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

Ikechukwu I. Udema *

Department of Chemistry and Biochemistry, Research Division, Ude International Concepts LTD (RC: 862217), B. B. Agbor, Delta State, Nigeria.

*Author to whom correspondence should be addressed.


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.

Keywords: Aspergillus oryzea alpha-amylase, apparent rate constants, larger intrinsic rate constants, intermolecular electrostatic potential energy, the probability of intermolecular distance

How to Cite

Udema, I. I. (2022). Larger Intrinsic Rate Constants of Alpha-amylase is Possible if Intrinsic Forward Rate Constant is ≠ Diffusion limited Rate of Encounter. Asian Journal of Chemical Sciences, 12(3), 1–14.


Download data is not yet available.


Udema II. A two-part approach to the determination of intrinsic rate constants of an alpha- amylase catalysed reaction. Asian J. Chem. Sci. 2020;8(2):8-21.

Schurr JM. The role of diffusion in bimolecular solution kinetics. Biophys. J. 1970;10:700-716.

Schurr JM.The role of diffusion in enzyme kinetics. Biophys. J. 1970;10:717-727.

Eser BE, Fitzpatrick PF. Measurement of intrinsic rate constants in the tyrosine hydroxylase reaction. Biochemistry. 2010; 49(3):645–652

Vijaykumar A, Bolhuis PG, Wolde PR. The intrinsic rate constants in diffusion influenced reactions. Faraday Discuss, 2016; 195: 421–441.

Levine IN. Physical chemistry Peterson, K.A. and Oberbroeckling, S.R. (Eds) 5th Ed.McGraw-Hill Companies, Inc.1221. Avenue of the Americas, New York, NY10020. 2002; 299-303.

Schnell S. Validity of the Michaelis–Menten equation – Steady-state or reactant stationary assumption: That is the question. FEBS J. 2014; 281: 464–472.

Udema II. The key to effective catalytic action is pre-catalytic site activity preceding enzyme- substrate complex formation. Adv. Res. 2017;9(3): 1-17.

Sugahara M, Takehira M, Yutani K. Effect of heavy atoms on the thermal stability of alpha-amylase from Aspergillus oryzea. PlosOne. 2013; 8(2):1 – 7.

Bernfeld P. Amylases, alpha and beta. Methods Enzymol.1955; 1:149 – 152.

Tomasik P. Specific physical and chemical properties of potato starch. Food (Special Issue 1): 2008; 45 – 56.

Pollard EC. The control of cell growth. In Cell Biology in Medicine (Bittar, E. E. ed). New York, London, Sydney, Toronto: John Wiley & Sons, Inc; 1973.

Udema II. Derivable equations and issues often ignored in the original Michaelis-Menten mathematical formalism. Asian J. Phys. Chem. Sci. 2019; 7(4): 1-13.

Udema II, Onigbinde AO. The experimentally determined velocity of catalysis could be higher in the absence of sequestration. Asian J. Res. Biochem. 2019;5(4):1-12.

Sassa A, Beard W.A., Shock D.D., Wilson S.H. Steady-state, Pre-steady-state, and single- turnover kinetic measurement for DNA glycosylase activity. J. Vis. Exp. 2013;(78):1-9.

Schnell S, Maini PK. Enzyme kinetics at high enzyme concentration. Bull Math. Biol. 2000;62:483-499.

Udema II. Non-equilibrium binding energy determined using alpha-amylase catalysed amylolysis of gelatinised starch as a probable generalisable model and importance. Asian J. Chem. Sci. 2020; 8 (3):9-23.

Olsen K, Svenssen B, Christensen U. Stopped flow fluorescence and steady-state kinetic studies of ligand-binding reactions of glucoamylase from Aspergillus niger. Eur. J. Biochem. 1992; 209: 777-784.

Paumann-Page M, Katz R-S, Bellei M, Schwartz T, Sevcnikar B et al. Pre-steady-state kinetics reveals the substrate specificity and mechanism of halide oxidation of truncated human peroxidasin. J. Biol. Chem. 2017;2921 (11): 4583–4592.

Cruys-Bagger N, Elmerdahl J, Praestgaard E, Tatsumi H, Spodsberg N, BorchK, Westh P. Pre-steady-state kinetics for hydrolysis of insoluble cellulose by cellobiohydrolase. J. Biol. Chem. 2012;287(22):18451–18458.

Petrášek Z, Eibinger M, Nidetzky B. Modeling the activity burst in the initial phase of cellulose hydrolysis by the processive cellobiohydrolase Cel7A. Biotechnol. Bioeng. 2019;116: 515- 525.

Ting CL, Makarov DE, Wang Z-G. A Kinetic Model for the Enzymatic Action of Cellulase. J. Phys. Chem. B. 2009; 113 (14): 4970-4977.

Kostylev M, Wilson D. A two-parameter kinetic model based on a time- dependent activity coefficient accurately describes enzymatic cellulose digestion. Biochemistry. 2013;52(33):5656–5664.

Webster IA. Intrinsic, inherent, and observed kinetic data with immobilised enzymes: The concept of rotational masking. Biotech. Bioeng. 1983; 25(10): 2479-2484.

Blais S. Lortie R. Determination of the intrinsic Michaelis constant of immobilized alpha- chymotrypsin. J. Biol. Chem. 1993; 268(25):18637-18639.

Agmon N, Szabo A. Theory of reversible diffusion-influenced reaction. J. Chem. Phys. 1990;92(9):5270 – 5284.

Lu B, McCammon JA. Kinetics of diffusion-controlled enzymatic reactions with charged substrates. PMC Biophys. 2010;3:1-5.

Gopich IV, Szabo A. Diffusion modifies the connectivity of kinetic schemes for multisite binding and catalysis. Proc. Natl. Acad. Sci. USA. 2013; 110(49):19784-19789.

Wolde PR, Beckar NB, Mugler AJ. Fundamental limits to cellular sensing. J. Stat. Phys. 2016;162:1395-14224.