A general expression for the Michaelis-Menten constant

ROSSI RC

Congreso; 56th Annual Meeting of the Biophysical Society; 2012

Biophysical Society

It is sometimes taken for granted that a change in the value of the Michaelis-Menten constant, Km, following the mutation of an enzyme’s amino acid is due to a modification in the intrinsic affinity of the active site for the substrate, leading to the unproven conclusion that the original amino acid is part of this site. This, as well as other misinterpretations could be avoided if a clear, general expression of Km were available. The following is proposed: Km = (k-1 fES∞ + kcat)/(k1 fE0), where k1 and k-1 are respectively the rate constants for binding and dissociation of the substrate, S, kcat is the catalytic constant, fES∞ is the fraction of enzyme present as the enzyme-substrate complex at [S] and fE0 is the fraction of enzyme able to bind the substrate at [S]=0. These quantities fES∞ and fE0 will be less than unity assuming the existence of intermediates other than the bound form ES and the free form E, respectively. Alternative forms for this expression can be obtained considering that kcat= k2’×fES∞, where k2’ is the net rate constant for the reaction from ES to the next intermediate in the forward direction (Cleland, 1975, Biochemistry 14:3220-3224). The above expression is model independent since for every model following Michaelis-Menten kinetics the rate constants k1 and k-1 will be present and the quantities fES∞, fE0, and kcat (or alternatively, k2’) can be defined. Analysis of models for the hydrolysis of ATP by the sodium pump, which during Na+-ATPase activity displays Michaelis-Menten kinetics, allows to explain why Km  KS, the equilibrium dissociation constant for ATP, although ATP is not in rapid equilibrium with its site on the enzyme. The case of the Na+/K+-ATPase activity will also be analyzed. With grants from CONICET and University of Buenos Aires, Argentina.