526 ANNALS NEW YORK ACADEMY OF SCIENCES 



Where v' is the velocity in the presence of the inhibitor, v in its ab- 

 sence, I is the concentration of the inhibitor, and Kj is the dissociation 

 constant of the enzyme-inhibitor complex. 



If the inhibition is competitive, then the following expression holds: 



^ + A'/ 1 + 



(-i) 



where the terms have the meanings as described in equations 1 and 3. 

 Kj may be calculated from the value of the dissociation constant, K's, 

 in the presence of a constant concentration of inhibitor, as follows: 



K: = ^r^— (4') 



The Michaelis-Menten derivation is based on the assumption that 

 the concentration of enzyme centers is constant and, as compared with 

 the concentration of any substance with which it could combine, so 

 small that it may be neglected. Recently, Straus and Goldstein," 

 elaborating upon the ideas of Easson and Stedman,^^ have submitted 

 a more general formulation for the effect of an inhibitor, which takes 

 into account those possibilities in which the concentration of enzyme 

 centers may not be negligible. In the presence of a large excess of 

 substrate, 



/ = ^. + iE . (5) 



1 — I 



total inhibitor free inhibitor bound inhibitor 

 where I is the concentration of total inhibitor, combined and free ; i is 

 the fraction of total enzyme combined with inhibitor; E is the concen- 

 tration of total enzyme; and Kj is the dissociation constant of the 

 enzyme-inhibitor complex. When the above equation is divided by Kj, 

 the following expression is obtained: 



/' - ^. + iE' (6) 



where /' = I/Kj and E' = E/Kj. 



Simplifications of these equations are possible, under conditions 

 where E' is very small, or very large, so that the other term on the right 

 hand side of the equation may be neglected. 



The implication of equation 6 is that the degree of inhibition de- 

 pends upon the value of £", namely, the ratio of the concentration of 

 enzyme centers to the dissociation constant of the complex. This may 

 be illustrated by taking values from a theoretical plot by Straus and 



