Rate-limiting step: a quantitative definition. Application to steady-state enzymic reactions.

The generality of the concept of a rate-limiting step in enzymic reactions recently has been questioned [Northrop, D. B. (1981) Biochemistry 20, 4056-4061] because, in simulated isotopic experiments, alterations of the step identified as rate limiting by current definitions do not consistently affect Vmax in the expected manner. In this paper a definition for a rate-limiting step is posed that eliminates such inconsistencies while the thrust of the original concept is retained. Thus, for any steady-state process involving a linear reaction sequence the rate-limiting step is taken as the "most sensitive" step, or the step which, if perturbed, causes the largest change in overall velocity, v. In both V and V/K enzymic systems the most sensitive step is identified by the relative magnitude of the sensitivity function, SFj, for the various forward steps. If forward steps are identified by kj, SFj is equal to delta(1/v)/[delta(1/kj)/(1/kj)], when the equilibrium constant for the step involving kj is maintained constant. The corresponding sensitivity index, SIj, is a normalized function of SFj (the normalizing factor is v) such that the sum of the values for SIj is equal to 1. In addition, there is an exact relationship between the sensitivity index for the isotopic step and the fraction of the intrinsic isotopic effect that is expressed in the overall rate of the reaction (when the intrinsic effect is taken as the fractional difference in reciprocal rate constant produced by the isotope). A procedure is described for approximating the sensitivity function for the various steps in a reaction sequence on the basis of the Gibbs energy profile for that reaction and thus identifying the most sensitive step. This approach also is used to consider the general question of whether a rate-limiting step should be specified for a multistep enzymic reaction. Identifying the rate-limiting step as the most sensitive step in a reaction sequence means that no aspect of the concept of minimal rate should be automatically considered as a property of a rate-limiting step.