Geometry theory of distribution shapes for autoregulatory gene circuits
Ying Sheng,
Genghong Lin,
Feng Jiao
et al.
Abstract:In this study, we provide a complete mathematical characterization of the phase diagram of distribution shapes in an extension of the two-state telegraph model of stochastic gene expression in the presence of positive or negative autoregulation. Using the techniques of second-order difference equations and nonlinear discrete dynamical systems, we prove that the feedback loop can only produce three shapes of steady-state protein distributions (decaying, bell-shaped, and bimodal), corresponding to three distinct… Show more
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