Diffusion of macromolecules in agarose gels: comparison of linear and globular configurations.

The diffusion coefficients (D) of different types of macromolecules (proteins, dextrans, polymer beads, and DNA) were measured by fluorescence recovery after photobleaching (FRAP) both in solution and in 2% agarose gels to compare transport properties of these macromolecules. Diffusion measurements were conducted with concentrations low enough to avoid macromolecular interactions. For gel measurements, diffusion data were fitted according to different theories: polymer chains and spherical macromolecules were analyzed separately. As chain length increases, diffusion coefficients of DNA show a clear shift from a Rouse-like behavior (DG congruent with N0-0.5) to a reptational behavior (DG congruent with N0-2.0). The pore size, a, of a 2% agarose gel cast in a 0.1 M PBS solution was estimated. Diffusion coefficients of the proteins and the polymer beads were analyzed with the Ogston model and the effective medium model permitting the estimation of an agarose gel fiber radius and hydraulic permeability of the gels. Not only did flexible macromolecules exhibit greater mobility in the gel than did comparable-size rigid spherical particles, they also proved to be a more useful probe of available space between fibers.     

Agarose/polyacrylamide minislab gel electrophoresis of intact cartilage proteoglycans and their proteolytic degradation products.

We have developed a procedure for the use of minislab gels to electrophoretically separate proteoglycans (PGs), large macromolecules with molecular masses greater than 2.5 million Da. Our procedure is a modification of the method of C.A. McDevitt and H. Muir (Anal. Biochem. 44, 612-622, 1971) for agarose/polyacrylamide, composite tube gels. These 1% agarose/1.2% acrylamide minigels are run at 35 mA for 75 min; bands are visualized by toluidine blue staining. The subtle size differences between the large aggregating PGs isolated from rat chondrosarcoma, bovine nasal septal cartilage, and adult bovine articular cartilage (which consists of two subpopulations) can be distinguished by their migration on these large pore gels. Chondroitin sulfate chains, added to all wells as a marker of constant mobility, ran immediately behind the dye front. The distance of migration into the gel of PGs incubated overnight with cathepsin B, carboxypeptidase A, papain, plasmin, elastase, or cathepsin G varied with the size of the cleavage products. We propose the use of this procedure for a convenient assessment of cartilage PGs and a rapid, reproducible assay for proteoglycanase activity.     

A subfraction of fragment D isolated from a plasmin hydrolysate of human fibrinogen.

Fragment D from a 4-hour plasminolysate of human fibrinogen was chromatographed on DEAE-cellulose and a nearly homogeneous subfraction obtained. It migrated as a single band in dodecylsulfate gel electrophoresis. Reduction yielded three peptide chains with approximate molecular weights of 45000, 295000 and 13000 as estimated from the electrophoretic migration rate in dodecylsulfate acrylamide gels. From these data the molecular weight of the Fragment D subfraction was calculated to be ca. 87500. The S-carboxymethylated peptide chains were separated by chromatography on DEAE-cellulose. They were correlated electrophoretically and their amino acid composition was determined. The peptide chains of molecular weight 45000 and 29500 showed a chromatographic microheterogeneity. The subfractions of these two chains, however, were not distinguished by their electrophoretic mobility in dodecylsulfate acry lamide gels and showed only insignificant differences in their amino acid composition.     

Electrophoretic mobility of high-molecular-weight, double-stranded DNA on agarose gels.

A new theoretical model for the migration of high-molecular-weight, double-stranded DNA on agarose gels is presented. This leads to the prediction that under certain conditions of electrophoresis, a linear relationship will exist between the molecular weight of a DNA molecule, raised to the (-2/3) power, and its electrophoretic mobility. Agarose gel electrophoresis of the fragments of bacteriophage lambda DNA produced by several restriction endonucleases confirms this relationship, and establishes some of the limits on its linearity. For this work, a polyacrylamide slab gel apparatus was modified for use with agarose gels. This apparatus has several advantages over others commercially available for agarose gel electrophoresis, including the abilities to run a larger number of samples at one time, to use lower-concentration gels, and to maintain better temperature stability across the width of the gel. The validation of the relationship developed here between molecular weight and electrophoretic mobility should make this a useful method for determining the molecular weights of DNA fragments.     

