Publications of Eduardo D. Sontag jointly with M. A. Al-Radhawi
Articles in journal or book chapters
  1. M. A. Al-Radhawi, D. Del Vecchio, and E. D. Sontag. Multi-modality in gene regulatory networks with slow gene binding. 2017. Note: Submitted. Preprint in arXiv:1705.02330, May 2017 rev Nov 2017. [PDF] Keyword(s): multistability, gene networks, Markov Chains, Master Equation, cancer heterogeneity, phenotypic variation, nonlinear systems, stochastic models, epigenetics.
    In biological processes such as embryonic development, hematopoietic cell differentiation, and the arising of tumor heterogeneity and consequent resistance to therapy, mechanisms of gene activation and deactivation may play a role in the emergence of phenotypically heterogeneous yet genetically identical (clonal) cellular populations. Mathematically, the variability in phenotypes in the absence of genetic variation can be modeled through the existence of multiple metastable attractors in nonlinear systems subject with stochastic switching, each one of them associated to an alternative epigenetic state. An important theoretical and practical question is that of estimating the number and location of these states, as well as their relative probabilities of occurrence. This paper focuses on a rigorous analytic characterization of multiple modes under slow promoter kinetics, which is a feature of epigenetic regulation. It characterizes the stationary distributions of Chemical Master Equations for gene regulatory networks as a mixture of Poisson distributions. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations and a trans-differentiation network.

Conference articles
  1. N.S. Kumar, M. A. Al-Radhawi, D. Del Vecchio, and E. D. Sontag. Stochasticity is necessary for multiple attractors in a class of differentiation networks. In 2017 American Control Conference (ACC), pages submitted, 2017. Keyword(s): systems biology, genetic regulatory, multistability, gene networks.
    Deterministic models remain the most common option for modeling gene regulatory networks even when the underlying assumptions of high copy numbers and fast promoter kinetics are unsatisfied. Here, we analyze a widely studied differentiation network motif known as the PU.1-GATA-1 circuit and we show that an ODE model of the biomolecular reactions consistent with known biology is incapable of exhibiting multistability, a defining behaviour for such a network. Thus, we consider the chemical master equation model of the same biomolecular reactions and using results recently developed by the authors, we analytically construct the stationary distribution. We show that this distribution is indeed capable of admitting a multitude of modes. We illustrate the results with a numerical example.



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Last modified: Thu Nov 23 10:40:56 2017
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