Graphic Analysis of Coupling in Biological Systems

We have developed a mathematical model in which we apply the graph theory to the problem of coupling in biological systems. Coupling in biological systems is represented as a network of digraph. We introduce a new "graphic transformation method", which is an extension of the graphic method of King & Altman (1956). We obtain the expression of the steady-state distribution of the coupled system as an extension of the Boltzmann distribution. We introduce the "coupling ratio" as a quantity which represents the direction in which chemical reaction proceeds. It is suggested that the largeness of the coupling ratio is closely related to the largeness of deviation from the Boltzmann distribution.