A Modelling Framework for Gene Regulatory Networks Including Transcription and Translation

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• 作者：R. Edwards ; A. Machina ; G. McGregor…
• 关键词：Gene regulation ; Piecewise ; linear ; Singular perturbation ; mRNA ; protein model ; Transcription鈥搕ranslation model ; 92C42 ; 34A36 ; 92C40
• 刊名：Bulletin of Mathematical Biology
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：77
• 期：6
• 页码：953-983
• 全文大小：1,015 KB
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• 作者单位：R. Edwards (1)
  A. Machina (1)
  G. McGregor (2)
  P. van den Driessche (1)
  
  1. Department of Mathematics and Statistics, University of Victoria, STN CSC, PO Box 1700, Victoria, BC, V8W 2Y2, Canada
  2. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 0B9, Canada
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  
• 出版者：Springer New York
• ISSN：1522-9602

文摘

Qualitative models of gene regulatory networks have generally considered transcription factors to regulate directly the expression of other transcription factors, without any intermediate variables. In fact, gene expression always involves transcription, which produces mRNA molecules, followed by translation, which produces protein molecules, which can then act as transcription factors for other genes (in some cases after post-transcriptional modifications). Suppressing these multiple steps implicitly assumes that the qualitative behaviour does not depend on them. Here we explore a class of expanded models that explicitly includes both transcription and translation, keeping track of both mRNA and protein concentrations. We mainly deal with regulation functions that are steep sigmoids or step functions, as is often done in protein-only models. We find that flow cannot be constrained to switching domains, though there can still be asymptotic approach to singular stationary points (fixed points in the vicinity of switching thresholds). This avoids the thorny issue of singular flow, but leads to somewhat more complicated possibilities for flow between threshold crossings. In the infinitely fast limit of either mRNA or protein rates, we find that solutions converge uniformly to solutions of the corresponding protein-only model on arbitrary finite time intervals. This leaves open the possibility that the limit system (with one type of variable infinitely fast) may have different asymptotic behaviour, and indeed, we find an example in which stability of a fixed point in the protein-only model is lost in the expanded model. Our results thus show that including mRNA as a variable may change the behaviour of solutions.