Detailed balance conditions for the irreversible cyclic reactions proceeding by a general modifier mechanism

Two kinetic schemes of the general modifier mechanism have been analysed in a quasi-steady state approximation, assuming that the reaction product concentration is negligible (a natural assumption for the initial rate method) and without additional simplifying assumptions. The characteristic equations have been obtained, allowing the calculation of quasi-steady state concentrations of all reaction participants and the initial rate (v0). Calculation algorithms are presented. It has been shown that the initial rate equations derived in the standard way (with the additional assumption that the total enzyme concentration (E0) is much lower than the total substrate (S0) and modifier (M0) concentrations) are identical to the equations obtained in the quasi-steady state approximation without additional simplifications, provided that E0 → 0. The “linearity criterion” has also been introduced, i.e. the limit towards which v0/E0 tends when E0 → 0. Several methods have been presented that allow finding both the conditions for reducing the initial rate equations, and the detailed balance conditions. It has been shown for the first time that more than one detailed balance condition may exist for the same irreversible cyclic mechanism, and that detailed balance conditions may also include quasi-steady state reactant concentrations. A universal detailed balance concept was introduced, which considers fluxes both at reversible and irreversible steps. Only by accounting for all pathways of substance formation and consumption can two balances be maintained simultaneously – the balance for substances and the balance for steps, i.e., ensuring concentration constancy and zero net flux at each composite reaction step