Optimal designs for enzyme inhibition kinetic models

TL;DR

This paper introduces a novel method for finding optimal experimental designs in enzyme inhibition kinetic models by transforming the problem into a response surface model, enabling explicit solutions for design optimization.

Contribution

It presents a new transformation-based approach that simplifies the optimal design problem for enzyme inhibition models, allowing explicit solutions where none were previously available.

Findings

Explicit D-optimal designs derived for enzyme inhibition models

Method simplifies complex nonlinear design problems

Transformations enable easier computation of optimal designs

Abstract

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.