THE NATURE OF ENZYME ACTION 293 



certain products of the reaction, it is possible to frame a mathe- 

 matical expression which not only includes the above three 

 stages of the hydrolytic part of the reaction, but also a stage of 

 zero change at the equilibrium point and a reversed velocity 

 beyond this point. The expression is undoubtedly a complex 

 one, although capable of simplification in particular cases. It 

 is, moreover, satisfactory to find that such an equation can be 

 formed on the basis of experimental data. 



Concentration of Enzyme. 



When we come to consider the various influences that are 

 capable of changing the rate of a reaction as catalysed by 

 enzymes, the first point that suggests itself is, how is this 

 velocity related to the amount of enzyme present ? We have 

 already seen that in the case of inorganic catalysts it has been 

 shown that the final equilibrium point is unaffected by the 

 amount of catalyst present. The time taken to reach this point 

 is alone affected. With regard to enzymes, it has been shown 

 by Croft Hill that the same law applies to the case of maltase, 

 and by Visser that it applies to invertase and emulsin. 



Various statements have been made from time to time with 

 respect to the relation of the concentration of enzyme to the 

 rate of the change produced by it. Indeed, when we consider 

 the different states of affairs in the three stages of the reaction, 

 we understand the cause of the disagreement amongst observers 

 as to this question. The relation cannot, in fact, be the same 

 at all stages of the reaction. In the first stage, so long as the 

 enzyme is in small proportion to the substrate, the rate of 

 change is in direct proportion to the amount of enzyme present ; 

 in the second (logarithmic) stage the ratio is some exponential 

 function of the enzyme concentration, so that when this is 

 doubled, for example, the rate of change is not also doubled, 

 but is usually multiplied by about 2^ to 2*; whereas in the 

 last stage, in which the enzyme is in excess, it is clear that the 

 rate of change will be independent of the amount of enzyme 

 present. These facts come out quite unmistakably in the cases 

 in which they have been looked for, such as lactase (E. F. Arm- 

 strong, trypsin (the present author), and others. The bearing 

 of the exponential function of the second stage on the nature of 

 the combination' between enzyme and substrate will be seen 

 later. 