Hindered diffusion in agarose gels: test of effective medium model.

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.     

Partitioning and diffusion of proteins and linear polymers in polyacrylamide gels.

The equilibrium partition coefficient (K) and diffusion coefficient (Dgel) of two proteins and two linear polymers were measured as a function of polymer content of a 2.7% cross-linked polyacrylamide (PA) gel. The gel concentration, expressed as a volume percentage of PA in the gel (phi), varied between 0 and 14%. The measurements were made by fluorescence spectroscopy; fluorescent dyes were covalently attached to the macromolecules. The dependence of K on phi for the proteins agrees with a model of the gel network as randomly placed, impenetrable rods. The diffusion data are interpreted in terms of an effective medium theory for the mobility of a sphere in a Brinkman fluid. Using values of the Brinkman parameter in the literature, the effective medium model with no adjustable parameters fits the diffusion data for the proteins very well but underpredicts Dgel for the linear polymers. The gel effect on partitioning is significantly greater than that on diffusion. The permeability (KDgel) of bovine serum albumin decreased by 10(3) over the range phi = 0 --> 8%, and the ratio of permeabilities for ribonuclease compared to BSA increased from 2 to 30.     

A technique for electrophoresis in multiple-concentration agarose gels

A technique has been developed for embedding several agarose gels (running gels), each of a different agarose concentration, within a single 1.5% agarose slab. Equal portions of a sample were placed at the origin of each running gel and were simultaneously subjected to electrophoresis. Protein within the running gels was detected by staining with Coomassie blue; 0.2% gels were the least concentrated gels that were stained without gel breakage. Using the above technique, the dependence of electrophoretic mobility on agarose concentration has been measured for bacteriophage T7 capsids and a capsid dimer.     

Use of holographic laser interferometry to study the diffusion of polymers in gels

The aim of this study was to demonstrate the potential for holographic interferometry to be used for diffusion studies of large molecules in gels. The diffusion and partitioning of BSA (67,000 g/mol) and pullulans (5,900-112,000 g/mol) in agarose gel were investigated. The gel diffusion coefficients obtained for BSA were higher when distilled water was used as a solvent compared to those obtained with 0.1 M NaCl as the solvent. Furthermore, the gel diffusion coefficient increased with increasing BSA concentration. The same trend was found for liquid BSA diffusion coefficients obtained by DLS. BSA partition coefficients obtained at different agarose gel concentrations (2-6%, w/w) decreased slightly with increasing gel concentration. However, all BSA gel diffusion coefficients measured were significantly lower than those in pure solvent and they decreased with increasing agarose concentration. The gel diffusion coefficients obtained for pullulans decreased with increasing pullulan molecular weight. The same effect from increased molecular weight was seen in the liquid diffusion coefficients measured by DLS. The pullulan partition coefficients obtained decreased with increasing molecular weight. However, pullulans with a larger Stokes' radius than BSA had partition coefficients that were higher or approximately the same as BSA. This implied that the pullulan molecules were more flexible than the BSA molecules. The results obtained for BSA in this study agreed well with other experimental studies. In addition, the magnitude of the relative standard deviation was acceptable and in the same range as for many other methods. The results thereby obtained showed that holographic interferometry is a suitable method for studying diffusion of macromolecules in gels.     

