This work presents a molecular thermodynamic theory to study protein interactions within a charge-regulating silica-like nanopore structure. The theory accounts for electrostatic interactions, steric repulsions, finite-size entropic effects, and protonation equilibrium of silanol groups on silica and protein residue side-chains. Coarse-grained representations of proteins based on their 3D crystallographic structures are employed. We evaluate the influence of pH, salt concentration, and pore size on the adsorption of selected proteins (cytochrome c, lysozyme, and myoglobin) in both single- and binary-protein solutions. The surface charge density on the nanopore walls is less negative than on the adjacent planar surface, primarily influenced by pH and salt concentration. Adsorption within the nanopore from single protein solutions exhibits a non-monotonic behavior with pH, increasing with decreasing salt concentration and diminishing pore size. Analysis of the effective interactions between proteins and silica surfaces indicates that adsorption is enhanced when the protein size matches that of the nanopore. Evaluation of various adsorption pathways indicates minimized free energy when the protein enters the nanopore through its edge and contacts its cylindrical walls. In binary solutions, the presence of another protein significantly alters the affinity of a protein for the silica surfaces, potentially preventing its adsorption, and affects its organization on these surfaces upon adsorption.
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