Bundschuh R, Hayot F, Jayaprakash C
Department of Physics, The Ohio State University, Columbus 43210-1106, USA.
Biophys J. 2003 Mar;84(3):1606-15. doi: 10.1016/S0006-3495(03)74970-4.
Computer simulations of large genetic networks are often extremely time consuming because, in addition to the biologically interesting translation and transcription reactions, many less interesting reactions like DNA binding and dimerizations have to be simulated. It is desirable to use the fact that the latter occur on much faster timescales than the former to eliminate the fast and uninteresting reactions and to obtain effective models of the slow reactions only. We use three examples of self-regulatory networks to show that the usual reduction methods where one obtains a system of equations of the Hill type fail to capture the fluctuations that these networks exhibit due to the small number of molecules; moreover, they may even miss describing the behavior of the average number of proteins. We identify the inclusion of fast-varying variables in the effective description as the cause for the failure of the traditional schemes. We suggest a different effective description, which entails the introduction of an additional species, not present in the original networks, that is slowly varying. We show that this description allows for a very efficient simulation of the reduced system while retaining the correct fluctuations and behavior of the full system. This approach ought to be applicable to a wide range of genetic networks.
大型遗传网络的计算机模拟通常极其耗时，因为除了生物学上有趣的翻译和转录反应外，许多不太有趣的反应，如DNA结合和二聚化反应也必须进行模拟。利用后者发生的时间尺度比前者快得多这一事实，消除快速且无趣的反应，仅获得慢速反应的有效模型，这是很有必要的。我们用三个自调控网络的例子表明，通常得到希尔型方程组的简化方法无法捕捉这些网络由于分子数量少而表现出的涨落；此外，它们甚至可能无法描述蛋白质平均数量的行为。我们确定在有效描述中包含快速变化的变量是传统方法失败的原因。我们提出一种不同的有效描述方法，即引入一个原始网络中不存在的、缓慢变化的额外物种。我们表明，这种描述方法能够在保留完整系统正确涨落和行为的同时，非常高效地模拟简化后的系统。这种方法应该适用于广泛的遗传网络。
