Design and analysis of protein binding experiments

The design and analysis of protein binding experiments for obtaining precise parameter estimates for a one-site and a two-site model treating fu, the fraction unbound as the experimentally determined quantity was investigated. Total drug concentrations were chosen at which the binding isotherm is determined to yield the most information about the parameters under study. The D-optimization information criterion was used to achieve this although other criteria are also discussed. For both the one-site and the two-site models the number of design points was always equal to the number of parameters being estimated. The results arrived at when dealing with constant variance and unconstrained total drug concentration were rather unique in that in most of the cases studied, all the optimal design points were away from the boundary conditions. For constant relative variance and unconstrained total drug concentrations, one of the design points was always placed at the smallest possible value of fu, the fraction unbound. For the one-site model the second point was always given by K(-1) + nP. The optimal designs arrived at lead to lower theoretical coefficients of variation in the parameters than the corresponding conventional ones. Simulated experiments supported these theoretical findings for both the one-site and the two-site models. For the one-site model, results from nonlinear regression were compared with Scatchard analysis and the optimal designs were also optimal in Scatchard space. We also show that using Scatchard analysis with the conventional strategy leads to poorly determined estimates particularly when the number of observations is low.