Self-loops favour diversification and asymmetric transitions between attractors in boolean network models

The process of cell differentiation manifests properties such as non-uniform robustness and asymmetric transitions among cell types. In this paper we adopt Boolean networks to model cellular differentiation, where attractors (or set of attractors) in the network landscape epitomise cell types. Since changes in network topology and functions strongly impact attractor landscape characteristics, in this paper we study how self-loops influence diversified robustness and asymmetry of transitions. The purpose of this study is to identify the best configuration for a network owning these properties. Our results show that a moderate amount of self-loops make random Boolean networks more suitable to reproduce differentiation phenomena. This is a further evidence that self-loops play an important role in genetic regulatory networks.