Potential landscape of high dimensional nonlinear stochastic dynamics with large noise

Abstract

Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including cell-fate decision in developmental processes as well as genesis and progression of cancers. While various attempts have been made to construct potential landscape in high dimensional systems and to estimate rare transitions, they are practically limited to cases where either noise is small or detailed balance condition holds. A general and practical approach to investigate nonequilibrium systems typically subject to finite or large multiplicative noise and breakdown of detailed balance remains elusive. Here, we formulate a computational framework to address this important problem. The current approach is based on a least action principle to efficiently calculate potential landscapes of systems under arbitrary noise strength and without detailed balance. With the deterministic stability structure preserving A-type stochastic integration, the potential barrier between different (local) stable stables is directly computable. We demonstrate our approach in a numerically accurate manner through solvable examples. We further apply the method to investigate the role of noise on tumor heterogeneity in a 38 dimensional network model for prostate cancer, and provide a new strategy on controlling cell populations by manipulating noise strength.