QUANTITATIVE EXPRESSION OF ENZYME INHIBITION 4 ( / 



profiles within such regions. The rate equations are quite complex but 

 the implications for inhibition are clear. For competitive inhibition, since 

 the substrate concentration is not constant throughout the cells, the degree 

 of inhibition varies in characteristic ways from one region of the cell to 

 another. The inhibition in such a case will be greater than predicted from 

 the external substrate concentration, providing the inhibitor penetrates 

 readily into the cells. Noncompetitive inhibitors by reducing the effective 

 enzyme concentration may exert complex effects on the rate when (S) 

 is high relative to K, (see Eq. 9-22), but when (S) is low the increased slope 

 of the Ijv — 1/(S) plot will be identical to that of the enzyme without geo- 

 metrical constraint. The other methods of plotting will frequently result 

 in nonlinearity but the present state of our knowledge would not justify 

 an accurate analysis of these relationships. 



The Factor of Intracellular Concentrations of Substrate and Inhibitor 



The intracellular concentration of an inhibitor may be different from 

 that in the external medium for reasons already discussed. It will now be 

 pertinent to investigate how this may modify the quantitative expression 

 of inhibition. The procedure is simple: the internal concentration, (I,), 

 is expressed in terms of the external concentration, (I^), and is substituted 

 in the equations of inhibition developed in previous chapters. The diffi- 

 culty lies in our ignorance of how to express (I,) in terms of (I^,). There 

 are actually many possible relations. One immediately thinks of the ex- 

 pression (I,) = ''((If) where /•, is simply the ratio of concentrations inside 

 and outside the cell. The fractional degree of noncompetitive inhibition 

 would then be given bv: 



rAle) 



(h 



rAle 



K. 



He 



{K,lr,) 



(9-24) 



When l/r, is plotted against 1/(S). the intercept on the I v axis will be 



1 



1 + 



K. 



and the slope will be 





K. 



Thus by this method one will obtain not K^ but K^jr^ by the usual calcu- 

 lation. The type D plot of l/v, against (I^,) will be linear with the same in- 

 tercept as for a noncellular enzyme (see Fig. 5-3), but the slope will now be 



1 + 





Dividing the intercept by the slope will not give K^ but K^h\. Likewise, 

 the intercept on the (I) axis will now be — K^'r^ instead of — K^. A type 

 F plot will result in a horizontal line but at K.jrj rather than K;. as may 



