Dessalles Renaud, Fromion Vincent, Robert Philippe
MaIAGE, INRA, Domaine de Vilvert, 78350, Jouy-en-Josas, France.
INRIA Paris, 2 rue Simone Iff, CS 42112, 75589, Paris Cedex 12, France.
J Math Biol. 2017 Nov;75(5):1253-1283. doi: 10.1007/s00285-017-1116-7. Epub 2017 Mar 13.
This paper analyzes, in the context of a prokaryotic cell, the stochastic variability of the number of proteins when there is a control of gene expression by an autoregulation scheme. The goal of this work is to estimate the efficiency of the regulation to limit the fluctuations of the number of copies of a given protein. The autoregulation considered in this paper relies mainly on a negative feedback: the proteins are repressors of their own gene expression. The efficiency of a production process without feedback control is compared to a production process with an autoregulation of the gene expression assuming that both of them produce the same average number of proteins. The main characteristic used for the comparison is the standard deviation of the number of proteins at equilibrium. With a Markovian representation and a simple model of repression, we prove that, under a scaling regime, the repression mechanism follows a Hill repression scheme with an hyperbolic control. An explicit asymptotic expression of the variance of the number of proteins under this regulation mechanism is obtained. Simulations are used to study other aspects of autoregulation such as the rate of convergence to equilibrium of the production process and the case where the control of the production process of proteins is achieved via the inhibition of mRNAs.
本文在原核细胞的背景下，分析了在通过自调控机制进行基因表达控制时蛋白质数量的随机变异性。这项工作的目标是评估调控限制给定蛋白质拷贝数波动的效率。本文所考虑的自调控主要依赖于负反馈：蛋白质是其自身基因表达的阻遏物。在假设两者产生相同平均蛋白质数量的情况下，将无反馈控制的生产过程的效率与具有基因表达自调控的生产过程进行比较。用于比较的主要特征是平衡时蛋白质数量的标准差。通过马尔可夫表示和简单的阻遏模型，我们证明，在标度 regime 下，阻遏机制遵循具有双曲线控制的希尔阻遏方案。得到了在此调控机制下蛋白质数量方差的显式渐近表达式。模拟用于研究自调控的其他方面，如生产过程达到平衡的收敛速率以及通过抑制 mRNA 实现蛋白质生产过程控制的情况。
