Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression
- 478 Downloads
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.
KeywordsStochastic modelling Gene expression Master equation Generating function
Mathematics Subject Classification (2000)92C40 60J27
Unable to display preview. Download preview PDF.
- Lestas I, Paulsson J, Ross N, Vinnicombe G (2008) Noise in gene regulatory networks. IEEE T Circuits-I 53: 189–200Google Scholar
- Lewin B (2000) Genes VII. Oxford University Press, OxfordGoogle Scholar
- Singh A, Hespanha J (2007) Stochastic analysis of gene regulatory networks using moment closure. In: Proceedings of the American control conferenceGoogle Scholar
- van Kampen N (2006) Stochastic processes in physics and chemistry. Elsevier, New YorkGoogle Scholar