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arXiv physics/0508112physics.bio-phphysics.chem-phphysics.comp-phq-bio.MN
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基因调控网络:一种粗粒度、无方程的多尺度计算方法

Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation

Radek Erban, Ioannis G. Kevrekidis, David Adalsteinsson, Timothy C. Elston

摘要:

我们提出了计算机辅助的方法来分析随机模型的基因调控网络。这种无方程分析的主要思想是设计和执行适当初始化的随机模拟短脉冲串;这些结果被处理以估计感兴趣的粗粒度数量,如介观输运系数。特别是,使用一个简单的模型的遗传切换开关,我们说明了计算的有效自由能和状态依赖的有效扩散系数,其特征在于一个不可用的有效福克-普朗克方程。此外,我们说明了连接方程的自由技术与连续的方法进行一种形式的随机“分叉分析”,估计平均开关时间的情况下,一个开关也实现了在这个方程的自由上下文中。我们的方法的准确性进行了测试,通过直接比较与长时间的随机模拟。这种类型的无方程分析似乎是一个很有前途的方法来计算功能的长时间,粗粒度的基因调控网络的某些类的复杂的随机模型的行为,避免了需要长时间的蒙特卡罗模拟。

英文摘要:

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy and of a state-dependent effective diffusion coefficient that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.

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