Matrices with compliance comparable to that of brain tissue select neuronal over glial growth in mixed cortical cultures

Cortical neurons and astrocytes respond strongly to changes in matrix rigidity when cultured on flexible substrates. In this study, existing polyacrylamide gel polymerization methods were modified into a novel method for making substrates capable of engaging specific cell-adhesion receptors. Embryonic cortical dissociations were cultured on polyacrylamide or fibrin gel scaffolds of varying compliance. On soft gels, astrocytes do not spread and have disorganized F-actin compared to the cytoskeletons of astrocytes on hard surfaces. Neurons, however, extend long neurites and polymerize actin filaments on both soft and hard gels. Compared to tissue culture plastic or stiff gel substrates coated with laminin, on which astrocytes overgrow neurons in mixed cultures, laminin-coated soft gels encourage attachment and growth of neurons while suppressing astrocyte growth. The number of astrocytes on soft gels is lower than on hard even in the absence of mitotic inhibitors normally used to temper the astrocyte population. Dissociated embryonic rat cortices grown on flexible fibrin gels, a biomaterial with potential use as an implant material, display a similar mechano-dependent difference in cell population. The stiffness of materials required for optimal neuronal growth, characterized by an elastic modulus of several hundred Pa, is in the range measured for intact rat brain. Together, these data emphasize the potential importance of material substrate stiffness as a design feature in the next generation of biomaterials intended to promote neuronal regeneration across a lesion in the central nervous system while simultaneously minimizing the ingrowth of astrocytes into the lesion area.     

Water dynamics in charged and uncharged polysaccharide gels by quasi-elastic neutron scattering

Using a microeV neutron spectrometer we have studied the mobility of water in gels formed by two polysaccharides: agarose and hyaluronic acid. Agarose is a nearly uncharged polysaccharide; its gels are fairly stiff, quasi-random networks of fibre bundles. Hyaluronic acid is a highly charged polysaccharide capable of retaining large amounts of water in entangled meshworks with unusual rheological properties. We have analysed sets of quasi-elastic lineshapes broadened by two proton populations with different degrees of freedom. The resulting microscopic mobility parameters and their temperature dependence reveal a complex behaviour. The overall effect of the biopolymer network is to increase translational as well as rotational relaxation times, but the changes observed are not dramatic and cannot fully account for the strikingly different macroscopic properties of these gels. Local electrostatic interactions (over 3 to 20 A) do not appear to influence significantly the rheological behaviour.     

Synthesis of biocompatible,stimuli-responsive,physical gels based on ABA triblock copolymers

ABA triblock copolymers [A = 2-(diisopropylamino)ethyl methacrylate), DPA or 2-(diethylamino)ethyl methacrylate), DEA; B = 2-methacryloyloxyethyl phosphorylcholine, MPC] prepared using atom transfer radical polymerization dissolve in acidic solution but form biocompatible free-standing gels at around neutral pH in moderately concentrated aqueous solution (above approximately 10 w/v % copolymer). Proton NMR studies indicate that physical gelation occurs because the deprotonated outer DPA (or DEA) blocks become hydrophobic, which leads to attractive interactions between the chains: addition of acid leads to immediate dissolution of the micellar gel. Release studies using dipyridamole as a model hydrophobic drug indicate that sustained release profiles can be obtained from these gels under physiologically relevant conditions. More concentrated DPA-MPC-DPA gels give slower release profiles, as expected. At lower pH, fast, triggered release can also be achieved, because gel dissolution occurs under these conditions. Furthermore, the nature of the outer block also plays a role; the more hydrophobic DPA-MPC-DPA triblock gels are formed at lower copolymer concentrations and retain the drug longer than the DEA-MPC-DEA triblock gels.     

An analysis of the molecular forms of the lipopolysaccharide from Pseudomonas syringae pv. atrofaciens IMV K-1025

Water extract and salt-EDTA extract of Pseudomonas syringae, pv. atrofaciens cells were fractionated by ultracentrifugation with following salting out of ultracentrifugal supernatant by ammonium sulphate at 55% saturation (pH 4.5). The composition and distribution of LPS molecular forms were studied in the obtained fractions by means of electrophoresis in 10% polyacrylamide gel with 1% sodium dodecylsulphate when staining gels by silver nitrate and cumassi. It is shown that ultracentrifugal supernatant and a sediment as well as sulphate sediment contain S-LPS and R-LPS. SR-LPS is not differentiated. Sulphate supernatant does not contain the determinable amount of S-LPS but it is enriched by the proteins with molecular weights of 65-15 kDalton. S-LPS is localized in the gel area which corresponds to mobilities of polypeptides with molecular weights 130-45 KDalton and the number of monomeric links in O-specific chains of its molecules reaches 25-30. R-LPS migrates under electrophoresis in gel to the mobility zone of polypeptides with molecular weights 14.5-16 kDalton.     

