Larger Intrinsic Rate Constants of Alpha-amylase is Possible if Intrinsic Forward Rate Constant is ≠ Diffusion limited Rate of Encounter

Abstract

Background: Previous research has shown that the intrinsic reverse (backward) and forward rate constants are larger than the effective or apparent rate constants for the formation and dissociation of an enzyme-substrate complex (ES). It is speculated that such intrinsic rate constants could be larger if an appropriate mathematical equation was adopted for their computation. 
 Methods: Theoretical, experimental (Bernfeld method), and computational methods.
 Objectives: 1) To rederive the equations for calculating the intrinsic rate constants for forward (k1) and reverse (i.e., backward) (k2) reactions; 2) to calculate the intrinsic rate constants; and 3) to show that the probability (1/g) (or req(r)) that an enzyme is at a distance from the substrate is a variable. 
 Results and Discussion: The equations for the determination of k2 and k1 were rederived. Unlike previous findings, the intrinsic (reverse) first order rate, k2 and forward second order rate, k1 were larger than their apparent counterparts, but they were, however, very similar in magnitude. The intrinsic rate constants were much larger than previously reported values when the enzyme (E) total concentration [ET] was much less than substrate’s total concentration [ST]. The k1 and apparent forward second order rate (kf) values where [ET] is much less than [ST] were > where [ET] is less than [ST]. Therefore, the magnitude of the second order rate constant is a function of [ET]. The values of k1 and k2 where [ET] is much less than [ST] and vice-versa were respectively, 7.41 exp. (+6) L/mol. min and 81.34 exp. (+4) /min, and 15.76 exp. (+6) L/mol. min and 58.08 exp.(+4) /min. It was discovered that the probability (1/g) (or req(r))) that an enzyme is at a distance from the substrate with the possibility of mutual attraction is not constant. 
 Conclusion: If the intrinsic forward rate constant (k1) is not equal to diffusion limited rate (kD) of encounter, the k1 and k2 values could be larger than values where k1 is equal to kD. The probability (1/g) (or req(r)) that an enzyme is at a distance from the substrate with the possibility of mutual attraction has been discovered to be a variable constant dependent on the concentration of the reaction mixture components and the enzyme's affinity for the substrate, and vice versa. Future research may attempt to derive an equation for the determination of an intrinsic catalytic rate constant for the formation of a product.