A Petri Net-Based Approach to Control of Boolean Networks

A Boolean network is a class of discrete-time nonlinear dynamical systems, and time evolution is expressed by a set of Boolean functions. This model is well known as one of the models of gene regulatory networks, and can express synchronous dynamics. In this paper, to express asynchronous dynamics, a new modeling method of Boolean networks with control inputs is proposed based on the Petri net framework. Furthermore, the optimal control problem of Petri nets expressing asynchronous dynamics of a Boolean network is formulated, and is reduced to an integer programming problem. The proposed approach will provide us one of the mathematical bases of control methods for gene regulatory networks.