Regulation On FPT Of Gene Expression And Its Dynamic Behaviors

All living organisms in the world,from bacteria to human beings,are composed of cells.Although the structure and composition of these cells are very similar,their functions are highly differentiated.Life for all organisms is based on various activities of cells.Cells are the basis of the growth and development of organism.The crucial decisions in cells like cell differentiation,cell development,lysis for -phage host cell,etc,and the switching of biologically important states,such as activation and inactivation of genes,rely on the timing that mRNA or protein levels reach a threshold.In the context of gene expression,the minimum time for the product of gene expression to reach a given number is formulated as the first-passage time(FPT)of gene expression.As the inherent stochasticity of gene expression generates random fluctuation of mRNA or protein copy numbers within a population of isogenic cells,FPT of gene expression is stochastic.It is an important index of stochasticity of gene expression,and has attracted attentions from many researchers.Gene expression is the core process of life activity.The dynamics of gene expression is the important context of systems molecular biology.Experimental results and theoretical researches have established that especially in eukaryotes,gene expression products are produced mainly in burst.The more and more biologists have accepted the viewpoint that bursty expression may cause phenotypic diversity among the cells of identical genes.The dynamics of bursty gene expression has attracted extensive attention in recent years.However,the influences of the burst on the noise and mean level of stable protein and its FPT have been elusive.In particular,there have been no scientists engaged in studying the impact of bursty forms on FPT of stable proteins.In Chapter 2,we focus on the impact of bursty gene expression on the dynamics of stable protein and its FPT.As a core process in living organisms,gene expression involves a series of molecular interactions,such as random collisions and reactions between the base pairs of DNA and many regulatory factors.The difference in regulatory mechanisms causes variation in gene expression.In order to gain a deep understanding of gene regulation in important cellular activities such as cell fate decision,functional and phenotypic switching,and the transfer of the biological system states,we need to study the random behavior of gene expression at the molecular level.To this end,we study effects of input signal on FPT in chapter 3 and chapter 4 with a goal to quantify the regulatory dynamics of FPT under the regulations of different stochastic signals.Transcription is the first step of gene expression.Its regulation has been thought to be the most important step in achieving regulation fidelity of gene expression.Naturally,the question of how transcription regulation affects FPT of gene products is put forward.In this paper,we concentrate on investigating the influences of transcription regulation of random signals and bursty gene expression on its FPT.Combining theoretical analyses with numerical simulations,we elucidate the relationship between the burst forms of gene expression with expression noise or FPT of stable proteins,and the relationship between the regulation of stochastic signal at steady-states with the noise of FPT of stable proteins,the regulation of stochastic signal from a birth-death process and the noise of FPT of mRNA(or protein)from the dynamical point of view.These results reveal some general laws of gene expression under stochastic signal regulation,which extend the connotation of stochasticity of FPT of gene expression.The major innovations of this thesis can be summarized as follows:(1)The research topic is novel.The first-passage time is defined as the minimum time that a stochastic process reaches a target.Although the analytical method of FPT is mature in the context of stochastic process,the study of FPT in gene expression is still in its infancy.Specially,a clear understanding of the regulation of signals on FPT has been elusive.(2)We initiate the study of the effect of different bursty forms of gene expression on its noise and FPT.(3)We first give formulae for the mean and variance of FPT of stable proteins under signal regulation by using Kolmogorov backward equation.With the aid of matlab,we demonstrate intuitively the impacts of random signal on FPT of proteins.(4)We initiate the study of the regulation of stochastic signal from a birth-death process on FPT of mRNA and proteins.This thesis is divided into five chapters.In Chapter 1,after briefly discussing the background of gene expression and its regulation,we introduce mathematical models.We then define some quantities characterizing the randomness of gene expression,and mention the methods such as Gillespie algorithm to calculate or approximate these quantities.To demonstrate the implications of these concepts in biology,we show how the main concept,FPT,can be used to help elucidate some interesting cellular behaviors observed in experiments.Meanwhile,Gillespie stochastic simulation algorithm is extended to the propensity function depending on both time and system states.In Chapter 2,we introduce a simplified model of bursty gene expression.We focus on the effect of different bursty forms of gene expression on its noise and FPT.Our results indicate that stochastic bursty expression increases the noise of gene expression under the same mean of burst expression and burst size.Under the same conditions,conditional geometric burst increases the mean and noise of FPT compared with geometric burst.In Chapter 3,we investigate the regulatory dynamics of stochastic signal in equilibrium state on FPT of protein without degradation.We first calculate the mean and variance of FPT in each case of transcription regulation of stochastic signal and its burst size regulation.It is found that random input signal tends to increase the mean and noise of FPT compared with constant input signal.It is also observed that burst size modulation tends to decrease the mean of FPT and increase the noise of FPT compared with burst frequency modulation.In Chapter 4,we study the regulation mechanism of random signal from a Markov birth-death process on FPT of gene expression product mRNA(protein).For gene expression products mRNA and protein,we obtain the probability density function,mean and second moment of its FPT under signal regulation by using Fokker-Planck equation.Our results indicate that stochastic signal tends to increase the mean and noise of FPT.The main results of this thesis is summarized in the final chapter,where we also introduce some unsolved problems in gene expression and its regulation,and mention some future research directions.