The binding interaction of protein on a charged surface using Poisson–Boltzmann equation: lysozyme adsorption onto SBA-15

A modified Poisson–Boltzmann model (PBEm) can be successfully used to determine the binding strength parameter, i.e., (Henry constant, K), for the protein adsorbent interaction in ion-exchanger columns. Lysozyme has been employed as a standard protein for the adsorption in a mesoporous silica adsorbent. The density of aminoacid groups and silanol groups were used as inputs to calculate the protein charge density as a function of pH, salt concentration, and type of salt. Using the electrostatic potential provided as solving the PBEm with the protein charge surface and silanol wall as boundaries conditions, we calculated the K through the potential of mean force to describe the whole set of experimental data. The unique estimated parameter in this work was the volumetric accessible surface area from isotherm data for different electrolyte conditions. The results show that the protocol applied includes a pH and ionic strength dependence in the Langmuir isotherm. A sensibility test with different anions ( $$\text {Cl}^{-}$$ , $$\text {Br}^{-}$$ , and $$\text {I}^{-}$$ ) showed an agreement with the Hofmeister series for the protein/adsorbent interaction. A modification in the electrolyte concentration and pH can change the behavior of the isotherm profile for a fixed value of saturation capacity, independently calculated for spheres packed in cylinders. The calculations provide here can be helpful for the optimization of the best condition for protein adsorption.