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

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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.