720 14. EFFECTS OF pH ON ENZYME INHIBITION 



Early work on the interfacial tension of films of the long-chain carbox- 

 ylates or amines showed that the inflections ijroduced by varying the pH 

 did not correspond to the p/C/s of the substances, indicating that the pH 

 in the film may not be the same as in the bulk phase. Danielli (1937) ex- 

 tended these observations and from the assumption of a Donnan equili- 

 brium between the film and the bulk phase calculated that the film pH 

 may be as much as 2 units different than the bulk phase pH. Hartley and 

 Roe (1940) calculated the distribution of ions near particles possessing 

 C-potentials and with respect to ])rotons obtained the following equation: 



{R+), = {R+),e-'^"'^ (14-160) 



where (H+), and (H+)j represent the concentrations at the surface and in 

 the bulk phase respectively and C is the electric potential between the 

 particle and the medium. This can be rewritten as: 



;■ 

 pH, = pHf, + 



62 



where C is in millivolts and the temperature is 37. 5o. Since potentials of 

 50 to 100 millivolts are quite common, it is seen that a significant difference 

 in pH is produced. They applied the theory to studies of amicroscopic mi- 

 celles of surfactant compounds and found for triethanolamine cetane sul- 

 fonate that p^j — pH, was around 1.5 units. The calculations of surface 

 pH values for proteins by either Donnan equilibria or electrokinetic data 

 were shown by Danielli (1941) to give comparable results. A plot of pH, — 

 pHj against pH^ for ovalbumin showed that the surface and bulk phase 

 has the same pH when pHj was 4.8; as pH^, is lowered, the pH, does not 

 decrease as rapidly and hence pH, — pH^ is positive, and upon raising the 

 pH^,, the difference becomes negative. At pH^ = 7, the difference was about 

 0.5 unit. The pH difference, of course, depends on many factors, such as the 

 ionic strength, the concentration of buffers, the amphoteric properties of 

 the protein, and the protein concentration, so that such results cannot be 

 directly applied to the cell. However, they do indicate the magnitude of 

 the effects to be expected. 



What is the importance of this spatial variation in pH for inhibitor stud- 

 ies ? Of greatest significance is the fact that it may lead to a heterogeneous 

 distribution of the inhibitor within the cell, if the inhibitor is a weak acid 

 or base. We have seen that the concentrations of total inhibitor and its 

 ionic forms depend on the pH, in buffered cells. In the same manner, the 

 concentration of inhibitor within any cell compartment will depend on 

 the pH of that compartment. The concentration of active inhibitor may vary 

 from region to region at equilibrium and different degrees of effect will be 

 exerted on the enzymes in these regions. Let us assume that the enzyme with 



