{"title":"Difficult control is related to instability in biologically inspired Boolean networks","authors":"Bryan C. Daniels, Enrico Borriello","doi":"arxiv-2402.18757","DOIUrl":null,"url":null,"abstract":"Previous work in Boolean dynamical networks has suggested that the number of\ncomponents that must be controlled to select an existing attractor is typically\nset by the number of attractors admitted by the dynamics, with no dependence on\nthe size of the network. Here we study the rare cases of networks that defy\nthis expectation, with attractors that require controlling most nodes. We find\nempirically that unstable fixed points are the primary recurring characteristic\nof networks that prove more difficult to control. We describe an efficient way\nto identify unstable fixed points and show that, in both existing biological\nmodels and ensembles of random dynamics, we can better explain the variance of\ncontrol kernel sizes by incorporating the prevalence of unstable fixed points.\nIn the end, the fact that these exceptions are associated with dynamics that\nare unstable to small perturbations hints that they are likely an artifact of\nusing deterministic models. These exceptions are likely to be biologically\nirrelevant, supporting the generality of easy controllability in biological\nnetworks.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-28","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-2402.18757","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
Previous work in Boolean dynamical networks has suggested that the number of
components that must be controlled to select an existing attractor is typically
set by the number of attractors admitted by the dynamics, with no dependence on
the size of the network. Here we study the rare cases of networks that defy
this expectation, with attractors that require controlling most nodes. We find
empirically that unstable fixed points are the primary recurring characteristic
of networks that prove more difficult to control. We describe an efficient way
to identify unstable fixed points and show that, in both existing biological
models and ensembles of random dynamics, we can better explain the variance of
control kernel sizes by incorporating the prevalence of unstable fixed points.
In the end, the fact that these exceptions are associated with dynamics that
are unstable to small perturbations hints that they are likely an artifact of
using deterministic models. These exceptions are likely to be biologically
irrelevant, supporting the generality of easy controllability in biological
networks.