SALT CONCENTRATION AND IONIC STRENGTH 821 



A sample calculation will illustrate the magnitude of the effects on 

 inhibition to be expected from variation of the ionic strength. Let us as- 

 sume that the ionic strength is changed from the normal physiological value 

 of 0.16 to 0.5 by the addition of KCl, for which K,^ = 0.0202. From Eq. 

 15-78 it is found that zJp^, will be — 0.10. The noncompetitive inhibition 

 at s = 0.16 for a system with K^= I mM and (I) = 1 mM is 50%. A 

 rise in the ionic strength to 0.5 will increase K^ to 1.26 milf and reduce the 

 inhibition to 44.2%. The effect on competitive inhibition will, in general, 

 be less because there will usually be an increase in K^, i.e., a decreased affi- 

 nity of the enzyme for the substrate. If the above system were competitive 

 and ^^ = 1 mM and (S) = 1 mM, the inhibition would be 33.3%; a rise in 

 the ionic strength to 0.5 would lower the inhibition to 30.7%. The effects 

 of even rather large changes in the ionic strength are quite small, particularly 

 when the range of ionic strength investigated is above 0.1. If the K^ is 1 mM 

 when s = and the ionic strength is increased to 0.16 with KCl, ^TpK^ may 

 be calculated to be — 0.264 and K^ would now be 1.84 mM, a much greater 

 effect than produced by an increase in the ionic strength from 0.16 to 0.5. 



The question may be raised as to whether the substrate and inhibitor 

 constants determined by the usual plotting i^rocedures are actually the 

 classic dissociation constants expressed by Eq. 15-72. If the derivation of 

 the Michaelis-Menten equation is made using activities and the thermody- 

 namic dissociation constants, K, and K, , the equation for the rate is: 



Vi = f 7^:^ ^^ (15-79) 



(S) + K,^ ^ 



YeVs 



1 +-1^ y^^i 



Thus the constants calculated from the analytical plotting procedures, e.g., 

 the \\v against 1/(S) plot, are dependent on the activity coefficients in the 

 way indicated above. 



From these theoretical considerations, some general i^rinciples regarding 

 the optimal approach to ionic strength studies emerge. In the first place, 

 one must be very accurate inasmuch as the changes to be expected are 

 small if the effect is purely related to the ionic strength. Secondly, one 

 should use as wide a range of ionic strengths as is compatible with the en- 

 zyme being investigated. Also it is often better to work at the low range 

 of ionic strengths (i.e., below s = 0.1) because the changes in the dissocia- 

 tion constants and the inhibitions are greater in this range (Fig. 15-17). 

 Finally, as pointed out previously, to eliminate specific ionic effects, it is 

 well to use two or more different salts to vary the ionic strength. 



We turn now to the problem of the effects of salts on nonelectrostatic 

 interactions between molecules. The decrease in the solubility of most non- 

 polar substances with increase in the salt concentration is a well-known 

 phenomenon and is often called the salting-out effect. This is an expression 



