Modeling And Analysis Of Post-Transcriptional Process Involving SRNA In Gene Expression

Gene expression is the process in which the genetic information stored in DNA sequence is used to generate protein molecules with specific biological function and structure via transcription and translation during the life process.In a simple point of view,gene expression consists of two processes: transcription and translation.Gene expression is highly accurate,and many life activities depend on the correct expression of the gene.Gene expression is actually a process of discrete bursting and stochasticity that can cause phenotypic differences in the same cells in genetic information.Therefore,it is critical for the cellular processes to understand how potential biochemical reactions cause changes in mRNA or protein levels.Recent technological developments have enabled single-cell measurements of cellular macromolecules which can shed new light on processes underlying gene expression.Correspondingly,there is a need for the development of theoretical tools to quantitatively model stochastic gene expression and its consequences for cellular processes.Given the fact that the gene expression is inherently stochastic,it is necessary to regulate this intrinsic variability of protein levels in the cell regulatory pathway,in particular those that bring about global changes in gene expression.It has been shown that a central component of regulatory networks is post-transcriptional control by regulatory proteins and by small RNAs(sRNAs)in bacteria and MicroRNAs(miRNAs)in higher organisms.Recent research points towards an increasingly important role for this mode of regulation in fine-tuning the noise in gene expression and in regulating important cellular processes.In our work,we have analyzed simple gene expression models involving transcriptional bursting and post-transcriptional regulation by sRNAs which plays a key role in diverse cellular processes such as development and differentiation.In the model,the genetic circuits is regulated by a high concentration regulator,and the kinetic behavior of the regulator cannot be ignored.The regulation of sRNA is acted by combined degradation with mRNA.Based on this stochastic model,the exact expression of the protein steady-state distribution were derived,and the mean of protein levels,the noise and random deviation of the system can be calculated.Then we focus on how posttranscriptional regulation mechanism involved sRNAs fine-tunes the process of stochastic gene expression.The main work of this paper is as follows:(1)Using a gene expression model involving transcriptional bursting mechanism and sRNA regulation,the chemical master equation for the joint probability distribution is written.The inherent nonlinearity caused by sRNA-mRNA interaction in this regulatory process together with the bursty production of mRNA and protein make the exact solution for this stochastic process intractable.This is particularly the case when quantifying the protein noise level,which has great impact on multiple cellular processes.The results obtained by the mean-field method are inaccurate in biological systems with non-linear reaction rates and low molecular abundance.Here we propose an approximate yet reasonably accurate solution for the gene expression noise with infrequent burst and strong regulation by sRNAs.According to the results,it is predicted that the sRNA regulation is a rescaling of the burst frequency.(2)Based on the previous results,we gradually released the constraints,move out from the hypothesis and come up with a protein burst distribution in probabilistic method.Then,a more accurate expression for protein steady-state distribution was derived by using burst synthesis approximation.It is noteworthy that our results are valid over for a wide range of parameters and validated by Gillespie simulation.(3)The noise of the protein can be derived from protein steady-state distribution,and the random deviation is used to quantify the variability caused by stochasticity.We find that the regulation amplifies the noise,reduces the protein level.The stochasticity in the regulation generates more proteins than what if the stochasticity is removed from the system.Once the sRNA level is fixed,the gain of proteins due to stochasticity will not change dramatically for the same value of noise,even mean mRNA burst size is different.We theoretically characterized the noise of gene expression regulated by sRNA and the variability in protein levels caused by stochasticity.The results provide analytical tools for more general studies of gene expression and strengthen our quantitative understandings of post-transcriptional regulation in controlling gene expression processes.