488 EFFECT OF ENZYME ON DIGESTION OF PROTEINS 



If the simplest case is considered in which there is no peptone present 

 at the beginning of the reaction the concentration of peptone at any- 

 time is X (since d is 0) and the formula becomes 



X 



This value for Q may now be substituted in equation (4) which 

 becomes 



dx _ KE{A - x) 

 at X 



in which A is the concentration of substrate at the beginning of the 

 reaction and x is the amount of substrate decomposed (or of peptone 

 formed) at the time T. For the first part of the reaction the value 

 of (A — x) will not differ much from the value of A and the equation 

 may be still further simplified to 



dx _ KEA 

 dt X 



which states that the rate of digestion at any moment is directly 

 proportional to the enzyme concentration and the substrate concen- 

 tration, and inversely proportional to the amount of substrate de- 

 composed. K in this equation is a new constant equal to the pro- 

 duct of k, the velocity constant, and K (equation (4)), the equilibrium 

 constant. This equation, as has been pointed out by Arrhenius,^^ 

 is the differential form of Schiitz's^^ rule, since on integration it 

 becomes 



TKEA = a;2 or x = K \/tEA 



That is X, the quantity of peptone formed, is proportional to the 

 square root of the time, the concentration of pepsin, and the con- 



^® Arrhenius, S., Medd. Kong, vetsakad. NobelinsL, 1908, i. An equation sim- 

 ilar to this but containing x ^ was found by Bodenstein and Fink (Bodenstein, 

 M., and Fink, C. G., Z. physik. Chem., 1907, Ix, 1) to represent the rate of oxi- 

 dation of SO2 in the presence of platinum. Dernby, K, G., Z. physiol. Chem., 

 1914, Ixxxix, 425. 



^^ Schiitz, E., Z. physiol. Chem., 1885, ix, 577. 



