Stochastic Models of Regulation of Transcription in Biological Cells

TL;DR

This paper models the regulation of transcription in biological cells by 6S RNAs using stochastic processes, analyzing efficiency and dynamics in different environmental regimes through mathematical scaling and averaging techniques.

Contribution

It introduces a stochastic model for transcription regulation by 6S RNAs and provides analytical results on its behavior in various environmental conditions.

Findings

Derived an averaging principle for the Markov process model.

Obtained an explicit expression for polymerase sequestration in stationary phase.

Analyzed system behavior in exponential and stationary regimes.

Abstract

In this paper we study an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment of the cell is not favorable. We investigate the efficiency of this mechanism with a scaling analysis of a stochastic model. The evolution equations of our model are driven by the law of mass action and the total number of polymerases is used as a scaling parameter. Two regimes are analyzed: exponential phase when the environment of the cell is favorable to its growth, and the stationary phase when resources are scarce. In both regimes, by defining properly occupation measures of the model, we prove an averaging principle for the associated multi-dimensional Markov process on a convenient timescale, as well as convergence results for fast variables of the system. An analytical expression of the asymptotic fraction of sequestrated polymerases in stationary phase is in particular obtained. The consequences of these results are discussed.