Developmental dynamics of multicellular organism is a process that takesplace in a multi-stable system in which each attractor state represents a celltype and attractor transitions correspond to cell differentiation paths. Thisnew understanding has revived the idea of a quasi-potential landscape, firstproposed by Waddington as a metaphor. To describe development one is interestedin the "relative stabilities" of N attractors (N>2). Existing theories of statetransition between local minima on some potential landscape deal with the exitin the transition between a pair attractor but do not offer the notion of aglobal potential function that relate more than two attractors to each other.Several ad hoc methods have been used in systems biology to compute a landscapein non-gradient systems, such as gene regulatory networks. Here we present anoverview of the currently available methods, discuss their limitations andpropose a new decomposition of vector fields that permit the computation of aquasi-potential function that is equivalent to the Freidlin-Wentzell potentialbut is not limited to two attractors. Several examples of decomposition aregiven and the significance of such a quasi-potential function is discussed.
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