A model based on continuum hydrodynamics and electrostatics was developed to predict the combined effects of molecular charge and size on the osmotic reflection coefficient (σo) of a macromolecule in a fibrous membrane, such as a biological hydrogel. The macromolecule was represented as a sphere with a constant surface charge density, and the membrane was assumed to consist of an array of parallel fibers of like charge, also with a constant surface charge density. The flow was assumed to be parallel to the fiber axes. The effects of charge were included by computing the electrostatic free energy for a sphere interacting with an array of fibers. It was shown that this energy could be approximated using a pairwise additivity assumption. Results for σo were obtained for two types of negatively charged fibers, one with properties like those of glycosaminoglycan chains, and the other for thicker fibers having a range of charge densities. Using physiologically reasonable fiber spacings and charge densities, σo for bovine serum albumin in either type of fiber array was shown to be much larger than that for an uncharged system. Given the close correspondence between σo and the reflection coefficient for filtration, the results suggest that the negative charge of structures such as the endothelial surface glycocalyx is important in minimizing albumin loss from the circulation.
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