Enzymatic Kinetic Issues and Controversies Surrounding Gibbs Free Energy of Activation and Arrhenius Activation Energy

Abstract

Background: The equation of the difference between reverse and forward Gibbs free energy of activation (ΔΔGES#) reflects Michaelis-Menten constant (KM) in both directions; this may not be applicable to all enzymes even if the reverse reaction is speculatively Michaelian. Arrhenius activation energy, Ea and (Ea - ΔGES#)/RT) are considered = ΔGES# and KM respectively. The equations are considered unlikely. Objectives: The objectives of this research are: 1) To derive what is considered as an appropriate equation for the determination of the difference in ΔGES# between the reverse and forward directions, 2) calculate the difference between the reverse and total forward ΔGES#, and 3) show reasons why Ea ≠ ΔGES#  in all cases. Methods: A major theoretical research and experimentation using Bernfeld method. Results and Discussion: A dimensionless equilibrium constant KES is given. Expectedly, the rate constants were higher at higher temperatures and the free energy of activation with salt was < the Arrhenius activation energy, Ea; ΔΔGES#ranges between 67 - 68 kJ/mol. Conclusion: The equations for the calculation of the difference in free energy of activation (ΔΔGES#) between the forward and reverse directions and a dimensionless equilibrium constant for the formation of enzyme-substrate (ES) were derivable. The large positive value of the ΔΔGES# shows that the forward reaction is not substantially spontaneous; this is due perhaps, to the nature of substrate. The equality of Arrhenius activation energy (Ea) and ΔGES# may not be ruled out completely but it must not always be the case; the presence of additive like salt can increase the magnitude of Ea well above the values of the ΔGES#. A dimensionless equilibrium constant for the net yield of ES seems to be a better alternative than KM. The Ea unlike ΔGES#  requires at least two different temperatures for its calculation.