A Mathematical Analysis of the Substrate Effect Observed in 3β-Hydroxysteroid Dehydrogenase Reactions of Rat Testicular Microsomes

Abstract

The substrate effect in enzyme reactions has been explained mostly in terms of an additional substrate binding site on the enzyme other than the catalytic site. A rate equation for the reaction is introduced according to the steady state mechanism as follows: v=(Ps³+Qs²+Rs)/(s³+Ls²+Ms+N), where the six parameters, L, M, N, P, Q, and R, can be determined by the least-squares method from the experimental points. The v vs. s curve has an asymptote parallel to the s abscissa, and can be classified into one of four types. The type A curve has an intersection with the asymptote and an apparent maximum velocity; the curve descends toward the asymptote. Type B has no intersection and no stationary point; the curve ascends toward the asymptote. Type C has two intersections and two stationary points, an apparent maximum velocity and a minimum velocity; the curve ascends toward the asymptote. Type D has no intersection and two stationary points; the curve ascends toward the asymptote. The equation was applied to the 3βhydroxysteroid dehydrogenase [EC 1.1.1.145] reaction of rat testicular microsomes. The conversion of 3β-hydroxyandrost-5-ene-17-one was represented by type C, with an apparent maximum velocity of 0.338 nmole/min/mg protein at 0.912 μM of the substrate concentration, minimum velocity of 0.108 nmole/min at 16.6 μM, and saturating velocity of 0.169 nmole/min at infinite concentration of the substrate. The conversion of 3β-hydroxy-pregn-5-ene-20-one was of type B, having two inflexion points, 0.320 nmole/min at 2.735 μM and 0.814 nmole/min at 12.39 μM, and a saturating velocity of 3.80 nmoles/ min at infinite concentration of the substrate.