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

ABSTRACT 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 concentration [ S T ] of the S must be > the concentration ([ E 0 ]) of the E for the quasi-steady-state assumption (or approximation) to hold. The SS kinetic parameters are not equivalent to zero-order parameters.