Diagrammatic approach to calculation of the fluctuation correlation matrix in a metabolic system

We present here a simple diagrammatic approach for the time evolution of the fluctuations in metabolite concentrations around the steady state. A fluctuation correlation matrix is introduced to characterise the response in the concentrations of metabolites to a singular initial fluctuation in one of the metabolites. We show how the temporal evolution of the correlation matrix can be represented in the form of a series with individual terms corresponding to pathways on a metabolic graph. The basic properties of such graphs are studied and it is shown how each term in the series can be evaluated. A Monte-Carlo procedure is outlined to calculate the fluctuation correlation matrix. We discuss various properties of the graphical representation and discuss links to information theory that arise from it.