# On the estimation errors of $K_M$ and $V$ from time-course experiments using the Michaelis-Menten equation

### Abstract

The conditions under which the Michaelis-Menten equation accurately captures the steady-state kinetics of a simple enzyme-catalyzed reaction is contrasted with the conditions under which the same equation can be used to estimate parameters, $K_M$ and $V$, from progress curve data. Validity of the underlying assumptions leading to the Michaelis-Menten equation are shown to be necessary, but not sufficient to guarantee accurate estimation of $K_M$ and $V$. Detailed error analysis and numerical experiments″ show the required experimental conditions for the independent estimation of both $K_M$ and $V$ from progress curves. A timescale, $t_Q$, measuring the portion of the time course over which the progress curve exhibits substantial curvature provides a novel criterion for accurate estimation of $K_M$ and $V$ from a progress curve experiment. It is found that, if the initial substrate concentration is of the same order of magnitude as $K_M$, the estimated values of the $K_M$ and $V$ will correspond to their true values calculated from the microscopic rate constants of the corresponding mass-action system, only so long as the initial enzyme concentration is less than $K_M$. (C) 2016 Elsevier B.V. All rights reserved.

Publication
BIOPHYSICAL CHEMISTRY 219, 17-27