Analysis of the substrate inhibition of complete and partial types

A simple graphical method was described for determining the kinetic parameters of substrate inhibition of complete and partial types. The method consists of plotting experimental data as $$v/\left( {V_{max} - v} \right)$$v/Vmax-v versus the reciprocals of the substrate concentrations, where Vmax represents the maximal velocity. The reaction rate constant of enzyme–substrate–inhibitor complex $$(k^{\prime } /k)$$(k′/k) can be calculated from the ordinate intercept of the linear relationship between $$v/\left( {V_{max} - v} \right)$$v/Vmax-v and the reciprocal of the substrate concentrations at the higher and inhibitory concentrations of the substrate: partial type $$(k^{\prime } /k < 1)$$(k′/k<1) of the substrate inhibition gives straight lines intersecting with the ordinate at $$(k^{\prime } /k)/( 1- k^{\prime } /k)$$(k′/k)/(1-k′/k), whereas complete substrate inhibition $$(k^{\prime } = 0)$$(k′=0) yields straight lines converging on the origin. The $$K_{i}^{\prime }$$Ki′ value also can be calculated from the slope by using the $$k^{\prime } /k$$k′/k value determined. Validity of the method was confirmed by analyzing the substrate inhibition of phosphofructokinase II from E. coli. The present method provides a simple way for determining kinetic parameters of the substrate inhibition irrespective of complete and partial types.