Deterministic models have been extensively used over the past decades to describe reaction phenomena. This approach, however, is inadequate for phenomena encountered in intracellular processes, in which the control volumes are on the order of some pico-liters: the inherent stochasticity of the reaction phenomena occurring in every single cell creates significant random fluctuations, termed “intrinsic noise”. Therefore, the underlying dynamics of transcription and translation, the protein-ligand interactions, and the degradation phenomena, must be described in probabilistic terms, with the use of stochastic models. Furthermore, this inherent, intracellular stochasticity contributes to phenotypic variations amongst isogenic cells of a cell population, thus leading to heterogeneous cell population dynamics. Even if one is only interested in accurate descriptions of bulk, average cell population dynamics, the two descriptions can give vastly different predictions in certain cases.

In this work, we present a detailed stochastic model describing the dynamics of the IPTG-inducible lac operon network. The model describes the constitutive expression of lacI repressor, the dynamics of lacY transcription and translation, the induced and facilitated transport of IPTG, and the degradation of the metabolizable species. Furthermore, we rigorously derive the equivalent deterministic model and by comparing its predictions with those of the stochastic model, we isolate the effects of intrinsic noise on system behavior. Moreover, we demonstrate how the asymptotic behavior and the phenotypic heterogeneity are affected by changes in several biomolecular parameters, such as promoter strength, binding affinities and plasmid copy numbers. Our results are expected to hold not only for the lac operon system, but for other systems with positive feedback architecture as well.