The total quasi-steady-state approximation is valid for reversible enzyme kinetics

The Briggs–Haldane approximation of the irreversible Michaelis–Menten scheme of enzyme kinetics is cited in virtually every biochemistry textbook and is widely considered the classic example of a quasi-steady-state approximation. Though of similar importance, the reversible Michaelis–Menten scheme is not as well characterized. This is a serious limitation since even enzymatic reactions that go to completion may be reversible. The current work derives a total quasi-steady-state approximation (tQSSA) for the reversible Michaelis–Menten and delineates its validity domain. The tQSSA allows the derivation of uniformly valid approximations for the limit of low enzyme concentrations, ET⪡ST+KM, and under certain more restrictive conditions also for high enzyme concentrations such that ST⪡ET+KM. Using these simple analytical approximations, a sequential experimental–theoretical method is suggested for unambiguously estimating all the kinetic parameters of the reversible Michaelis–Menten scheme.