The frequency of cyclic processes in biological multistate systems

Cyclic processes in stochastic models of macromolecular biological systems are considered. The diagram solution of the model equations (master equation) gives rise to special functions of the rate constants, called the circuit (or one-way cycle) fluxes. As Hill has shown, these functions are the fundamental theoretical components of the operational fluxes, i.e., of the rates of reaction, of transport, of energy conversion, etc. Evidence recently has been found by Monte Carlo simulations that the circuit fluxes can be interpreted as the frequencies of circuit completions. Making use of the theory of graphs, we prove that this physical interpretation of the circuit fluxes is generally valid.