Calculation And Analysis Of Exact Formulas For MRNA Dynamic Probability Distribution In Several Stochastic Gene Transcription Models

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells.The large distribution data used to quantify fluctuations in mRNA levels can be theoretically characterized by dynamic probability distribution P_m(t),where P_m(t)represents the probability of producing m mRNA molecules at time t.Solving the exact expression of P_m(t)in different stochastic gene transcription is beneficial to understanding different gene regulatory mechanisms and the influence of system parameters on the random behavior of gene transcription.Tremendous efforts have been made to derive analytical forms of P_m(t),which rely on solving infinite arrays of the master equations of models.Much work has been done to explore the calculation of P_m(t)in steady-state(t→∞)or specific parameter regions.In this dissertation,we propose a calculation method for computing exact expression of P_m(t)in all parameter regions.We apply this method to classical two-state model and three-state model,and multiscale model coupled with RNA polymerase kinetics.This thesis is mainly divided into three chapters,the details of which are as follows:In Chapter 1,the background of stochastic gene transcription and the existing theories for the exact expression of dynamic probability distribution P_m(t)are introduced.In addition,the main research content of this dissertation is discussed.In Chapter 2,we use the classical two-state model and three-state model as examples to illustrate our method of solving the exact expression P_m(t).We found that two-state model and three-state model can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.In Chapter 3,we explore the multiscale model coupling classical two-state model and the RNA polymerase kinetics,and calculate exact expression of dynamic probability distribution.Further,we combine the probability distribution,mean,and second-order moment of dynamic and steady-state to explore the connection and difference between two-state model and multiscale model.We generalize this research idea to wider range of three-state model,cross-talking pathways model,and multiscale model coupled with RNA polymerase kinetics.