{"title":"A necessary condition for non-monotonic dose response, with an application to a kinetic proofreading model -- Extended version","authors":"Polly Y. Yu, Eduardo D. Sontag","doi":"arxiv-2403.13862","DOIUrl":null,"url":null,"abstract":"Steady state non-monotonic (\"biphasic\") dose responses are often observed in\nexperimental biology, which raises the control-theoretic question of\nidentifying which possible mechanisms might underlie such behaviors. It is well\nknown that the presence of an incoherent feedforward loop (IFFL) in a network\nmay give rise to a non-monotonic response. It has been conjectured that this\ncondition is also necessary, i.e. that a non-monotonic response implies the\nexistence of an IFFL. In this paper, we show that this conjecture is false, and\nin the process prove a weaker version: that either an IFFL must exist or both a\npositive loop and a negative feedback loop must exist. Towards this aim, we\ngive necessary and sufficient conditions for when minors of a symbolic matrix\nhave mixed signs. Finally, we study in full generality when a model of immune\nT-cell activation could exhibit a steady state non-monotonic dose response.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuanBio - Molecular Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.13862","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Steady state non-monotonic ("biphasic") dose responses are often observed in
experimental biology, which raises the control-theoretic question of
identifying which possible mechanisms might underlie such behaviors. It is well
known that the presence of an incoherent feedforward loop (IFFL) in a network
may give rise to a non-monotonic response. It has been conjectured that this
condition is also necessary, i.e. that a non-monotonic response implies the
existence of an IFFL. In this paper, we show that this conjecture is false, and
in the process prove a weaker version: that either an IFFL must exist or both a
positive loop and a negative feedback loop must exist. Towards this aim, we
give necessary and sufficient conditions for when minors of a symbolic matrix
have mixed signs. Finally, we study in full generality when a model of immune
T-cell activation could exhibit a steady state non-monotonic dose response.