98 3. KINETICS OF ENZYME INHIBITION 



The inhibition is thus less than for the usual competitive situation where 

 the inhibitor is stable and, since VJV, = kjjk,, the reduction factor in 

 the numerator is [1 + 1/(S')] kjk,. If the ratio kjkg is quite low, as it of- 

 ten is, the behavior approaches that of typical competitive inhibition. 

 However, k^ may be comparable to k^, or even greater, in which case it is 

 better to consider both reactants as substrates, since the inhibition Eq. 

 3-99 will not apply, the over-all rate being greater than for substrate. 

 In fact,Eq. 3-99 is valid only when k,lk, < (S')/[(S') + 1]. 



The ratio KjIKg may sometimes be determined by measurements made 

 on the maximal rates. If (I) = (S), Eq. 3-98 leads to an expression for the 

 maximal rate in the equimolar mixture: 



F,„ = [VJK, - V^IK,] / [IIK, + I IK,] (3-100) 



from which it follows that: 



K V - V 



(3-101) 



and thus the ratio of the affinities may be calculated from determinations 

 of the maximal rates with substrate alone, inhibitor alone, and both in 

 equimolar proportions. 



An interesting example of such inhibition is provided by sweet potato 

 phosphatase where various combinations of glycerate-3-phosphate, pyro- 

 phosphate, phenyl-phosphate, ATP, and other phosphates give kinetics 

 in accord with the treatment above (Ito et al., 1955). All of these substances 

 give values of K, or K^ in the same range and compete with one another 

 for the same active center. 



SOME FACTORS OCCASIONALLY IMPORTANT IN 

 INHIBITION 



Many factors may modify the formulations of inhibition kinetics as they 

 have been presented in this chapter. Of particular importance are pH, ion- 

 ic strength, buffer effects, temperature, purity of the enzyme, and similar 

 factors; these will be considered in Chapters 14 and 15. However, there are 

 some aspects which may profitably be discussed at this point. 



The Enzyme Becomes Progressively Inactivated during the Reaction 



The determination of reaction rates and inhibition requires measurement 

 of some quantity over an interval of time, occasionally only a few minutes 

 but often an hour or longer. During this interval the enzyme may be pro- 

 gressively inactivated either spontaneously or as the result of secondary 



