Diffusion and partitioning of proteins in charged agarose gels.

The effects of electrostatic interactions on the diffusion and equilibrium partitioning of fluorescein-labeled proteins in charged gels were examined using fluorescence recovery after photobleaching and gel chromatography, respectively. Measurements were made with BSA, ovalbumin, and lactalbumin in SP-Sepharose (6% sulfated agarose), in phosphate buffers at pH 7 and ionic strengths ranging from 0.01 to 1.0 M. Diffusivities in individual gel beads (D) and in the adjacent bulk solution (D infinity) were determined from the spatial Fourier transform of the digitized two-dimensional fluorescence recovery images. Equilibrium partition coefficients (phi) were measured by recirculating protein solutions through a gel chromatography column until equilibrium was reached, and using a mass balance. Diffusion in the gel beads was hindered noticeably, with D/D infinity = 0.4-0.5 in each case. There were no effects of ionic strength on BSA diffusivities, but with the smaller proteins (ovalbumin and lactalbumin) D infinity increased slightly and D decreased at the lowest ionic strength. In contrast to the modest changes in diffusivity, there were marked effects of ionic strength on the partition coefficients of these proteins. We conclude that for diffusion of globular proteins through gel membranes of like charge, electrostatic effects on the effective diffusivity (Deff = phi D) are likely to result primarily from variations in phi with only small contributions from the intramembrane diffusivity.     

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.     

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited.     

Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads.

Fluorescence correlation spectroscopy (FCS) has been used to measure the diffusion of fluorescently labeled beads in solutions of polymerized actin or buffer. The results, obtained at actin concentrations of 1 mg/ml, show that small beads (0.09 micron in diameter) diffuse nearly as rapidly in the actin gel as in buffer, whereas the largest beads tested (0.5 micron in diameter) are immobilized. Measured autocorrelation times for motions of beads with intermediate sizes show that the diffusion is retarded (relative to buffer) and that the time behavior cannot be represented as a single diffusive process. In addition to the retarded diffusion observed over distances > 1 micron, 0.23-micron beads also show a faster motion over smaller distances. Based on the measured rate of this faster motion, we estimate that the beads may be constrained within a cage approximately 0.67 micron on a side, equal to a filament length of approximately 250 subunits. Fluorescence correlation spectroscopy measurements made in the same small spot (radius of 1.4 microns) of the gel vary over time. From the variations of both the autocorrelation functions and the mean fluorescence, we conclude that, corresponding to a spatial scale of 1.4 microns, the actin gel is a dynamic structure with slow rearrangement of the gel occurring over periods of 20-50 s at 21-22 degrees C. This rearrangement may result from local reorganization of the actin matrix. Data for the retardation of beads by the actin gel are consistent with a detailed theory of the diffusion of particles through solutions of rigid rods that have longitudinal diffusion coefficients much less than that of the particles (Ogston, A. G., B. N. Preston, and J. D. Wells. 1973. Proc. R. Soc. Lond. A. 333:297-316).     

Study of the translational diffusion of macromolecules in beads of gel chromatography by the FRAP method

We measured the translational diffusion of fractions of dextrans labelled with fluorescein isothiocyanate, in Sephadex gel beads permeated by aqueous solutions of these molecules. The molecular weights of these fractions were between 5400 and 200,000 and measurements of their diffusion coefficients inside a gel bead (D) and in the free solution (D0), were performed using the fluorescence recovery after photobleaching method (FRAP). We also determined the coefficient of partitioning (Kav) of these fractions between the gel and the free solvent, with a new microfluorimetric method. We found that, for Sephadex G-50, G-75, G-100, G-150 and G-200 gels, Kav varied with the Stokes radius (rs) of the dextran molecules, in agreement with the formula of Laurent and Killander (J. Chromatogr. 14 (1964) 317). For Sephadex G-100, G-150 and G-200 gels, D/D0 varied with rs, according to the theory of Ogston et al. (Proc. R. Soc. Lond. 333 (1973) 297). In addition, these theories predict a relation linking D/D0 to Kav which was well verified. Our work is the first systematic study of the translational diffusion of macromolecules in a chromatography gel. These measurements should allow a better evaluation of the factors which influence the resolution in exclusion chromatography. In addition, the diffusion of macromolecules in gels may provide models for the diffusion of these molecules in the cytoplasm of living cells and in connective biological tissues.     

