Abstract
A common model of stochastic auto-regulatory gene expression describes promoter switching via cooperative protein binding, effective protein production in the active state and dilution of proteins. Here we consider an extension of this model whereby colored noise with a short correlation time is added to the reaction rate parameters—we show that when the size and timescale of the noise is appropriately chosen it accounts for fast reactions that are not explicitly modeled, e.g., in models with no mRNA description, fluctuations in the protein production rate can account for rapid multiple stages of nuclear mRNA processing which precede translation in eukaryotes. We show how the unified colored noise approximation can be used to derive expressions for the protein number distribution that is in good agreement with stochastic simulations. We find that even when the noise in the rate parameters is small, the protein distributions predicted by our model can be significantly different than models assuming constant reaction rates.
Highlights
Proteins perform a large range of cellular functions and it is of great interest to understand how the genes that produce them operate
In figure 10(A) we show how effective the unified colored noise approximation (UCNA) can be in approximating the protein distribution from the full system described in equation (79), where we have for simplicity assumed that there are three mRNA states: M1, M2 and M3 (i.e., N = 3)
In this paper we have explored the addition of colored noise onto the reaction rates for a cooperative auto-regulatory circuit
Summary
Proteins perform a large range of cellular functions and it is of great interest to understand how the genes that produce them operate. The focus of the present article is threefold: (i) to provide a general method by which one can obtain analytical expressions for the steady-state protein distributions of auto-regulatory gene circuits with fluctuating rate parameters, through the use of the unified colored noise approximation (UCNA) [27], (ii) to use this method to investigate the effects that extrinsic noise of different magnitude and timescales has on auto-regulatory gene expression and (iii) to show how the colored noise formalism can be used to describe complex models of autoregulation that involve multi-stage protein production and multi-stage protein degradation.
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