VARIATION OF ENZYME INHIBITION WITH pH 699 



charge on the ^^'s of ionizing groups on proteins have been treated in sev- 

 eral different ways and we shall utilize these approaches in discussing the 

 effects on K^. 



The total free energy for the formation of the EI complex is given by: 



AF, = AF.r^t + AF,,,, (14-123) 



where zl-f'j,;^ is the intrinsic association energy when the enzyme is in the 

 isoelectric state and AF ^i^^ is the contribution arising from electrostatic 

 interaction with the net enzyme charge. Tanford (1955), postulated that 

 /\Fgigc is proportional to the total net charge on the protein and desig- 

 nated the proportionality factor as 2RTw. Thus: 



AFi = AF,„t + 2RTwz (14-124) 



where z is the total number of charged groups and may be either positive 

 or negative. Substituting RT In K^ for AFi and RT In K^ for JF^,^^ and 

 solving for K^: 



Ki = K] e^"'^ (14-125) 



K° is the inhibitor constant for the isoelectric enzyme and K^ is the inhi- 

 bitor constant when there is a net charge on the enzyme. 



A convention must be adopted with regard to the sign of z in applying 

 these equations to inhibition. For acidic dissociation there is no problem 

 because the proton is always positively charged and the true sign of z 

 will indicate whether K^ is larger or smaller than K°^. However, an inhi- 

 bitor may be negatively charged and the opposite effects would be expected. 

 Thus we may formulate the following rule: when the charges on the inhi- 

 bitor and the enzyme are of the same sign, z is positive, and when the char- 

 ges are of opposite sign, z is negative. Thus for a negatively charged inhi- 

 bitor and a positively charged enzyme (on the acidic side of the isoelectric 

 point), 2 will be negative and, from Eq. 14-125, it is seen that K^ will be 

 smaller than A^, as anticipated. It may also be noted that the sign conven- 

 tion in Eq. 14-124 is different from that of Tanford because the free energy 

 changes here are related to the formation rather than to the dissociation of 

 the EI complex. 



These equations cannot be applied until the electrostatic factor, w, 

 is defined and determined in some way. The definition of w is such that 

 2RTwz is the electrostatic energy involved in bringing a unit charge from 

 infinity up to the enzyme. The value of w was expressed by Scatchard 

 (1949) in terms of the Debye-Hiickel theory as: 



~ - -^ 1 (14-126) 



1 + xa 



