540 12. RATES OF INHIBITION 



to derive an expression for the initial rate by differentiating Eq. 12-3 and 

 setting ^ = 0, from which it is found that: 



(dildt)o = aif (12-5) 



It is worthwhile noting that the initial rate of inhibition is directly pro- 

 portional to the final equilibrium inhibition reached. Once the total course 

 of the inhibition is established, it is thus possible to obtain useful data 

 from readings taken for a short period after addition of the inhibitor. In- 

 deed, the early portion of the curve is often more accurate to use inasmuch 

 as secondary effects occasionally distort the course of the inhibition later. 



An approach such as this was applied to the inhibitions of respiration 

 and glycolysis in mammaliam tissues by HgCla and other heavy metal 

 salts in the early work of Jowett and Brooks (1928). They used the equa- 

 tion Vj = ^06"°' and determined the values of a for the various inhibitions. 

 However, it should be pointed out that this equation implies that complete 

 inhibition is eventually reached, so that Eq. 12-1 is generally preferable. 



No certain physical meaning can be attached to the constant a in com- 

 plex systems in which the factors governing the rate of inhibition are un- 

 known, unless it can be proved that the over-all rate measured is propor- 

 tional to the activity of the enzyme upon which the inhibitor acts, in 

 which case a may be related to the true rate constants for the association 

 and dissociation of the enzyme-inhibitor complex as described in the 

 following section. 



If the course of the inhibition is neither logarithmic nor linear with 

 time, and the data cannot be easily represented by any equation, it is 

 necessary to inquire into the best way of presenting the kinetics. The time 

 required to reach a certain chosen degree of inhibition, e.g. 50%, is often 

 given but this is not entirely satisfactory when comparisons are to be made 

 between inhibitors. It is generally true that the early rate of inhibition 

 will bear some relationship to the final inhibition (as shown above for the 

 exponential variation) and thus it is important if two inhibitors are to be 

 compared with respect to the rate of action, that the concentrations of 

 each are chosen so that the final inhibitions produced will be approximately 

 equal. This may be illustrated in Fig. 12-4 showing the experimental 

 curves for two inhibitors acting on the same system. One might be tempted 

 to say that inhibitor 1 acts more rapidly than inhibitor 2 because dildt 

 is obviously greater for the former and the time required to reach 50% 

 inhibition is also shorter. This statement would be true if one were compar- 

 ing the inhibitors at concentrations that gave quite different final inhibitions 

 but this is a dangerous procedure. Actually it is seen that inhibitor 2 pro- 

 duces half of its final inhibition in a shorter time than does inhibitor 1 

 and for this reason might be considered to be the more rapidly acting. This 

 can also be expressed mathematically for the case in which the inhibition 



