The accuracy of the rapid equilibrium assumption in steady-state enzyme kinetics in the case of a multipath arbitrary enzyme mechanism with a number of equilibrium segments

A quantitative evaluation of the accuracy of the rapid-equilibrium assumption in steady-state enzyme kinetics was obtained for a multipath arbitrary enzyme mechanism with a number of equilibrium segments. Explicit expressions for estimating the contribution of any equilibrium segment to the accuracy of the rapid-equilibrium assumption were obtained. This allowed us to determine the accuracy of the rapid-equilibrium assumption (Δ) in general: 1 + Δ = (1 + Δ₁)(1 + Δ₂)... (1 + Δ_k), where Δ₁, Δ₂,..., Δ_k is the contribution of each individual equilibrium segment. The accuracy depends only on the structure and properties of equilibrium segments, which have been accounted for in the rapid-equilibrium assumption, but it is independent of the number of paths in the mechanism of the enzymatic reaction and on the structure and properties of the remaining part (steady-state) of the kinetic scheme.