Revealing temporal genetic regulatory networks from steady-state distributions

The design of dynamical networks from steady-state distributions usually presents some inherent limitations. The dynamical behavior of the system can not be determined from the steady-state, it can only be constrained by it. In general, there is a huge number of dynamical systems that can produce the same steady-state. Nevertheless, it is possible to further constrain the possibilities by adopting the Probabilistic Genetic Networks model which is based on axioms that usually make sense in biological systems. In this work we introduce a new method for the inference of dynamical systems, and their underlying logical structures, from a steady-state distribution. Our method is based on the assumption that biological systems are quasi-deterministic. The technique is based on an integer programming model that selects stochastic matrices with a known limit distribution. These transition matrices reveal how the dynamical system evolves, allowing the application of standard inference methods to discover dependencies among elements of the system.