  Finite dynamical systems (e.g. Boolean networks and logical models) have been
used in modeling biological systems to focus attention on the qualitative
features of the system, such as the wiring diagram. Since the analysis of such
systems is hard, it is necessary to focus on subclasses that have the
properties of being general enough for modeling and simple enough for
theoretical analysis. In this paper we propose the class of AND-NOT networks
for modeling biological systems and show that it provides several advantages.
Some of the advantages include: Any finite dynamical system can be written as
an AND-NOT network with similar dynamical properties. There is a one-to-one
correspondence between AND-NOT networks, their wiring diagrams, and their
dynamics. Results about AND-NOT networks can be stated at the wiring diagram
level without losing any information. Results about AND-NOT networks are
applicable to any Boolean network. We apply our results to a Boolean model of
Th-cell differentiation.
