Stochastic Boolean Networks

Stochasticity is a fundamental property of biological networks, and it can have a significant impact on the dynamics of these networks. To account for the stochasticity in various molecular processes, several versions of stochastic Boolean networks exist including probabilistic Boolean networks, perturbed Boolean networks, and probabilistic edge operators. This chapter will focus on the stochastic framework that is usually referred as Stochastic Discrete Dynamical Systems (SDDS). The SDDS framework introduces stochasticity by assigning propensity parameters for activation and degradation to each function in the Boolean network. We will describe how obtain information of the long-term dynamics of an SDDS as well as how to tune the propensity parameters. Finally, we will describe a toolbox for simulation using SDDS and discuss potential applications for the control and optimal control of discrete systems.