Michaelis-Menton equation derivation

Equation 9 is a hyperbolic relationship, similar to the Michaelis-Menton equation derived for enzyme kinetics (104) the Langmuir equation as applied to adsorption on soils (105), and an adaptation of these models for dechlorination by Fe that we published previously (13). As such, all four models are capable of describing site saturation phenomena commonly found in heterogenous systems however, only the new model (equations 8 and 9) explicitly distinguishes thermodynamically-related parameters from the kinetic constants. 

When accurate data can be obtained over a range of both concentrations and temperatures, it is possible from the Michaelis-Menton model to obtain data on the first-order rate constant kz and the constant Km = kz + kz)/ki and their apparent activation energies Ez and Unfortunately, most of the values quoted in the literature for the activation energies of enzyme-catalyzed reactions are derived from the use of overly simple first-order equations to describe the reaction. Consequently these values are a composite of Kmj kzy and the other constants in the Michaelis-Menton equation and cannot be used for interpretive purposes. Where the constants have been separated it is found that the values of Ez are low and of order of magnitude of 5 to 15 Kcal/mole. It is of interest to note that enzyme preparations from different biological sources, which may show different specific activity for a given reaction, have very nearly the same temperature coefficient for their specific rate constants. ... 

The procedure used in deriving the Michaelis-Menton equation is readily generalized. Equation (3-73) supposes that the decomposition of complex X is reversible, but suppose that it is not that is... 

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