13","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"_id":"1485","author":[{"full_name":"De Martino, Daniele","first_name":"Daniele","orcid":"0000-0002-5214-4706","last_name":"De Martino","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87"}],"date_published":"2016-01-29T00:00:00Z","publisher":"IOP Publishing Ltd.","year":"2016","language":[{"iso":"eng"}],"doi":"10.1088/1478-3975/13/1/016003","type":"journal_article"},{"date_updated":"2021-01-12T06:50:23Z","status":"public","day":"27","publication_status":"published","oa_version":"Preprint","abstract":[{"text":"The solution space of genome-scale models of cellular metabolism provides a map between physically\r\nviable flux configurations and cellular metabolic phenotypes described, at the most basic level, by the\r\ncorresponding growth rates. By sampling the solution space of E. coliʼs metabolic network, we show\r\nthat empirical growth rate distributions recently obtained in experiments at single-cell resolution can\r\nbe explained in terms of a trade-off between the higher fitness of fast-growing phenotypes and the\r\nhigher entropy of slow-growing ones. Based on this, we propose a minimal model for the evolution of\r\na large bacterial population that captures this trade-off. The scaling relationships observed in\r\nexperiments encode, in such frameworks, for the same distance from the maximum achievable growth\r\nrate, the same degree of growth rate maximization, and/or the same rate of phenotypic change. Being\r\ngrounded on genome-scale metabolic network reconstructions, these results allow for multiple\r\nimplications and extensions in spite of the underlying conceptual simplicity.","lang":"eng"}],"ec_funded":1,"citation":{"ama":"De Martino D, Capuani F, De Martino A. Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli. <i>Physical Biology</i>. 2016;13(3). doi:<a href=\"https://doi.org/10.1088/1478-3975/13/3/036005\">10.1088/1478-3975/13/3/036005</a>","apa":"De Martino, D., Capuani, F., &#38; De Martino, A. (2016). Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli. <i>Physical Biology</i>. IOP Publishing Ltd. <a href=\"https://doi.org/10.1088/1478-3975/13/3/036005\">https://doi.org/10.1088/1478-3975/13/3/036005</a>","ista":"De Martino D, Capuani F, De Martino A. 2016. Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli. Physical Biology. 13(3), 036005.","short":"D. De Martino, F. Capuani, A. De Martino, Physical Biology 13 (2016).","mla":"De Martino, Daniele, et al. “Growth against Entropy in Bacterial Metabolism: The Phenotypic Trade-off behind Empirical Growth Rate Distributions in E. Coli.” <i>Physical Biology</i>, vol. 13, no. 3, 036005, IOP Publishing Ltd., 2016, doi:<a href=\"https://doi.org/10.1088/1478-3975/13/3/036005\">10.1088/1478-3975/13/3/036005</a>.","ieee":"D. De Martino, F. Capuani, and A. De Martino, “Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli,” <i>Physical Biology</i>, vol. 13, no. 3. IOP Publishing Ltd., 2016.","chicago":"De Martino, Daniele, Fabrizio Capuani, and Andrea De Martino. “Growth against Entropy in Bacterial Metabolism: The Phenotypic Trade-off behind Empirical Growth Rate Distributions in E. Coli.” <i>Physical Biology</i>. IOP Publishing Ltd., 2016. <a href=\"https://doi.org/10.1088/1478-3975/13/3/036005\">https://doi.org/10.1088/1478-3975/13/3/036005</a>."},"project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7"}],"scopus_import":1,"issue":"3","main_file_link":[{"url":"https://arxiv.org/abs/1601.03243","open_access":"1"}],"publication":"Physical Biology","title":"Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli","doi":"10.1088/1478-3975/13/3/036005","language":[{"iso":"eng"}],"year":"2016","publisher":"IOP Publishing Ltd.","type":"journal_article","author":[{"orcid":"0000-0002-5214-4706","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87","last_name":"De Martino","first_name":"Daniele","full_name":"De Martino, Daniele"},{"first_name":"Fabrizio","full_name":"Capuani, Fabrizio","last_name":"Capuani"},{"last_name":"De Martino","first_name":"Andrea","full_name":"De Martino, Andrea"}],"_id":"1394","oa":1,"date_published":"2016-05-27T00:00:00Z","article_number":"036005","date_created":"2018-12-11T11:51:46Z","department":[{"_id":"GaTk"}],"acknowledgement":"The research leading to these results has received funding from the from the Marie\r\nCurie Action ITN NETADIS, grant agreement no. 290038.