Workshop on Topology: Identifying Order in Complex Systems

We first describe mathematical foundation of DSGRN (Dynamic Signatures Generated by Regulatory Networks), an approach that provides a queryable description of global dynamics of a network over its entire param- eter space. We describe a connection to Boolean network models that allows us to view DSGRN as a platform for bifurcation theory of Boolean maps.

We describe several applications. We show how to use DSGRN to (1) design a network that performs a biological function; (2) diagnose why a synthetic network failed, and (3) delineate dynamics of network that governs epithelial-mesenchynal transition, which allows cells to escape confinement of a tissue and migrate.