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.
Rojdestvenski
I
I
Department of Plant Physiology, Umea University, 90187, Umea, Sweden. rojdestvenski@plantphys.umu.se
Cottam
M G
MG
D000818:Animals; D006801:Humans; D008660:Metabolism; D008962:Models, Theoretical; D009010:Monte Carlo Method