MUTUAL DEPLETION SYSTEMS 75 



The designation of zones and the choice of the appropriate equations to 

 be used for a particular inhibition cannot generally be predicted but must be 

 decided upon after sufficient data have been accumulated to characterize 

 the behavior of the system. 



Boundary Conditions for Competitive Inhibition 



From Eq. 3-50 the boundary conditions corresponding to Eqs. 3-40 and 

 3-41 are obtained for competitive inhibition: 



Zone A, — zone Jt5,: = — - -. — :; r (3-o4) 



(S') +1 I (1 - I - Ai)(l - i) 



Zone B, - zone C,: ' = -- -~ r (3-55) 



(o ) + 1 zli 1 — ^ 



so that the same boundaries exist as for noncompetitive inhibition (Fig. 

 3-11) but they refer to (E,)/[(S') + 1] instead of (E/). Since (S') + l wiU be 

 greater than unity (sometimes much greater) and (E/) determines the zone, 

 systems that would be in zone B^ for noncompetitive inhibitors might well 

 be translated into zone A for competitive inhibition. In the experiments of 

 Goldstein on cholinesterase, for example, (S/) was usually 64.4. It is reason- 

 able that competitive systems, compared with noncompetitive, would less 

 likely be in zone B, because binding of substrate to the enzyme reduces 

 the amount of enzyme capable of binding the inhibitor and decreasing the 

 concentration of its free form. 



Steady-State Kinetics of Mutual Depletion Systems 



Throughout the formulation it has been assumed that the Michaelis con- 

 stant is a dissociation constant and the terms (S,)/^, and {'Eii)lK^ have been 

 used. However, if K„^ = {k_^-\-k2)lk-^ it may be substituted for K^ in the 

 equations above, but the specific concentrations do not have their usual 

 significance, since now, for example, (S/) = (S()/iiC„;. Although this does not 

 affect the validity of the theory or the equations, it is important in deter- 

 minations of the individual rate constants from the kinetic data, just as 

 in zone A systems. Indeed, the rate constants for cholinesterase calculated 

 by Goldstein have been shown to be in error by Myers (1952 b) and this pa- 

 per may be consulted for a detailed analysis of the problems involved in 

 such determinations. 



Independence of Zone C Inhibition on K, 



Straus and Goldstein pointed out the very interesting fact that in zone 

 C all inhibitors, whatever their affinities for the enzyme, will produce the 

 same effect. This follows from Eqs. 3-36 and 3-54 which may be written 



