Experimental designs for the Adair model

Abstract

The Adair equation is used to model biological macro-molecule reactions. This equation relates the saturation rate to the free ligand concentration. But, the latter is not a variable completely under the control of the experimenter. The ligand is a random variable depending on an initial ligand added by the experimenter, which can be designed, but the dependence of the saturation rate on the initial ligand has not been considered in the literature. In this paper a transformed model based on the Adair model of first order (monomer) is derived in order to obtain a proper model that depends on the initial ligand. This model will allow proper fitting and optimal designs using the initial ligand. It will be called the transformed Adair model (TAM). Optimal designs as well as seven-point quasi-optimal designs forced to follow a harmonic, geometric or uniform progression, are computed. The parameters are estimated and compared for simulated data from these designs. A sensitivity analysis against the choice of nominal values of the parameters is also performed for the TAM. The analytic version of the transformed model is only possible for the first class model. But the good efficiencies of the optimal designs obtained directly from the monomer model for fitting the TAM justify doing something similar for the second order model (dimer). Designs were computed numerically in this case.