Background: There has been recent shift from the core issue of Michaelian kinetics to issues regarding various kinds of quasi-steady-state assumptions. Derivable equations with which to determine reverse rate constant for the dissociation of enzyme-substrate complex (ES) is given less attention. Objectives: The objectives of this research are: 1) to derive other equations from differential equations whose evaluation leads to MM equation and 2) quantify based on derived equations the kinetic parameters given less attention and duration of catalytic events. Methods: A major theoretical research and experimentation using Bernfeld method. Results and Discussion: The durations for ES dissociation (ESD) into free substrate, S and enzyme, E were much shorter than the duration of ESD into E and product, P in 3 minutes duration of assay with low [S]; it was the shortest and longest in 3 and 5 minutes durations respectively with high [S]. The durations of ESD into E and P was shortest in 3 minutes duration of assay with high [S]. The values of reverse rate constant, k-1 for ESD into S and E in 3 minutes duration of assay with high [S] was » the rate constant, k2 for product formation and they are much higher than in other duration of assay. Conclusion: The equations for the determination of the durations of various events, in a given catalytic cycle were derived. The various time regimes for each event and the rate constant for the dissociation of the ES can be graphically and calculationally determined as the case may be. Substrate concentration regime and duration of assay affects rate constants.

Background: Researchers who have shown interest in the consequence of introducing dry biomolecules or a solution of it into cosolvents generally known as osmolyte, have applied many models for the elucidation of the scientific basis of the results obtained. The Kirkwood and Buff theory (KBT) or its reverse form has been the basis for the interpretation of the effect of the osmolyte. There seems to be no generally acceptable definition of terms in the basic KBT mathematical formalism. There is also error in stated equations describing solution structure and misapplication of Wyman linkage relation. Therefore, the objectives of this research are 1) to show how the equation of preferential interaction parameter is derived based on KBT, 2) to show the appropriate way in which Wyman linkage relation can be applied, 3) to apply biochemical approach (using generated data) to the equation of preferential interaction parameter (preferential interaction parameter is symbolised as ) for its calculation and calculation of parameters linked to KBT derived equations. Methods: The research is mainly theoretical and partly experimental. The experiment entails Bernfeld method of enzyme assay for the generation of data. Results and Discussion: The change in solvation preference upon the ethanol partial denaturation of the enzyme and the corresponding change in preferential interaction parameter were respectively positive and negative in sign. Unexpectedly ethanol was preferentially excluded from the enzyme. Conclusion: The equations of preferential interaction parameters were derived. The appropriate way is either by calculation or measurement of preferential interaction parameter. Therefore,  or  for the change, cannot be a constant (or slope) and an instrumentation–based measurable parameter at the same time. Based on Wyman linkage relation, purely biochemical thermodynamic parameter is linked to preferential interaction parameters which are therefore, thermodynamic parameters.

No abstract

Backed by kinetic schemes, attempts had been made to derive equations for the calculation of all zero-order first-order rate constants (ZOFORC) for the activation of the enzyme-substrate (ES) complex and its deactivation. The values of ZOFORC, including the kind for the dissociation of the enzyme-product complex (EP) to free enzyme (E) and product (P), are hardly reported. The methods of research were primarily Bernfeld and Lineweaver methods. The goal of the research was to determine ways for the utilization of experimental data for the determination of verifiable and quantifiable rate constants, with the following objectives: 1) To derive equations for the first order rate constants, for the activation of ES and its deactivation, respectively; 2) to quantify by calculation the first order rate constant for product release; 3) ultimately quantify the rate constants, and 4) to advise the reactor, process, chemical engineers, etc. in different industrial concerns on the usefulness of the rate constants. The value of ZOFORC for the dissociation of EP to free E and P is 3.155 exp. (+5)/min; the values of the rate constant for activation and deactivation are 3.513 exp. (+4) and 2.377 exp. (+8)/min, respectively. Ultimately, it is imperative for all stakeholder groups to devise means of controlling the enzymatic rate of catalysis by manipulating the magnitudes of the rate constant for activation and deactivation in particular. The derived equations can be fitted to the experimentally generated and calculated data. A future research project should entail conducting the assay under optimum conditions so as to verify possible variations in the ZOFORC values when compared with values generated outside optimum conditions. Keywords: Alpha-amylase; first-order rate constants; activation and deactivation of enzyme-substrate complex; zero-order kinetic parameters.

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 much less than the zero-order Michaelian value, and the difference is approximately equal to 97.59 % of the zero-order value; the SS catalytic rate differed from the zero-order catalytic rate by approximately equal to 76.41 % of the latter value; and it was approximately equal to 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 concentration [ST] of the S must be greater 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 and dissociation constant equations; Aspergillus oryzea alpha-amylase