Chain-chain interactions for methyl polygalacturonate: models for high methyl-esterified pectin junction zones

The ability of pectins to form gels in the presence of calcium is well-known, and it implies the interaction of carboxylate groups and bivalent ions. However, even when most of the galacturonic units are methyl esterified, pectins are able to form gels but only under certain experimental conditions. In this case, hydrogen bonding and hydrophobic interactions are believed to be responsible for gel formation, and it is likely, as in the other mechanisms of polysaccharide gel formation, that stable junction zones consist of cooperatively ordered chains linked together throughout nonbonded interactions to provide a three-dimensional network. To investigate the junction zones in HM-pectin gels, we investigated, by molecular modeling, all of the ways to associate two, and then three, fully methyl-esterified galacturonic acid chains. Two models are obtained: the first one is based on a packing of parallel chains; it agrees with the hypothetical model derived from fiber diffraction study; the second one displays an antiparallel orientation of the chains; it presents a better arrangement of the chains and, theoretically, a much lower potential energy. In both cases, all of the favorable associations occur within a network of hydrogen bonds and of hydrophobic contacts.     

Steady-state and pulsed NMR studies of gelation in aqueous agarose

Steady-state and pulsed NMR techniques have been used to investigate molecular motion in sols and gels of agarose. In passing through the sol–gel transition, the molecular mobility of water molecules is reduced only by a small amount, whereas motion of the polymer chains is greatly attenuated. The results are discused in terms of the network theory of gelation, with references to the role of water in the process and the nature of the “junction zones” between polymer chains. T₂ and line-width measurements are dominated by exchange broadening. The effects of exchange rate and differences in relaxation time between the exchanging sites are discussed. The temperature hysteresis behavior of agarose gels has been investigated and the effects of “ageing” correlated with changes in nuclear relaxation times. The synergistic increase in gel strength obtained on adding locust bean gum (LBG) to agarose has been investigated. The results indicate that LBG does not form double-helix junctions and may decrease rates of gelation by steric effects. At high agarose concentration, the LBG remains mainly in solution in interstitial water, but at low agarose concentration, it is suggested that the LBG can link gel aggregates together into a self-supporting structure, producing a synergistic increase in gel strength. Comparisons have been made between the nature of the agarose–LBG interaction and agarose–cellulose interactions in biological systems.     

Trans-elution: a method for the purification of components of complex biological extracts

Trans-elution is a simple and rapid technique allowing the purification of macromolecules trapped in polyacrylamide gels following electrophoresis. This method of purification consists of the sideways transfer of the macromolecules under the influence of an electric field from the gel slab toward an inert support. In contrast to the role of nitrocellulose used in the "Western blotting" technique, in this case the support does not bind the macromolecules. It consists of a network capable of retaining the buffer by capillary. The electroeluted proteins remain in solution in the buffer and it is thus easy to recover them by spin-drying the support. The support material is either glue-free paper or glass fiber paper. Small concentrated samples are obtained at high yield. The procedure does not require gel slicing, thus avoiding both manipulation of the gel and errors in the localization of the fractions to be purified. In a single step all the proteins fractionated on the gel may be eluted. The trans-elution technique has been applied to the purification of Plasmodium falciparum and Toxoplasma gondii antigens, the causative agents of malaria and toxoplasmosis, respectively.     

