Hindered convection of proteins in agarose gels

Physical chemistry of gastric digestion of proteins gels

In this paper, we present the rich physics and chemistry of the gastric digestion of protein gels. Knowledge of this matter is important for the development of sustainable protein foods that are based on novel proteins sources like plant proteins or insects. Their digestibility is an important question in the design of these new protein foods. As polyelectrolyte gels, they can undergo volume changes upon shifts in pH or ionic strengths, as protein gels experience when entering the gastric environment. We show that these volume changes can be modelled using the Flory-Rehner theory, combined with Gibbs-Donnan theory accounting for the distribution of electrolytes over gel and bath. In-vitro experiments of soy protein gels in simulated gastric fluid indeed show intricate swelling behaviour, at first the gels show swelling but at longer times they shrink again. Simulations performed with the Flory-Rehner/Gibbs-Donnan theory reproduce qualitatively similar behaviour. In the final part of the paper, we discuss how the model must be extended to model realistic conditions existing in the in-vivo gastric environment.

Gel formation in protein amyloid aggregation: a physical mechanism for cytotoxicity

Amyloid fibers are associated with disease but have little chemical reactivity. We investigated the formation and structure of amyloids to identify potential mechanisms for their pathogenic effects. We incubated lysozyme 20 mg/ml at 55C and pH 2.5 in a glycine-HCl buffer and prepared slides on mica substrates for examination by atomic force microscopy. Structures observed early in the aggregation process included monomers, small colloidal aggregates, and amyloid fibers. Amyloid fibers were observed to further self-assemble by two mechanisms. Two or more fibers may merge together laterally to form a single fiber bundle, usually in the form of a helix. Alternatively, fibers may become bound at points where they cross, ultimately forming an apparently irreversible macromolecular network. As the fibers assemble into a continuous network, the colloidal suspension undergoes a transition from a Newtonian fluid into a viscoelastic gel. Addition of salt did not affect fiber formation but inhibits transition of fibers from linear to helical conformation, and accelerates gel formation. Based on our observations, we considered the effects of gel formation on biological transport. Analysis of network geometry indicates that amyloid gels will have negligible effects on diffusion of small molecules, but they prevent movement of colloidal-sized structures. Consequently gel formation within neurons could completely block movement of transport vesicles in neuronal processes. Forced convection of extracellular fluid is essential for the transport of nutrients and metabolic wastes in the brain. Amyloid gel in the extracellular space can essentially halt this convection because of its low permeability. These effects may provide a physical mechanism for the cytotoxicity of chemically inactive amyloid fibers in neurodegenerative disease.

Biphasic finite element model of solute transport for direct infusion into nervous tissue

Infusion-based techniques are promising drug delivery methods for treating diseases of the nervous system. Direct infusion into tissue parenchyma circumvents the blood-brain barrier, localizes delivery, and facilitates transport of macromolecular agents. Computational models that predict interstitial flow and solute transport may aid in protocol design and optimization. We have developed a biphasic finite element (FE) model that accounts for local, flow-induced tissue swelling around an infusion cavity. It solves for interstitial fluid flow, tissue deformation, and solute transport in surrounding isotropic gray matter. FE solutions for pressure-controlled infusion were validated by comparing with analytical solutions. The influence of deformation-dependent hydraulic permeability was considered. A transient, nonlinear relationship between infusion pressure and infusion rate was determined. The sensitivity of convection-dominated solute transport (i.e., albumin) over a range of nervous tissue properties was also simulated. Solute transport was found to be sensitive to pressure-induced swelling effects mainly in regions adjacent to the infusion cavity (r/a 0 <or= 5 where a 0 is the outer cannula radius) for short times infusion simulated (3 min). Overall, the biphasic approach predicted enhanced macromolecular transport for small volume infusions (e.g., 2 microL over 1 h). Solute transport was enhanced by decreasing Young's modulus and increasing hydraulic permeability of the tissue.

