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. A computational model based on switching networks is generated from the regulatory network. The phase space dimension of this model equals the number of nodes and the associated parameter space consists of one parameter for each node (a decay rate), and three parameters for each edge (low level of expression, high level of expression, and 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 a compact representation of the global dynamics called an annotated Morse graph that identifies recurrent and nonrecurrent dynamics. 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 dynamical 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 of 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.

中文翻译：

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交换网络的参数空间的组合表示。

我们描述了遗传管理网络动态签名（DSGRN）数据库的理论和计算框架。动机来自迫切需要了解具有至少5至10个节点，涉及多种相互作用和数十年参数的生物学相关信号转导/基因调控网络的全球动态。数据库计算的输入是调节网络，即，有向图的边表示向上或向下调节。从交换网络生成基于交换网络的计算模型。此模型的相空间维等于节点数，并且相关的参数空间由每个节点一个参数（衰减率）和每个边缘三个参数（低表达水平，高表达水平，以及表达水平变化的阈值）。由于开关系统的非线性是分段恒定的，因此相空间自然分解为单元，可以根据状态转换图组合描述动力学。反过来，这导致了全局动力学的紧凑表示，称为带注释的摩尔斯图，用于标识循环和非循环动力学。本文的重点是将参数空间自然地可计算的有限分解构造为动态的带注释的摩尔斯图描述恒定的区域。我们使用这种分解来构建一个SQL数据库，该数据库可以有效地搜索诸如双稳态，稳定或不稳定的振荡以及稳定的平衡之类的动态签名。我们包括两个简单的3节点网络，以提供有关DSGRN数据库中存储的信息类型的小型显式示例。为了演示该系统的计算能力，我们考虑一个与p53相关的简单网络，该网络涉及5个节点和29维参数空间。