1904] 



Studies on Enzyme Action, 



513 



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 com- 

 binations : the proportion 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 II. — 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 

 change will escape notice. O'Sullivan and Tompson seem to have used 

 a relatively large proportion of enzyme, and therefore it is easy to* 

 understand why they found the action of invertase to follow the 

 logarithmic law, whilst subsequent observers using relatively small 

 quantities of enzyme have noted departures from this law. 



Case III. — When the amount of the enzyme does not remain constant 

 but for some reason decreases, the magnitude of the active system will 

 not only be a function of the amount of sugar but also of that of the 

 enzyme ; it will therefore be represented by an equation of the second 

 order, in which both of two interacting substances decrease — as, for 

 example, is the case in the interaction of an alkali and methylic 

 acetate. Such an expression corresponds to a curve falling off from a 

 logarithmic curve and therefore giving a series of decreasing values 

 for K when this is calculated for the simple logarithmic law. In such 

 a case, the change in its early stages will still be a linear function of 

 the time, as the diminution in the amount of enzyme will not at first 

 materially influence the magnitude of the active system. 



Stated shortly, the ordinary equation of mass action 



§ = K( S-.,), 



where S is the total sugar and x the amount changed in time t r 

 is applicable - only to the period during which a constant relatively 

 large proportion of enzyme is present together with a continually 

 decreasing amount of sugar but uninfluenced by the products of 

 change. 



During the final period, when the products of change exercise an. 

 influence by withdrawing enzyme from the sphere of action, 



| = K(S 



