Qualitative Studies And Application Of Cross-talking Pathways In Stochastic Gene Expression

Gene expression plays an essential role in life and is a hot topic in molecular biology.It has attracted the attention of scholars and experts in various fields such as mathematics,statistics,computer science,chemistry,physics,in addition to biology and medicine.The central dogma of gene expression,DNA directs the production of RNA,while RNA directs the production of proteins,mainly includes transcription and translation,each of which contains a large amount of biochemical reactions.Gene transcription is the core of all life and the first stage of gene expression.Therefore,it is very important to elucidate the molecular mechanism of transcription and its regulatory principles.This thesis was driven by experimental data to study gene transcription and the distribution of mRNA copy numbers in individual cells by two-pathway transcription model.The details are outlined as follows:In Chapter 1,the biological background,current research and development prospects of gene expression are introduced.In addition,the main content and the structure of this dissertation are discussed.It has been a central question to understand how genes in single cells re-sponse to environmental changes.Recent measurements have generated massive data on expression dynamics and noise.The theoretical fit,notoriously,requires synchronous modulation of gene activation and inactivation,mRNA synthesis and the following feedback in mathematical models.In Chapter 2 and Chapter 3,we integrated a usually neglected weak basal pathway into the classical two-state model,which competes with the signaling pathway to activate the gene.We re-vealed rich cross-talking regulations of two pathways and good agreement with those data.This simple framework only modulates gene activation and may open a new avenue for future biophysical studies.In Chapter 2 and Chapter 3,we model gene activation as the competitive cross-talk between a weak basal pathway and an inducible signaling pathway,and reveal rich expression dynamics and intricate dependence of noise and fano factor on mean expression.An encouraging observation is that those theoretical results are in good agreement with numerous data in E.coli,yeast and mammalian cells.Further theoretical analysis and supporting biological evidences then converge to a trade-off that governs sharp up-and-down regulation of expression,and an or-dered scenario that activates the gene under varying conditions.These regulation modes,together with cross-talking pathways,may provide new interpretations on experimental observations.In Chapter 2,our endeavor theoretically shows that the dynamical profile of gene mean expression takes either the monotonic growth or up-and-down pattern.We reveal rich cross-talking regulation modes on the mean expression dynamics,and yields a good theoretical fit to the three groups of representative data for 180TNF induced mouse fibroblast genes.Especially,the sharp up-and-down dynamics can be achieved by the trade-off between a strong and frequently selected signaling pathway that up-regulates expression rapidly to a high level,and a rarely selected weak basal pathway that down-regulates expression from its peak to the base line.Interestingly,the transition of such negative regulation from mRNA to protein levels totally depends on the stability of protein molecules and a threshold.To demonstrate more explicitly the non-monotonic expression dynamics,we assume that the gene inactivation rate is larger than mRNA degradation rate.We derive a threshold?for the selection probability₂of the signaling pathway.The mean expression displays growing pattern when₂??and switches to the up-and-down dynamics once₂is enhanced above?.Note that the two-state model and its extensions with single activation pathway cannot capture such non-monotonic dynamics.This observation suggests that natural selection may favor the cross-talking regulation to induce the signaling pathway for fulfilling two contradictory requirements:The rapid up-regulation of gene expression to contribute to the adaptation of acute external stresses;the subsequent repression to avoid over-exuberant expression which may have detrimental side-effects.Finally,we obtain the exact forms of the average level of mRNA8)??and protein?6??,and analyze their properties.According to the dependence of8???and(6??,we further discuss their dynamical behaviors.In Chapter 3,our endeavor reveals a general cross-talking regulation scenario that may explain the stationary expression data of distinct promoters under vary-ing conditions.We display different stationary curves of noise and fano factor against mean expression level by changing the selection probability₂or strength rate₂of the signaling pathway.An encouraging observation is that those the-oretical results are in good agreement with a large data set in E.coli,yeast and mammalian cells.This reveals that the regulation of₂is the main feature in re-sponse to external signals and₂is modulated greatly across different chromatin environments.To gain deeper insight on pivotal roles of₂and₂in gene regula-tion,we focus on analyzing the transcription data for three E.coli promoters and HIV LTR promoter,and reverse data set to the variations of₂and₂against mean expression.This reveals a robust regulation mode:₂is modulated when expression is low,while₂is modulated when the expression becomes higher.Such ordered regulation shows that the accumulation of signal-induced TFs primarily navigates gene activation more frequently through the stronger signaling pathway.Once TFs concentration and retention time reach the ceiling,the scenario switches to increasing strength rate of the signaling pathway,such as enhancing accessibility of DNA binding sites hampered by chromatin structure.We use two-state model to fit the stationary data from different promoters requires distinct regulation modes that alter mRNA synthesis,gene activation and inactivation.In comparation,our model requires modulating only the signaling pathway in gene activation process.The good theoretical fits by the two models reveal two alternative views:The promoter specific regulation that may be deter-mined by promoter architecture;the promoter nonspecific regulation that reflects global cellular constraintsMeanwhile,the analytical forms of average level,noise and Fano factor?noise intensity?of the cross-talking pathways model at steady state are obtained,and the more complex correlation between them and the two-state model are discussed.In Chapter 4,we initiate a theoretical study on mRNA distribution dynamics for the stochastic transcription model that involves cross-talking signaling path-ways to direct gene activation in response to external signals.We first express the distribution in mathematical dynamical formulas under both moderate and high transcriptional upregulations.In each scenario,our further numerical examples display an observed dynamical transition type among three distribution modes for stress genes in yeast.In particular,the intermediate bimodal stage sustains within a certain length of early time and lasts much longer than that generated by the single pathway.This shows the general and robust bimodal transcription regulated by the cross-talk of signaling pathways.At last,we give a brief summary of the whole dissertation and look forward to the future of research work.