We describe the theoretical and computational framework for the Dynamic Signatures for Genetic Regulatory Network (DSGRN) database. The motivation stems from urgent need to understand the global dynamics of biologically relevant signal transduction/gene regulatory networks that have at least 5 to 10 nodes, involve multiple interactions, and decades of parameters. The input to the database computations is a regulatory network, i.e.\ a directed graph with edges indicating up or down regulation, from which a computational model based on switching networks is generated. The phase space dimension equals the number of nodes. The associated parameter space consists of one parameter for each node (a decay rate), and three parameters for each edge (low and high levels of expression, and a threshold at which expression levels change). Since the nonlinearities of switching systems are piece-wise constant, there is a natural decomposition of phase space into cells from which the dynamics can be described combinatorially in terms of a state transition graph. This in turn leads to compact representation of the global dynamics called an annotated Morse graph that identifies recurrent and nonrecurrent. The focus of this paper is on the construction of a natural computable finite decomposition of parameter space into domains where the annotated Morse graph description of dynamics is constant. We use this decomposition to construct an SQL database that can be effectively searched for dynamic signatures such as bistability, stable or unstable oscillations, and stable equilibria. We include two simple 3-node networks to provide small explicit examples of the type information stored in the DSGRN database. To demonstrate the computational capabilities of this system we consider a simple network associated with p53 that involves 5-nodes and a 29-dimensional parameter space.
翻译:我们描述基因监管网络动态签名(DSGRN)数据库的理论和计算框架。动力来自迫切需要了解生物相关信号转换/基因监管网络的全球动态,这些网络至少有5至10个节点,涉及多个互动和数十年参数。数据库计算输入是一个监管网络,即带有显示上下调调控的边緣的定向图形,由此生成一个基于切换网络的计算模型。阶段空间维度等于节点的数量。相关的参数空间包括每个节点的一个参数(一个衰减率)和每个边缘的三个参数(一个低和高的表达水平,一个表达水平变化的阈值)。由于切换系统的非线性常态常态,将阶段空间自然地分解到细胞中,从边际图中可以对动态进行轮廓式描述。这反过来导致全球动态的缩略表示,需要一份附加注释的 Morse 图表,用以识别经常性和非经常性的。本文的焦点是构建一个稳定的空间动态网络,其中含有稳定的磁性变变变变的系统, 包括一个稳定的磁的系统,我们用来构建一个稳定的磁变变变变的磁的系统。