BOD AN SKY: CHOLINESTERASE 527 



Goldstein. Thus, the log values of /', at i = 0.5 (50 per cent inhibi- 

 tion) are as follows, for various values of E': 



E' log r 



0.1 0.00 



10 0.79 



100 1.71 



1000 2.70 



It may, thus, be seen that dilution of the enzyme influences the £" 

 value, and hence, the extent of inhibition. 



The values of Kj and E may be calculated from the experimental 

 determination of the inhibition, i, at various concentrations, /, of in- 

 hibitor. Equation 5 may be transposed, as follows: 



l = KjX j^. + E (7) 



A plot of - against :j -. should, therefore, yield a straight line, the 



slope of which would be Kj and the intercept on the F-axis would be E. 

 Goldstein'' has also developed an expression for competitive equilib- 

 rium between enzyme, substrate, and inhibitor: 



/' 



total free combined 



Where /' = I/Kr, S' = S/Ks, E'l = E/Ki, 



Es = E/Ks, and a = 1 — z or fractional activity of the enzyme. 



Another type of derivation is possible, if E{, the amount of free 

 enzyme, is considered negligible in comparison with the amount of 

 enzyme combined with inhibitor and substrate. Then: 



/' =iS'-aEs')l- -]^{l-a)Er (9) 



total free combined. 



Various simplifications of equations 8 or 9 are possible, depending 

 upon whether we assume Ej' or Eg- to be small enough to be neglected, 

 or so large that other terms not involving them become negligible. 



The investigations on in vitro inhibition may now be summarized. 

 In TABLE 2, are shown those results which have been formulated, in 

 terms of the dissociation constants of an inhibitor-enzyme complex, in 

 accordance with the equations already discussed. Several points of 

 interest may be noted. First, the dissociation constants of the enzyme 

 complexes of physostigmine and prostigmine are of a low order of mag- 

 nitude, about 10"^ to 10"^, as compared with the dissociation constants 

 of the cholinesterase-morphine derivative complexes, 10"^ to 10~*. The 



