Stochastic modeling of cellular networks.

Noise and stochasticity are fundamental to biology because they derive from the nature of biochemical reactions. Thermal motions of molecules translate into randomness in the sequence and timing of reactions, which leads to cell-cell variability ("noise") in mRNA and protein levels even in clonal populations of genetically identical cells. This is a quantitative phenotype that has important functional repercussions, including persistence in bacterial subpopulations challenged with antibiotics, and variability in the response of cancer cells to drugs. In this chapter, we present the modeling of such stochastic cellular behaviors using the formalism of jump Markov processes, whose probability distributions evolve according to the chemical master equation (CME). We also discuss the techniques used to solve the CME. These include kinetic Monte Carlo simulations techniques such as the stochastic simulation algorithm (SSA) and method closure techniques such as the linear noise approximation (LNA).