Stochastic Modeling of Gene Regulation by Noncoding Small RNAs in the Strong Interaction Limit

Noncoding small RNAs (sRNAs) are known to play a key role in regulating diverse cellular processes, and their dysregulation is linked to various diseases such as cancer. Such diseases are also marked by phenotypic heterogeneity, which is often driven by the intrinsic stochasticity of gene expression. Correspondingly, there is significant interest in developing quantitative models focusing on the interplay between stochastic gene expression and regulation by sRNAs. We consider the canonical model of regulation of stochastic gene expression by sRNAs, wherein interaction between constitutively expressed sRNAs and mRNAs leads to stoichiometric mutual degradation. The exact solution of this model is analytically intractable given the nonlinear interaction term between sRNAs and mRNAs, and theoretical approaches typically invoke the mean-field approximation. However, mean-field results are inaccurate in the limit of strong interactions and low abundances; thus, alternative theoretical approaches are needed. In this work, we obtain analytical results for the canonical model of regulation of stochastic gene expression by sRNAs in the strong interaction limit. We derive analytical results for the steady-state generating function of the joint distribution of mRNAs and sRNAs in the limit of strong interactions and use the results derived to obtain analytical expressions characterizing the corresponding protein steady-state distribution. The results obtained can serve as building blocks for the analysis of genetic circuits involving sRNAs and provide new insights into the role of sRNAs in regulating stochastic gene expression in the limit of strong interactions.     

The stochastic nature of biochemical networks

Cell behaviour and the cellular environment are stochastic. Phenotypes vary across isogenic populations and in individual cells over time. Here we will argue that to understand the abilities of cells we need to understand their stochastic nature. New experimental techniques allow gene expression to be followed in single cells over time and reveal stochastic bursts of both mRNA and protein synthesis in many different types of organisms. Stochasticity has been shown to be exploited by bacteria and viruses to decide between different behaviours. In fluctuating environments, cells that respond stochastically can out-compete those that sense environmental changes, and stochasticity may even have contributed to chromosomal gene order. We will focus on advances in modelling stochasticity, in understanding its effects on evolution and cellular design, and on means by which it may be exploited in biotechnology and medicine.     

Effect of feedback regulation on stochastic gene expression

Stochastic noise in gene expression arises as a result of species in small copy number undergoing transitions between discrete chemical states. Here the noise in a single gene network is investigated using the Omega-expansion techniques. We show that the linear noise approximation implies an invariant relationship between the normalized variances and normalized covariance in steady-state statistics. This invariant relationship provides an exactly statistical interpretation for why the stochastic noise in gene expression should be measured by the normalized variance. The nature of the normalized variance reveals the basic relationship between the stochasticity and system size in gene expression. The linear noise approximation implies also that for both mRNA and protein, the total noise can be decomposed into two basic components, one concerns the contribution of average number of molecules, and other the contribution of interactions between mRNA and protein. For the situation with linear feedback, our results clearly show that for two genes with the same average number of protein molecules, the gene with negative feedback will have a small protein noise, i.e., the negative feedback will reduce the protein noise. For the effect of the burst size on the protein noise, we show also that the protein intrinsic noise will decrease with the increase of the burst size, but the protein extrinsic noise is independent of the burst size.