A stochastic model for a closed biochemical system at equilibrium.

This paper presents a stochastic model, a theoretical multi-variate probability function describing concentrations of reactants in a closed biochemical system at equilibrium. The theory applies to the complete range of biochemical systems from single enzyme reactions to combinations of reactions to complete pathways. Prior to examining the general system, probability functions are derived for the following systems as examples: a reaction with a competitive inhibitor. a bisubstrate reaction using the ping-pong mechanism and a series of two mono-substrate reactions. The theory of Markov processes is used to derive the probability functions for each of the example systems and then for the general system which includes the example systems as special cases. The probability function for any appropriate biochemical system proves to be the product of independent Poisson probabilities conditioned on the conservation equations. Finally, the implications of the theory are briefly discussed and possible extensions proposed.