Alternative to the steady-state method: derivation of reaction rates from first-passage times and pathway probabilities.

An alternative method for deriving rate equations in enzyme kinetics is presented. An enzyme is followed as it moves along the various pathways allowed by the reaction scheme. The times spent in various sections of the scheme and the pathway probabilities are computed, using simple rules. The rate equation obtains as a function of times and probabilities. The results are equivalent to those provided by the steady-state formalism. While the latter applies uniformly to all schemes, the formalism presented here requires adaptation to each additional class of schemes. However, it has the merit of allowing one to leave unspecified many details of the scheme, including topological ones. Furthermore, it allows one to decompose a scheme into subschemes, analyze the parts separately, and use the intermediate results to derive the rate equation of the complete scheme. The method is applied here to derive general equations for one- and two-entry site enzymes.