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Analytical study of an exclusive genetic switch

By J. Venegas-Ortiz and M. R. Evans

Abstract

The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be repressed. The model may be thought of as a minimal model of the power struggle between two competing parties. Exact solutions are given for the limits of vanishing binding/unbinding rates and infinite binding/unbinding rates. A mean field theory is introduced which is exact in the limit of vanishing binding/unbinding rates. The mean field theory and numerical simulations reveal that generically bistability occurs and the system is in a symmetry broken state. An exact perturbative solution which in principle allows the nonequilibrium stationary state to be computed is also developed and computed to first and second order.Comment: 28 pages, 6 figure

Topics: Condensed Matter - Statistical Mechanics, Quantitative Biology - Molecular Networks, 82
Year: 2011
DOI identifier: 10.1088/1751-8113/44/35/355001
OAI identifier: oai:arXiv.org:1105.0301
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