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.
Permutation theory governs long-term dynamics of critical Boolean networks
University of California, Los Angeles（加州大学洛杉矶分校）；University of Florida（佛罗里达大学）；Watchung Hills Regional High School（瓦丘山地区高中）；Ponte Vedra High School（蓬特韦德拉高中）；Iowa State University（爱荷华州立大学）