The human erythrocyte membrane skeleton may be an ionic gel

Biochemical and biophysical observations indicate that the erythrocyte membrane skeleton is composed of a swollen network of long, flexible and ionizable macromolecules located at the cytoplasmic surface of the fluid membrane lipid bilayer. We have analyzed the mechanochemical properties of the erythrocyte membrane assuming that the membrane skeleton constitutes an ionic gel (swollen ionic elastomer). Using recently established statistical thermodynamic theory for such gels, our analysis yields mathematical expressions for the mechanochemical properties of erythrocyte membranes that incorporate membrane molecular parameters to an extent not achieved previously. The erythrocyte membrane elastic shear modulus and maximum elastic extension ratio predicted by our membrane model are in quantitative agreement with reported values for these parameters. The gel theory predicts further that the membrane skeleton modulus of area compression, K _G, may be small as well as large relative to the membrane elastic shear modulus, G, depending on the environmental conditions. Our analysis shows that the ratio between these two parameters affects both the geometry and the stability of the favoured cell shapes.     

Prostatic binding protein. A steriod-binding protein secreted by rat prostate.

Rat prostatic cytosol contains a high concentration of a prostatic binding protein with peculiar steroid-binding properties. Indeed, in spite of a relatively low affinity, charcoal adsorption can be used for its measurement. Furthermore, the binding is not specific for particular steroids and increases very strongly after delipidation. In delipidated cytosol the concentration of the binding site is 3.1 micronmol/g protein and the apparent affinity for pregenolone 1.7 X 10(6) M-1. The high concentration of prostatic binding protein in prostatic fluid shows that this substance is secreted by the prostate. Prostatic binding protein has the following physicochemical characteristics: it is precipitated by ammonium sulfate between 50 and 70% saturation; the elution position from a Sephadex G-100 column corresponds to a molecular weight of 51000; it sediments in sucrose density gradients at 3.7 S and is eluted from DEAE-cellulose columns at about 0.25 M KCl. On polyacrylamide gel electrophoresis the binding activity coincides with the major cytosolic protein band. This band has the same mobility as serum albumin in 7% gels, but a higher mobility in more concentrated gels.     

The nuclear pore complex mystery and anomalous diffusion in reversible gels

The exchange of macromolecules between the cytoplasm and the nucleus of eukaryotic cells takes place through the nuclear pore complex (NPC), which contains a selective permeability barrier. Experiments on the physical properties of this barrier appear to be in conflict with current physical understanding of the rheology of reversible gels. This paper proposes that the NPC gel is anomalous and characterized by connectivity fluctuations. It develops a simplified model to demonstrate the possibility of enhanced diffusion constants of macromolecules trapped in such a gel.     

Equilibrium Modeling of the Mechanics and Structure of the Cancer Glycocalyx

The glycocalyx is a thick coat of proteins and carbohydrates on the outer surface of all eukaryotic cells. Overproduction of large, flexible or rod-like biopolymers, including hyaluronic acid and mucins, in the glycocalyx strongly correlates with the aggression of many cancer types. However, theoretical frameworks to predict the effects of these changes on cancer cell adhesion and other biophysical processes remain limited. Here, we propose a detailed modeling framework for the glycocalyx incorporating important physical effects of biopolymer flexibility, excluded volume, counterion mobility, and coupled membrane deformations. Because mucin and hyaluronic biopolymers are proposed to extend and rigidify depending on the extent of their decoration with side chains, we propose and consider two limiting cases for the structural elements of the glycocalyx: stiff beams and flexible chains. Simulations predict the mechanical response of the glycocalyx to compressive loads, which are imposed on cells residing in the highly confined spaces of the solid tumor or invaded tissues. Notably, the shape of the mechanical response transitions from hyperbolic to sigmoidal for more rod-like glycocalyx elements. These mechanical responses, along with the corresponding equilibrium protein organizations and membrane topographies, are summarized to aid in hypothesis generation and the evaluation of future experimental measurements. Overall, the modeling framework developed provides a theoretical basis for understanding the physical biology of the glycocalyx in human health.