Figure 1.

Mapping Waddington's epigenetic landscape. (A) The "epigenetic landscape" proposed by Conrad Waddington shows a ball rolling down valleys separated by ridges on an inclined surface, as a visual metaphor for the branching pathways of cell fate determination. Figure reproduced from original text by Waddington [5]. (B) The computed epigenetic landscape for a two-gene (x and y) regulatory network with mutual inhibition and positive autoregulation, where the elevation represents a path-integral quasi-potential derived from the deterministic rate equations describing the interactions of the two genes. We show that the "valleys" on this computed surface correspond to stable steady states (attractors) of the network, while the "ridges" separating the valleys represent barriers to stochastic transitions among multiple steady states. Colored circles represent a population of stochastically simulated "cells" (multiple instances of the network) residing in different stable steady states.