182 



5. DETERMINATION OF MECHANISMS AND CONSTANTS 



are simplified. Even for partially competitive or partially noncompetitive 

 inhibitions, however, calculations must be based on plots made at different 

 inhibitor concentrations, or results from two or more types of plotting. 

 It has already been pointed out that the type E plot of Iji against 1/(1) 

 is particularly useful for calculation of a or /5 in cases of partially com- 

 petitive or noncompetitive inhibitions since the intercepts involve only 

 a or /? and known quantities. 



Determination of K^jKj 



It is frequently of interest, especially in competitive inhibition, to know 

 the relative affinities of the enzyme for substrate and inhibitor, inasmuch 

 as any estimation of comparative binding energies, to relate with the struc- 

 ture or topography of the active site, depends upon an accurate determi- 

 nation of the ratio KJKj as discussed in Chapter 3. It is usually easy 

 to determine the ratio K^JK- where K- represents a calculated inhibition 

 constant that need not correspond to the true dissocition constant of the 

 EI complex. Thorn (1953) has outlined three methods applicable to com- 

 petitive inhibition. 



{a) The values of K^,, and K^ may be determined separately by the plot- 

 ting procedures previously described and the ratio of them secondarily 

 calculated. 



(b) The ratio may be determined directly by rearranging the rate Eq. 3-12 

 for competitive inhibition to: 



F,„ , a;„ a',„ (I) 



(S) + K, (S) 



= 1 + 



(5-30) 



and plotting F,„/^i against (I) at constant substrate concentration, from 

 the slope of which the ratio of the constants may be obtained. This is es- 

 sentially type D plotting as described above (Fig. 5-1 D). 



(c) An approximate method involves transformation of Eq. 5-30 as 

 follows: 



F„ 



1 + 



Km 



+ 



_JUI)_ 



F™A',(S) 



+ 



Km{\) 



VmKA^) 



(5-31) 



where v is the rate in the absence of inhibitor. The ratio is thus found to be: 



1 



K,n ^ (S) r V 



K, (1) L^'^ 



when (S) is sufficiently high so that v is approximately equivalent to V 

 This can also be written as: 



K,n _ (S) "_ 



Ki 'il) [l 



5-32) 



(5-33) 



