Analytical study of an exclusive genetic switch

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.

28 pages, 6 figures

References in corpus (6)

• Analytical distributions for stochastic gene expression
• Genetic Toggle Switch Without Cooperative Binding
• Exact solution of a model DNA-inversion genetic switch with orientational control
• Conversion of graded to binary response in an activator-repressor system
• Statistical physics of a model binary genetic switch with linear feedback
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Cited by in corpus (5)

• Bacterial growth: a statistical physicist's guide
• Bistable switching asymptotics for the self regulating gene
• Genetic Toggle Switch in the Absence of Cooperative Binding: Exact Results
• Dynamics of the Chemical Master Equation, a strip of chains of equations in d-dimensional space
• Counting statistics for genetic switches based on effective interaction approximation