Optimum Designs for the Equality of Parameters in Enzyme Inhibition Kinetic Models

A general model for enzyme kinetics with inhibition, the “mixed” inhibition model, simplifies to the non-competitive inhibition model when two of the parameters are equal. We reparamaterise the model and provide designs for investigating the equality of parameters, which corresponds to a scalar parameter δ being zero. For linear models T-optimum designs for discriminating between models in which δ is, and is not, equal to zero are identical to designs in which the estimate of δ has minimum variance. We show that this equality does not hold for our nonlinear model, except as δ approaches zero. We provide optimum discriminating designs for a series of parameter values. An Appendix presents analytical expressions for the D-optimum design for the four parameters of the mixed inhibition model.