In vitro starch digestion kinetic, formal analysis and new kinetic model

Abstract

Describing mathematically the kinetics of the enzymatic hydrolysis of starch is a crucial part of nutrition and industrial applications studies. The majority of math models aim to fit the hydrolysis-extent curve ($X\_t$), so-called digestogram, whose simple shape which can be fitted equally well by various math models. A relevant model of starch digestion kinetics should be more specific of the phenomenon. This study proposes a novel analytical framework that jointly fits the hydrolysis-extent curve ($X\_t$) and the instantaneous reaction-rate coefficient ($k\_a(t)$). A large dataset comprising 672 wheat-starch time-course measurements (including normal, waxy, and high-amylose genotypes), and additional experiments on other botanical starches was analysed. Standard First-Order and Weibull models were compared with two newly derived kinetic formulations \eqref{Eq.11} and \eqref{Eq.12} based on expected starch hydrolysis' phenomenon by which $k\_a(t)$ tends with time towards an asymptotic-rate constant value, $k\_e$, following a characteristic relaxation time ($τ$). A mathematical proof of the existence of $k\_e$, specific of the type of starch, is provided, based on an analysis of the Weibull's parameters. Model ability to fit both $X\_t$ and $k\_a(t)$ was assessed by examining coefficients of determination ($R^2$) for both data types, and its adjusted version ($R^2\_{adj}$) was used to compare performances between models. All models fit very well $X\_t$ data, while $k\_a(t)$ is much more discriminant of the model formulation. Wheat starch types are well distinguished, regarding ke, by the new models, with higher susceptibility to amylase for waxy samples ($\approx 5.7\times 10^{-3} min^{-1}$), than normal ($\approx 2.2\times 10^{-3} min^{-1}$) and high-amylose ($\approx 1.7\times 10^{-3} min^{-1}$) ones. The new models outperformed the other models for monotonic evolution of $k\_a(t)$, particularly digestion of high-amylose, and allow a more accurate estimation of $k\_e$. However, the analysis also highlighted limitations for modelling non-monotonic kinetics observed for waxy wheat starch digestion, suggesting a need for more sophisticated differential-equation descriptions for $k\_a(t)$. Overall, the combined fitting strategy provides a robust method for extracting physically meaningful kinetic parameters, facilitating deeper insight into the factors controlling starch digestion and supporting the development of more accurate predictive models for glycaemic response and food processing.