KINETICS OF PROTEIN HYDROLYSIS 407 



So far we have, in essentials, made only two assumptions, the 

 one the original assumption that the ferment acts as a "carrier" 

 of water, the other that one molecule of ferment reacts with one 

 -COH.N- bond. 

 Combining the above two equations we obtain : 



(C) -COH.N- + HFFOH = -COOH + H2N- + FF 



from which it is evident that the point of equilibrium in the 

 reaction : 



(D) FF + H2O ^ HFFOH 



must be shifted in some measure towards the left by the presence 

 of the substrate and the extent of this shift must bear a constant 

 proportion (a) to (a — x). But this equilibrium must also be 

 shifted towards the right by the presence of the products of the 

 hydrolysis of the protein, and this shift must bear a constant 

 proportion (/3) to x^. 



Let us now analyse the physical meaning of Henri's equation. 

 This equation, as we have seen in Chap. XV, may be written: 



log {- ax = kFt, (v) 



a — X 



in which a and k are constants and F is the total mass of ferment 

 present in the system. 



Differentiating this equation we obtain: 



dx F 



-TT = rn — 7 ^ k{a — x), (vi) 



at 1 + a (a — x) ^ ^ 



which means that the actual "active mass" of the proteolytic 

 ferment, that proportion, namely, which accelerates the hydrol- 

 ysis by multiplying the velocity-constant, is not F but 



F 



■ • 



1 -\- a{a — x) 



In other words, the process of combination between the ferment 

 and the substrate and its products which Henri depicts, results 

 in the inactivation of a certain constant proportion of the ferment 

 by each molecule of the substrate. The mechanism of this will 

 be clear from equation (C); by the same equation it will also 

 be clear that a proportion of the ferment is at the same time 

 activated (rendered available for the acceleration of the hydrolysis). 

 The quantity of ferment thus activated must evidently bear a 



