Abstract
Several mathematical properties associated with the simple Michaelis-Menten mechanism for enzymatic reactions are proven. In particular it is shown that the usual interpretation of the slope of the experimental Michaelis-Menten rate law in terms of the reaction constants of the mechanism can be obtained, in the approximation in which the total concentration of the enzyme is small compared with the Michaelis-Menten constant, independently of the ratio between the total initial concentrations of the enzyme and substrate. Furthermore, the ratio of the total concentration of the enzyme to the Michaelis-Menten constant allows for the elimination of a fast variable in a singular perturbation method, yielding the Michaelis-Menten rate law as a first order approximation.
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