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

The maximum velocity (V_max) of catalysis and the substrate concentration ([S_T]) at half the V_max, the K_M, 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 1^st 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 2^nd order rate constant for the formation of enzyme-substrate complex. The equations of time-dependent rate constants, K_M, and dissociation constants were derived. The magnitude of [S_T] 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.