Unexpected loss of genomic DNA from agarose gel plugs

Intact chromosomal DNAs are routinely prepared by embedding cells in agarose plugs before lysis. The large sizes of the genomic DNAs cause their retention while other macromolecules diffuse into and out of the gel matrix during lysis, washing and restriction cleavage incubations. However, in an analysis of agarose-embedded chromosomal DNAs cleaved with restriction enzymes, fragments larger than 30 kilobases were found to have eluted from the gel plugs. Since loss of fragments from gel plugs may affect qualitative and quantitative interpretations of electrophoretic patterns, an analysis of the diffusion of DNA segments from agarose plugs was performed. The two variables monitored were the time dependence and the DNA fragment size dependence of the diffusion process. The results indicate that small fragments (less than or equal to 2 kilobases) are quickly lost from 1% agarose gel plugs; moreover, significant amounts of large DNA segments (i.e., the 48.5-kilobase lambda phage chromosome) are also lost. In addition to urging caution in the analysis of restriction cleavage data, these observations suggest that intact small organelle genomes and extrachromosomal DNAs also may be lost from genomic DNAs prepared in agarose gel plugs.     

Glucose diffusion in crosslinked proteins containing streptomyces

Summary Diffusion measurements of glucose in a crosslinked water-swollen protein matrix containingStreptomyces thermovulgaris strain 127, are described. Solute diffusion coefficients in the gel phase were found to be considerably lower than for free diffusion. The range of diffusion coefficients was 0.83×10⁻¹⁰ to 2.68×10⁻¹⁰m²/s at corresponding ratios to free diffusion values 0.11 to 0.38. It is shown that polymer structure does not pose any significant effect on mass transfer for the small glucose molecule.     

Electronic speckle pattern interferometry: a tool for determining diffusion and partition coefficients for proteins in gels

The aim of this study was to demonstrate electronic speckle pattern interferometry (ESPI) as a powerful tool in determining diffusion coefficients and partition coefficients for proteins in gels. ESPI employs a CCD camera instead of a holographic plate as in conventional holographic interferometry. This gives the advantage of being able to choose the reference state freely. If a hologram at the reference state is taken and compared to a hologram during the diffusion process, an interferometric picture can be generated that describes the refraction index gradients and thus the concentration gradients in the gel as well as in the liquid. MATLAB is then used to fit Fick's law to the experimental data to obtain the diffusion coefficients in gel and liquid. The partition coefficient is obtained from the same experiment from the flux condition at the interface between gel and liquid. This makes the comparison between the different diffusants more reliable than when the measurements are performed in separate experiments. The diffusion and partitioning coefficients of lysozyme, BSA, and IgG in 4% agarose gel at pH 5.6 and in 0.1 M NaCl have been determined. In the gel the diffusion coefficients were 11.2 +/- 1.6, 4.8 +/- 0.6, and 3.0 +/- 0.3 m(2)/s for lysozyme, BSA, and IgG, respectively. The partition coefficients were determined to be 0.65 +/- 0.04, 0.44 +/- 0.06, and 0.51 +/- 0.04 for lysozyme, BSA, and IgG, respectively. The current study shows that ESPI is easy to use and gives diffusion coefficients and partition coefficients for proteins with sufficient accuracy from the same experiment.     

Diffusion in kappa-carrageenan gel beads

Using a well-mixed and temperature-led vessel, the diffusion characteristics of various solutes into spherical kappa-carrageenan gel beads were experimentally investigated. The diffusion coefficient of glucose was markedly affected by the glucose concentration and the operating temperature. In all cases the diffusivity obtained was noticeably smaller than that of glucose in pure water. The experimental data also indicated an inverse relationship between the diffusivity and the polymer concentration used in the gel preparation. As well, the glucose diffusivity was affected by the presence of other solutes in the glucose solution. Electrolytes such as ammonium sulfate, KCl, and CaCl(2) were observed to enhance the diffusion coefficient. On the other hand, the addition of arginine or bovine serum albumin had an adverse effect on the diffusivity. No diffusion of albumin into the gel beads was observed, and such a solute created a significant mass transfer resistance during the diffusion process.     

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.     

Enhanced Tethered-Particle Motion Analysis Reveals Viscous Effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl₂ or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.     

Solute and macromolecule diffusion in cellular aqueous compartments.

Diffusion of solutes and macromolecules in aqueous cellular compartments is required for numerous cellular processes including metabolism, second messenger signaling and protein-protein interactions. The view of the cell interior has evolved from that of a viscous gel to that of a watery but crowded compartment. Recent measurements of fluorescent probe diffusion using photobleaching, correlation microscopy and time-resolved anisotropy methods, have indicated unexpectedly high mobilities of small solutes and macromolecules. This review evaluates experimental evidence defining the rates and barriers for molecular diffusion in cells. Possible implications of regulated molecular diffusion as a rate-limiting step in cell metabolism, and with respect to the delivery of therapeutic agents, are discussed.     