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":"        13","month":"05","publist_id":"5815","quality_controlled":"1","volume":13},{"author":[{"orcid":"0000-0002-5214-4706","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87","last_name":"De Martino","first_name":"Daniele","full_name":"De Martino, Daniele"},{"last_name":"Masoero","full_name":"Masoero, Davide","first_name":"Davide"}],"_id":"1188","oa":1,"date_published":"2016-12-30T00:00:00Z","doi":"10.1088/1742-5468/aa4e8f","language":[{"iso":"eng"}],"year":"2016","publisher":"IOPscience","type":"journal_article","month":"12","publist_id":"6165","quality_controlled":"1","volume":2016,"article_number":"123502","date_created":"2018-12-11T11:50:37Z","department":[{"_id":"GaTk"}],"acknowledgement":"D De Martino is supported by the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007–2013) under REA grant agreement no. [291734]. D Masoero is supported by the FCT scholarship, number SFRH/BPD/75908/2011. D De Martino thanks the Grupo de Física Matemática of the Universidade de Lisboa for the kind hospitality. We also wish to thank Matteo Osella, Vincenzo Vitagliano and Vera Luz Masoero for useful discussions, also late at night.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":"      2016","day":"30","oa_version":"Preprint","publication_status":"published","abstract":[{"text":"We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modelling. \r\nIn the asymptotic regime of slow\r\ndiffusion, that coincides with the relevant experimental range, the resulting\r\nnon-linear Fokker–Planck equation is solved for the steady state in the WKB\r\napproximation that maps it into the ground state of a quantum particle in an\r\nAiry potential plus a centrifugal term. We retrieve scaling laws for growth rate\r\nfluctuations and time response with respect to the distance from the maximum\r\ngrowth rate suggesting that suboptimal populations can have a faster response\r\nto perturbations.","lang":"eng"}],"ec_funded":1,"date_updated":"2021-01-12T06:48:57Z","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.09048"}],"publication":" Journal of Statistical Mechanics: Theory and Experiment","title":"Asymptotic analysis of noisy fitness maximization, applied to metabolism &amp; growth","citation":{"ieee":"D. De Martino and D. Masoero, “Asymptotic analysis of noisy fitness maximization, applied to metabolism &#38;amp; growth,” <i> Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2016, no. 12. IOPscience, 2016.","chicago":"De Martino, Daniele, and Davide Masoero. “Asymptotic Analysis of Noisy Fitness Maximization, Applied to Metabolism &#38;amp; Growth.” <i> Journal of Statistical Mechanics: Theory and Experiment</i>. IOPscience, 2016. <a href=\"https://doi.org/10.1088/1742-5468/aa4e8f\">https://doi.org/10.1088/1742-5468/aa4e8f</a>.","ama":"De Martino D, Masoero D. Asymptotic analysis of noisy fitness maximization, applied to metabolism &#38;amp; growth. <i> Journal of Statistical Mechanics: Theory and Experiment</i>. 2016;2016(12). doi:<a href=\"https://doi.org/10.1088/1742-5468/aa4e8f\">10.1088/1742-5468/aa4e8f</a>","short":"D. De Martino, D. Masoero,  Journal of Statistical Mechanics: Theory and Experiment 2016 (2016).","apa":"De Martino, D., &#38; Masoero, D. (2016). Asymptotic analysis of noisy fitness maximization, applied to metabolism &#38;amp; growth. <i> Journal of Statistical Mechanics: Theory and Experiment</i>. IOPscience. <a href=\"https://doi.org/10.1088/1742-5468/aa4e8f\">https://doi.org/10.1088/1742-5468/aa4e8f</a>","ista":"De Martino D, Masoero D. 2016. Asymptotic analysis of noisy fitness maximization, applied to metabolism &#38;amp; growth.  