Design of Boolean networks based on prescribed singleton attractors

Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an integer linear programming problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.