The lipid bilayers of cell membranes are primarily responsible for the low passive transport of nonelectrolytes across cell membranes, and for the pronounced size selectivity of such transport. The size selectivity of bilayer permeation has been hypothesized to originate from the hindered transport of solutes across the ordered-chain region. In this paper, we develop a theoretical description that provides analytical relationships between the permeation properties of the ordered-chain region of the lipid bilayer (partition and diffusion coefficients) and its structural properties, namely, lipid chain density, free area, and order parameter. Emphasis is placed on calculating the size selectivity of solute partitioning, diffusion, and overall permeability across the ordered-chain region of the lipid bilayer. The size selectivity of solute partitioning is evaluated using scaled-particle theory, which calculates the reversible work required to create a cavity to incorporate a spherical solute into the ordered-chain region of the lipid bilayer. Scaled-particle theory is also used to calculate the work required to create a diffusion path for solutes in the interfacial region of the lipid bilayer. The predicted size dependence of the bilayer permeability is comparable to that observed experimentally. The dependence of solute partition and diffusion coefficients on the bilayer structural parameters is also discussed.

Solute permeation across human stratum corneum (SC) was examined in terms of the fundamental bilayer transport properties. A mathematical model was developed to describe the macroscopic SC permeation via the interkeratinocyte lipid domain in terms of (i) the structure and dimensions of the SC, and (ii) the microscale lipid bilayer transport properties, which include the bilayer/water partition coefficient, the lateral diffusion coefficient, the interfacial transbilayer mass transfer coefficient, and the intramembrane transbilayer mass transfer coefficient. The relative importance of the diffusive resistances associated with the bilayer transport properties was evaluated with the model and experimental data. Lateral diffusion coefficients in SC lipid bilayers were calculated from 120 human skin permeability measurements, and compared with previously reported measurements made in SC-extracted lipids. Good qualitative and quantitative agreement was observed, indicating that, in the context of the model, the diffusive resistance associated with lateral diffusion is sufficient to explain the overall resistance of solute permeation through the SC. A similar analysis shows that the diffusive resistance associated with interfacial transbilayer transport is not capable of explaining the experimental permeation values, thus supporting this finding. The lateral diffusion analysis also revealed a bifunctional size dependence of transport within the SC, with a strong size dependence for small solutes (<300 Da) and a weak size dependence for larger solutes.

An image-based technique of fluorescence recovery after photobleaching (video-FRAP) was used to measure the lateral diffusion coefficients of a series of nine fluorescent probes in two model lipid bilayer systems, dimyristoylphosphatidylcholine (DMPC) and DMPC/cholesterol (40 mol%), as well as in human stratum corneum-extracted lipids. The probes were all lipophilic, varied in molecular weight from 223 to 854 Da, and were chosen to characterize the lateral diffusion of small compounds in these bilayer systems. A clear molecular weight dependence of the lateral diffusion coefficients in DMPC bilayers was observed. Values ranged from 6.72 x 10(-8) to 16.2 x 10(-8) cm2/s, with the smaller probes diffusing faster than the larger ones. Measurements in DMPC/cholesterol bilayers, which represent the most thorough characterization of small-solute diffusion in this system, exhibited a similar molecular weight dependence, although the diffusion coefficients were lower, ranging from 1.62 x 10(-8) to 5.60 x 10(-8) cm2/s. Lateral diffusion measurements in stratum corneum-extracted lipids, which represent a novel examination of diffusion in this unique lipid system, also exhibited a molecular weight dependence, with values ranging from 0.306 x 10(-8) to 2.34 x 10(-8) cm2/s. Literature data showed that these strong molecular weight dependencies extend to even smaller compounds than those examined in this study. A two-parameter empirical expression is presented that describes the lateral diffusion coefficient in terms of the solute's molecular weight and captures the size dependence over the range examined. This study illustrates the degree to which small-molecule lateral diffusion in stratum corneum-extracted lipids can be represented by diffusion in DMPC and DMPC/cholesterol bilayer systems, and may lead to a better understanding of small-solute transport across human stratum corneum.

A theory has been developed to predict the effects of electrostatic interactions on the equilibrium partition coefficient (Φ) of spherical macromolecules in gels, the gels being modeled as random arrays of fibers. The partitioning theory derived by Ogston (Trans. Faraday Soc.54, 1754–1757 (1958)) for neutral macromolecules and fibers was extended by using a Boltzmann factor, containing an electrostatic free energy, to modify the probability of fitting a sphere in a space between fibers. This approach, which is limited to dilute solutions of macromolecules, is approximate in that the only electrostatic interactions considered are those between the sphere and the nearest fiber. The electrostatic free energy was calculated from finite-element solutions to the linearized Poisson–Boltzmann equation for a sphere interacting with a long cylinder, both with specified surface charge densities. Free energies calculated for many combinations of sphere radius, fiber radius, separation distance, Debye length, and the surface charge densities of the sphere and fiber are presented as a correlation involving the various dimensionless parameters. When the sphere and fiber have like charges, Φ decreases with increases in the sphere size, the volume fraction of fibers, the Debye length, and either surface charge density; results are presented to illustrate each of these effects. Predictions from the theory are in good agreement with recent measurements of Φ for proteins in moderately charged gels.

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.

The permeabilities of many steroids through human skin have been previously measured and reported in the literature. Analysis of these data reveals that significant discrepancies exist between the measurements of Scheuplein et al.1and those of other groups. Six of the 14 steroids which were examined by Scheuplein et al., aldosterone, corticosterone, estradiol, hydrocortisone, progesterone, and testosterone, have also been examined by other groups. For each of these steroids, the permeability measurements of Scheuplein et al. are lower than those reported by other groups by factors of between 5.0 and 77. Eight independent measurements of the permeability of estradiol are in good agreement with one another, but are greater than the value reported by Scheuplein et al. by factors of between 11 and 20. Several possible sources of experimental error, including the variability of the skin samples, the differences in the experimental temperature, the establishment of steady‐state conditions, the use of radiolabeled drugs, and the skin preparation technique, have been considered and do not appear to account for the magnitude of the observed discrepancies nor for the fact that the data of Scheuplein et al. are consistently lower than those reported by other groups.