Theory and applications of refractive index-based optical microscopy to measure protein mass transfer in spherical adsorbent particles

This work provides the theoretical foundation and a range of practical application examples of a recently developed method to measure protein mass transfer in adsorbent particles using refractive index-based optical microscopy. A ray-theoretic approach is first used to predict the behavior of light traveling through a particle during transient protein adsorption. When the protein concentration gradient in the particle is sharp, resulting in a steep refractive index gradient, the rays bend and intersect, thereby concentrating light in a sharp ring that marks the position of the adsorption front. This behavior is observed when mass transfer is dominated by pore diffusion and the adsorption isotherm is highly favorable. Applications to protein cation-exchange, hydrophobic interaction, and affinity adsorption are then considered using, as examples, the three commercial, agarose-based stationary phases SP-Sepharose-FF, Butyl Sepharose 4FF, and MabSelect. In all three cases, the method provides results that are consistent with measurements based on batch adsorption and previously published data confirming its utility for the determination of protein mass transfer kinetics under a broad range of practically relevant conditions.