Parabolic inhibition in monosubstrate reactions

In addition to hyperbohc inhibition, we may also encounter different parabolic types of inhibition. In such cases, the family of straight hues in primary plots i/Vo versus 1/A, at different fixed concentrations of an inhibitor, have or will not have a common intersection point to the left of the vertical axis. However, in each case, the replot of Slopei/A and/or Intercept,/a function from the primary plots versus increasing / will be a nonlinear parabolic function (Rudolph, 1979 Fromm, 1995). 

In this case, we shall revert again to monosubstrale reactions in order to obtain a simple kinetic expressions and to facilitate the explanation of parabolic patterns. 

Parabolic types of inhibition may take several forms. They can be parabolic competitive, 5-linear /-parabolic noncompetitive, 5-parabolic /-linear noncom petitive, or 5-parabolic /-parabolic noncompetitive. The general rate equations for these four types of inhibition are 

Consider the first case, a parabolic competitive inhibition. This case occurs in a monosubstrate reaction in which an enzyme can bind two molecules of the same competitive inhibitor, in a random manner at different sites (Yonetani, 1982). The binding of I at either site is sufficient to exclude the substrate. 

The rate equation for this case, derived from rapid equilibrium assumptions, is  

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