[{"has_accepted_license":"1","citation":{"mla":"Sokolowski, Thomas R., et al. “Deriving a Genetic Regulatory Network from an Optimization Principle.” <i>Proceedings of the National Academy of Sciences</i>, vol. 122, no. 1, e2402925121, National Academy of Sciences, 2025, doi:<a href=\"https://doi.org/10.1073/pnas.2402925121\">10.1073/pnas.2402925121</a>.","ieee":"T. R. Sokolowski, T. Gregor, W. Bialek, and G. Tkačik, “Deriving a genetic regulatory network from an optimization principle,” <i>Proceedings of the National Academy of Sciences</i>, vol. 122, no. 1. National Academy of Sciences, 2025.","chicago":"Sokolowski, Thomas R, Thomas Gregor, William Bialek, and Gašper Tkačik. “Deriving a Genetic Regulatory Network from an Optimization Principle.” <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences, 2025. <a href=\"https://doi.org/10.1073/pnas.2402925121\">https://doi.org/10.1073/pnas.2402925121</a>.","ista":"Sokolowski TR, Gregor T, Bialek W, Tkačik G. 2025. Deriving a genetic regulatory network from an optimization principle. Proceedings of the National Academy of Sciences. 122(1), e2402925121.","apa":"Sokolowski, T. R., Gregor, T., Bialek, W., &#38; Tkačik, G. (2025). Deriving a genetic regulatory network from an optimization principle. <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2402925121\">https://doi.org/10.1073/pnas.2402925121</a>","ama":"Sokolowski TR, Gregor T, Bialek W, Tkačik G. Deriving a genetic regulatory network from an optimization principle. <i>Proceedings of the National Academy of Sciences</i>. 2025;122(1). doi:<a href=\"https://doi.org/10.1073/pnas.2402925121\">10.1073/pnas.2402925121</a>","short":"T.R. Sokolowski, T. Gregor, W. Bialek, G. Tkačik, Proceedings of the National Academy of Sciences 122 (2025)."},"article_number":"e2402925121","corr_author":"1","OA_type":"hybrid","issue":"1","OA_place":"publisher","language":[{"iso":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":"       122","ddc":["570"],"acknowledgement":"We thank Nicholas H. Barton for his comments on the manuscript, Benjamin Zoller for helpful discussions, and Aleksandra Walczak and Curtis Callan for early collaborations that shaped this work. Special thanks to Eric F. Wieschaus for many persistently inspiring conversations. This work was supported in part by the Human Frontiers Science Program; the Austrian Science Fund (FWF P28844); by the European Research Council grant DynaTrans (101118866); by U.S. NSF, through the Center for the Physics of Biological Function (PHY–1734030); by NIH Grants R01GM097275, U01DA047730, and U01DK127429; by the John Simon Guggenheim Memorial Foundation; and by the LOEWE priority program “Center for Multiscale Modeling in Life Sciences” (CMMS), sponsored by the Hessian Ministry for Science and Research, Arts and Culture (HMWK).","department":[{"_id":"GaTk"}],"author":[{"first_name":"Thomas R","id":"3E999752-F248-11E8-B48F-1D18A9856A87","full_name":"Sokolowski, Thomas R","last_name":"Sokolowski","orcid":"0000-0002-1287-3779"},{"first_name":"Thomas","full_name":"Gregor, Thomas","last_name":"Gregor"},{"full_name":"Bialek, William","last_name":"Bialek","first_name":"William"},{"orcid":"0000-0002-6699-1455","full_name":"Tkačik, Gašper","last_name":"Tkačik","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","first_name":"Gašper"}],"publication_status":"published","isi":1,"month":"01","volume":122,"abstract":[{"text":"Many biological systems operate near the physical limits to their performance, suggesting that aspects of their behavior and underlying mechanisms could be derived from optimization principles. However, such principles have often been applied only in simplified models. Here, we explore a detailed mechanistic model of the gap gene network in the Drosophila embryo, optimizing its 50+ parameters to maximize the information that gene expression levels provide about nuclear positions. This optimization is conducted under realistic constraints, such as limits on the number of available molecules. Remarkably, the optimal networks we derive closely match the architecture and spatial gene expression profiles observed in the real organism. Our framework quantifies the tradeoffs