Search for Steady States of Piecewise-Linear Differential Equation Models of Genetic Regulatory Networks

The analysis of the attractors of a genetic regulatory network gives a good indication of the possible functional modes of the system. In this paper, we are concerned with the problem of finding all steady states of genetic regulatory networks described by piecewise-linear differential equation (PLDE) models. We show that the problem is NP-hard and translate it into the problem of finding all valuations of a propositional satisfiability (SAT) formula. This allows the use of existing, efficient SAT solvers and has enabled the development of a steady state search module of the computer tool genetic network analyzer (GNA). The practical use of this module is demonstrated by means of the analysis of a number of relatively small bacterial regulatory networks, as well as randomly generated networks of several hundred genes.