Quasi-potential landscape in complex multi-stable systems
2012 (English)In: Journal of the Royal Society Interface, ISSN 1742-5662, E-ISSN 1742-5689, Vol. 9, no 77, 3539-3553 p.Article in journal (Refereed) Published
The developmental dynamics of multicellular organisms is a process that takes place in a multi-stable system in which each attractor state represents a cell type, and attractor transitions correspond to cell differentiation paths. This new understanding has revived the idea of a quasi-potential landscape, first proposed by Waddington as a metaphor. To describe development, one is interested in the 'relative stabilities' of N attractors (N > 2). Existing theories of state transition between local minima on some potential landscape deal with the exit part in the transition between two attractors in pair-attractor systems but do not offer the notion of a global potential function that relates more than two attractors to each other. Several ad hoc methods have been used in systems biology to compute a landscape in non-gradient systems, such as gene regulatory networks. Here we present an overview of currently available methods, discuss their limitations and propose a new decomposition of vector fields that permits the computation of a quasi-potential function that is equivalent to the Freidlin-Wentzell potential but is not limited to two attractors. Several examples of decomposition are given, and the significance of such a quasi-potential function is discussed.
Place, publisher, year, edition, pages
2012. Vol. 9, no 77, 3539-3553 p.
multi-stable dynamical system, non-equilibrium dynamics, quasi-potential, state transition, epigenetic landscape, Freidlin-Wentzell theory
Social Sciences Interdisciplinary
IdentifiersURN: urn:nbn:se:kth:diva-107063DOI: 10.1098/rsif.2012.0434ISI: 000310573100035ScopusID: 2-s2.0-84868578989OAI: oai:DiVA.org:kth-107063DiVA: diva2:574967
QC 201212072012-12-072012-12-062012-12-07Bibliographically approved