Background

Gene 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.

Results

The 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.

Conclusions

In 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.

Gene regulatory networks are multistable dynamical systems in which attractor states represent cell phenotypes. Spontaneous, noise-induced transitions between these states are thought to underlie critical cellular processes, including cell developmental fate decisions, phenotypic plasticity in fluctuating environments, and carcinogenesis. As such, there is increasing interest in the development of theoretical and computational approaches that can shed light on the dynamics of these stochastic state transitions in multistable gene networks. We applied a numerical rare-event sampling algorithm to study transition paths of spontaneous noise-induced switching for a ubiquitous gene regulatory network motif, the bistable toggle switch, in which two mutually repressive genes compete for dominant expression. We find that the method can efficiently uncover detailed switching mechanisms that involve fluctuations both in occupancies of DNA regulatory sites and copy numbers of protein products. In addition, we show that the rate parameters governing binding and unbinding of regulatory proteins to DNA strongly influence the switching mechanism. In a regime of slow DNA-binding/unbinding kinetics, spontaneous switching occurs relatively frequently and is driven primarily by fluctuations in DNA-site occupancies. In contrast, in a regime of fast DNA-binding/unbinding kinetics, switching occurs rarely and is driven by fluctuations in levels of expressed protein. Our results demonstrate how spontaneous cell phenotype transitions involve collective behavior of both regulatory proteins and DNA. Computational approaches capable of simulating dynamics over many system variables are thus well suited to exploring dynamic mechanisms in gene networks.

Macrophages are versatile cells of the immune system that play an important role in both advancing and resolving inflammation. Macrophage activation has been described as a continuum, and different stimuli lead to M1, M2, or mixed phenotypes. In addition, macrophages expressing markers associated with both M1 and M2 function are observed in vivo. Using flow cytometry, we examine how macrophage populations respond to combined M1 and M2 activation signals, presented either simultaneously or sequentially. We demonstrate that macrophages exposed to a combination of LPS, IFN-γ, IL-4, and IL-13 acquire a mixed activation state, with individual cells expressing both M1 marker CD86 and M2 marker CD206 instead of polarizing to discrete phenotypes. Over time, co-stimulated macrophages lose expression of CD86 and display increased expression of CD206. In addition, we find that exposure to LPS/IFN-γ potentiates the subsequent response to IL-4/IL-13, whereas pre-polarization with IL-4/IL-13 inhibits the response to LPS/IFN-γ. Mathematical modeling of candidate regulatory networks indicates that a complex inter-dependence of M1- and M2-associated pathways underlies macrophage activation. Specifically, a mutual inhibition motif was not by itself sufficient to reproduce the temporal marker expression data; incoherent feed-forward of M1 activation as well as both inhibition and activation of M2 by M1 were required. Together these results corroborate a continuum model of macrophage activation and demonstrate that phenotypic markers evolve with time and with exposure to complex signals.