  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.
