Towards a calculus of biological networks

In this paper we present a new framework for studying the dynamics of biological networks. A specific class of dynamical systems, Sequential Dynamical Systems (SDS), is introduced. These systems allow one to investigate the interplay between structural properties of the network and its phase space. We will show in detail how to find a reduced system that captures key features of a given system. This reduction is based on a special graph-theoretic relation between the two networks. We will study the reduction of SDS over n-cubes in detail and we will present several examples.