  Families of ODE models characterized by a common sign structure of their
Jacobi matrix are investigated within the formalism of qualitative differential
equations. In the context of regulatory networks the sign structure of the
Jacobi matrix carries the information about which components of the network
inhibit or activate each other. Information about constraints on the behavior
of models in this family is stored in a so called qualitative state transition
graph. We showed previously that a similar approach can be used to analyze a
model pool of Boolean functions characterized by a common interaction graph.
Here we show that the opposite approach is fruitful as well. We show that the
qualitative state transition graph can be reduced to a "skeleton" represented
by a Boolean function conserving the reachability properties. This reduction
has the advantage that approaches such as model checking and network inference
methods can be applied to the "skeleton" within the framework of Boolean
networks. Furthermore, our work constitutes an alternative to approach to link
Boolean networks and differential equations.
