MRna Degradation Models And Its Dynamic Behavior

Gene expression is a complex probabilistic process,which involves numerous components and biochemical processes.It includes two important steps: the first step is transcription that the genetic information stored in DNA is converted into messenger RNA(mRNA)by using four free ribonucleotides as raw materials,catalyzed by enzymes such as helicase and RNA polymerase,and the second step is translation that proteins are generated from mRNAs.Transcription is inherently a biochemical and dynamical process,which contains the binding of transcription factors to the promoter,the production and degradation of mRNAs,etc.Especially,mRNA degradation plays a crucial role in the gene regulation.The balance between mRNA synthesis and decay is a key aspect in the regulation of gene expression.Variation and randomness in these events would bring the stochastic behavior of transcripts even in the hypothetically identical cellular environment.Randomness in the transcription process mainly comes from random switching between“gene on” and “gene off”.In almost all experimental studies in gene transcription,after transcription is completely blocked by the incorporation of rifampicin or other means that inhibit the initiation or elongation of RNA polymerases,it has been conventionally assumed that mRNA degradation follows an exponential decay,such as [1–6].However,in many recent experiments in different organisms it was found that large amounts of the decay patterns are not exponential.One surprising example was given for S.cerevisiae(a yeast model organism)[7],which shows that only 11 out of 424(selected)mRNAs obey an exponential decay.Similarly in E.coli only 11 out of 103 and in the marine cyanobacterium Prochlorococcus 117 out of 1102 mRNAs resemble an exponential decay [8].Hence,a description with this simple exponential decay kinetic model seems inappropriate in light of the knowledge of the degradation mechanisms.Reducing the gap between observed decay patterns and degradation pathway is one of the main challenges facing the scientist.The most difficult issue is the fact that intermediate states of the degradation pathway is still unknown or difficult to quantify.Hence,a series of modifications are required for degradation,each process contributes with its specific decay rate.The mechanism of mRNA degradation is mainly caused by its physiological structure.The 5?-7-methylguanosine cap and the 3?-poly(A)tail are two key parts of the integral stability determinants of mRNAs in eukaryotic cells.This two structures interact with the cytoplasmic proteins eIF4 E and the poly(A)-binding protein(PABP),respectively,to protect the transcript from exonucleases.To initiate mRNA decay,either one of these two structures must be compromised or the mRNA must be cleaved internally by endonucleolytic attack.Nevertheless,once mRNAs are degraded,one of two routes must be taken.Within the more common degradation pathway,the 5?-cap is removed by a process known as decapping which takes place in the small cytoplasmic processing Body(P-body)[9,10].Hence,this process allows the mRNA body to be degraded in the5?? 3?direction by the XRN1 exoribonuclease.Before the decapping of mRNA,the poly(A)tail is deadenylated to an oligo(A).The deadenylation is a crucial step,which makes mRNAs susceptible for decapping.The next pathway is that the mRNAs can be degraded from the unprotected 3?end from a complex called the exosome,which takes advantage of different co-factors.In this thesis,we are interested in analyzing a modified version of the classical exponential model,which is driven by biological experimental data.we will first establish the models of the non-exponential decay of mRNA molecules.In particular,we will identify the novel feature of the temporal profile of the mean transcription level and its noise strength at steady-state.And then we obtain several basic principles on the monotonicity of the mean mRNAs.The major innovations are summarized as follows:(1)The criteria for exponential decay and non-exponential decay is obtained.(2)We will first establish the models of the non-exponential decay of mRNA.One model is that mRNA molecules is regulated by two pathways denoted by 3?? 5?and 5?? 3?,the other is mRNAs are degraded in two rate-limiting steps or multiple steps.(3)We get some conclusions on the kinetics of the mean of newly accumulated transcripts in the non-exponential decay model.(4)We prove an interesting result that the two-step degradation always produces noisier transcription,and the maximum noise occurs when the two rates 1and 2are the same.This thesis is organized as follows.In Chapter 1,we give a brief background on the stochastic gene expression,mechanism of mRNA degradation,and present experimental data of non-exponential degradation.In Chapter 2,we give the criteria for the nonexponential decay.When mRNA molecules are degraded in two consecutive rate-limiting steps,we show that it's a non-exponential degradation and get the range of the half-life1/2.And then we obtain several basic principles on the monotonicity of the mean level of mRNAs regulated by two rate-limiting steps.In Chapter 3,we prove an interesting result that the two-step degradation always produces noisier transcription,and the maximum noise occurs when the two rates are the same.In Chapter 4,we will first establish a model of mRNA regulation by two pathways denoted by 3?? 5?and 5?? 3?for short.It is proved that(1)the newly mean level is strictly increasing in and ,but is strictly decreasing in ,here , and are the initial activation frequency,the activation rate and the inactivation rate,respectively;(2)the newly mean level is strictly decreasing in both 2and 3,remarkably,is strictly increasing in 1when 2< 3and decreasing when 2> 3and(3)the newly mean level is strictly increasing in time when < /( + ).In Chapter 5,we will first establish the mRNA non-exponential multiple-steps degradation model.And then we get some conclusions on the kinetics of the mean of newly accumulated transcripts is strictly increasing in ,but is strictly decreasing in .Finally,we discuss the prospective on our future study in Chapter 5.