KINETICS OF PROTEIN HYDROLYSIS 401 



If we assume, however, (i) that the ferment does not enter 

 appreciably into combination with the substrate or products 

 and hence does not shift the equihbrium between the protein 

 and its products, (ii) that the products of the reaction do not 

 appreciably depress the velocity of hydrolysis, and (iii) that 

 the reaction of the digest either does not affect the velocity of 

 hydrolysis or is unaltered by its progress, then for a certain period 

 of the hydrolysis, we may regard the transformation as concerning, 

 on the whole, only one molecular species, and the equation 



log -^ = kt (i) 



a — X 



should hold good. 



It will be well, before proceeding further, to clearly understand 

 what is implied in the statement that this equation will hold 

 good for a certain period of the hydrolysis. When the first 

 — COH.N— bond in the protein molecule splits (considering, 

 for the present, only one of the possible parallel reactions, since, 

 in a system of parallel reactions of the same order, the reaction- 

 constants of the different reactions simply add themselves to- 

 gether to produce the gross resultant) a product p, is the result. 

 This product, however, now becomes the substrate for a second 

 reaction involving the splitting of another —COH.N— bond 

 and the production of a second substance p2. Two possibilities 

 now exist. The transformation pi -^ p^ may be specifically more 

 rapid than the transformation p — > pi or it may be specifically 

 less rapid. In either case it will initially be in an absolute sense 

 less rapid than the primary reaction since its substrate-concen- 

 tration is initially zero and, consequently, the absolute velocity of 

 the second reaction will rise until it attains a maximum value, and 

 the combined reactions will then proceed with the velocity and 

 time-relations of the specifically slowest reaction. If this should 

 chance to be the primary reaction then equation (i) will hold 

 throughout; if it should chance to be the secondary reaction 

 then equation (i) will hold after the secondary reaction has attained 

 its maximum velocity but not before. 



The meaning and derivation of equation (i) will be clear when 

 it is recollected that the reaction of protein hydrolysis consists 

 in the addition of a molecule of water to a —COH.N— bond 

 in the protein molecule. In dilute solutions the active mass of 



