260 6. INTEKACTIONS OF INHIBITORS WITH ENZYMES 



IONIC ATMOSPHERE 



The energy involved in ionic interactions in solution must be further 

 corrected for the ionic atmosphere that surrounds each ion. Each ion in 

 the solution attracts ions of opposite charge and, although the ions retain 

 their mobility, there is established an ion distribution the characteristics 

 of which can be predicted by statistical theory. The presence of this ionic 

 atmosphere around an ion alters the electrical field of the central ion and 

 hence the interaction energy. The ionic atmosphere will be contributed to 

 mainly by small ions such as Na+, K+, Cl~, and others. It is evident that 

 the greater the concentration of these ions, the smaller will be the inter- 

 action energy between ionic groups, such as on an enzyme or inhibitor. 

 This situation may be conceived as a competition between the numerous 

 small inorganic ions and the inhibitor ionic group for the enzyme ionic 

 group; as the inhibitor approaches the enzyme, energy is required to dis- 

 place part or all of the ionic atmosphere. 



The electrical potential in the neighborhood of an ion can be shown to be: 



F = ^ -^^ (6-85) 



dD 1 + xTo 



where d is the distance from the ion to the point where the potential is 

 considered and Tq is the closest approach of the ionic atmosphere to the ion. 

 The Debye-Hiickel constant x is given by: 



where n^ is the number of ions per ml, z^ is their charge, and s is the ionic 

 strength. The potential in Eq. 6-85 is actually made up of two separate 

 potentials, one due to the central ion and one to the atmosphere. The 

 potential of an ion will be reduced by the ionic atmosphere and the mag- 

 nitude of this reduction will depend primarily on the ionic radii and the 

 ionic strength. The potential energy of two interacting ions will now be 

 given by: 



rp = ^i^ ^-^ (6-87) 



dD 1 + xTq 



The evaluation of the potential energy requires an estimation of x and r^. 

 At 37.50 and assuming D = 74.1: 



;< =0.332^/71-1 (6-88) 



In most enzyme studies under physiological conditions, the ionic strength 

 s = 0.16, in which case x = 0.133 A"^. The radius of the ionic atmosphere, 



