title: Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression.
abstract: Gene expression at the single-cell level incorporates reaction mechanisms which are intrinsically stochastic as they involve molecular species present at low copy numbers. The dynamics of these mechanisms can be described quantitatively using stochastic master-equation modelling; in this paper we study a generic gene-expression model of this kind which explicitly includes the representations of the processes of transcription and translation. For this model we determine the generating function of the steady-state distribution of mRNA and protein counts and characterise the underlying probability law using a combination of analytic, asymptotic and numerical approaches, finding that the distribution may assume a number of qualitatively distinct forms. The results of the analysis are suitable for comparison with single-molecule resolution gene-expression data emerging from recent experimental studies.
authors.affiliation: Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK. pavol.bokes@fmph.uniba.sk
authors.forename: Pavol
authors.initials: P
authors.lastname: Bokes
authors.forename: John R
authors.initials: JR
authors.lastname: King
authors.forename: Andrew T A
authors.initials: AT
authors.lastname: Wood
authors.forename: Matthew
authors.initials: M
authors.lastname: Loose
mesh_terms: D018628:Gene Dosage; D008957:Models, Genetic; D014176:Protein Biosynthesis / Q000235:genetics; D011506:Proteins / Q000235:genetics / Q000378:metabolism*; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism*; D013269:Stochastic Processes; D014158:Transcription, Genetic
chemical_list: D011506:Proteins; D012333:RNA, Messenger