32 2. THE KINETICS OF ENZYME REACTIONS 



in binding may be reflected in the rate since the concentration of complex 

 (ES) will be determined by this affinity, but otherwise no necessary rela- 

 tionship may be assumed. Thus an inhibitor by reducing the affinity of the 

 enzyme for the substrate may slow the reaction by reducing (ES); on the 

 other hand, it may retard the breakdown of the complex, with or without 

 effect on K^. A reduction in the maximal rate by an inhibitor does not, of 

 course, reflect a decrease in k^ but generally a reduction in total concentra- 

 tion of enzyme active centers, since F,,, = h^i^i)', an increase in K^,^ does 

 not necessarily imply a reduction in affinity unless it is certain that K^,^ = 

 Kg. Thus the usual kinetic analysis is not adequate generally to differentiate 

 between action of an inhibitor on K^ or k.^. For this purpose one of the spe- 

 cial methods of independently determining ko or K^ must be used and applied 

 to both normal and inhibited systems. This has been done only rarely. 

 The more complex the reaction and the more steps it is assumed to include, 

 the more possibilities exist for effects upon a variety of rate processes and 

 equilibria. 



The binding of the activated complex to the enzyme must also be consi- 

 dered since it is the energy and entropy of activation that determines the 

 reaction rate constant. Comparing the over-all reactions: 



A + B ^ AB* ^ C + D 

 A + B + E ;^ EAB* ^ E + C + D 



the energy contributed by the binding in the EAB* complex may be respon- 

 sible for the reduction in activation energy and the accelerated rate. Thus 

 the possible effects of inhibitors on this binding of the activated complex 

 must be considered, the inhibitor in this case raising the activation energy. 



KINETICS OF SOME COMPLEX ENZYME REACTION TYPES 



The purpose in presenting several more complex, but commonly observed, 

 types of reaction is, first, to provide kinetic rate equations that may be 

 applied later in discussing the effects of inhibitors and, second, to emphasize 

 the manifold possibilities in enzyme reactions in order to help disj^erse 

 whatever illusions the reader may have concerning the uniformity of enzyme 

 mechanisms and kinetics. Special and unique reactions will be dealt with 

 in those chapters where the kinetics will be pertinent to inhibition. 



General Procedure For Derivation of Rate Equations 



Rate equations for any type of reaction — including those involving 

 activators, coenzymes, hydrogen ions, inhibitors, multiple substrates, or 

 interdependent active centers — may be derived assuming a steady 



