Analytical and numerical approaches to the analysis of progress curves: A methodological comparison

Accurate models of the reaction kinetics of enzymatic reactions are essential for the design of biocatalytic processes. While many experimental studies still build on initial slope analysis, progress curve analysis offers the potential for modelling enzymatic reactions with a significantly lower experimental effort in terms of time and costs, but requires the solution of a dynamic nonlinear optimization problem. There are many different approaches for solving this problem for parameter regression, building on the experimental progress curve data. In order to provide some guidance for selecting an appropriate approach, this study presents a detailed comparison of two analytical and two numerical approaches analysing their strengths and weaknesses on the basis of three case studies. The analytical approaches build on the implicit and explicit integrals of the respective reaction rate equations, while the numerical approaches consider the direct numerical integration of the differential mass balance equations as well as the transformation of the dynamic problem to an algebraic problem by means of spline interpolation of the reaction data. In particular, the dependence of the results on the initial parameter estimates is evaluated, showcasing that the numerical solution with spline interpolation shows a lower dependence on the initial values providing parameter estimates comparable to the analytical approaches, which are however limited in applicability.