ON CHEMICAL REACTION RATES; ENZYMES 



205 



that obtained by measuring rates at various concentrations of substrate and 

 enzyme. 



The "catalyst law" (for enzymes, the Michaelis-Menten expression) rear- 

 ranges to 



[S\ 



W£]„ - K 



eq 



from which it is seen that the slope of a plot ofv/[S] vs v gives K (= 1/A" m ) 

 directly as the negative of the slope. Figure 8-7 is such a plot for the hy- 

 drolysis of a particular dipeptide for which the stomach enzyme, pepsin, is a 

 specific catalyst. The value of K m obtained is 0.0014 moles liter -1 . This 

 result is typical. The inverse, the value of K at 25°, will usually be found 

 to be between 100 and 600 liters/mole, which means that the substrate must 

 be in excess 100- to 600-fold over the enzyme if the catalyst is to be more 

 than 90 per cent complexed (i.e., "worked hard") at all times. 



There are cases (certain chymotrypsin-catalyzed reactions, for example) 

 in which the binding of the complex is much stronger. By contrast, the 

 myosin-adenosine triphosphate complex, formed during muscle contraction 

 is relatively a very weak complex .... The value of K m is numerically equal 

 to that value of the substrate concentration at which one-half the enzyme 

 molecules are tied up as complexes. Electrical attractions and repulsions 

 as well as the geometry of the molecules E and S determine the extent of 



K eq = 700 



Figure 8-7. Determination of the Binding Constant of the Intermediate Complex in a 

 Catalyzed Reaction (pepsin-catalyzed hydrolysis of carbobenzoxy-glutamyl-tyrosine 

 ethyl ester, a dipeptide). Values plotted are those of initial rates found experimentally 

 for six different initial concentrations of substrate. 



