Hindered diffusion in agarose gels: test of effective medium model

Abstract

The diffusivities of uncharged macromolecules in gels (D) are typically lower than in free solution (D infinity), because of a combination of hydrodynamic and steric factors. To examine these factors, we measured D and D infinity for dilute solutions of several fluorescein-labeled macromolecules, using an image-based fluorescence recovery after photobleaching technique. Test macromolecules with Stokes-Einstein radii (rs) of 2.1-6.2 nm, including three globular proteins (bovine serum albumin, ovalbumin, lactalbumin) and four narrow fractions of Ficoll, were studied in agarose gels with agarose volume fractions (phi) of 0.038-0.073. The gels were characterized by measuring the hydraulic permeability of supported agarose membranes, allowing calculation of the Darcy permeability (kappa) for each gel sample. It was found that kappa, which is a measure of the intrinsic hydraulic conductance of the gel, decreased by an order of magnitude as phi was increased over the range indicated. The diffusivity ratio D/D infinity, which varied from 0.20 to 0.63, decreased with increases in rs or phi. Thus as expected, diffusional hindrances were the most severe for large macromolecules and/or relatively concentrated gels. According to a recently proposed theory for hindered diffusion through fibrous media, the diffusivity ratio is given by the product of a hydrodynamic factor (F) and a steric factor (S). The functional form is D/D infinity = F(rs/k1/2) S(f), where f = [(rs+rf)/rf]2 phi and rf is the fiber radius. Values of D/D infinity calculated from this effective medium theory, without use of adjustable parameters, were in much better agreement with the measured values than were predictions based on other approaches. The strengths and limitations of the effective medium theory for predicting diffusivities in gels are discussed.