involved in maximizing functional performance and allows for the exploration of alternative network configurations, addressing the question of which features are necessary and which are contingent. Our results suggest that multiple solutions to the optimization problem might exist across closely related organisms, offering insights into the evolution of gene regulatory networks.","lang":"eng"}],"title":"Deriving a genetic regulatory network from an optimization principle","quality_controlled":"1","publisher":"National Academy of Sciences","file":[{"date_updated":"2025-01-20T10:10:04Z","success":1,"content_type":"application/pdf","checksum":"8dbfc7d495413340225ebfae69b0cf9a","file_id":"18862","relation":"main_file","date_created":"2025-01-20T10:10:04Z","access_level":"open_access","file_size":19073585,"creator":"dernst","file_name":"2025_PNAS_Sokolowski.pdf"}],"publication_identifier":{"eissn":["1091-6490"],"issn":["0027-8424"]},"doi":"10.1073/pnas.2402925121","date_updated":"2026-02-16T12:26:51Z","status":"public","project":[{"call_identifier":"FWF","grant_number":"P28844-B27","name":"Biophysics of information processing in gene regulation","_id":"254E9036-B435-11E9-9278-68D0E5697425"},{"name":"Transcription in 4D: the dynamic interplay between chromatin architecture and gene expression in developing pseudo-embryos","grant_number":"101118866","_id":"7bfe6a29-9f16-11ee-852c-c0da5e2045d9"},{"_id":"2665AAFE-B435-11E9-9278-68D0E5697425","name":"Can evolution minimize spurious signaling crosstalk to reach optimal performance?","grant_number":"RGP0034/2018"}],"tmp":{"short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_type":"original","oa":1,"pmid":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","date_created":"2025-01-19T23:01:50Z","external_id":{"isi":["001392772400001"],"pmid":["39752518"]},"_id":"18849","date_published":"2025-01-07T00:00:00Z","year":"2025","file_date_updated":"2025-01-20T10:10:04Z","day":"07","article_processing_charge":"Yes (in subscription journal)","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Proceedings of the National Academy of Sciences"},{"file_date_updated":"2024-02-23T14:20:16Z","year":"2024","date_published":"2024-02-23T00:00:00Z","_id":"15020","acknowledged_ssus":[{"_id":"ScienComp"}],"date_created":"2024-02-23T14:02:04Z","type":"dissertation","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","article_processing_charge":"No","day":"23","publication_identifier":{"issn":["2663-337X"]},"file":[{"date_created":"2024-02-23T13:50:53Z","relation":"main_file","creator":"mhledik","access_level":"open_access","file_size":7102089,"file_name":"hledik thesis pdfa 2b.pdf","date_updated":"2024-02-23T13:50:53Z","success":1,"checksum":"b2d3da47c98d481577a4baf68944fe41","content_type":"application/pdf","file_id":"15021"},{"date_updated":"2024-02-23T14:20:16Z","file_id":"15022","checksum":"eda9b9430da2610fee7ce1c1419a479a","content_type":"application/zip","relation":"source_file","date_created":"2024-02-23T13:50:54Z","access_level":"closed","file_size":14014790,"creator":"mhledik","file_name":"hledik thesis source.zip"}],"publisher":"Institute of Science and Technology Austria","abstract":[{"text":"This thesis consists of four distinct pieces of work within theoretical biology, with two themes in common: the concept of optimization in biological systems, and the use of information-theoretic tools to quantify biological stochasticity and statistical uncertainty.\r\nChapter 2 develops a statistical framework for studying biological systems which we believe to be optimized for a particular utility function, such as retinal neurons conveying information about visual stimuli. We formalize such beliefs as maximum-entropy Bayesian priors, constrained by the expected utility. We explore how such priors aid inference of system parameters with limited data and enable optimality hypothesis testing: is the utility higher than by chance?