Theoretical Modeling

Jeon et al. built a mathematical model to explain the protein-rejecting abilities of PEG coatings [26, 27]. The authors considered the case of a hydrophobic surface covered with a brush of terminally attached PEG chains at a distance D from one another [27]. Proteins approaching these surfaces by diffusion were assimilated to homogeneous spherical particles with hydrophobic surfaces. Optimal surface densities to avoid adsorption were calculated as a function of protein radius. For example, in the case of a PEG brush with a molecular weight of 5280 g/mole, the calculated optimal D values were 9-11, 11-15, and 13-17 A for protein radius, respectively, equal to 20, 40, and 60-80 A. Furthermore, at optimal surface densities, the longest PEG chain length was best for protein-resistance properties.

More recently, Torchilin et al. [28, 29] built a simple model for understanding the steric repulsion induced by PEG layers. The authors highlighted the importance of polymer flexibility to avoid protein adsorption. Indeed, a polymer chain in solution statistically exists as a distribution or cloud of probable conformations. The higher the polymer flexibility, the higher its ability to occupy, with high frequency, many surrounding locations, which are thus made inaccessible for proteins. By opposition with the very flexible PEG chains, nonflexible polymers terminally attached to a surface form a broad but loose and, thus, protein-permeable cloud.

Szleifer [30] developed a theoretical approach based on the single-chain mean-field theory to study protein adsorption on surfaces grafted with polymers. The polymerprotein-solvent layer at the surface was considered inhomo-geneous in the direction perpendicular to the surface. It was found that the main parameter in determining the ability of a polymeric layer to prevent protein adsorption is the density of the polymer segments close to the surface.

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