174 5. DETERMINATION OF MECHANISMS AND CONSTANTS 



Two Inhibitor Molecules Are Bound to the Enzyme 



There are many possibilities of behavior depending upon the exact mech- 

 anism and only two cases have been illustrated in Figs. 5-15 and 5-16. It 

 is seen that noncompetitive inhibition yields the same type curves as for 

 the simple case of a single inhibitor molecule, but again the slopes and 

 intercepts are different and more complex. The exceptions are types D 

 and E where deviations from linearity may occur. If only the double-reci- 

 procal plot type A is made and simple competitive inhibition is assumed, the 

 determination of K^ is subject to error. If an inhibitor concentration of 0.3 

 mM increases the slope two-fold, K^ would be found to be 0.3 mM assuming 

 only one inhibitor molecule is reacting; however, A', would range from 0.186 

 to 0.486 mM if two inhibitor molecules are involved, depending on the 

 value of ^. It is possible, but laborious, to determine /? from several plots 

 of type A-C at different inhibitor concentrations. The difficulty is in de- 

 termining the values of both a and /? if one is not known; in fact it is unex- 

 pectedly difficult to distinguish between inhibitions with one and two in- 

 hibitor molecules, and cases where there are multiple sites with interaction 

 or intrinsically different A/s are impossible to deal with by the ordinary 

 procedures. Suffice to say that in such cases, even when the kinetics fol- 

 low simple patterns, the determined inhibition constants may correspond 

 to no actual constants. 



Substrate Inhibition 



If the concentration of substrate has not been increased to where inhi- 

 bition is obvious by a definite drop in the rate, this type of inhibition is 

 usually detected in plots of type A by a rise in the curve as it approaches 

 the \jv axis. It is not difficult to calculate a constant for the inhibiting 

 substrate molecule but, as pointed out in the previous chapter, it is not 

 easy to interpret this constant in the general case. Values for 7„, and K^ 

 may be obtained from the slope at lower substrate concentrations and the 

 intercept of the prolongation of the linear part of the curve on the 1/v 

 axis. This V ,,^ is the theoretical maximal rate if substrate inhibition did 

 not occur; the actual maximal rate -^'ocan only be determined experimentally. 

 The value of a in the simplified scheme 4-6 may be calculated from the peak 

 in the rate curve which occurs at (Sq) ^ K, V a . Another method in- 

 volves a plot of llv against (S), for from the reciprocal of Eq. 4-7: 



±=^ + _^- + -^- (5-24) 



V F„. ^ aV„K, ^ F„,(S) 



it is seen that when (S) is high the last term is negligible, the slope at 

 high (S) being l/aF,„A,, and the intercept of this line prolonged on the 



