Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Holcman, David, Dao Duc, Khanh, Jones, Anna, Byrne, Helen, & Burrage, Kevin (2015) Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem. Journal of Mathematical Biology, 70(4), pp. 805-828.

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Abstract

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

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ID Code: 88776
Item Type: Journal Article
Refereed: Yes
Keywords: Stochastic process, Markov chain, Gene expression, mean first passage time, Fokker Planck equation, PTEN, mRNA
DOI: 10.1007/s00285-014-0782-y
ISSN: 0303-6812
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: © 2014 Springer-Verlag Berlin Heidelberg
Deposited On: 29 Oct 2015 04:16
Last Modified: 29 Oct 2015 04:28

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