Effects of Solute Concentration on Equilibrium Partitioning of Flexible Macromolecules in Fibrous Membranes and Gels

Bath Concentration of Anionic Contrast Agents Does Not Affect Their Diffusion and Distribution in Articular Cartilage In Vitro

OBJECTIVE

Differences in contrast agent diffusion reflect changes in composition and structure of articular cartilage. However, in clinical application the contrast agent concentration in the joint capsule varies, which may affect the reliability of contrast enhanced cartilage tomography (CECT). In the present study, effects of concentration of x-ray contrast agents on their diffusion and equilibrium distribution in cartilage were investigated.

DESIGN

Full-thickness cartilage discs (d = 4.0 mm, n = 120) were detached from bovine patellae (n = 24). The diffusion of various concentrations of ioxaglate (5, 10, 21, 50 mM) and iodide (30, 60, 126, 300 mM) was allowed only through the articular surface. Samples were imaged with a clinical peripheral quantitative computed tomography scanner before immersion in contrast agent, and after 1, 5, 9, 16, 25, and 29 hours in the bath.

RESULTS

Diffusion and partition coefficients were similar between different contrast agent concentrations. The diffusion coefficient of iodide (473 ± 133 µm(2)/s) was greater (P ≤ 0.001) than that of ioxaglate (92 ± 46 µm(2)/s). In full-thickness cartilage, the partition coefficient (at 29 h) of iodide (71 ± 5%) was greater (P ≤ 0.02 with most concentrations) than that of ioxaglate (62 ± 6%).

CONCLUSIONS

Significant differences in partition and diffusion coefficient of two similarly charged (-1) contrast agents were detected, which shows the effect of steric interactions. However, the increase in solute concentration did not increase its partition coefficient. In clinical application, it is important that contrast agent concentration does not affect the interpretation of CECT imaging.

Artificial molecular sieves and filters: a new paradigm for biomolecule separation

Patterned regular sieves and filters with comparable molecular dimensions hold great promise as an alternative to conventional polymeric gels and fibrous membranes to improve biomolecule separation. Recent developments of microfabricated nanofluidic sieves and filters have demonstrated superior performance for both analytical and preparative separation of various physiologically relevant macromolecules, including proteins. The insights gained from designing these artificial molecular sieves and filters, along with the promising results gathered from their first applications, serve to illustrate the impact that they can have on improving future separation of complex biological samples. Further development of artificial sieves and filters with more elaborate geometrical constraints and tailored surface functionality is believed to provide more promising ideals and results for biomolecule separation, which has great implications for proteomic research and biomarker discovery.

Darcy permeability of agarose-glycosaminoglycan gels analyzed using fiber-mixture and donnan models

Agarose-glycosaminoglycan (GAG) membranes were synthesized to provide a model system in which the factors controlling the Darcy (or hydraulic) permeability could be assessed in composite gels of biological relevance. The membranes contained a GAG (chondroitin sulfate) that was covalently bound to agarose via terminal amine groups, and the variables examined were GAG concentration and solution ionic strength. The addition of even small amounts of GAG (0.4 vol/vol %) resulted in a twofold reduction in the Darcy permeability of 3 vol/vol % agarose gels. Electrokinetic coupling, caused by the negative charge of the GAG, resulted in an additional twofold reduction in the open-circuit permeability when the ionic strength was decreased from 1 M to 0.01 M. A microstructural hydrodynamic model was developed, based on a mixture of neutral, coarse fibers (agarose fibrils), and fine, charged fibers (GAG chains). Heterogeneity within agarose gels was modeled by assuming that fiber-rich, spherical inclusions were distributed throughout a fiber-poor matrix. That model accurately predicted the Darcy permeability when the ionic strength was high enough to suppress the effects of charge, but underestimated the influence of ionic strength. A more macroscopic approach, based on Donnan equilibria, better captured the reductions in Darcy permeability caused by GAG charge.

