44 2. THE KINETICS OF ENZYME REACTIONS 



where k is the rate constant for the formation of products from the complex, 

 Ki and K2 are dissociation constants for the complexes of substrate with 

 its own site and the water-site respectively, F,„ = k(Ei) ^2/(^i+-^2) ^^^ 

 K^ = Ky K^liK^+K^. Such a mechanism leads to inhibition at high sub- 

 strate concentrations since both sites are predominantly occupied by urea, 

 and water cannot enter into the reaction. Equation 2-64 is plotted in Fig. 2-8 

 to illustrate how relative values of the ^'s affect the dependence of the rate 

 on the substrate concentration. The degree of inhibition increases, of course, 

 with the increasing affinity of the water-site for the urea. 



lOOOmM 



Fig. 2-8. Rate plots for an enzyme reaction involving two substrates, one of which 

 is the solvent (Eq. 2-64). F,„ = 100. Curve 1: i^i = 1 mM, K^ = OO; curve 2: Xi = 1 

 mM, K^ = 100 mil/; curve 3: A'l = 1 mM, K^ = 10 mM; curve 4: Ky = 1 mM, 



K, = 1 mM. 



The most direct evidence for a specific water-site has come from a study 

 of myosin ATPase where the activity of water relative to methanol in 

 the splitting of adenosine triphosphate (ATP) is perhaps greater than 1000. 

 Since the activities in non-enzymic splitting are comparable, it is possible 

 that an active center capable of binding water much more tightly than 

 methanol exists on this enzyme; however, other explanations, such as a 

 site for hydrated ATP, are tenable (Koshland and Herr, 1957). The general 

 importance of a specific water-site for inhibition kinetics lies in the possi- 

 bility that certain inhibitors affect or compete for this site instead of the 

 site binding the ordinarily considered substrate. 



When water enters into a hydrolytic reaction sequence, it is necessary 

 to include it in the kinetic expressions. For example, in the reactions pos- 



