The determination of the binding constant of metalloenzymes for their active site metal ion from ligand inhibition data: Theoretical analysis and application to the inhibition of thermolysin by 1,10-phenanthroline

An equation is found relating the fractional activity, (v/v₀), of an enzyme assay mixture to the total concentrations of metalloenzyme, active site metal ion, metal-binding ligand and substrate and the stability constants of the complexes present. When (v/v₀) is measured as a function of the total ligand concentration, this equation offers a way of data-plotting which yields straight lines and permits the calculation of the metal-binding constant K_ME from either the slope or the intercept, provided that mixed complexes (enzyme-metal ion-ligand) do not contribute significantly to the change in (v/v₀). Since deviations from linearity occur in the latter case, the proposed inhibition plot serves as a diagnostic tool for the recognition of such complexes. Application to the inhibition of thermolysin by 1,10-phenanthroline gives a value of 2.1 × 10¹¹m⁻¹ for K_ZnE, the binding constant of the active site zinc ion, at pH 7.50, 25°C and ionic strength 0.1. The equation also allows the rapid calculation of the ligand concentration necessary to attain a desired degree of inhibition when the total enzyme and active site metal ion concentrations of the solution are known.