Characteristics of protein partitioning in an aqueous micellar-gel system

Partitioning of proteins has been studied experimentally in a system combining a gel-bead phase and a nonionic micellar phase. The micellar phase consists of cylindrically shaped micelles, which are completely excluded from the gel-bead phase. Partitioning of single-component protein solutions (myoglobin, ovalbumin, and BSA) is determined by excluded-volume interactions in the micellar phase, and as a result the proteins prefer the gel-bead phase to the micellar phase. The protein concentration inside the gel beads increases with an increase in volume fraction of the micelles and increases with an increase in the size of the proteins. The protein partition coefficients obtained for a binary mixture of myoglobin and bovine serum albumin (BSA) show the same protein concentration dependence as the single-component protein partition coefficients.

Solute diffusivity correlates with mechanical properties and matrix density of compressed articular cartilage

The biomechanical functions of articular cartilage are governed largely by the composition and density of its specialized extracellular matrix. Relationships between matrix density and functional indices such as mechanical properties or interstitial solute diffusivities have been previously explored. However, direct correlations between mechanical properties and solute transport parameters have received less attention, despite potential application of this information for cartilage functional assessment both in vivo and in vitro. The objective of this study was therefore to examine relationships among solute diffusivities, mechanical properties, and matrix density of compressed articular cartilage. Matrix density varied due to natural variation among explants and due to applied static compression. Matrix density of statically compressed cartilage explants was characterized by glycoaminoglycan (GAG) weight fraction and fluid volume fraction, while diffusion coefficients of a wide range of solutes were measured to characterize the transport environment. Explant mechanical properties were characterized by a non-linear Young's modulus (axial stress-strain ratio) and a non-linear Poisson's ratio (radial-to-axial strain ratio). Solute diffusivities were consistently correlated with Young's modulus, as well as with explant GAG weight and fluid volume fractions. Therefore, in vitro mechanical tests may provide a means of assessing transport environments in cartilage-like materials, while in vivo measurements of solute transport (for example with magnetic resonance imaging) may be a useful complement in identifying localized differences in matrix density and mechanical properties.

Hydrodynamic radius ladders of proteins

We introduce hydrodynamic radius ladders of proteins as a new tool to isolate and measure the role of hydrodynamic size on transport properties of proteins. Radius ladders are collections of derivatives of a protein that differ incrementally in number of polyethylene glycol (PEG) chains grafted to their surface. The addition of these chains causes the hydrodynamic size of the protein to increase. Capillary electrophoresis (CE) separates these derivatives into individual peaks or "rungs" of a ladder composed of proteins that have the same number of PEG chains, and provides a way to measure the values of hydrodynamic radius of proteins that constitute the rungs of the ladder. We demonstrate the utility of this approach by measuring the partitioning of radius ladders into polymer hydrogels. The combination of radius ladders and CE produces a large amount of internally consistent data on hydrodynamic size. This technique will have applicability to the study of the role of hydrodynamic size on transport.

Solute convection in dynamically compressed cartilage

Chondrocytes depend upon solute transport within the avascular extracellular matrix of articular cartilage for many of their biological activities. Alterations to solute transport parameters may therefore mediate the cell response to tissue compression. While interstitial solute transport may be supplemented by convection during dynamic tissue compression, matrix compression is also associated with decreased diffusivities. Such trade-offs between increased convection and decreased diffusivities of solutes in dynamically compressed cartilage remain largely unexplored. We measured diffusion and convection coefficients of a wide range of solutes in mature bovine cartilage explant disks subjected to radially unconfined axial ramp compression and release. Solutes included approximately 500 Da fluorophores bearing positive and negative charges, and 10 kDa dextrans bearing positive, neutral, and negative charges. Significantly positive values of convection coefficients were measured for several different solutes. Findings therefore support a role for solute convection in mediating the cartilage biological response to dynamic compression.

