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 $$v/\left( {V_{max} - v} \right)$$ versus the reciprocals of the substrate concentrations, where V max represents the maximal velocity. The reaction rate constant of enzyme–substrate–inhibitor complex $$(k^{\prime } /k)$$ can be calculated from the ordinate intercept of the linear relationship between $$v/\left( {V_{max} - v} \right)$$ and the reciprocal of the substrate concentrations at the higher and inhibitory concentrations of the substrate: partial type $$(k^{\prime } /k < 1)$$ of the substrate inhibition gives straight lines intersecting with the ordinate at $$(k^{\prime } /k)/( 1- k^{\prime } /k)$$ , whereas complete substrate inhibition $$(k^{\prime } = 0)$$ yields straight lines converging on the origin. The $$K_{i}^{\prime }$$ value also can be calculated from the slope by using the $$k^{\prime } /k$$ 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.