DNA diffusion in mucus: effect of size, topology of DNAs, and transfection reagents

DNA represents a promising therapeutic and prophylactic macromolecule in treating genetic diseases, infectious diseases and cancers. The therapeutic potential of DNA is directly related to how DNA transports within the targeted tissue. In this study, fluorescence photobleaching recovery was used to examine the diffusion of plasmid DNAs with various size (2.7-8.3 kb), topology, and in the presence of transfection reagents in mucus. We observed that DNAs diffused slower when size of DNAs increased; supercoiled DNAs diffused faster than linear ones; mucus did not reduce the diffusion of linear DNAs but retarded the diffusion of supercoiled DNAs. Diffusion data were fitted to models of a polymer chain diffusing in gel systems. Diffusion of linear DNAs in mucus were better described by the Zimm model with a scaling factor of -0.8, and supercoiled DNAs showed a reptational behavior with a scaling factor of -1.3. Based on the Zimm model, the pore size of bovine mucus was estimated and agreed well with previous experimental data. In the presence of transfection reagents, e.g., liposomes, the diffusion of DNAs increased by a factor of 2 in mucus. By using bovine mucus as a model system, this work suggests that DNA size, topology, and the presence of transfection reagents may affect the diffusion of DNA in tissues, and thus the therapeutic effects of DNA.     

Fluorescence photobleaching with spatial Fourier analysis: measurement of diffusion in light-scattering media.

A new method for the measurement of diffusion in thick samples is introduced, based upon the spatial Fourier analysis of Tsay and Jacobson (Biophys. J. 60: 360-368, 1991) for the video image analysis of fluorescence recovery after photobleaching (FRAP). In this approach, the diffusion coefficient is calculated from the decay of Fourier transform coefficients in successive fluorescence images. Previously, the application of FRAP in thick samples has been confounded by the optical effects of out-of-focus light and scattering and absorption by the sample. The theory of image formation is invoked to show that the decay rate is the same for both the observed fluorescence intensity and the true concentration distribution in the tissue. The method was tested in a series of macromolecular diffusion measurements in aqueous solution, in agarose gel, and in simulated tissue consisting of tumor cells (45% v/v) and blood cells (5% v/v) in an agarose gel. For a range of fluorescently labeled proteins (MW = 14 to 600 kD) and dextrans (MW = 4.4 to 147.8 kD), the diffusion coefficients in aqueous solution were comparable to previously published values. A comparison of the spatial Fourier analysis with a conventional direct photometric method revealed that even for the weakly scattering agarose sample, the conventional method gives a result that is inaccurate and dependent on sample thickness whereas the diffusion coefficient calculated by the spatial Fourier method agreed with published values and was independent of sample thickness. The diffusion coefficient of albumin in the simulated tissue samples, as determined by the spatial Fourier analysis, varied slightly with sample thickness.(ABSTRACT TRUNCATED AT 250 WORDS)     

Enhanced Tethered-Particle Motion Analysis Reveals Viscous Effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl₂ or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.     

Microencapsulation of nanoparticulate complexes of DNA with cationic lipids and polymers in pectin beads for targeted gene delivery

Nanoparticulate complexes of plasmid DNA (pDNA) with cationic liposomes/polymer, of approx 200 nm diameter, were encapsulated with a high degree of efficiency within calcium pectinate gel beads. Electron microscopy showed the DNA nanocomplexes to be evenly distributed throughout the gel matrix. Controlled release of pDNA-lipid nanocomplexes was achieved by the action of pectinase enzymes, whereas release of naked and polymer-complexed DNA was found to be more greatly influenced by the swelling behavior of the polysaccharide matrices in buffer alone. Physical degradation of pDNA within pectin beads was found to be accelerated during bead drying, most probably as a result of shear forces generated within the gel matrices by the evaporation of water. Plasmid complexation with cationic liposomes provided a greater degree of protection for the DNA during bead drying than complexation with cationic polymer, and was shown to successfully transfect cultured cells after release from the beads, via the action of pectinase. Observations concerning the physical stability of nanocomplexed pDNA, and its encapsulation within and release from pectin gel beads, are discussed with reference to the electrostatic interactions existing between the various components.     

Determination of glucose and ethanol effective diffusion coefficients in Ca-alginate gel.