\r\nChapter 3 examines the ultimate biological optimization process: evolution by natural selection. As some individuals survive and reproduce more successfully than others, populations evolve towards fitter genotypes and phenotypes. We formalize this as accumulation of genetic information, and use population genetics theory to study how much such information can be accumulated per generation and maintained in the face of random mutation and genetic drift. We identify the population size and fitness variance as the key quantities that control information accumulation and maintenance.\r\nChapter 4 reuses the concept of genetic information from Chapter 3, but from a different perspective: we ask how much genetic information organisms actually need, in particular in the context of gene regulation. For example, how much information is needed to bind transcription factors at correct locations within the genome? Population genetics provides us with a refined answer: with an increasing population size, populations achieve higher fitness by maintaining more genetic information. Moreover, regulatory parameters experience selection pressure to optimize the fitness-information trade-off, i.e. minimize the information needed for a given fitness. This provides an evolutionary derivation of the optimization priors introduced in Chapter 2.\r\nChapter 5 proves an upper bound on mutual information between a signal and a communication channel output (such as neural activity). Mutual information is an important utility measure for biological systems, but its practical use can be difficult due to the large dimensionality of many biological channels. Sometimes, a lower bound on mutual information is computed by replacing the high-dimensional channel outputs with decodes (signal estimates). Our result provides a corresponding upper bound, provided that the decodes are the maximum posterior estimates of the signal.","lang":"eng"}],"title":"Genetic information and biological optimization","oa":1,"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"},{"_id":"2665AAFE-B435-11E9-9278-68D0E5697425","name":"Can evolution minimize spurious signaling crosstalk to reach optimal performance?","grant_number":"RGP0034/2018"},{"name":"Understanding the evolution of continuous genomes","grant_number":"101055327","_id":"bd6958e0-d553-11ed-ba76-86eba6a76c00"}],"keyword":["Theoretical biology","Optimality","Evolution","Information"],"status":"public","doi":"10.15479/at:ista:15020","date_updated":"2026-04-07T12:59:25Z","page":"158","oa_version":"Published Version","language":[{"iso":"eng"}],"month":"02","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"NiBa"},{"_id":"GaTk"}],"author":[{"id":"4171253A-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Hledik","full_name":"Hledik, Michal"}],"ddc":["576","519"],"corr_author":"1","citation":{"short":"M. Hledik, Genetic Information and Biological Optimization, Institute of Science and Technology Austria, 2024.","ama":"Hledik M. Genetic information and biological optimization. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:15020\">10.15479/at:ista:15020</a>","apa":"Hledik, M. (2024). <i>Genetic information and biological optimization</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:15020\">https://doi.org/10.15479/at:ista:15020</a>","ista":"Hledik M. 2024. Genetic information and biological optimization. Institute of Science and Technology Austria.","chicago":"Hledik, Michal. “Genetic Information and Biological Optimization.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:15020\">https://doi.org/10.15479/at:ista:15020</a>.","ieee":"M. Hledik, “Genetic information and biological optimization,” Institute of Science and Technology Austria, 2024.","mla":"Hledik, Michal. <i>Genetic Information and Biological Optimization</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:15020\">10.15479/at:ista:15020</a>."},"alternative_title":["ISTA Thesis"],"ec_funded":1,"degree_awarded":"PhD","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"7606"},{"relation":"part_of_dissertation","id":"12081","status":"public"},{"id":"7553","status":"public","relation":"part_of_dissertation"}]},"has_accepted_license":"1","OA_place":"publisher","supervisor":[{"orcid":"0000-0002-8548-5240","last_name":"Barton","full_name":"Barton, Nicholas H","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Tkačik","full_name":"Tkačik, Gašper","orcid":"0000-0002-6699-1455","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","first_name":"Gašper"}]},{"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"20357"}]},"has_accepted_license":"1","issue":"44","OA_type":"hybrid","article_number":"e2402340121","corr_author":"1","citation":{"ama":"Ruzickova N, Hledik M, Tkačik G. Quantitative omnigenic model discovers interpretable genome-wide associations. