VELOCITY OF REACTION 73 



conception of an " active system " is introduced on the hypo- 

 thesis that the enzyme acts upon a portion of the sugar only 

 at any given time, if S be the total amount of sugar, and s that 

 portion which is in combination with an amount of enzyme e ; 

 " it will be convenient to speak of the combination s + e as the 

 active system." 



The author divides the consideration of the question into four 

 sets of conditions, which may be given in his own words, as 

 follows : 



" Case /., in which, whatever the amount of sugar present, the 

 quantity of enzyme is relatively small. 



" Case //., in which there is a difference from Case I., inasmuch as 

 the quantity of enzyme is relatively considerable. 



" Case III., in which the amount of enzyme diminishes as the action 

 proceeds. 



" Case IV., in which the amount of sugar present is varied. 



" Case I. As hydrolysis proceeds, assuming that the enzyme itself 

 is not affected by the work it does, since the magnitude of the active 

 system depends on the amount of enzyme present, it is obvious that 

 in the initial stages if the total amount of the sugar present S be 

 large compared with s, the enzyme will be in presence of enough 

 sugar molecules to establish the maximum possible number of 

 effective combinations ; or, in other words, the magnitude of the 

 active system will remain constant and the change will be expres- 

 sible, as Brown and Glendinning have pointed out, as a linear 

 function of the time. As hydrolysis proceeds, the amount S of 

 sugar present decreases until it is no longer negligible compared 

 with that of the active part s, and hence the enzyme will no longer 

 effect the maximum possible number of combinations : the propor- 

 tion of sugar s undergoing change will then be a function of the 

 total mass, and the formation of active systems will be governed by 

 the law of mass action. The rate of change will be a logarithmic 

 function of the time. 



"This explanation is fairly in accordance with the observed facts 

 in the case of invertase and diastase, the only enzymes hitherto 

 experimented with, which have always been used in very small 

 quantities. 



" Case IL If, on the other hand, the quantity of enzyme used be 

 relatively large, the active mass will be a function of the total 

 mass from the very beginning of the experiment, so that the linear 

 part of the curve will escape notice. O'Sullivan and Tompson seem 

 to have used a relatively large proportion of enzyme, and therefore 



