Least-squares problems for Michaelis-Menten kinetics

The Michaelis-Menten kinetics is fundamental in chemical and physiological reaction theory. The problem of parameter identification, which is not well posed for arbitrary data, is shown to be closely related to the Chebyshev sum inequality. This inequality yields sufficient conditions for existence of feasible solutions both for nonlinear and for linear least-squares problems. The conditions are natural and practical as they are satisfied if the data show the expected monotone and concave behaviour.