MUTUAL DEPLETION SYSTEMS 



69 



Boundary Conditions for Zone Behavior 



It is necessary now to determine for practical purposes the conditions 

 under which zone B and C kinetics should be used, rather than the usual 

 zone A equations. One may do this by establishing the boundaries between 

 the three zones. These boundaries are, to some extent, arbitrary since they 

 depend upon the accuracy desired in the treatment; i.e., zone A kinetics can 

 be used over a wider range if the experiments do not require a rigorously 

 quantitative expression. Straus and Goldstein (1943) determined the boun- 

 dary conditions assuming certain values for the acceptable error in the degree 

 of inhibition obtained from the various equations. They considered values 

 of Ai, the acceptable deviation in i; it might be more generally preferable 

 to consider values of Jiji, which would be a measure of the per cent error 

 at any level of inhibition. The following treatment and the boundary curves 

 obtained thus differ in this respect from those of Straus and Goldstein. 



(E,)- 



FiG. 3-10. Variation of the fractional inhibition with the specific enzyme concen- 

 tration for different inhibitor concentrations. K^ = 10^^ milf. Curve 1: pi = 7; 

 curve 11: pi = 6; curve III: pi = 5. 



The derivation of boundary equations may be done as follows. The general 

 Eq. 3-33 is accurate and actually applies to all zones. Thus if one introduces 

 the acceptable deviation J{ into the special equations for zone A and zone C 

 and equates these, since (I/) is constant, with the general equation, one 

 obtains: 



Zone A - zone B: 



i{E/) 



Ai 



1 



Ai 



(3-38) 



Zone B - zone C: 



1 - i 



+ i(E,') = [i -r Ai){E/) 



(3-39) 



