Molecular noise modulates transitions in the cell-fate differentiation landscape

Waddington's epigenetic landscape has become one of biology's cornerstone metaphors, widely used both conceptually and computationally. Cell types are often associated with the stable stationary points or valleys of this landscape. In previous work, we showed that the molecular noise dominating sub-cellular dynamics can distort and profoundly reshape this landscape. In non-equilibrium systems, an equally profound question arises: to what extent does noise alter the transition paths between valleys in such dynamic landscapes. We tackle this question using a set of illustrative exemplars, and show that noise gives rise to paths that differ substantially from the canonical least-action paths calculated under deterministic dynamics. We dissect the dynamics of these exemplars and determine the reactive density and transition currents, which show us, respectively, where and how transitions occur for different realisations of stochastic dynamics. Our analysis unambiguously demonstrates that reaction paths for stochastic dynamics diverge non-trivially from their deterministic least-action paths or simple barrier crossing models.