Load-dependent surface diffusion model for analyzing the kinetics of protein adsorption onto mesoporous materials

The adsorption of cytochrome c in water onto organic and carbon xerogels with narrow pore size distributions has been studied by carrying out transient and equilibrium batch adsorption experiments. It was found that equilibrium adsorption exhibits a quasi-Langmuirian behavior (a g coefficient in the Redlich-Peterson isotherms of over 0.95) involving the formation of a monolayer of cyt c with a depth of ∼4nm on the surface of all xerogels for a packing density of the protein inside the pores of 0.29gcm^-3. A load-dependent surface diffusion model (LDSDM) has been developed and numerically solved to fit the experimental kinetic adsorption curves. The results of the LDSDM show better fittings than the standard homogeneous surface diffusion model. The value of the external mass transfer coefficient obtained by numerical optimization confirms that the process is controlled by the intraparticle surface diffusion of cyt c. The surface diffusion coefficients decrease with increasing protein load down to zero for the maximum possible load. The decrease is steeper in the case of the xerogels with the smallest average pore diameter (∼15nm), the limit at which the zero-load diffusion coefficient of cyt c also begins to be negatively affected by interactions with the opposite wall of the pore.