Markov State Models of gene regulatory networks

Abstract

BackgroundGene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have the potential to guide cell-reprogramming strategies. Networks are often modeled by the stochastic Chemical Master Equation, but methods for systematic identification of key properties of the global dynamics are currently lacking.ResultsThe method identifies the number, phenotypes, and lifetimes of long-lived states for a set of common gene regulatory network models. Application of transition path theory to the constructed Markov State Model decomposes global dynamics into a set of dominant transition paths and associated relative probabilities for stochastic state-switching.ConclusionsIn this proof-of-concept study, we found that the Markov State Model provides a general framework for analyzing and visualizing stochastic multistability and state-transitions in gene networks. Our results suggest that this framework—adopted from the field of atomistic Molecular Dynamics—can be a useful tool for quantitative Systems Biology at the network scale.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-017-0394-4) contains supplementary material, which is available to authorized users.

Learning dynamical information from static protein and sequencing data

“…3B). In agreement with previous studies 52, 53 , the identified metastable states were not recovered from deterministic simulations of the governing ordinary differential equations (Supplementary Information), but could only be identified directly from the stochastic data (Fig. 3A,B).…”

“…By contrast, we show here that protein folding pathways and rates can be recovered without explicit knowledge of the time-dependent trajectories, provided the system is sufficiently ergodic and equilibrium distributions are sampled accurately. Furthermore, we show that the dynamics of state-switching or phenotype-switching in gene regulatory networks 51 can be inferred directly from static snapshots of protein abundances in regimes where deterministic modeling only captures a single steady state 52,53 . The agreement of our FIG.…”

Analysis of Single-Cell Gene Pair Coexpression Landscapes by Stochastic Kinetic Modeling Reveals Gene-Pair Interactions in Development

“…We define two types of model systems. The Mutual Inhibition/Self-Activation (MISA) model encodes a common network motif that is understood to control a variety of cell fate decisions (Graf and Enver, 2009;Huang, 2013) and has been extensively studied by mathematical modeling (Huang et al, 2007;Feng and Wang, 2012;Chu et al, 2017). In contrast, the Two-Gene Flex model flexibly encodes a variety of regulatory interactions, as described below.…”

“…That is, it assumes the propensity of reactions that lead to mRNA numbers exceeding M − 1 is 0. This assumption is justified when M is chosen to be sufficiently large compared to g/k (Chu et al, 2017). We confirmed that the probability of mRNAs exceeding M-1 for our parameter values is negligible (Supplement, Section 2.2) and we further confirmed that increasing M (from 21, the value used in calculations throughout the manuscript, to 36) had negligible impact on quasipotential landscape shape and all subsequent analysis of single cell RNA sequencing (scRNA-seq) data ( Figure S2).…”

Learning Dynamical Information from Static Protein and Sequencing Data

“…By contrast, we show here that protein-folding pathways and rates can be recovered without explicit knowledge of the time-dependent trajectories, provided the system is sufficiently ergodic and equilibrium distributions are sampled accurately. Furthermore, we show that the dynamics of state-switching or phenotype-switching in generegulatory networks 40 can be inferred directly from static snapshots of protein abundances in regimes where deterministic modeling only captures a single steady state 41,42 . The agreement of our inferred results with two separate sets of time-dependent measurements suggests that the inference of complex transition networks via reconstructed energy landscapes can provide a viable and often more efficient alternative to traditional timeseries estimates, particularly as new experimental techniques will offer unprecedented access to high-dimensional ensemble data.…”