Periodic orbits and equilibria in glass models for gene regulatory networks

Abstract

Glass models are frequently used as models for gene regulatory networks. This paper proposes algorithmic methods for the synthesis of Glass networks with specific dynamics, including periodic orbits and equilibrium states. In contrast to existing work, bi-periodic networks and networks possessing both stable equilibria and periodic trajectories are considered. The robustness of the attractor is also addressed, which gives rise to hypercube paths with non-dominated nodes and double coils. These paths correspond to novel combinatorial problems, for which initial experimental results are presented. Finally, a classification of Glass networks with respect to their corresponding gene interaction graphs for the case of graphs with three edges is presented.