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Publications about 'chemical master equations'
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. PLoS Computational Biology, 15:e1006784, 2019. [PDF] Keyword(s): multistability, gene networks, Markov Chains, Master Equation, cancer heterogeneity, phenotypic variation, nonlinear systems, stochastic models, epigenetics.
    Abstract:
    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.


  2. E.D. Sontag. Examples of computation of exact moment dynamics for chemical reaction networks. In R. Tempo, S. Yurkovich, and P. Misra, editors, Emerging Applications of Control and Systems Theory, volume 473 of Lecture Notes in Control and Inform. Sci., pages 295-312. Springer-Verlag, Berlin, 2018. [PDF] Keyword(s): chemical master equations, stochastics, moments, chemical reaction networks, incoherent feedforward loop, feedforward, IFFL.
    Abstract:
    The study of stochastic biomolecular networks is a key part of systems biology, as such networks play a central role in engineered synthetic biology constructs as well as in naturally occurring cells. This expository paper reviews in a unified way a pair of recent approaches to the finite computation of statistics for chemical reaction networks.



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Last modified: Fri Jul 12 13:41:34 2019
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