A general framework for noise propagation in a cascade of metabolic transformations

This note investigates how noise propagates in cascades of metabolic transformations. Motivation stems from recent single cell experiments that have shown that noise generated in gene expression and enzymes fluctuations propagates to growth rate through metabolic fluxes. A stochastic approach based on Continuous-Time Markov Chains (CTMC) is exploited to model all reactions, with a special interest in the substrate production, assumed to happen in bursts. Different noise features are dealt with, including correlation of intermediate players, noise impact on the end-product and the role of a feedback from the end-product that may control the substrate production. Most results are given in terms of analytical solutions of the CTMC, in some cases exploiting linear approximations; in all these cases, the findings are validated via Monte Carlo stochastic simulations. The proposed results highlight how substrate production in bursts, cascade length and distance among species affect fluctuations and correlations, with the feedback possibly playing a crucial role in favor of noise propagation.