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.

1. The suggestion by Segel & 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 (a) 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 those suggested by Segel & Martin. 2. Examination of residual King-Altman patterns for the general modifier model of Botts & Morales [(1953) Trans. Faraday Soc. 49, 696-707] revealed the reasons for the erroneous conclusions reached by Segel & 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 kcat/Km is briefly discussed.