Fractional Kinetic Modelling of the Adsorption and Desorption Processes From Experimental SPR Curves

ABSTRACT The application of surface plasmon resonance (SPR) has transformed the study of interactions between a ligand immobilized on the surface of a sensor chip () and an analyte in solution (). This technique enables the real‐time monitoring of binding processes with high sensitivity. The adsorption–desorption dynamics, , are commonly described by a set of coupled integer‐order differential equations. However, such formulations exhibit limited ability to account for temperature distributions, diffusion, and transport effects involved in the reaction process. Fractional kinetic models provide a natural framework for incorporating nonlocal and memory effects into the description of complex reaction dynamics. In this study, a fractional‐order kinetic model based on the Caputo derivative is applied to analyze experimental SPR data for the interaction between immobilized Baru protein (IBP) and Congo Red dye (CR), at concentrations ranging from 7.5 to 97.5 M, pH 7.4, and 16°C. The dependence of the kinetic parameters on the model order is systematically investigated, and it is shown that the classical integer‐order formulation fails to adequately reproduce the experimental sensorgrams. The results demonstrate that the fractional‐order model captures the intrinsic complexity of the adsorption–desorption process observed in SPR experiments, providing a significantly improved representation of the experimental data.