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. 2024;121(44). doi:<a href=\"https://doi.org/10.1073/pnas.2402340121\">10.1073/pnas.2402340121</a>","apa":"Ruzickova, N., Hledik, M., &#38; Tkačik, G. (2024). Quantitative omnigenic model discovers interpretable genome-wide associations. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2402340121\">https://doi.org/10.1073/pnas.2402340121</a>","short":"N. Ruzickova, M. Hledik, G. Tkačik, Proceedings of the National Academy of Sciences of the United States of America 121 (2024).","ieee":"N. Ruzickova, M. Hledik, and G. Tkačik, “Quantitative omnigenic model discovers interpretable genome-wide associations,” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 121, no. 44. National Academy of Sciences, 2024.","chicago":"Ruzickova, Natalia, Michal Hledik, and Gašper Tkačik. “Quantitative Omnigenic Model Discovers Interpretable Genome-Wide Associations.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2024. <a href=\"https://doi.org/10.1073/pnas.2402340121\">https://doi.org/10.1073/pnas.2402340121</a>.","mla":"Ruzickova, Natalia, et al. “Quantitative Omnigenic Model Discovers Interpretable Genome-Wide Associations.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 121, no. 44, e2402340121, National Academy of Sciences, 2024, doi:<a href=\"https://doi.org/10.1073/pnas.2402340121\">10.1073/pnas.2402340121</a>.","ista":"Ruzickova N, Hledik M, Tkačik G. 2024. Quantitative omnigenic model discovers interpretable genome-wide associations. Proceedings of the National Academy of Sciences of the United States of America. 121(44), e2402340121."},"APC_amount":"3062,93 EUR","OA_place":"publisher","oa_version":"Published Version","language":[{"iso":"eng"}],"acknowledgement":"N.R.acknowledges the support of the Austrian Academy of Sciences through the Doctoral Fellowship Programme (DOC) of the Austrian Academy of Sciences 26917. M.H. and G.T. were supported in part by the Human Frontiers Science Program Grant RGP0034/2018. We thank Nicholas H. Barton, Fyodor Kondrashov, and Matthew R. Robinson for fruitful discussions.","intvolume":"       121","ddc":["570"],"scopus_import":"1","month":"10","volume":121,"isi":1,"publication_status":"published","department":[{"_id":"GaTk"},{"_id":"NiBa"}],"author":[{"full_name":"Ruzickova, Natalia","last_name":"Ruzickova","first_name":"Natalia","id":"D2761128-D73D-11E9-A1BF-BA0DE6697425"},{"full_name":"Hledik, Michal","last_name":"Hledik","first_name":"Michal","id":"4171253A-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-6699-1455","last_name":"Tkačik","full_name":"Tkačik, Gašper","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","first_name":"Gašper"}],"file":[{"checksum":"d930e2ccf9ec900c7d7509a78cfb3564","file_id":"18536","content_type":"application/pdf","success":1,"date_updated":"2024-11-11T09:31:00Z","file_name":"2024_PNAS_Ruzickova.pdf","creator":"dernst","access_level":"open_access","file_size":25529709,"date_created":"2024-11-11T09:31:00Z","relation":"main_file"}],"publisher":"National Academy of Sciences","abstract":[{"lang":"eng","text":"As their statistical power grows, genome-wide association studies (GWAS) have identified an increasing number of loci underlying quantitative traits of interest. These loci are scattered throughout the genome and are individually responsible only for small fractions of the total heritable trait variance. The recently proposed omnigenic model provides a conceptual framework to explain these observations by postulating that numerous distant loci contribute to each complex trait via effect propagation through intracellular regulatory networks. We formalize this conceptual framework by proposing the “quantitative omnigenic model” (QOM), a statistical model that combines prior knowledge of the regulatory network topology with genomic data. By applying