Fractional kinetic modelling of the adsorption and desorption process from experimental SPR curves

Abstract: The application of surface plasmon resonance (SPR) has transformed the field of study of interactions between a ligand immobilized on the surface of a sensor chip, designated as $L_S$, and an analyte in solution, referred to as $A$. This technique enables the real-time measurement of interactions with high sensitivity. The dynamics of adsorption-desorption process, $A+L_S \rightarrow AL_S$, can be expressed mathematically as a set of coupled integer-order differential equations. However, this approach has limited ability to acoount for temperature distribution, diffusion and transport effects involved in the reaction process. The fractional kinetic model provides a methodology for incorporating non-local effects into the problem. In this study, the proposed model was applied to analyze data to the interaction between Immobilized Baru Protein (IBP) and Congo Red dye (CR) at concentrations ranging from $7.5$ to $97.5$ $\mu M$, at pH $7.4$ and $16^o$ C. The variation in the kinetic constants was studied, and it was demonstrated that the integer-order model is unable to adequately represent the experimental data. This work has shown that the fractional-order model is capable of capturing the complexity of the adsorption-desorption process involved in the SPR data.