27 Congreso Nacional de Estad´ ıstica e Investigaci´ on Operativa Lleida, 8–11 de abril de 2003 OPTIMAL DESIGNS FOR DISCRIMINATION BETWEEN THE MICHAELIS-MENTEN MODEL AND LINEAR REGRESSION C. Trandafir, J.L´opez-Fidalgo Departamento de Estad´ ıstica Universidad de Salamanca, Plaza de los Ca´ ıdos s/n 37008 Salamanca, Espa˜ na E-mail:fidalgo@usal.es, a110619@usal.es ABSTRACT In this paper the problem of estimating and designing experiments in a non- linear regression model used in enzyme-kinetics is studied. In particular, an extension of the popular chemical model of Michaelis-Menten is considered when the linear regression model is another alternative. Key words and phases: D-optimal design, linear regression, locally optimal design, Michaelis-Menten model, Lagrange interpolation polynomial. AMS Classification: 62K05 1 Introduction The Michaelis-Menten (MM) model is used in biology to describe the equlibrium kinetics of the enzyme system and in analysis of data from drug, neurotransmit- ter and hormone receptor assay. (See, for instance, Cressie and Keightley (1981); Raaijimakers (1987); Dunn (1985)). The MM model is also used in compartmental models to modelize the rate of change from one compartment to another. A general theory for enzyme kinetics was first developed by Michaelis and Menten (1913). This model predicts the velocity rate, ν , of formation of a product in a chemical reaction given the substrate concentration, x. The Michaelis-Menten model is: E[ν ]= Vx K + x , var[ν ]= σ 2 , x ∈ χ = [0, ∞) 1