Multi-modality in gene regulatory networks with slow gene binding. Al-Radhawi, M. A., Del Vecchio, D., & Sontag, E. D. , 2018. Submitted. Preprint in arXiv:1705.02330, May 2017 rev Nov 2017abstract bibtex 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.
@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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