Noise propagation in feedback coupling between cell growth and metabolic activity

Size control is usually exerted in living cells by properly sensing the external inputs (like nutrients) and, accordingly, by activating the metabolic pathways in order to set and adjust their own growth rate. In this framework, experimental results have recently highlighted the role of metabolic noise, usually neglected because of its averaging over the great deal of reactions involved in metabolic networks. In this note, a basic model of the interplay among metabolic enzymes activity, resource allocation and growth rate is introduced. A noise source is supposed to affect the enzymatic activity. The model includes a feedforward action of the resource on the enzyme dynamics (modulated by growth), as well as a feedback of the enzyme on the resource production rate. A Stochastic Hybrid System formulation is exploited to investigate how the noise propagates through the metabolic pathway. Model-based results support the hypothesis that fluctuations in the enzyme production perturb cellular growth, and not vice versa, because of an apparent delay in the cross-correlation function. This result is coherent with single-cell recent experimental results.