our model to gene expression traits in yeast, we demonstrate that QOM achieves similar gene expression prediction performance to traditional GWAS with hundreds of times less parameters, while simultaneously extracting candidate causal and quantitative chains of effect propagation through the regulatory network for every individual gene. We estimate the fraction of heritable trait variance in cis- and in trans-, break the latter down by effect propagation order, assess the trans- variance not attributable to transcriptional regulation, and show that QOM correctly accounts for the low-dimensional structure of gene expression covariance. We furthermore demonstrate the relevance of QOM for systems biology, by employing it as a statistical test for the quality of regulatory network reconstructions, and linking it to the propagation of nontranscriptional (including environmental) effects."}],"title":"Quantitative omnigenic model discovers interpretable genome-wide associations","quality_controlled":"1","publication_identifier":{"eissn":["1091-6490"],"issn":["0027-8424"]},"project":[{"name":"Collective behaviour of cells in pancreatic Islets of Langerhans","_id":"7bec9174-9f16-11ee-852c-ded9fe5f810e"},{"_id":"2665AAFE-B435-11E9-9278-68D0E5697425","name":"Can evolution minimize spurious signaling crosstalk to reach optimal performance?","grant_number":"RGP0034/2018"}],"status":"public","doi":"10.1073/pnas.2402340121","date_updated":"2026-08-10T07:47:55Z","oa":1,"tmp":{"short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_type":"original","date_published":"2024-10-29T00:00:00Z","external_id":{"pmid":["39441639"],"isi":["001349462600001"]},"_id":"18525","date_created":"2024-11-10T23:01:59Z","pmid":1,"file_date_updated":"2024-11-11T09:31:00Z","year":"2024","article_processing_charge":"Yes","day":"29","publication":"Proceedings of the National Academy of Sciences of the United States of America","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"article_processing_charge":"No","day":"29","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Proceedings of the National Academy of Sciences of the United States of America","license":"https://creativecommons.org/licenses/by/4.0/","pmid":1,"date_created":"2022-09-11T22:01:55Z","date_published":"2022-08-29T00:00:00Z","external_id":{"isi":["000889278400014"],"pmid":["36037343"]},"_id":"12081","year":"2022","file_date_updated":"2022-09-12T08:08:12Z","project":[{"grant_number":"250152","name":"Limits to selection in biology and in evolutionary computation","_id":"25B07788-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"2665AAFE-B435-11E9-9278-68D0E5697425","name":"Can evolution minimize spurious signaling crosstalk to reach optimal performance?","grant_number":"RGP0034/2018"}],"doi":"10.1073/pnas.2123152119","status":"public","date_updated":"2026-04-07T12:59:24Z","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publisher":"National Academy of Sciences","abstract":[{"text":"Selection accumulates information in the genome—it guides stochastically evolving populations toward states (genotype frequencies) that would be unlikely under neutrality. This can be quantified as the Kullback–Leibler (KL) divergence between the actual distribution of genotype frequencies and the corresponding neutral distribution. First, we show that this population-level information sets an upper bound on the information at the level of genotype and phenotype, limiting how precisely they can be specified by selection. Next, we study how the accumulation and maintenance of information is limited by the cost of selection, measured as the genetic load or the relative fitness variance, both of which we connect to the control-theoretic KL cost of control. The information accumulation rate is upper bounded by the population size times the cost of selection. This bound is very general, and applies across models (Wright–Fisher, Moran, diffusion) and to arbitrary forms of selection, mutation, and recombination. Finally, the cost of maintaining information depends on how it is encoded: Specifying a single allele out of two is expensive, but one bit encoded among many weakly specified loci (as in a polygenic