An investigation of the relationships between rate and driving force in simple uncatalysed and enzyme-catalysed reactions with applications of the findings to chemiosmotic reactions

Abstract

Both the rate and the driving force of a reaction can be expressed in terms of the concentrations of the reactants and products. Consequently, rate and driving force can be expressed as a function of each other. This has been done for a single-reactant, single-product, uncatalysed reaction and its enzyme-catalysed equivalent using the van't Hoff reaction isotherm and Haldane's generalized Michaelis-Menten rate equation, the primary objective being explanation of the exponential and sigmoidal relationships between reaction rate and delta mu H+ commonly observed in studies on chemiosmotic reactions. Acquisition of a purely thermodynamic rate vs. driving-force relationship requires recognition of the intensive and extensive variables and maintenance of the extensive variables constant. This relationship is identical for the two reactions and is hyperbolic or sigmoidal, depending on whether the equilibrium constant is smaller or larger than unity. In the case of the catalysed reaction, acquisition of the purely thermodynamic relationship requires the assumption that the enzyme be equally effective in catalysing the forward and backward reactions. If this condition is not met, the relationship is modified by the enzyme in a manner which can be determined from the ratio of the Michaelis constants of the reactant and product. Under conditions of enzyme saturation in respect to reactant+product, the rate vs. driving-force relationship is determined exclusively by the thermodynamics of the reaction and a single kinetic parameter, the magnitude of which is determined by the relative effectiveness of the enzyme in catalysing the forward and backward reactions. In view of this finding, it is pointed out that, since the catalytic components of chemiosmotic reactions appear to be saturated with respect to the reactant-product pair that is varied in experimental rate vs. delta mu H+ determinations, and that, since many complex enzymic reactions conform to the simple Michaelis-Menten equation with respect to a single reactant-product pair when the concentrations of all other reactants and products are maintained constant, one might expect to be capable of simulating the experimental relationships simply from knowledge of the thermodynamics of the reaction and the relative effectiveness of the catalytic component in catalysing the forward and backward reactions using the simple Michaelis-Menten equation. That this expectation appears to be largely correct is demonstrated with model reactions.(ABSTRACT TRUNCATED AT 400 WORDS)