Derivation of steady-state first-order rate constant equations for enzyme-substrate complex dissociation, as well as zero-order rate constant equations in relation to background assumptions
Department of Chemistry and Biochemistry, Research Division, Ude International Concepts LTD (862217), B. B. Agbor, Delta State, Nigeria.
Research Article
GSC Biological and Pharmaceutical Sciences, 2022, 21(03), 175-189.
Article DOI: 10.30574/gscbps.2022.21.3.0482
Publication history:
Department of Chemistry and Biochemistry, Research Division, Ude International Concepts LTD (862217), B. B. Agbor, Delta State, Nigeria.
Abstract:
The maximum velocity (Vmax) of catalysis and the substrate concentration ([ST]) at half the Vmax, the KM, are regarded as steady-state (SS) parameters even though they are the outcomes of zero-order kinetics (ZOK). The research was aimed at disputing such a claim with the following objectives: To: 1) carry out an overview of issues pertaining to the validity of assumptions; 2) derive the needed steady-state (SS) equations distinct from Michaelian equations that can be fitted to both experimental variables and kinetic parameters; 3) calculate the SS first-order rate constant for the dissociation of enzyme-substrate complex (ES) to free substrate, S and enzyme, E; 4) derive the equation of rate constant as a function of the reciprocal of the duration of each catalytic event in the reaction pathway. The experimental values of the data were generated by Bernfeld and Lineweaver-Burk methods. The calculated SS 1st order-order rate constant was « the zero-order Michaelian value, and the difference is ≈ 97.59 % of the zero-order value; the SS catalytic rate differed from the zero-order catalytic rate by ≈ 76.41 % of the latter value; and it was ≈ 93.87 % with respect to the 2nd order rate constant for the formation of enzyme-substrate complex. The equations of time-dependent rate constants, KM, and dissociation constants were derived. The magnitude of [ST] must be > the concentration ([E0]) of the E for the quasi-steady-state assumption (or approximation) to hold. The SS kinetic parameters are not equivalent to zero-order parameters.
Keywords:
Steady-state rate constants; Steady-state dissociation constant; Zero-order rate constants; Michaelian constant; Derivation of steady-state rate; Dissociation constant equations; Aspergillus oryzae alpha-amylase
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