trait) is cheap.","lang":"eng"}],"title":"Accumulation and maintenance of information in evolution","quality_controlled":"1","file":[{"relation":"main_file","date_created":"2022-09-12T08:08:12Z","file_size":2165752,"creator":"dernst","access_level":"open_access","file_name":"2022_PNAS_Hledik.pdf","date_updated":"2022-09-12T08:08:12Z","success":1,"file_id":"12091","content_type":"application/pdf","checksum":"6dec51f6567da9039982a571508a8e4d"}],"publication_identifier":{"eissn":["1091-6490"],"issn":["0027-8424"]},"ddc":["570"],"intvolume":"       119","scopus_import":"1","acknowledgement":"We thank Ksenia Khudiakova, Wiktor Młynarski, Sean Stankowski, and two anonymous reviewers for discussions and comments on the manuscript. G.T. and M.H. acknowledge funding from the Human Frontier Science Program Grant RGP0032/2018. N.B. acknowledges funding from ERC Grant 250152 “Information and Evolution.”","isi":1,"publication_status":"published","department":[{"_id":"NiBa"},{"_id":"GaTk"}],"author":[{"id":"4171253A-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","full_name":"Hledik, Michal","last_name":"Hledik"},{"first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","last_name":"Barton","full_name":"Barton, Nicholas H"},{"id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","first_name":"Gašper","orcid":"1","last_name":"Tkačik","full_name":"Tkačik, Gašper"}],"volume":119,"month":"08","language":[{"iso":"eng"}],"oa_version":"Published Version","has_accepted_license":"1","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"15020","status":"public"}]},"corr_author":"1","article_number":"e2123152119","citation":{"ista":"Hledik M, Barton NH, Tkačik G. 2022. Accumulation and maintenance of information in evolution. Proceedings of the National Academy of Sciences of the United States of America. 119(36), e2123152119.","chicago":"Hledik, Michal, Nicholas H Barton, and Gašper Tkačik. “Accumulation and Maintenance of Information in Evolution.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2022. <a href=\"https://doi.org/10.1073/pnas.2123152119\">https://doi.org/10.1073/pnas.2123152119</a>.","ieee":"M. Hledik, N. H. Barton, and G. Tkačik, “Accumulation and maintenance of information in evolution,” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 119, no. 36. National Academy of Sciences, 2022.","mla":"Hledik, Michal, et al. “Accumulation and Maintenance of Information in Evolution.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 119, no. 36, e2123152119, National Academy of Sciences, 2022, doi:<a href=\"https://doi.org/10.1073/pnas.2123152119\">10.1073/pnas.2123152119</a>.","short":"M. Hledik, N.H. Barton, G. Tkačik, Proceedings of the National Academy of Sciences of the United States of America 119 (2022).","ama":"Hledik M, Barton NH, Tkačik G. Accumulation and maintenance of information in evolution. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. 2022;119(36). doi:<a href=\"https://doi.org/10.1073/pnas.2123152119\">10.1073/pnas.2123152119</a>","apa":"Hledik, M., Barton, N. H., &#38; Tkačik, G. (2022). Accumulation and maintenance of information in evolution. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2123152119\">https://doi.org/10.1073/pnas.2123152119</a>"},"issue":"36"},{"publication_identifier":{"issn":["0027-8424"],"eissn":["1091-6490"]},"publisher":"National Academy of Sciences","quality_controlled":"1","abstract":[{"lang":"eng","text":"In prokaryotes, thermodynamic models of gene regulation provide a highly quantitative mapping from promoter sequences to gene-expression levels that is compatible with in vivo and in vitro biophysical measurements. Such concordance has not been achieved for models of enhancer function in eukaryotes. In equilibrium models, it is difficult to reconcile the reported short transcription factor (TF) residence times on the DNA with the high specificity of regulation. In nonequilibrium models, progress is difficult due to an explosion in the number of parameters. Here, we navigate this complexity by looking for minimal nonequilibrium enhancer models that yield desired regulatory phenotypes: low TF residence time, high specificity, and tunable cooperativity. We find that