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 + H 2 N- + FF 



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

 reaction : 



(D) FF + H 2 <= 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 (0) to x 2 . 



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) 



tt 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 7 / \ / -\ 



37 = 1-1 1 \ k(a x), (vi) 



dt I + 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 



l + 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 