Dilation and degradation of the brain extracellular matrix enhances penetration of infused polymer nanoparticles

This study investigates methods of manipulating the brain extracellular matrix (ECM) to enhance the penetration of nanoparticle drug carriers in convection-enhanced delivery (CED). A probe was fabricated with two independent microfluidic channels to infuse, either simultaneously or sequentially, nanoparticles and ECM-modifying agents. Infusions were performed in the striatum of the normal rat brain. Monodisperse polystyrene particles with a diameter of 54 nm were used as a model nanoparticle system. Because the size of these particles is comparable to the effective pore size of the ECM, their transport may be significantly hindered compared with the transport of low molecular weight molecules. To enhance the transport of the infused nanoparticles, we attempted to increase the effective pore size of the ECM by two methods: dilating the extracellular space and degrading selected constituents of the ECM. Two methods of dilating the extracellular space were investigated: co-infusion of nanoparticles and a hyperosmolar solution of mannitol, and pre-infusion of an isotonic buffer solution followed by infusion of nanoparticles. These treatments resulted in an increase in the nanoparticle distribution volume of 51% and 123%, respectively. To degrade hyaluronan, a primary structural component of the brain ECM, a pre-infusion of hyaluronidase (20,000 U/mL) was followed after 30 min by infusion of nanoparticles. This treatment resulted in an increase in the nanoparticle distribution of 64%. Our results suggest that both dilation and enzymatic digestion can be incorporated into CED protocols to enhance nanoparticle penetration.

Binding of glycosaminoglycans to cyano-activated agarose membranes: kinetic and diffusional effects on yield and homogeneity

Methods were developed for binding a glycosaminoglycan (GAG, a 50 kDa chondroitin sulfate) to thin agarose membranes using 1-cyano-4-(dimethylamino)pyridinium tetrafluoroborate (CDAP) as the activating agent. Process conditions were optimized to achieve high yields and spatially uniform concentrations of bound ligand. Yields were varied mainly by manipulating the duration and temperature of the aqueous washes prior to coupling, which affected the concentration of active sites available for subsequent GAG binding. The rate constants for degradation of the active cyanate esters in 0.1M bicarbonate solutions were 0.24+/-0.02 h(-1) at 4 degrees C and 0.08+/-0.03 h(-1) at 0 degrees C. Steric limitations in the 3% agarose gels severely restricted binding, with only about 0.1% of active sites being accessible to GAG molecules. The GAG binding occurred primarily in the outer 50-70 microm of the membranes, so that coupling was homogeneous only for thin gels. A model of GAG diffusion and reaction in the coupling step was developed to explain the observed effects of parameters such as the GAG concentration in solution and the membrane thickness. An analysis of the key time scales in the synthesis provides design principles that should be useful also for other cyanylating agents, other ligands, and for beads as well as membranes.

Interstitial flow and its effects in soft tissues

Interstitial flow plays important roles in the morphogenesis, function, and pathogenesis of tissues. To investigate these roles and exploit them for tissue engineering or to overcome barriers to drug delivery, a comprehensive consideration of the interstitial space and how it controls and affects such processes is critical. Here we attempt to review the many physical and mathematical correlations that describe fluid and mass transport in the tissue interstitium; the factors that control and affect them; and the importance of interstitial transport on cell biology, tissue morphogenesis, and tissue engineering. Finally, we end with some discussion of interstitial transport issues in drug delivery, cell mechanobiology, and cell homing toward draining lymphatics.

A sensitive in vivo model for quantifying interstitial convective transport of injected macromolecules and nanoparticles

Effective interstitial transport of particles is necessary for injected drug/diagnostic agents to reach the intended target; however, quantitative methods to estimate such transport parameters are lacking. In this study, we develop an in vivo model for evaluating interstitial convection of injected macromolecules and nanoparticles. Fluorescently labeled macromolecules and particles are coinfused with a reference solute at constant infusion pressure intradermally into the mouse tail tip, and their relative convection coefficients are determined from spatial and temporal interstitial concentration profiles. Quantifying relative solute velocity with a coinfused reference solute eliminates the need to estimate interstitial fluid velocity profiles, greatly reducing experimental variability. To demonstrate sensitivity and usefulness of this model, we compare the effects of size (dextrans of 3, 40, 71, and 2,000 kDa and 40-nm diameter particles), shape (linear dextran 71 kDa vs. 69 kDa globular protein albumin), and charge (anionic vs. neutral dextran 3 kDa) on interstitial convection. We find significant differences in interstitial transport rates between each of these molecules and confirm expected transport phenomena, testifying to sensitivity of the model in comparing solutes of different size, shape, and charge. Our data show that size exclusion (within a specific size range) dominates molecular convection, while mechanical hindrance slows larger molecules and nanoparticles; proteins convect slower than linear molecules of equal molecular mass, and negative surface charges increase convection through matrix repulsion. Our in vivo model is presumably a sensitive and reliable tool for evaluating and optimizing potential drug/diagnostic vehicles that utilize interstitial and lymphatic delivery routes.

