Cell phenotypes are controlled by complex interactions between genes, proteins, and other molecules within a cell, along with extracellular signals. Gene regulatory networks (GRNs), which describe these interactions mathematically, are multi-stable dynamical systems, in which attractor states represent cell phenotypes. Transitions between these states are thought to underlie critical cellular processes, including cell fate-decisions, phenotypic plasticity, and carcinogenesis. In principle, a GRN model can produce a map of possible cell phenotypes and phenotype-transitions, potentially informing experimental strategies for controlling cell phenotypes. Such a map could have a profound impact on many medical fields, ranging from stem cell therapies to wound healing. As such, there is increasing interest in the development of theoretical and computational approaches that can shed light on the dynamics of these state-transitions in multi-stable gene networks. In this work, we approach the problem of understanding cellular decision-making on two fronts. First, we develop and extend rare-event stochastic simulation methods, toward efficient characterization of the global dynamics of multi-stable stochastic systems, such as GRNs. When applied to a mutual inhibition network motif and a model of pluripotency in stem cells, our sampling methods demonstrate that spontaneous cell phenotype transitions involve collective behavior of both regulatory proteins and DNA, and that transition dynamics are sensitive to parameters governing transcription factor-DNA binding kinetics. Our approach significantly expands the capability of stochastic simulation to investigate gene regulatory network dynamics. In the second portion of this work, we model the dynamic response of macrophages to complex stimuli by inferring cell-decision networks from data, in the absence of detailed molecular information. Macrophage activation has been described as a continuum, and different stimuli lead to M1, M2, or mixed phenotypes. Flow cytometry experiments performed in the Liu lab at UCI found discovered that macrophages acquire a mixed activation state when exposed to a combination of LPS, IFN-$\gamma$, IL-4, and IL-13. Additionally, mathematical modeling of candidate regulatory networks indicates that a complex inter-dependence of M1- and M2-associated pathways underlies macrophage activation. Together these results corroborate a continuum model of macrophage activation and demonstrate that phenotypic markers evolve with time and with exposure to complex signals.

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