138 GENERAL BIOCHEMISTRY 



and more than one kind of intermediate complex. Moreover, in an 

 equilibrium system such as this, the concentrations of the products 

 affect the reaction rates. Usually it is customary to simplify considera- 

 tion of the rates by examining the reaction under special conditions. 

 In the first place, attention is restricted to initial rates, that is, the 

 rate in the absence of products, and this rate is determined by some 

 method of extrapolating back to the time of mixing of enzyme and 

 reactants. Next, in the many systems involving two or more reactants, 

 it is customary to provide a large excess of all reactants but one. In 

 this way the rate is made to appear proportional to t?lie concentration 

 of the single limiting substrate. 



Actually in the hydrolysis of sucrose in solutions of ordinary con- 

 centration catalyzed by invertase (sucrase) the rate is controlled by 



invertase , , <- " 



Sucrose -\- H2O > glucose -f- tructose 



the concentration of sucrose, and the relatively small changes in the 

 water concentration concurrent with changing sucrose concentration 

 normally have no detectable effect. However, at high sucrose concen- 

 trations, anomalies in the application of the simplified equations 

 occur, apparently because the effective concentration of the water 

 becomes important. When a gas is taken up during a reaction, this 

 dependence of rate on all reactants is even more manifest. In such 

 cases the partial pressure controls the solubility and thus the rate 

 of reaction. 



Regardless of any simplifying assumptions made for mathematical 

 purposes, the rate of reaction depends upon the concentration of 

 enzyme. In some characteristic range of concentration, there is direct 

 proportionality. Above this range the relationship changes until finally 

 further increases in enzyme concentration have no effect on the rate. 

 In this respect an enzyme behaves like an ordinary reactant. 



Assuming that the concentration of only one reactant is limiting, 

 the initial reaction velocity, v, is given by 



A-3[E][S] 

 V = 



A',. + [S] 



where [E] and [S] are the concentrations of enzyme and substrate, 

 respectively, and k^ and K,^ are constants characteristic of the enzyme. 

 Thus, in enzyme-catalyzed reactions the initial velocity is proportional 

 to enzyme concentration and related to substrate concentration. Al- 

 though the constants can be evaluated and are characteristic of the 



