Stochastic simulation of enzymatic reactions under transcriptional feedback regulation

The interaction between gene expression and metabolism is a form of feedback control that allows cells to up- or downregulate specific reactions according to the environmental conditions. Although gene expression is an inherently stochastic process, the effect of genetic feedback on the propagation of noise to the metabolic layer remains largely unexplored. These systems operate in two timescales, and a major challenge is to devise stochastic simulation techniques that can cope with this stiffness in reasonable computational time. We propose a simulation technique, based on the slow-scale Stochastic Simulation Algorithm, to rapidly compute realizations of the Markov process associated to an enzymatic reaction under genetic feedback regulation. We show that in the case of constant substrate, the enzyme-substrate complexes have a binomial stationary distribution. With this result we can avoid the explicit simulation of the binding/dissociation of the enzyme and substrate, leading to a significant improvement in computational speed. We discuss the extension of the algorithm to networks of enzymatic reactions. The proposed method can be used to systematically compute the stationary distributions of the species for different combinations of model parameters, thus opening the way for the identification of the cellular processes that can modulate the amplification or attenuation of genetic noise in enzymatic reactions.