Large Deviations and Driven Processes for Stochastic Models of Gene Expression and Its Regulation

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This project will develop mathematics to predict and characterize rare, random events affecting gene expression in a population of cells. The survival and evolution of cell populations under stress often depends on a small fraction of outlier cells. For example, drug exposure leads to cell death for most cancer cells in a tumor, but a small fraction survive and lead to development of drug resistance. Recent research shows that such cellular differences are driven by rare events during gene expression, and there is a need to develop quantitative models of rare events in stochastic descriptions of gene expression. This project, supported jointly by the Divisions of Mathematical Sciences and Molecular and Cellular Biology, will develop and apply approaches from non-equilibrium statistical mechanics and large deviation theory to create a framework for rare events in gene expression and its regulation in diverse cell processes. The theory will address current research questions: (1) How do cell regulatory mechanisms control probability of rare events in gene expression? (2) How can one characterize gene expression conditional on rare event occurrences? (3) Can control mechanisms be determined to realize desirable rare events? The answers will have applications ranging from synthetic biology to understanding latency in HIV-1 infections. Graduate and undergraduate students will be mentored in interdisciplinary research on biological systems, and research activities will be effectively integrated with teaching at graduate and undergraduate levels. The integrated research, teaching and outreach activities will prepare future scientists to apply stochastic mathematics to molecular biology.Rare events which lead to phenotypic transitions are a recurring theme in current biological research. In several cases phenotypic switching is driven by the intrinsic stochasticity of gene expression. Correspondingly, there is a need to develop a theoretical framework for analyzing rare events in stochastic models of gene expression. Recent developments in non-equilibrium statistical mechanics, using large deviation theory, have led to a framework for analyzing Markovian processes conditioned on rare events and for representing such processes by conditioning-free driven processes. The goal of this project is to apply and further develop this theoretical framework to quantitatively characterize large deviations in stochastic models of gene expression and its regulation. The specific aims will focus on developing analytical and computational approaches for characterizing large deviations in general models of gene expression with a) promoter-based regulation, b) post-transcriptional regulation and c) feedback regulation. This research will lead to quantitative insights into how cellular regulatory mechanisms impact rare event probabilities which can be used to design optimal control mechanisms for realization of desired rare events. A particular focus will be modeling latency in HIV-1 viral infections. The analysis requires tools and approaches from physics and applied mathematics which will be integrated with teaching efforts to effectively train students and future scientists focusing on interdisciplinary research in the life sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.