a single extra parameter, interpretable as the “linking rate,” by which bound TFs interact with Mediator components, enables our models to escape equilibrium bounds and access optimal regulatory phenotypes, while remaining consistent with the reported phenomenology and simple enough to be inferred from upcoming experiments. We further find that high specificity in nonequilibrium models is in a trade-off with gene-expression noise, predicting bursty dynamics—an experimentally observed hallmark of eukaryotic transcription. By drastically reducing the vast parameter space of nonequilibrium enhancer models to a much smaller subspace that optimally realizes biological function, we deliver a rich class of models that could be tractably inferred from data in the near future."}],"title":"Nonequilibrium models of optimal enhancer function","file":[{"access_level":"open_access","file_size":1199247,"creator":"dernst","relation":"main_file","date_created":"2021-01-11T08:37:31Z","file_name":"2020_PNAS_Grah.pdf","date_updated":"2021-01-11T08:37:31Z","content_type":"application/pdf","checksum":"69039cd402a571983aa6cb4815ffa863","file_id":"9004","success":1}],"tmp":{"short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_type":"original","oa":1,"project":[{"name":"Can evolution minimize spurious signaling crosstalk to reach optimal performance?","grant_number":"RGP0034/2018","_id":"2665AAFE-B435-11E9-9278-68D0E5697425"},{"_id":"267C84F4-B435-11E9-9278-68D0E5697425","name":"Biophysically realistic genotype-phenotype maps for regulatory networks"}],"date_updated":"2025-05-14T10:57:50Z","doi":"10.1073/pnas.2006731117","status":"public","year":"2020","file_date_updated":"2021-01-11T08:37:31Z","pmid":1,"date_created":"2021-01-10T23:01:17Z","date_published":"2020-12-15T00:00:00Z","_id":"9000","external_id":{"pmid":["33268497"],"isi":["000600608300015"]},"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Proceedings of the National Academy of Sciences of the United States of America","article_processing_charge":"No","day":"15","corr_author":"1","citation":{"mla":"Grah, Rok, et al. “Nonequilibrium Models of Optimal Enhancer Function.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 117, no. 50, National Academy of Sciences, 2020, pp. 31614–22, doi:<a href=\"https://doi.org/10.1073/pnas.2006731117\">10.1073/pnas.2006731117</a>.","chicago":"Grah, Rok, Benjamin Zoller, and Gašper Tkačik. “Nonequilibrium Models of Optimal Enhancer Function.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2020. <a href=\"https://doi.org/10.1073/pnas.2006731117\">https://doi.org/10.1073/pnas.2006731117</a>.","ieee":"R. Grah, B. Zoller, and G. Tkačik, “Nonequilibrium models of optimal enhancer function,” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 117, no. 50. National Academy of Sciences, pp. 31614–31622, 2020.","ista":"Grah R, Zoller B, Tkačik G. 2020. Nonequilibrium models of optimal enhancer function. Proceedings of the National Academy of Sciences of the United States of America. 117(50), 31614–31622.","apa":"Grah, R., Zoller, B., &#38; Tkačik, G. (2020). Nonequilibrium models of optimal enhancer function. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2006731117\">https://doi.org/10.1073/pnas.2006731117</a>","ama":"Grah R, Zoller B, Tkačik G. 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Tkačik, Proceedings of the National Academy of Sciences of the United States of America 117 (2020) 31614–31622."},"issue":"50","has_accepted_license":"1","related_material":{"link":[{"relation":"press_release","url":"https://ist.ac.at/en/news/new-compact-model-for-gene-regulation-in-higher-organisms/","description":"News on IST Homepage"}]},"language":[{"iso":"eng"}],"page":"31614-31622","oa_version":"Published Version","publication_status":"published","isi":1,"author":[{"last_name":"Grah","full_name":"Grah, Rok","orcid":"0000-0003-2539-3560","first_name":"Rok","id":"483E70DE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Zoller, Benjamin","last_name":"Zoller","first_name":"Benjamin"},{"last_name":"Tkačik","full_name":"Tkačik, Gašper","orcid":"0000-0002-6699-1455","first_name":"Gašper","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"GaTk"}],"volume":117,"month":"12","ddc":["570"],"intvolume":"       117","scopus_import":"1","acknowledgement":"G.T. was supported by Human Frontiers Science Program Grant RGP0034/2018. R.G. was supported by the Austrian Academy of Sciences DOC Fellowship. R.G. thanks S. Avvakumov for helpful discussions."