Convection and diffusion in charged hydrated soft tissues: a mixture theory approach

The extracellular matrix of cartilage is a charged porous fibrous material. Transport phenomena in such a medium are very complex. In this study, solute diffusive flux and convective flux in porous fibrous media were investigated using a continuum mixture theory approach. The intrinsic diffusion coefficient of solute in the mixture was defined and its relation to drag coefficients was presented. The effect of mechanical loading on solute diffusion in cartilage under unconfined compression with a frictionless boundary condition was analyzed numerically using the model developed. Both strain-dependent hydraulic permeability and diffusivity were considered. Analyses and results show that (1) In porous media, the convective velocity for each solute phase is different. (2) The solute convection in tissue is governed by the relative convective velocity (i.e., relative to solid velocity). (3) Under the assumption that all the frictional interactions among solutes are negligible, the relative convective velocity for alpha-solute phase is equal to the relative solvent velocity multiplied by its convective coefficient (H (alpha)) which is also known as the hindrance factor in the literature. The relationship between the convective coefficient and the relative diffusivity of solute is presented. (4) Solute concentration profile within the cartilage sample depends on the phase of dynamic compression.

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.

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.

Hindered convection of macromolecules in hydrogels

Hindered convection of macromolecules in gels was studied by measuring the sieving coefficient (theta) of narrow fractions of Ficoll (Stokes-Einstein radius, r(s) = 2.7-5.9 nm) in agarose and agarose-dextran membranes, along with the Darcy permeability (kappa). To provide a wide range of kappa, varying amounts of dextran (volume fractions < or = 0.011) were covalently attached to agarose gels with volume fractions of 0.040 or 0.080. As expected, theta decreased with increasing r(s) or with increasing concentrations of either agarose or dextran. For each molecular size, theta plotted as a function of kappa fell on a single curve for all gel compositions studied. The dependence of theta on kappa and r(s) was predicted well by a hydrodynamic theory based on flow normal to the axes of equally spaced, parallel fibers. Values of the convective hindrance factor (K(c), the ratio of solute to fluid velocity), calculated from Theta and previous equilibrium partitioning data, were unexpectedly large; although K(c) < or = 1.1 in the fiber theory, its apparent value ranged generally from 1.5 to 3. This seemingly anomalous result was explained on the basis of membrane heterogeneity. Convective hindrances in the synthetic gels were quite similar to those in glomerular basement membrane, when compared on the basis of similar solid volume fractions and values of kappa. Overall, the results suggest that convective hindrances can be predicted fairly well from a knowledge of kappa, even in synthetic or biological gels of complex composition.

Mathematical modelling of skeletal repair

Tissue engineering offers significant promise as a viable alternative to current clinical strategies for replacement of damaged tissue as a consequence of disease or trauma. Since mathematical modelling is a valuable tool in the analysis of complex systems, appropriate use of mathematical models has tremendous potential for advancing the understanding of the physical processes involved in such tissue reconstruction. In this review, the potential benefits, and limitations, of theoretical modelling in tissue engineering applications are examined with specific emphasis on tissue engineering of bone. A central tissue engineering approach is the in vivo implantation of a biomimetic scaffold seeded with an appropriate population of stem or progenitor cells. This review will therefore consider the theory behind a number of key factors affecting the success of such a strategy including: stem cell or progenitor population expansion and differentiation ex vivo; cell adhesion and migration, and the effective design of scaffolds; and delivery of nutrient to avascular structures. The focus will be on current work in this area, as well as on highlighting limitations and suggesting possible directions for future work to advance health-care for all.

