JOHN H. NORTHROP 253 



above (therefore Qd becomes constant) . Since the velocity of hydroly- 

 sis is proportional to Q and to the concentration of substrate the 



dx 

 differential expression for the course of hydrolysis would be — = QA , 



j^i/ ctt 



where A is the amount of substrate. Substituting — - for Q we have 



a 



dx _ ^^^4_ 



dt~ d ^^' 



Since d, the inhibiting substance, is the same as x, the products of 

 hydrolysis, we may substitute x for d. A may be considered a con- 

 stant for the first few per cents of the hydrolysis. In any case, 

 although A is decreasing, the term {E — Q) (which has also been 

 considered a constant in the numerator) is increasing so that the 

 product of the two will be more nearly constant than either of the 

 two quantities themselves. It is this product that really enters 

 into the equation. Substituting x for d in equation (2) and inte- 

 grating we obtain 



^ xdx= Ck" a dt or -x'- = K^T or x = K^i/f 



That is, X, the products formed, is proportional to the square root 

 of the elapsed time. This derivation makes it clear that Schiitz's 

 rule will only hold when the concentration of the products formed is 

 large with respect to the amount of enzyme. The author has 

 shown that the same experiments may be performed with pepsin.^ 

 In the case of these two enzymes, at least, therefore, there is direct 

 experimental evidence for Arrhenius' explanation. 



Effect of Constant Quantity of Inhibitor on Increasing Amounts 



of Trypsin. 



In all the foregoing experiments the concentration of trypsin has 

 been the same in any one series of experiments and the concentration 

 of inhibitor varied. If the mechanism proposed is correct it should 

 be possible to predict equally well the result of an experiment in 

 which the concentration of inhibitor was kept constant and the 

 amount of trypsin varied. That this is the case is shown in Fig. 2. 

 The calculated results for this experiment were obtained by using the 



