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

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.