@ARTICLE{mali_delvecchio_sontag_slow_gene_binding_2017,
   AUTHOR       = {M. A. Al-Radhawi and Del Vecchio, D. and E. D. Sontag},
   JOURNAL      = {},
   TITLE        = {Multi-modality in gene regulatory networks with slow 
      gene binding},
   YEAR         = {2018},
   OPTMONTH     = {},
   NOTE         = {Submitted. Preprint in arXiv:1705.02330, May 2017 rev Nov 2017},
   OPTNUMBER    = {},
   OPTPAGES     = {},
   OPTVOLUME    = {},
   KEYWORDS     = {multistability, gene networks, Markov Chains, 
      Master Equation, cancer heterogeneity, phenotypic variation, 
      nonlinear systems, stochastic models, epigenetics},
   PDF          = {https://arxiv.org/pdf/1705.02330.pdf},
   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.}
}

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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.","bibtex":"@ARTICLE{mali_delvecchio_sontag_slow_gene_binding_2017,\n AUTHOR = {M. A. Al-Radhawi and Del Vecchio, D. and E. D. Sontag},\n JOURNAL = {},\n TITLE = {Multi-modality in gene regulatory networks with slow \n gene binding},\n YEAR = {2018},\n OPTMONTH = {},\n NOTE = {Submitted. Preprint in arXiv:1705.02330, May 2017 rev Nov 2017},\n OPTNUMBER = {},\n OPTPAGES = {},\n OPTVOLUME = {},\n KEYWORDS = {multistability, gene networks, Markov Chains, \n Master Equation, cancer heterogeneity, phenotypic variation, \n nonlinear systems, stochastic models, epigenetics},\n PDF = {https://arxiv.org/pdf/1705.02330.pdf},\n ABSTRACT = { In biological processes such as embryonic development, \n hematopoietic cell differentiation, and the arising of tumor \n heterogeneity and consequent resistance to therapy, mechanisms of \n gene activation and deactivation may play a role in the emergence of \n phenotypically heterogeneous yet genetically identical (clonal) \n cellular populations. Mathematically, the variability in phenotypes \n in the absence of genetic variation can be modeled through the \n existence of multiple metastable attractors in nonlinear systems \n subject with stochastic switching, each one of them associated to an \n alternative epigenetic state. An important theoretical and practical \n question is that of estimating the number and location of these \n states, as well as their relative probabilities of occurrence. This \n paper focuses on a rigorous analytic characterization of multiple \n modes under slow promoter kinetics, which is a feature of epigenetic \n regulation. It characterizes the stationary distributions of Chemical \n Master Equations for gene regulatory networks as a mixture of Poisson \n distributions. As illustrations, the theory is used to tease out the \n role of cooperative binding in stochastic models in comparison to \n deterministic models, and applications are given to various model \n systems, such as toggle switches in isolation or in communicating \n populations and a trans-differentiation network.}\n}\n\n","author_short":["Al-Radhawi, M. A.","Del Vecchio, D.","Sontag, E. 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