536 12. RATES OF INHIBITION 



rate determinations of inhibition that certain kinetic data bearing on the 

 nature of the reaction of the inhibitor molecule with the enzyme surface 

 can be obtained. Thus the activation energy of the inhibition, which may 

 be derived from the variation of the rate constant with temperature, can 

 provide some information on the course of the reaction, or the approach 

 of the inhibitor to the active site, and the alteration of the activation energy 

 upon changing the experimental conditions (such as pH or ionic strength) 

 may indicate the physical nature of the energy barriers that must be cross- 

 ed. The number of quantitative studies on inhibition rates is, however, 

 regrettably small and the more recent techniques for the rapid recording 

 of enzyme reactions have not been applied as yet to this problem. 



The rate of inhibition will be designated by dijdt, the change in the 

 fractional inhibition with time. This is usually not constant throughout an 

 experimental period and therefore when comparing two or more inhibitors 

 or comparing the rates of action of a single inhibitor under a variety of con- 

 ditions, a rate constant should be calculated if possible, this constant 

 being of such a nature that it relates the inhibition rate with the concen- 

 trations of reactants, e.g., dildt = A-(E)(S)(I).... The two constants, k and 

 K^, the latter characterizing the final equilibrium state and the former 

 the rate at which this is reached, are fundamental arid adequately describe 

 the quantitative aspects of an enzyme inhibition. 



GENERAL WAYS OF EXPRESSING THE RATE OF INHIBITION 



The time course of inhibition in any system may be expressed either 

 graphically or by equations. The three commonest ways of plotting are 

 shown in Fig. 12-1. Despite the preference of many investigators for plots 

 of type A, these may be considered the least satisfactory because it is very 

 difficult by inspection of such curves to visualize the actual inhibition at 

 any time (since this would involve a comparison of the slopes of the curves 

 at a chosen time) and more difficult to trace the time course of the inhi- 

 bition.* The belief that it is better to plot directly obtained data rather 

 than derived data has no sound basis unless there is a specific reason for 

 indicating the absolute rates. Plots of types B and C are both satisfactory 



* In a study of the rates at which iodoaeetate inhibited respiration of brain tissue, 

 Fuhrman and Field (194.3) presented curves showing the cumulative oxygen uptake 

 against time and stated that this type of plotting has "the further advantage of pre- 

 senting original rather than derived data" compared to plotting inhibition against 

 time. Additional advantages are evident: (1) there is no necessity to waste time cal- 

 culating the results, which can be left to others to do, and (2) the data plotted by this 

 method usually look better, especially if the results have not been obtained very 

 accurately, and hence fewer experiments (sometimes only one) need be performed 

 to give the impression that the results are quantitatively reliable. 



