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.

Uncertainty quantification (UQ) analysis may help identify model error; however, efficacy of UQ to filter predictions varies considerably between datasets and featurization/model types.AMPL is open source and available for download at

Stochastic simulation has been a powerful tool for studying the dynamics of gene regulatory networks, particularly in terms of understanding how cell-phenotype stability and fate-transitions are impacted by noisy gene expression. However, gene networks often have dynamics characterized by multiple attractors. Stochastic simulation is often inefficient for such systems, because most of the simulation time is spent waiting for rare, barrier-crossing events to occur. We present a rare-event simulation-based method for computing epigenetic landscapes and phenotype-transitions in metastable gene networks. Our computational pipeline was inspired by studies of metastability and barrier-crossing in protein folding, and provides an automated means of computing and visualizing essential stationary and dynamic information that is generally inaccessible to conventional simulation. Applied to a network model of pluripotency in Embryonic Stem Cells, our simulations revealed rare phenotypes and approximately Markovian transitions among phenotype-states, occurring with a broad range of timescales. The relative probabilities of phenotypes and the transition paths linking pluripotency and differentiation are sensitive to global kinetic parameters governing transcription factor-DNA binding kinetics. Our approach significantly expands the capability of stochastic simulation to investigate gene regulatory network dynamics, which may help guide rational cell reprogramming strategies. Our approach is also generalizable to other types of molecular networks and stochastic dynamics frameworks.

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.