Linear relationships between the ligand binding energy and the activation energy of time-dependent inhibition of steroid 5alpha-reductase by delta 1-4-azasteroids

The inhibition of steroid 5alpha-reductase (5AR) by Delta(1)-4-azasteroids is characterized by a two-step time-dependent kinetic mechanism where inhibitor combines with enzyme in a fast equilibrium, defined by the inhibition constant K(i), to form an initial reversible enzyme-inhibitor complex, which subsequently undergoes a time-dependent chemical rearrangement, defined by the rate constant k(3), leading to the formation of an apparently irreversible, tight-binding enzyme-inhibitor complex (Tian, G., Mook, R. A., Jr., Moss, M. L., and Frye, S. V. (1995) Biochemistry 34, 13453-13459). A detailed kinetic analysis of this process with a series of Delta(1)-4-azasteroids having different C-17 substituents was performed to understand the relationships between the rate of time-dependent inhibition and the affinity of the time-dependent inhibitors for the enzyme. A linear correlation was observed between ln(1/K(i)), which is proportional to the ligand binding energy for the formation of the enzyme-inhibitor complex, and ln(1/(k(3)/K(i))), which is proportional to the activation energy for the inhibition reaction under the second order reaction condition, which leads to the formation of the irreversible, tight-binding enzyme-inhibitor complex. The coefficient of the correlation was -0.88 +/- 0.07 for type 1 5AR and -1.0 +/- 0.2 for type 2 5AR. In comparison, there was no obvious correlation between ln(1/K(i)) and ln(1/k(3)), which is proportional to the activation energy of the second, time-dependent step of the inhibition reaction. These data are consistent with a model where ligand binding energies provided at C-17 of Delta(1)-4-azasteroids is fully expressed to lower the activation energy of k(3)/K(i) with little perturbation of the energy barrier of the second, time-dependent step.