844 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



AVj* to the formation of the ES* activated complex, and JF2* to the acti- 

 vated complex in the breakdown of the ES complex to products. When the 

 substrate concentration is close to ^,„ or K„^ is (A'g + A-_i)/A"j, the relation- 

 ships are somewhat more complex and intermediate between the extreme 

 situations. These equations may be easily derived by substituting the values 

 for k^ and K^^ obtained from Eq. 15-109 and 15-111. 



The gas constant R = 82.05 ml-atm deg-i mole-^ and thus this value 

 may be used when the pressure is in atmospheres and the volume change 

 in milliliters. The above equations may be written in the general form: 



V PAV 



where AV represents any specified volume change. At temperatures around 

 370: 



V P(atm)JF(ml) n^^^'^^ 



log — = ^^^^^^ (15-117) 



Vo 58,590 



A sample calculation will illustrate the magnitude of the changes to be ex- 

 pected. The electrostriction is about 10 ml/mole for singly charged ions 

 of the type of — C00~ and — NH3+. A reaction involving the appearance 

 of two ionic groups w^ould therefore result in a 20 ml-reduction of the solvent 

 volume. If we assume that this is the major volume change and that the 

 pressure is increased to 500 atm (within a range often used in enzyme 

 studies), the rate is found to increase by a factor of 1.48. The effect of 

 pressure on the binding of an inhibitor to an enzyme may be similarly 

 found, for from Eq. 15-108 we may write: 



PAV 



VK, - p/i. - — r (15-118) 



" 2.303i2r 



If the inhibition involves the appearance of two ionic groups, as above, 

 and the pressure were increased to 500 atm, the pJ^, w^ould be increased by 

 0.17. 



It would be expected that volume changes might be in general correlated 

 with entropy changes if disturbances of the solvent structure are of major 

 significance, inasmuch as the transfer of water molecules from a free to a 

 bound state, or vice versa, is accompanied by entropy changes. For example, 

 if ionic groups are produced in a reaction, the volume will decrease due to 

 the solvent electrostriction; simultaneously there will be a decrease in 

 the entropy because of the immobility imposed on the water molecules. 

 In other words, the volume and entropy changes should be roughly parallel, 

 and this has been found to be true for many reactions, including enzyme 

 catalysis (Laidler, 1958). Pressure studies can, thus, supplement the more 

 classic thermodynamic approaches in probing the movements and fluctua- 

 tions in the electric field during the various phases of a reaction. 



