490 EFFECT OF ENZYME ON DIGESTION OF PROTEINS 



dx _ KE {A - x) 

 dt ~ X 



which on integration becomes 



A 

 Aln X 



—^-^ = K (6) 



ET 



If the foregoing hypothesis correctly expresses the mechanism of 

 the reaction, the results calculated from Schiitz's rule and equation 

 (6) should agree with the experimental results as soon as x has reached 

 a value ten or fifteen times as large as the quantity of active pepsin 

 present. Before x has reached such a value, the results calculated 

 from equation (6) or Schiitz's rule, using the values of K at which 

 they are constant, will be higher than those found by experiment. 

 That is, the value of K in Schiitz's rule or equation (6) increases for 

 the first 10 or 20 per cent of the total digestion. As was pointed out 

 above, this discrepancy is due to the fact that the formulas are de- 

 rived on the assumption that the relative change in the pepsin con- 

 centration is inversely proportional to the change in the peptone 

 concentration, a condition which does not hold until the peptone is 

 present in large excess. After this point is reached both equations 

 should correctly represent the course of the reaction until the changes 

 in substrate become large. After this change in substrate concentra- 

 tion becomes significant Schiitz's rule will no longer hold since there 

 is no term in it that provides for the change in substrate concentra- 

 tion. ^^ Equation (6) should hold {i.e. give a constant value for K) 

 until the end of the reaction, since this equation takes account of 

 the changes in substrate concentration. Table VII and Fig. 5 give 

 the results of an experiment in which the rate of hydrolysis of an egg 



^^ If the substrate concentration is high {i.e. more than 1 to 2 per cent) 

 Schiitz's rule will be found to hold throughout the greater part of the reaction. 

 This is due to the fact that the rate of digestion in concentrated solutions is 

 nearly independent of the substrate concentration. The falling off in the rate 

 of reaction is therefore almost entirely due to the changes in the pepsin con- 

 centration. This change is correctly expressed by Schiitz's rule. In high con- 

 centration of albumin Schiitz's rule therefore fits better than Arrhenius' 

 equation. 



