SALT CONCENTEATION AND IONIC STRENGTH 819 



the thermodynamic activities of the substances. For a simple EI complex : 

 £,= J^=i5><^Z^ (15-71, 



" ttei (EI) yei 



where the y's represent the activity coefficients. K^ is the true thermody- 

 namic dissociation constant of the EI complex. The classic or observed dis- 

 sociation constant is (E)(1) /(EI) which we may designate in the usual man- 

 ner by K^ and thus: 



K,=K.-^^~ (15-72) 



yeVi 



Since an increase in the ionic strength reduces the activity coefficients of 

 ions, it will lead to a rise in the observed K^. The activity coefficients are 

 usually expressed in the simple limiting form of the Debye-Hiickel equa- 

 tion: 



log y = - 0.509z^ VT (15-73) 



where z is the charge on the ion under consideration. Taking the logarithm 

 of each side of Eq. 15-72 and substituting from Eq. 15-73: 



p^, - pZ,„ - 0.509 VTiz; +z] - z'J (15-74) 



Since in most cases, z^^ = z^ + z{. 



pZ, = vKi^ + 1.022,2, \/ 7 (15-75) 



If the charges on the inhibitor and the enzyme active site are opposite, as 

 is usually the case, and are unity: 



vKi = vKi^ - 1.02 vT (15-76) 



A i^lot of the observed i>K^ against \/Y would give a straight line, from the 

 slope of which some idea of the charge on the enzyme site might be obtained, 

 knowing the charge on the inhibitor. 



Although this treatment leads to simple equations that may be readily 

 plotted, it is not accurate enough when the ionic strength is over 0.05, as 

 it is in most studies on enzymes; indeed deviations from Eq. 15-73 appear 

 when the ionic strength reaches 0.01. Therefore, we must use a more refined 

 treatment to express the variation of the activity coefficient. Equation 

 15-68 affords an expression that is reasonably accurate for ionic strengths 

 up to 1 and will be satisfactory for most enzyme work. Substituting from 

 this equation in Eq. 15-72 and assuming that r,, = 4 A, the resulting 

 expression for p^^ is similar to Eq. 15-75 with the corrections for finite 

 ion size and change in the dielectric constant: 



1.022,Zi V S |^nrrJ. 



pKi = pKi H -=^ + K,oS (15-77) 



1 + 1.31 V s 



