17:3/ Enzyme Kinetics of Hydrolytic Reactions 



323 



The foregoing stoichiometric equations can be rewritten as differential 

 rate equations. These are 



j t = k 1 (e-p)x - k 2 p - k 3 p (2) 



j t = -k 1 {e-p)x + k 2 p (3) 



The reaction rate V at which substrate is consumed is defined by 



dx 



V = - j t = k 1 (e-p)x - k 2 p (4) 



These three equations can agree qualitatively with the empirical 

 observations presented in Figures 1-4, provided suitable values are 



+ S 



Very 

 Rapid 



<(> OO Products 



Figure 5. Diagrammatic representation of a hydrolytic reaction 

 according to the Michaelis-Menten scheme. The shapes 

 chosen here are purely for illustrative purposes and have no 

 physical significance. 



chosen for the rate constants k 1 , k 2 , and k 3 . Because, in general, only 

 one measured quantity, namely V, must be fitted by these data, it is 

 perhaps not too surprising that suitable values can be found. If p could 

 be observed directly, this would permit a separation of the constants and 

 add considerable strength to the theory. For the more complex cases of 

 catalase and peroxidase discussed in the next chapter, the intermediates 

 can be observed, but for the hydrolytic reactions the intermediates 

 never have been observed directly. Nonetheless, the success of this 

 theory with the added approximations presented below has led to its 



