DAE

Abstract

Enzymes are biological catalysts that act on substrates. The speed of reaction as a function of substrate concentration typically follows the nonlinear Michaelis-Menten model. The reactions can be modified by the presence of inhibitors, which can act by several different mechanisms, leading to a variety of models, all also nonlinear.

The talk will describe the models and derive optimum experimental designs for model building. When the model is known these include D-optimum designs for all the parameters for which we obtain analytical solutions. Ds-optimum designs for the inhibition constant are also of scientific importance.

When the model is not known, the choice is often between two three-parameter models. These can be combined in a single four-parameter model. Ds-optimum designs for the parameter of combination provide a means of establishing which model is true. However, T-optimum designs for departures from the individual models provide tests of maximum power for departures from the models. With two models on an equal footing, compound T-optimum designs are required. Their properties are compared with those of the Ds-optimum designs in the combined model, which have the advantage of being easier to compute.