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.

Mapping of statistical physics to information theory with application to biological systems

The problem of achieving a mapping of formalisms in statistical physics and theoretical biology to information theory is discussed using an example for canonical ensembles. We extend the meaning of the Handscomb Monte-Carlo method to a general recipe for the transformation from a "configuration" space to a "sentence" space. The ensemble of "sentences" and its corresponding source uncertainty function are introduced. A possible mapping procedure based on a generalization of the Handscomb representation is described. For a biological illustration, we present a way to introduce a pathway representation to describe metabolic processes in living systems.