826 15. EFFECTS OF VAKIOUS FACTORS ON INHIBITION 



Substituting such values in Eq. 15-83 gives: 



log k = log ho + {K,o^ + K,o, - K.ojs (15-93) 



Log k should vary with the first power of the ionic strength instead of with 

 the square root and the effect of ionic strength changes should be much 

 smaller than in ion-ion interactions. Actually, K^^s is usually around 5-10% 

 of the total value of log k in Eq. 15-85. If the {K.^ -f K,„^ — K,gjs term 

 is small compared to unity, it is possible to write as an approximation: 



k = k,{l + 2.303Kso's) (15-94) 



where K' g^ = Kgg^ -f- K^^^ — K,.g^, and k should be proportional to the ionic 

 strength. These relationships have been found to describe the variations of 

 the rate constants of certain organic reactions, such as the attack by hy- 

 droxyl ions on acetals. These types of interactions are probably of fairly 

 frequent occurrence in enzyme catalysis and inhibition, and this is another 

 reason for using the more complete Debye-Hiickel equation. 



When K,,i is not the substrate dissociation constant but the kinetic con- 

 stant, k2lk-i, the dependence on the ionic strength is quite different from 

 that of Kf.. We may write for the individual rate constants: 



k2 = k2 (ES) ^^ (15-95) 



h = A-: (E)(S) -^^^ (15-96) 



where the activated complexes may be identified in the following sequence: 

 E + S ^ Xi ^ ES ^ X2 -» E + P (15-97) 



The Michaelis constant is thus given by: 



ki^ (E)(S) yeysV^^ Kso y^i ^-lo y^i 



Such a Michaelis constant will vary with the ionic strength in a manner de- 

 pending on the activity coefficients of the two activated complexes. These 

 two complexes can certainly have different charges but the direction of 

 the ionic strength effect is more difficult to predict than in the case of the 

 dissociation constant. 



Effects of Changes in the Ionic Strength on Enzyme Reactions 



A number of enzyme kinetic studies in which the effects of increasing 

 the salt concentration appear to be due mainly to changes in the ionic 

 strength will be briefly discussed, particularly from the standpoint of the 



