An algorithm for detecting fixed points of boolean network

In the applications of Boolean networks to modeling biological systems, an important computational problem is the detection of the fixed points of these networks. There have been various attempts to develop algorithms to address the computation need for large size networks. The existing methods are usually based on known algorithms and thus limited to the situations where these known algorithms can apply. In this paper, we show how to divide the polynomial equation system which defines the fixed points of a Boolean network into subsystems according to the number of variables involved, so that each of these subsystems can be readily solved. After solving these subsystems and thus reducing the number of states involved, we can combine the solutions to obtain all fixed points of the given network. This approach does not depend on other algorithms and it is easy to implement. We show that this method can handle large size Boolean networks, and demonstrate its effectiveness by using MAPLE to compute the fixed points of Boolean networks with hundreds of nodes and thousands of interactions.