A general expression for the Michaelis-Menten constant

R. C. ROSSI

San Miguel de Tucumán

Congreso; XLI Reunión Anual de la Sociedad Argentina de Biofísica; 2012

Sociedad Argentina de Biofísica

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 fESoo + 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, fESoo is the fraction of enzyme present as the enzyme-substrate complex at [S] tending to infinity and fE0 is the fraction of enzyme able to bind the substrate at [S]=0. Fractions fESoo and fE0 will be less than unity assuming the existence of other intermediates besides the bound species ES and the free species E, respectively. Alternative forms for this expression can be obtained considering that kcat= k2´ fESoo, where k2´ is the net rate constant for the reaction from ES to the next intermediate in the forward direction. The above expression is general in the sense that for every model following Michaelis-Menten kinetics the rate constants k1 and k-1 will be present and the quantities fESoo, fE0, and kcat (or alternatively, k2´) can be defined. We use the present formalism to analyze an ordered sequential system and a "ping-pong" system. 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 is approximately equal to 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 is also analyzed, revealing an apparent incongruence between the observed value of Km and that predicted from the rate limiting step at very low [ATP].