Variable-free exploration of stochastic models: A gene regulatory network example
Variable-free exploration of stochastic models: A gene regulatory network example
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DOI：
10.1063/1.2718529
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发表时间：
2007-04-21
影响因子：
4.4
通讯作者：
Kevrekidis, Ioannis G.
中科院分区：
文献类型：
--
作者：
Erban, Radek;Frewen, Thomas A.;Kevrekidis, Ioannis G.
在基因调控网络的复杂随机模型分析中，寻找粗粒度、低维的描述是一项重要的任务。这项任务涉及（a）识别最能描述这些复杂系统状态的可观测量，以及（B）表征可观测量的动态。在以前的论文[R. Erban，J.Chem.Phys.124，084106（2006）]，作者假设良好的可观测量是先验已知的，并且提出了一种无方程方法来近似粗粒度的量（即，有效漂移和扩散系数），其表征了观测量的长期行为。这里我们使用扩散映射[R. Coifman，Proc. Natl. Acad. Sci. U.S.A. 102，7426（2005）]以自动方式提取适当的可观测量（“归约坐标”）;这些涉及从网络模拟数据构建的图上的加权拉普拉斯算子的前导特征向量。我们提出了提升和限制物理变量和这些基于数据的观测值之间的转换程序。这些程序使我们能够通过设计和处理在基于数据的观测值的适当值处初始化的随机模拟的短突发来执行无方程的粗粒度计算，以表征长期动态。(c)2007年，美国物理学会。
Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [R. Erban , J. Chem. Phys. 124, 084106 (2006)] the authors assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e., effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [R. Coifman , Proc. Natl. Acad. Sci. U.S.A. 102, 7426 (2005)] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free, coarse-grained computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables. (c) 2007 American Institute of Physics.