},{"project":[{"_id":"2665AAFE-B435-11E9-9278-68D0E5697425","name":"Can evolution minimize spurious signaling crosstalk to reach optimal performance?","grant_number":"RGP0034/2018"},{"name":"Biophysically realistic genotype-phenotype maps for regulatory networks","_id":"267C84F4-B435-11E9-9278-68D0E5697425"}],"doi":"10.1101/2020.04.08.029405","status":"public","date_updated":"2026-07-06T12:43:43Z","das_tickbox":"1","oa":1,"abstract":[{"lang":"eng","text":"In prokaryotes, thermodynamic models of gene regulation provide a highly quantitative mapping from promoter sequences to gene expression levels that is compatible with in vivo and in vitro bio-physical measurements. Such concordance has not been achieved for models of enhancer function in eukaryotes. In equilibrium models, it is difficult to reconcile the reported short transcription factor (TF) residence times on the DNA with the high specificity of regulation. In non-equilibrium models, progress is difficult due to an explosion in the number of parameters. Here, we navigate this complexity by looking for minimal non-equilibrium enhancer models that yield desired regulatory phenotypes: low TF residence time, high specificity and tunable cooperativity. We find that a single extra parameter, interpretable as the “linking rate” by which bound TFs interact with Mediator components, enables our models to escape equilibrium bounds and access optimal regulatory phenotypes, while remaining consistent with the reported phenomenology and simple enough to be inferred from upcoming experiments. We further find that high specificity in non-equilibrium models is in a tradeoff with gene expression noise, predicting bursty dynamics — an experimentally-observed hallmark of eukaryotic transcription. By drastically reducing the vast parameter space to a much smaller subspace that optimally realizes biological function prior to inference from data, our normative approach holds promise for mathematical models in systems biology."}],"title":"Normative models of enhancer function","related_material":{"record":[{"relation":"dissertation_contains","id":"8155","status":"public"}]},"corr_author":"1","citation":{"short":"R. Grah, B. Zoller, G. Tkačik, BioRxiv (2020).","ama":"Grah R, Zoller B, Tkačik G. Normative models of enhancer function. <i>bioRxiv</i>. 2020. doi:<a href=\"https://doi.org/10.1101/2020.04.08.029405\">10.1101/2020.04.08.029405</a>","apa":"Grah, R., Zoller, B., &#38; Tkačik, G. (2020). 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Tkačik, “Normative models of enhancer function,” <i>bioRxiv</i>. 2020.","chicago":"Grah, Rok, Benjamin Zoller, and Gašper Tkačik. “Normative Models of Enhancer Function.” <i>BioRxiv</i>, 2020. <a href=\"https://doi.org/10.1101/2020.04.08.029405\">https://doi.org/10.1101/2020.04.08.029405</a>.","mla":"Grah, Rok, et al. “Normative Models of Enhancer Function.” <i>BioRxiv</i>, 2020, doi:<a href=\"https://doi.org/10.1101/2020.04.08.029405\">10.1101/2020.04.08.029405</a>."},"main_file_link":[{"url":"https://doi.org/10.1101/2020.04.08.029405 ","open_access":"1"}],"article_processing_charge":"No","biorxivid":1,"day":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","type":"preprint","author":[{"first_name":"Rok","id":"483E70DE-F248-11E8-B48F-1D18A9856A87","last_name":"Grah","full_name":"Grah, Rok","orcid":"0000-0003-2539-3560"},{"first_name":"Benjamin","last_name":"Zoller","full_name":"Zoller, Benjamin"},{"first_name":"Gašper","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","full_name":"Tkačik, Gašper","last_name":"Tkačik","orcid":"0000-0002-6699-1455"}],"department":[{"_id":"CaGu"},{"_id":"GaTk"}],"month":"04","publication":"bioRxiv","date_created":"2020-04-23T10:12:51Z","date_published":"2020-04-09T00:00:00Z","external_id":{"biorxivid":["10.1101/2020.04.08.029405"]},"_id":"7675","year":"2020","language":[{"iso":"eng"}],"oa_version":"Preprint"}]