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

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• 作者：D. Holcman (1)
  K. Dao Duc (1)
  A. Jones (2)
  H. Byrne (3)
  K. Burrage (4)
  
  1. Applied Mathematics and Computational Biology ; IBENS ; Ecole Normale Sup茅rieure ; 46 rue d鈥橴lm ; 75005聽 ; Paris ; France
  2. Computational Biology Group ; Department of Computer Science ; University of Oxford ; Wolfson Building ; Parks Rd ; Oxford聽 ; OX1 3QD ; UK
  3. Oxford Centre for Collaborative and Applied Mathematics ; Mathematical Institute ; University of Oxford ; 24-29 St Giles鈥? Oxford聽 ; OX1 3LB ; UK
  4. School of Mathematical Sciences ; Queensland University of Technology ; Brisbane ; Australia
  
• 关键词：Stochastic process ; Markov chain ; Gene expression ; mean first passage time ; Fokker Planck equation ; PTEN ; mRNA ; 92B05 ; 60J28 ; 60J70
• 刊名：Journal of Mathematical Biology
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：70
• 期：4
• 页码：805-828
• 全文大小：809 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  Applications of Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1416

文摘

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 calculation 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 reducing 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.