  In this paper we present a new method for determining optimal designs for
enzyme inhibition kinetic models, which are used to model the influence of the
concentration of a substrate and an inhibition on the velocity of a reaction.
The approach uses a nonlinear transformation of the vector of predictors such
that the model in the new coordinates is given by an incomplete response
surface model. Although there exist no explicit solutions of the optimal design
problem for incomplete response surface models so far, the corresponding design
problem in the new coordinates is substantially more transparent, such that
explicit or numerical solutions can be determined more easily. The designs for
the original problem can finally be found by an inverse transformation of the
optimal designs determined for the response surface model. We illustrate the
method determining explicit solutions for the $D$-optimal design and for the
optimal design problem for estimating the individual coefficients in a
non-competitive enzyme inhibition kinetic model.