Dynamic alterations of glomerular charge density in fixed rat kidneys suggest involvement of endothelial cell coat

In a previous paper, we found that low ionic strength (I) reversibly reduced the glomerular charge density, suggesting increased volume of the charge-selective barrier. Because glutaraldehyde makes most structures rigid, we considered the isolated, perfusion-fixed rat kidney to be an ideal model for further analysis. The fixed kidneys were perfused with albumin solutions containing FITC-Ficoll at two different Is (I = 151 and 34 mM). At normal I, the fractional clearance () for albumin was 0.0049 (SE -0.0017, +0.0027, n = 6), whereas for neutral Ficoll35.5A of similar size was significantly higher 0.104 (SE 0.010, n = 5, P < 0.001). At low I, for albumin was 0.0030 (SE -0.0011, +0.0018, n = 6, not significant from albumin at normal I) and for Ficoll35.5A was identical to that at normal I, 0.104 (SE 0.015, n = 6, P < 0.01 compared with albumin at low I). According to a heterogeneous charged fiber model, low I reduced the fiber density from 0.056 to 0.0315, suggesting a 78% gel volume expansion. We conclude that 1) there is a significant glomerular charge barrier. 2) Solutions with low I increase the volume of the charge barrier even in kidneys fixed with glutaraldehyde. Our findings suggest that polysaccharide-rich structures, such as the endothelial cell coat, are key components in the glomerular barrier.

Glomerular size and charge selectivity in the mouse after exposure to glucosaminoglycan-degrading enzymes

This is the first functional study of glomerular size and charge selectivity in mice. The aim was to investigate the controversial issue of glomerular permselectivity in animals exposed to glucosaminoglycan-degrading enzymes, hyaluronidase, and heparinase. Fractional clearances (theta) for FITC-Ficoll and albumin were estimated in isoflurane anesthetized mice in vivo and in cooled isolated perfused kidneys (cIPK). In cIPK, a significant increase of theta(albumin) from 0.0023 (95% confidence interval, 0.0014 to 0.0033) in controls to 0.0130 (95% confidence interval, 0.0055 to 0.0206) was seen after hyaluronidase treatment. The theta for neutral Ficoll of similar size as albumin was 0.063 to 0.093 in all groups. According to a heterogeneous charged fiber model, the fiber volume fraction of negatively charged fibers decreased by 10% after enzyme treatments. It is concluded that glomerular size and charge selectivity in mice is similar to that previously shown for rats. Moreover, hyaluronic acid, chondroitin sulfate, and heparan sulfate are of importance for charge selectivity.

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.

Structural determinants of glomerular permeability

Recent progress in relating the functional properties of the glomerular capillary wall to its unique structure is reviewed. The fenestrated endothelium, glomerular basement membrane (GBM), and epithelial filtration slits form a series arrangement in which the flow diverges as it enters the GBM from the fenestrae and converges again at the filtration slits. A hydrodynamic model that combines morphometric findings with water flow data in isolated GBM has predicted overall hydraulic permeabilities that are consistent with measurements in vivo. The resistance of the GBM to water flow, which accounts for roughly half that of the capillary wall, is strongly dependent on the extent to which the GBM surfaces are blocked by cells. The spatial frequency of filtration slits is predicted to be a very important determinant of the overall hydraulic permeability, in keeping with observations in several glomerular diseases in humans. Whereas the hydraulic resistances of the cell layers and GBM are additive, the overall sieving coefficient for a macromolecule (its concentration in Bowman's space divided by that in plasma) is the product of the sieving coefficients for the individual layers. Models for macromolecule filtration reveal that the individual sieving coefficients are influenced by one another and by the filtrate velocity, requiring great care in extrapolating in vitro observations to the living animal. The size selectivity of the glomerular capillary has been shown to be determined largely by the cellular layers, rather than the GBM. Controversial findings concerning glomerular charge selectivity are reviewed, and it is concluded that there is good evidence for a role of charge in restricting the transmural movement of albumin. Also discussed is an effect of albumin that has received little attention, namely, its tendency to increase the sieving coefficients of test macromolecules via steric interactions. Among the unresolved issues are the specific contributions of the endothelial glycocalyx and epithelial slit diaphragm to the overall hydraulic resistance and macromolecule selectivity and the nanostructural basis for the observed permeability properties of the GBM.