Effects of concentration on the partitioning of macromolecule mixtures in agarose gels

To test the effects of solute concentration on the equilibrium partitioning of single macromolecules and macromolecule mixtures between bulk solutions and gels, the partition coefficient in agarose was measured for BSA and for four narrow fractions of Ficoll with Stokes radii of 30-59 A. Solutions of each test macromolecule were equilibrated with a known volume of gel, final liquid concentrations measured, and partition coefficients (gel concentration divided by bulk concentration) calculated by applying a material balance. The partition coefficient of each macromolecule was measured in 4 and 6% gels under dilute conditions and with BSA present at initial concentrations up to 13.5 g/dl. As expected, the partition coefficients decreased with increasing agarose concentration and with increasing macromolecular size. Moreover, increasing the BSA concentration increased the partition coefficient of BSA itself and that of all four Ficolls. This effect was most pronounced for the largest test solutes. Measurements at two ionic strengths confirmed that electrostatic interactions were negligible under the conditions used. The experimental results were compared with predictions from a previously developed excluded volume theory for the partitioning of mixtures of rigid, spheroidal macromolecules in fibrous media. Agarose was represented as a randomly oriented array of cylindrical fibers, BSA as a prolate spheroid, and Ficoll as a sphere. The quantitative agreement between the model predictions and the data was generally quite good, indicating that steric interactions among solute molecules and between solute molecules and gel fibers could explain the partitioning results. The theory is simple enough computationally to be applied to a variety of processes that are influenced by the equilibrium partitioning of macromolecules.

Equilibrium partitioning of Ficoll in composite hydrogels

Equilibrium partition coefficients (phi, the concentration in the gel divided by that in free solution) of fluorescein-labeled Ficolls in pure agarose and agarose-dextran composite gels were measured as a function of gel composition and Ficoll size. The four narrow fractions of Ficoll, a spherical polysaccharide, had Stokes-Einstein radii ranging from 2.7 to 5.9 nm. Gels with agarose volume fractions of 0.040 and 0.080 were studied, with dextran volume fractions (calculated as if the chain were a long fiber) up to 0.011. As expected, phi generally decreased as the Ficoll size increased (for a given gel composition) or as the amount of dextran incorporated into the gel increased (for a given agarose concentration and Ficoll size). The decrease in phi that accompanied dextran addition was predicted well by an excluded volume theory in which agarose and dextran were both treated as rigid, straight, randomly positioned and oriented fibers. Modeling dextran as a spherical coil within a fibrous agarose gel produced much less accurate predictions. The diffusional permeabilities of these gels were assessed by combining the current partitioning data with relative diffusivities (Kd, the diffusivity in the gel divided by that in free solution) reported previously. The values of phi Kd for a synthetic gel with 8.0% agarose and 1.1% dextran (by volume) were found to be very similar to those for the glomerular basement membrane, a physiologically important material which also has a total solids content of approximately 10%.

Agarose-dextran gels as synthetic analogs of glomerular basement membrane: water permeability

Novel agarose-dextran hydrogels were synthesized and their suitability as experimental models of glomerular basement membrane was examined by measuring their Darcy (hydraulic) permeabilities (kappa). Immobilization of large dextran molecules in agarose was achieved by electron beam irradiation. Composite gels were made with agarose volume fractions (phi(a)) of 0.04 or 0.08 and dextran volume fractions (phi(d)) ranging from 0 to 0.02 (fiber volume/gel volume), using either of two dextran molecular weights (500 or 2000). At either agarose concentration and for either size of dextran, kappa decreased markedly as the amount of dextran was increased. Statistically significant deviations from the value of kappa for pure agarose were obtained for remarkably small volume fractions of dextran: phi(d) > or = 0.0003 for phi(a) = 0.04 and phi(d) > or = 0.001 for phi(a) = 0.08. The Darcy permeabilities were much more sensitive to phi(d) than to phi(a), and were as much as 26 times smaller than those of pure agarose. Although phi(d) was an important variable, dextran molecular weight was not. The effects of dextran addition on kappa were described fairly well using simple structural idealizations. At high agarose concentrations, the dextran chains behaved as fine fibers interspersed among coarse agarose fibrils, whereas, at low concentrations, the dextran molecules began to resemble spherical obstacles embedded in agarose gels. The ability to achieve physiologically relevant Darcy permeabilities with these materials (as low as 1.6 nm2) makes them an attractive experimental model for glomerular basement membrane and possibly other extracellular matrices.