Classification of transient behaviours in a time-dependent toggle switch model

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  • dc.contributor.author Verd Fernández, Berta, 1984-ca
  • dc.contributor.author Crombach, Antonca
  • dc.contributor.author Jaeger, Johannes, 1973-ca
  • dc.date.accessioned 2015-03-19T08:37:44Z
  • dc.date.available 2015-03-19T08:37:44Z
  • dc.date.issued 2014ca
  • dc.description.abstract Background: Waddington’s epigenetic landscape is an intuitive metaphor for the developmental and evolutionary potential of biological regulatory processes. It emphasises time-dependence and transient behaviour. Nowadays, we can derive this landscape by modelling a specific regulatory network as a dynamical system and calculating its so-called potential surface. In this sense, potential surfaces are the mathematical equivalent of the Waddingtonian landscape metaphor. In order to fully capture the time-dependent (non-autonomous) transient behaviour of biological processes, we must be able to characterise potential landscapes and how they change over time. However, currently available mathematical tools focus on the asymptotic (steady-state) behaviour of autonomous dynamical systems, which restricts how biological systems are studied. Results: We present a pragmatic first step towards a methodology for dealing with transient behaviours in non-autonomous systems. We propose a classification scheme for different kinds of such dynamics based on the simulation of a simple genetic toggle-switch model with time-variable parameters. For this low-dimensional system, we can calculate and explicitly visualise numerical approximations to the potential landscape. Focussing on transient dynamics in non-autonomous systems reveals a range of interesting and biologically relevant behaviours that would be missed in steady-state analyses of autonomous systems. Our simulation-based approach allows us to identify four qualitatively different kinds of dynamics: transitions, pursuits, and two kinds of captures. We describe these in detail, and illustrate the usefulness of our classification scheme by providing a number of examples that demonstrate how it can be employed to gain specific mechanistic insights into the dynamics of gene regulation. Conclusions: The practical aim of our proposed classification scheme is to make the analysis of explicitly time-dependent transient behaviour tractable, and to encourage the wider use of non-autonomous models in systems biology. Our method is applicable to a large class of biological processes.en
  • dc.description.sponsorship This work was supported by a ’la Caixa’ fellowship awarded to BV. AC was supported by the BioPreDyn consortium, funded by European Commission grant FP7-KBBE-2011-5/289434. The laboratory of JJ is funded by the MEC-EMBL agreement for the EMBL/CRG Research Unit in Systems Biology. Additional financial support was provided by SGR Grant 406 from the Catalan funding agency AGAUR, and by grants BFU2009- 10184 and BFU2012-337758 from the Spanish Ministerio de Economia y Competitividad (MINECO)en
  • dc.format.mimetype application/pdfca
  • dc.identifier.citation Verd B, Crombach A, Jaeger J. Classification of transient behaviours in a time-dependent toggle switch model. BMC Systems Biology. 2014; 8: 43. DOI 10.1186/1752-0509-8-43ca
  • dc.identifier.doi http://dx.doi.org/10.1186/1752-0509-8-43
  • dc.identifier.issn 1752-0509ca
  • dc.identifier.uri http://hdl.handle.net/10230/23226
  • dc.language.iso engca
  • dc.publisher BioMed Centralca
  • dc.relation.ispartof BMC Systems Biology. 2014; 8: 43
  • dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/289434ca
  • dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/BFU2009-10184
  • dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/BFU2012-337758
  • dc.rights © 2014 Verd et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver () applies to the data made available in this article, unless otherwise stated.ca
  • dc.rights.accessRights info:eu-repo/semantics/openAccessca
  • dc.rights.uri http://creativecommons.org/licenses/by/2.0
  • dc.subject.other Transcripció genètica -- Regulacióca
  • dc.subject.other Sistemes biològics -- Mètodes de simulacióca
  • dc.title Classification of transient behaviours in a time-dependent toggle switch modelen
  • dc.type info:eu-repo/semantics/articleca
  • dc.type.version info:eu-repo/semantics/publishedVersionca

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