Figure 3.

Topologies of transitions that connect interconverting phenotypes. The dynamics of systems in molecular abundance space are often represented by the motions of weights sliding around potential energy surfaces at roughly terminal velocity in an ambient medium, with thermal excitation. (a) Reversible transitions proceed back and forth between a pair of states in a bistable system. This corresponds to two energy valleys. (b) Transitions can occur in stepwise fashion along a continuous spectrum or graded discrete collection of states. (c) Higher-dimensional topologies introduce the possibility of connecting an initial state, i, to a final state, f, through multiple paths (i.e. green path going around energy peak and red path passing through intermediate valley). The typical time required to move from state i to state f along these two paths may differ.