KINETICS OF PROTEIN HYDROLYSIS 



409 



regain the monomolecular formula. If /Sa^ is large in comparison 

 with 1 and a is small then we obtain the relation 



log 



a 



x^ 



kF 



a- x'^ a^ 2 a} fio?^' 



(x) 



which, when x is small, yields the relation: 



kFt (equation (iii)). 



X 



a 



It is obvious from equation (vii) that if the velocity constant 

 k were to be calculated from the monomolecular formula through- 

 out the reaction of hydrolysis, k would tend to fall off as hydrolysis 

 proceeded, i.e., as x increased, and also, it will be evident, even 

 for small values of x the constant would decrease with increasing 

 initial substrate-concentration. This obviously accords with the 

 facts observed. 



The way in which the relationship expressed in equation (ix) 

 may simulate the monomolecular formula, the Schiitz rule, etc., 

 under certain conditions, is very well shown by the following 

 table. The values of t corresponding to various values of x 

 are calculated from formula (ix) on the assumption that a = 10 

 and that ^„ _i_ ^^ « ]^p 



a-\- fia 



/3 



= 1. 



1 - /3a2 2 (1 - ^a?) (1 - fia^) 



From these values of t and the given values of x are calculated 

 the constants corresponding to the law of direct proportionality 

 between the quantity digested and the time, to the Schiitz rule 

 {t = kx^) and to the monomolecular formula: 



1.144 

 1.244 

 1.545 

 2.046 

 3.049 

 4.051 

 5.055 

 6.060 

 7.066 

 8.075 

 9.087 

 9.889 



k = 



l2 



11.44 

 6.22 

 3.09 

 2.05 

 1.52 

 1.35 

 1.26 

 1.21 

 1.18 

 1.15 

 1.14 

 1.21 



logK 



26.0 



28.3 



34.6 



44.5 



62.9 



78.4 



91.1 



100.7 



106.5 



108.1 



104.0 



89.0 



