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A probabilistic model of a prokaryotic gene and its regulation

The previous chapter described several different kinds of models that are used to model gene regulation. This chapter focuses exclusively on stochastic models (Van Kampen, 1992),(McQuarrie, 1967). As mentioned in the previous chapter, the stochastic framework is important when the number of molecules involved is small, the time scale is short, or both. This chapter will not rehash the theoretical underpinnings of the previous chapter, but rather, will provide an extensive example, which illustrates many of the biological processes involved in (prokaryotic) gene regulation and also many of the stochastic processes used to model these biological processes. The system to be modeled is part of the regulatory circuitry of lambda phage, and is a small subset of the complete model in (Arkin et al., 1998).