Mapping Epigenetic Landscapes of Gene Regulatory Networks by Adaptive Weighted Ensemble Sampling

Abstract

Nonlinear interactions in gene regulatory networks (GRNs) give rise to multiple steady states, where attractor states represent stable gene expression profiles, or cell phenotypes. Phenotypic changes such as differentiation, reprogramming, and carcinogenesis have been described as dynamic processes occurring over a rugged landscape. Computational methods that predict how GRN features govern state-structure and dynamics over the global epigenetic landscape can potentially inform strategies for cellular reprogramming. Stochastic simulations of reaction network dynamics provide a flexible approach, because they are not inherently limited to small networks and can treat events that are single-molecule in nature, such as epigenetic control of gene activity. However, brute-force stochastic simulations have limited efficiency for mapping multi-stable dynamic landscapes due to trapping in local attractors. Rare event sampling methods provide a means of sampling global distributions without sacrificing molecular mechanistic detail. We demonstrate the use of adaptive Weighted Ensemble (WE) sampling methods for efficiently computing the global quasi-potential landscape for complex multi-gene networks underlying stem cell differentiation. The WE method, combined with adaptive partitioning methods for efficient discretization of state space, provides computational speedups over brute force stochastic simulations in parameter regimes where spontaneous transitioning between states is rare. Our simulations reveal how network parameters governing kinetics of regulatory interactions at promoters can significantly alter the structure of the global landscape.