Sigmoidal substrate saturation curves in Michaelis-Menten mechanism as an artefact

The conditions under which sigmoidal substrate saturation curves are to be expected in the simple Michaelis-Menten mechanism and the Michaelis-Menten mechanism combined with the concomitant partial inactivation of the enzyme have been determinee solved numerically for different sets of rate constants by computer simulation on the basis of the second order Runge-Kutta method. In order to simulate the real experimental conditions, the substrate saturation curves have also been derived from velocity values in the quasi-steady state, by using the non-linear least squares fitting method. In the framework of the Michaelis-Menten mechanism there is a sigmoidal relationship between initial velocity and substrate concentration only in the case of a Van Slyke mechanism, i.e. if k2 greater than k-1 and therefore K=k2/k1 is a "kinetic constant" if the velocity is determined in the quasi-steady state. If the enzyme is inactivated during the course of velocity measurement in the quasi-steady state, a sigmoidal or a degenerated hyperbolic saturation curve is obtained. A sigmoidal saturation curve can be obtained in the case of the Van Slyke mechanism, independent of the rate constant of the inactivation of the enzyme, or in the case of Michaelis-Menten or Briggs-Haldane mechanism, if k3 is sufficiently high. The inflexion point of such substrate saturation curves is determined by the rate constants, i.e. S0 less than or approximately k3/k1 and k-1/k1 and/or k2/k1. The higher the value of k3 the more pronounced is the sigmoidicity. The Michaelis constant can precisely be determined only if the velocities are measured in the very steady state at all substrate concentrations used. If the measurements are made in the quasi-steady state, the KM is always underestimated.