A Modelling Framework for Gene Regulatory Networks Including Transcription and Translation
A Modelling Framework for Gene Regulatory Networks Including Transcription and Translation
复制标题
DOI：
10.1007/s11538-015-0073-9
复制
发表时间：
2015-06-01
影响因子：
3.5
通讯作者：
van den Driessche, P.
中科院分区：
文献类型：
--
作者：
Edwards, R.;Machina, A.;van den Driessche, P.
基因调控网络的定性模型通常考虑转录因子直接调控其他转录因子的表达，而不需要任何中间变量。事实上，基因表达总是涉及转录，产生 mRNA 分子，然后是翻译，产生蛋白质分子，然后蛋白质分子可以充当其他基因的转录因子（在某些情况下是在转录后修饰之后）。抑制这些多个步骤隐含地假设定性行为不依赖于它们。在这里，我们探索一类明确包括转录和翻译的扩展模型，跟踪 mRNA 和蛋白质浓度。我们主要处理陡峭 sigmoid 或阶跃函数的调节函数，就像在纯蛋白质模型中经常做的那样。我们发现，尽管仍然可以对奇异驻点（切换阈值附近的固定点）进行渐近处理，但流不能被限制在切换域。这避免了奇异流的棘手问题，但导致阈值交叉之间的流的可能性更加复杂。在 mRNA 或蛋白质速率的无限快限制下，我们发现解在任意有限时间间隔上均匀地收敛到相应的仅蛋白质模型的解。这留下了一种可能性，即极限系统（具有无限快的一种类型的变量）可能具有不同的渐近行为，事实上，我们发现了一个例子，其中仅蛋白质模型中的固定点的稳定性在扩展模型中丢失了。因此，我们的结果表明，将 mRNA 作为变量可能会改变解决方案的行为。
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.