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 reparameterize the model and provide designs for investigating the equality of parameters, which corresponds to a scalar parameter δδ being zero. For linear models T-optimum designs for discriminating between models in which δδ is, and is not, equal to zero are identical to designs in which the estimate of δδ has minimum variance. We show that this equality does not hold for our nonlinear model, except as δδ approaches zero. We provide optimum discriminating designs for a series of parameter values. Appendix A presents analytical expressions for the D-optimum design for the four parameters of the mixed inhibition model.