Journal of Statistical Mechanics: Theory and Experiment. 2016(12), 123502.","mla":"De Martino, Daniele, and Davide Masoero. “Asymptotic Analysis of Noisy Fitness Maximization, Applied to Metabolism &#38;amp; Growth.” <i> Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2016, no. 12, 123502, IOPscience, 2016, doi:<a href=\"https://doi.org/10.1088/1742-5468/aa4e8f\">10.1088/1742-5468/aa4e8f</a>."},"project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"scopus_import":1,"issue":"12"},{"quality_controlled":"1","publist_id":"6065","month":"06","article_type":"original","volume":27,"department":[{"_id":"GaTk"}],"article_number":"1650067","date_created":"2018-12-11T11:51:00Z","intvolume":"        27","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"_id":"1260","author":[{"orcid":"0000-0002-5214-4706","id":"3FF5848A-F248-11E8-B48F-1D18A9856A87","last_name":"De Martino","first_name":"Daniele","full_name":"De Martino, Daniele"}],"date_published":"2016-06-01T00:00:00Z","publisher":"World Scientific Publishing","year":"2016","language":[{"iso":"eng"}],"doi":"10.1142/S0129183116500674","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1505.02963"}],"external_id":{"arxiv":["1505.02963"]},"title":"The dual of the space of interactions in neural network models","publication":"International Journal of Modern Physics C","citation":{"ama":"De Martino D. The dual of the space of interactions in neural network models. <i>International Journal of Modern Physics C</i>. 2016;27(6). doi:<a href=\"https://doi.org/10.1142/S0129183116500674\">10.1142/S0129183116500674</a>","short":"D. De Martino, International Journal of Modern Physics C 27 (2016).","apa":"De Martino, D. (2016). The dual of the space of interactions in neural network models. <i>International Journal of Modern Physics C</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129183116500674\">https://doi.org/10.1142/S0129183116500674</a>","ista":"De Martino D. 2016. The dual of the space of interactions in neural network models. International Journal of Modern Physics C. 27(6), 1650067.","mla":"De Martino, Daniele. “The Dual of the Space of Interactions in Neural Network Models.” <i>International Journal of Modern Physics C</i>, vol. 27, no. 6, 1650067, World Scientific Publishing, 2016, doi:<a href=\"https://doi.org/10.1142/S0129183116500674\">10.1142/S0129183116500674</a>.","ieee":"D. De Martino, “The dual of the space of interactions in neural network models,” <i>International Journal of Modern Physics C</i>, vol. 27, no. 6. World Scientific Publishing, 2016.","chicago":"De Martino, Daniele. “The Dual of the Space of Interactions in Neural Network Models.” <i>International Journal of Modern Physics C</i>. World Scientific Publishing, 2016. <a href=\"https://doi.org/10.1142/S0129183116500674\">https://doi.org/10.1142/S0129183116500674</a>."},"arxiv":1,"issue":"6","scopus_import":1,"abstract":[{"lang":"eng","text":"In this work, the Gardner problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis is addressed under a dual perspective. By means of duality arguments, an integer linear system is defined whose solution space is the dual of the Gardner space and whose solutions represent mutually unstable patterns. We propose and discuss Monte Carlo methods in order to find and remove unstable patterns and uniformly sample the space of interactions thereafter. We illustrate the problem on a set of real data and perform ensemble calculation that shows how the emergence of phase dominated by unstable patterns can be triggered in a nonlinear discontinuous way."}],"publication_status":"published","oa_version":"Preprint","day":"01","date_updated":"2021-01-12T06:49:28Z","status":"public"}]