Summary: Gene expression profiles exhibit variability due to stochasticity in cellular processes such as transcription and translation. This variability results in probabilistic dynamics, where under the same conditions one may observe slightly or very different responses. A comprehensive analysis of the stochasticity in cellular processes is an important challenge in systems biology because biological networks are large and complex. Boolean networks are popular models for gene regulation due to their intuitive approach and relative simplicity for analysis. To incorporate the stochasticity of gene regulatory processes into the models, several stochastic extensions of the deterministic Boolean network framework have been developed. For simplicity of the presentation, we will focus on a class of stochastic models which we will refer to as stochastic discrete dynamical systems. However, the methods discussed in this chapter can also be applied in other stochastic settings such as probabilistic Boolean networks. This chapter will cover three important problems in stochastic discrete modeling: (1) long-term dynamical properties, (2) parameter estimation techniques, and finally, (3) optimal control methods and their limitations.
For the entire collection see [Zbl 1404.92006].