Glucose and ethanol diffusion coefficients in 2% Ca-alginate gel were measured using the experimental technique based on solute diffusion into or out of gel beads in a well-stirred solution. The aim of the study was to make the measurements under typical conditions found in alcoholic fermentations, such as the concentrations of glucose (100 g l-1) and ethanol (50 g l-1), the simultaneous counter-diffusion of glucose and ethanol, and the presence of cells in the gel beads at a level of 10(9) cells g-1 of beads. Previously, an evaluation of the error associated with the methodology used indicated how the experimental procedure would minimize the error. The individual measurement of glucose and ethanol coefficients in 2% Ca-alginate with no cells gave values of 5.1 and 9.6 x 10(-6) cm2 s-1, respectively, which are lower than those in water. When the effect of counter-diffusion was investigated, both coefficients decreased: glucose by 14% and ethanol by 28%. When cells were incorporated into the beads, only the ethanol coefficient decreased significantly, while the glucose coefficient apparently increased its value to 6.9 10(-6) cm2 s-1.     

Stability of hydrogels used in cell encapsulation: An in vitro comparison of alginate and agarose

The present studies were undertaken to evaluate the in vitro gel stability of the hydrogels alginate and agarose. Gel strength (of alginate and agarose) and protein diffusion (of alginate only) were shown to correlate with gel stability and to be useful techniques to monitor gel stability over time. The gel strengths of alginate and agarose were followed for a 90-day period using gel strength as a measure of gel stability. The gel strength of agarose diminished in the presence of cells because the cells likely interfered with the hydrogen bond formation required for agarose gelation. In the presence of cells, the gel strength of agarose decreased by an average of 25% from time 0 to 60 days, thereafter maintaining that value to 90 days. The gel strength of calcium- or barium-crosslinked alginate decreased over 90 days, with an equilibrium gel strength being achieved after 30 days. The presence of cells did not further decrease alginate gel strength. The gel strengths of calcium- and barium-crosslinked alginates were similar at 60 days-350 +/- 20 g and 300 +/- 60 g, respectively-indicating equivalence in their stability. The stability of calcium-crosslinked sodium alginate gels over a 60-day time period was monitored by diffusion of proteins ranging in molecular weight from 14.5 to 155 kD. From these diffusion measurements, the average pore size of the calcium-crosslinked alginate gels was estimated, using a semi-empirical model, to increase from approximately 176 to 289 A over a period of 60 days. (c) 1996 John Wiley & Sons, Inc.     

Protein osmotic pressure and the state of water in frog myoplasm

We measured the osmotic pressure of diffusible myoplasmic proteins in frog (Rana temporaria) skeletal muscle fibers by using single Sephadex beads as osmometers and dialysis membranes as protein filters. The state of the myoplasmic water was probed by determining the osmotic coefficient of parvalbumin, a small, abundant diffusible protein distributed throughout the fluid myoplasm. Tiny sections of membrane (3.5- and 12-14-kDa cutoffs) were juxtaposed between the Sephadex beads and skinned semitendinosus muscle fibers under oil. After equilibration, the beads were removed and calibrated by comparing the diameter of each bead to its diameter measured in solutions containing 3-12% Dextran T500 (a long-chain polymer). The method was validated using 4% agarose cylinders loaded with bovine serum albumin (BSA) or parvalbumin. The measured osmotic pressures for 1.5 and 3.0 mM BSA were similar to those calculated by others. The mean osmotic pressure produced by the myoplasmic proteins was 9.7 mOsm (4 degrees C). The osmotic pressure attributable to parvalbumin was estimated to be 3.4 mOsm. The osmotic coefficient of the parvalbumin in fibers is approximately 3.7 mOsm mM(-1), i.e., roughly the same as obtained from parvalbumin-loaded agarose cylinders under comparable conditions, suggesting that the fluid interior of muscle resembles a simple salt solution as in a 4% agarose gel.     

Evaluation of densitometry data using interactive computer graphics: Application to DNA agarose gels

A method of analyzing DNA agarose gels using interactive computer graphics is described. After electrophoresis in an alkaline agarose gel, DNA is neutralized, stained with ethidium bromide and excited with ultraviolet radiation. The resulting fluorescent distribution on the gel is photographed, and the negative scanned by a digitizing densitometer. The data is subsequently analyzed using a computer program developed to facilitate manipulation and selection of data from the densitometer trace. The method has been applied to determine pyrimidine dimer yields in DNA from human lymphocytes exposed to UV radiation. The technique significantly reduces the time required to analyze such data, while also providing greater accuracy. The method could be easily adapted to assist in similar analyses of other macromolecules such as RNA or proteins.