A quantitative analysis of the glomerular charge barrier in the rat

Modifying the ionic strength (I) is a gentle way to alter charge interactions, but it cannot be done for studies of the glomerular sieving of proteins in vivo. We therefore perfused 18 isolated rat kidneys with albumin solutions of different ionic strengths at a low temperature (cIPK) to inhibit tubular uptake and protease activity. Four anionic proteins were studied, namely albumin (Alb), orosomucoid (Oro), ovalbumin (Ova), and anionic horseradish peroxidase (aHRP), together with the neutral polymer Ficoll. With normal ionic strength of the perfusate (152 mM), the fractional clearance (theta) was 0.0018 +/- 0.0003 for Alb, 0.0033 +/- 0.0003 for Oro, 0.090 +/- 0.008 for Ova, and 0.062 +/- 0.002 for aHRP. These theta values were all lower than for Ficoll of similar hydrodynamic size; e.g., theta(Ficoll 36 A) was >20 times higher than theta for albumin. Low ionic strength (34 mM) increased size selectivity as theta for anionic proteins and Ficoll fell, suggesting a reduction in small-pore radius from 44 +/- 0.4 to 41 +/- 0.5 A, P < 0.01. In contrast, low I reduced the charge density of the membrane, omega, to one-quarter of the 20--50 meq/l estimated at normal I. These dynamic changes in omega seem to be due to volume alterations of the charged gel, fluid shifts that easily are accounted for by the changes in electroosmotic pressures. The finding that low ionic strength induces inverse effects on size selectivity and charge density strongly suggests that separate structures of the glomerular wall are responsible for the two properties.

A gel-membrane model of glomerular charge and size selectivity in series

We have analyzed glomerular sieving data from humans, rats in vivo, and from isolated perfused rat kidneys (IPK) and present a unifying hypothesis that seems to resolve most of the conflicting results that exist in the literature. Particularly important are the data obtained in the cooled IPK, because they allow a variety of experimental conditions for careful analysis of the glomerular barrier; conditions that never can be obtained in vivo. The data strongly support the classic concept of a negative charge barrier, but separate components seem to be responsible for charge and size selectivity. The new model is composed of a dynamic gel and a more static membrane layer. First, the charged gel structure close to the blood compartment has a charge density of 35-45 meq/l, reducing the concentration of albumin to 5-10% of that in plasma, due to ion-ion interactions. Second, the size-selective structure has numerous functional small pores (radius 45-50 A) and far less frequent large pores (radius 75-115 A), the latter accounting for 1% of the total hydraulic conductance. Both structures are required for the maintenance of an intact glomerular barrier.

Effects of Multisolute Steric Interactions on Membrane Partition Coefficients

A key parameter in membrane and chromatographic separations is the partition coefficient, the equilibrium ratio of the solute concentration in a porous or fibrous material to that in bulk solution. The theoretical effects of solute size on partition coefficients in straight pores or randomly oriented fiber matrices have been investigated previously for very dilute solutions, where solute-solute interactions are negligible, and also for more concentrated solutions consisting of spherical solutes of uniform size. For concentrated solutions it has been found that steric and other repulsive interactions among solutes increase the partition coefficient above the dilute limit. To extend the results for porous or fibrous media to include concentrated mixtures of solutes with different sizes or shapes, we used an excluded volume approach. In this formulation, which describes steric interactions only, partition coefficients were computed by summing all volumes excluded to a solute molecule by virtue of its finite size, the finite size of other solutes, and the presence of fixed obstacles (pore walls or fibers). For a mixture of two spherical solutes, the addition of any second solute at finite concentration increased the partition coefficient of the first solute. That increase was sensitive to the size of the second solute; for a given volume fraction of the second solute, the smaller its radius, the larger the effect. When the total volume fraction of solutes was fixed, an increase in the amount of a second, smaller solute increased the partition coefficient of the first solute, whereas an increase in the amount of a second, larger solute had the opposite effect. Results were obtained also for oblate or prolate spheroidal solutes and for fibrous media containing fibers of different radii. For constant total fiber volume fraction, an increase in the amount of a second, smaller fiber decreased the partition coefficient of a spherical solute, whereas an increase in the amount of a second, larger fiber had the opposite effect. Overall, the theory suggests that the introduction of heterogeneities, whether as mixtures of solute sizes or mixtures of fiber sizes, may cause partition coefficients to differ markedly from those of uniform systems. Copyright 2000 Academic Press.