Optimum design of experiments for enzyme inhibition kinetic models.

We find closed-form expressions for the D-optimum designs for three- and four-parameter nonlinear models arising in kinetic models for enzyme inhibition. We calculate the efficiency of designs over a range of parameter values and make recommendations for design when the parameter values are not well known. In a three-parameter experimental example, a standard design has an efficiency of 18.2% of the D-optimum design. Experimental results from a standard design with 120 trials and a D-optimum design with 21 trials give parameter estimates that are in close agreement. The estimated standard errors of these parameter estimates confirm our theoretical results on efficiency and thus on the serious savings that can be made by the use of D-optimum designs.