title: Quasi-potential landscape in complex multi-stable systems.
abstract: 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.
authors.affiliation: Institute for Systems Biology, Seattle, WA, USA. joseph.zhou@systemsbiology.org
authors.forename: Joseph Xu
authors.initials: JX
authors.lastname: Zhou
authors.forename: M D S
authors.initials: MD
authors.lastname: Aliyu
authors.forename: Erik
authors.initials: E
authors.lastname: Aurell
authors.forename: Sui
authors.initials: S
authors.lastname: Huang
mesh_terms: D053263:Gene Regulatory Networks; D008962:Models, Theoretical; D049490:Systems Biology / Q000379:methods*