268 



1.0 



6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



T 



6 KcaL/mole 



Fig. 6-15. Variation of the fractional inhibition with the free energy of interaction 



between the enzyme and the inhibitor (Eq. 6-102). Curve A: (I)/x = 0.1; curve B: 



(I)/x = 0.01; curve C: {l)/x = 0.001; curve D: (I)/x = 0.0001. 



Determination of Relative Interaction Energies 



The over-all free energy change may be calculated from the value of K^ 

 but this usually includes energy terms other than for the direct interaction 

 of enzyme and inhibitor. These other terms, such as for the displacement 

 of water or ionic atmosphere, are difficult to evaluate accurately. Thus it is 

 generally impossible to derive a value for the enzyme-inhibitor interaction 

 alone. However, it is often this energy that is of the most significance in 

 deriving accurate spatial relations of the binding and evaluating the spe- 

 cific contributions of various groups on the inhibitor. Although it is not 

 always possible to obtain an absolute value for this interaction energy, 

 one can occasionally determine with sufficient accuracy the relative bind- 

 ing energies of two or more related inhibitors and attribute these differences 

 to variations in the properties of the inhibitors. 



Let us consider two structurally related competitive inhibitors. From 

 the relations: 



AF, = 1.422 log K, JF, = 1.422 log K, (6-103) 



K. 



di) (1 - ^^) 



Ki. 



(I2) (1 - ^2) 



(6-104) 



