RATES OF INHIBITION OF PURE ENZYMES 559 



occurring at a molecular level as the inhibitor approaches and contacts the 

 enzyme. Very few data are at present available. The subject will be treated 

 here in a rather cursory fashion for this reason but it is believed that this 

 approach in the future will be necessary to solve some of the problems con- 

 nected with the forces occurring between enzyme and inhibitor molecules. 

 It is also of some interest to examine the thermodynamic quantities that 

 determine the rate of inhibition. 



The inhibition rate constant is given in transition state kinetics as: 



IcT kT 



k, = -— e-<J^*/-R?') = e-(-'ff*/«7') g(Js*//2) (12-39) 



h h 



where k is the Boltzmann constant (1.38X 10-^^ erg deg-^), h is the Planck 

 constant (6.624 x lO"-' erg sec), and AF*, AH*, and AS* all refer to the 

 activated state EI*. The rate constant thus depends upon the change in 

 free energy involved in the formation of the activated complex from the 

 individual components. Therefore, just as in the formation of the normal 

 complex, EI, as discussed in Chapter 6, the rate will depend upon changes 

 in both enthalpy and entropy. Equation 12-39 may be rewritten as: 



Ji- \S* \H*' 



l„i,^l„^H-l„r+— -^ <12-40) 



AS* AH* 



log ^, = 10.32+ log r + ^^ -^^ (12-41) 



A plot of log ki against l/T will, therefore, not be strictly a straight line 

 but over the limited range of temperatures possible for enzymic study it 

 will show so little curvature that it may be neglected. The slope may be 

 obtained by differentiating Eq. 12-41: 



slope ^ iO^iM ^_JH^ __ ^ ,12-42) 



^ da IT) 2.SR 2.3 



and from this the enthalpy of activation, J^*, may be calculated. A typ- 

 ical plot is shown in Fig. 12-19 for an inhibition in which AH* is 15 kcal/ 

 mole and J»S'* is 5 cal/mole/deg. The linearity over this temperature range 

 is evident and is due to the relatively small contribution of the T/2.3 term. 

 The relation between the enthalpy of activation and the apparent energy 

 of activation, as determined by the commonly used method of Arrhenius, 

 is easily shown. Arrhenius assumed the rate constant to be expressed by: 



k,=Aexp{- -^1 (12-43) 



