Out-of-Equilibrium Fluctuations Drive Correlations Between Enzyme and Metabolic Product Levels

Enzyme-driven catalysis of a substrate into a product forms the fundamental backbone of cellular metabolic pathways. In the deterministic formulation of such a reaction scheme, the equilibrium level of the metabolic product is independent of the steady-state enzyme, so that any perturbation in enzyme levels causes a transient change in metabolic product levels that perfectly adapts to the original enzyme-independent steady state. In this work, we consider a stochastic formulation of the problem, where enzyme levels constantly fluctuate due to the inherently noisy gene expression process as well as to the extrinsic noise in substrate availability. Our results show that such out-of-equilibrium fluctuations can result in positive (or negative) enzyme-product and substrate-product correlations, whose behavior qualitatively and quantitatively changes in different scenarios characterized by perturbations of nominal parameters and variable noise levels.