Asynchronous stochastic Boolean networks as gene network models.

Logical models have widely been used to gain insights into the biological behavior of gene regulatory networks (GRNs). Most logical models assume a synchronous update of the genes' states in a GRN. However, this may not be appropriate, because each gene may require a different period of time for changing its state. In this article, asynchronous stochastic Boolean networks (ASBNs) are proposed for investigating various asynchronous state-updating strategies in a GRN. As in stochastic computation, ASBNs use randomly permutated stochastic sequences to encode probability. Investigated by several stochasticity models, a GRN is considered to be subject to noise and external perturbation. Hence, both stochasticity and asynchronicity are considered in the state evolution of a GRN. As a case study, ASBNs are utilized to investigate the dynamic behavior of a T helper network. It is shown that ASBNs are efficient in evaluating the steady-state distributions (SSDs) of the network with random gene perturbation. The SSDs found by using ASBNs show the robustness of the attractors of the T helper network, when various stochasticity and asynchronicity models are considered to investigate its dynamic behavior.