194 EXPERIMENTAL OBSERVATIONS ON 



proceeding in the opposite direction, as, for example, in any of 

 the syntheses by enzymes mentioned on previous pages. Here the 

 reaction slows down also as it nears the equilibrium point, and we 

 might consider the slowing as due to the product of reaction, and 

 state that this combined with the enzyme and removed it from 

 the sphere of action. But for the reaction proceeding from left 

 to right, it is just this combination of enzyme and product of 

 reaction (now substratum) which is regarded as giving rise to the 

 action of the enzyme. It is evident, then, that our explanation 

 must be symmetrical on both sides of the equilibrium point, and 

 that it is better to regard the relationship between enzyme and 

 substratum on the one hand, or cleavage product on the other, as 

 favouring the reaction in a determinate direction in each case, 

 rather than as doing this in one case, and simply inertly removing 

 enzyme in the other. 



Returning to the mathematical consideration of a formula to suit 

 the entire course of the reaction, it becomes clear after the above dis- 

 cussion that in the first place we must not remove the expression 

 k 2 x 2 representing reversibility in those formula) deduced earlier in the 

 work, or there will be experimental obscuration in the later stages 

 increasing as the equilibrium point is neared; and, secondly, that into 

 the portion of each expression which represents the action of the 

 enzyme we must introduce a factor expressing that this action is not 

 constant throughout, but intensifies as the concentration of the sub- 

 stratum diminishes; and here it must be remembered that for the 

 expression k^a - x) the concentration of the substratum is a - x, and 

 for the second expression in the equation of velocity of reaction & 2 2 , 

 the concentration of the substratum is x. In other words, the influence 

 of the enzyme in either direction is not a constant, but is some function 

 of the concentration of the substratum. As a simple approximation 



the factor introduced by Henri f 1 .-f f- J may be used, so that k becomes 



I + eM; only it must be remembered that such a correction equally 



applies to the reversed reaction, and hence instead of k 2 we must put 



k 2 ( 1 - e x - - J, when the equation for velocity of reaction becomes 



dx 



This formula is too complicated for application to experimental results 

 on integration, but it includes all the observed experimental cases 



