Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm

Biochemical dynamics are often determined by series of single molecule events such as gene expression and reactions involving protein concentrations at nanomolar concentrations. Molecular fluctuations, consequently, may be of biological significance. For example, heterogeneity in clonal populations is believed to arise from molecular fluctuations in gene expression. A realistic description, therefore, requires a probabilistic description of the biochemical dynamics as deterministic descriptions cannot capture the inherent molecular fluctuations. The Gillespie algorithm [D. T. Gillespie, J. Phys. Chem. 81, 2350 (1977)] is a stochastic procedure for simulating chemical systems at low concentrations. A limitation…