In defence of the general validity of the Cha method of deriving rate equations: The importance of explicit recognition of the thermodynamic box in enzyme kinetics

Abstract

1 The suggestion by Segel and Martin [(1988) J. Theor. Biol. 135, 445-453] that the well-known schematic method for the derivation of rate equations for combined quasi-equilibrium-steady-state models proposed by Cha [(1968) J. Biol. Chem. 243, 820-825] may not be generally applicable was shown to be incorrect. By contrast Cha's method was shown to yield correct initial-rate equations that are exact and (b) not to require any constraints on the relative magnitudes of rate constants for slow steps outside the quasi-equilibrium segments of the kinetic model, including these suggested by Segel and Martin. 2 Examination of residual King Altman patterns for the general modifier model of Botts and Morales [(1953) Trans Faraday Soc 49, 696-707] revealed the reasons for the erroneous conclusions reached by Segel and Martin. The errors arise from the failure to take account of fluxes in parallel pathways that connect the two isolated groups of enzyme species existing in quasi-equilibrium with the modifier. 3 A similar failure to take explicit account of parallel pathways in a thermodynamic box that delayed proper appreciation of the form of pH-dependence of k(cat)/K(m) is briefly discussed.