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 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.     

Electrophoresis of DNA in oriented agarose gels

Oriented agarose gels were prepared by applying an electric field to molten agarose while it was solidifying. Immediately afterwards, DNA samples were applied to the gel and electrophoresed in a constant unidirectional electric field. Regardless of whether the orienting field was applied parallel or perpendicular to the eventual direction of electrophoresis, the mobilities of linear and supercoiled DNA molecules were either faster (80% of the time) or slower (20% of the time) than observed in control, unoriented gels run simultaneously. The difference in mobility in the oriented gel (whether faster or slower) usually increased with increasing DNA molecular weight and increasing voltage applied to orient the agarose matrix. In perpendicularly oriented gels linear DNA fragments traveled in lanes skewed toward the side of the gel; supercoiled DNA molecules traveled in straight lanes. If the orienting voltage was applied parallel to the direction of electrophoresis, both linear and supercoiled DNA molecules migrated in straight lanes. These effects were observed in gels cast from different types of agarose, using various agarose concentrations and two different running buffers, and were observed both with and without ethidium bromide incorporated in the gel. Similar results were observed if the agarose was allowed to solidify first, and the orienting electric field was then applied to the gel for several hours before the DNA samples were added and electrophoresed. The results suggest that the agarose matrix can be oriented by electric fields applied to the gel before and probably during electrophoresis, and that orientation of the matrix affects the mobility and direction of migration of DNA molecules. The skewed lanes observed in the perpendicularly oriented gels suggest that pores or channels can be created in the matrix by application of an electric field. The oriented matrix becomes randomized with time, because DNA fragments in oriented and unoriented gels migrated in straight lanes with identical velocities 24 hours later.     

Diffucison of OXYGEN, Nitrogen and water in hyluronate solutions.

A method is reported for the measurement of the diffusion coefficients in water of some sparingly soluble gases. The results obtained for the diffusion coefficients of oxygen and nitrogen gas through water at 25 degrees C are 2.12. 10-5 and 2.61 . 10-5 cm-2 . s-1, respectively. A check on the accuracy of the teachnique using tritiated water as the diffusing substance gave a value of 2.15 . 10-5 cm-2 . s-1 which agrees within 3% with recent values from the literature. The method was applied to the measurement of oxygen, nitrogen, and tritiated water diffusion coefficients through agarose gels and through agarose gels containing hyluronate. The results indicate that the hyaluronate had only a small effect as a barrier to the diffusion of such low molecular weight substance.     

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.     

Diffusion-ordered NMR spectroscopy: a versatile tool for the molecular weight determination of uncharged polysaccharides

Diffusion-ordered NMR spectroscopy (DOSY) experiments have been carried out on dilute aqueous solutions of uncharged saccharide systems and, in particular, on six well characterized pullulan fractions of different molecular weights. The values of diffusion coefficients and hydrodynamic radii determined for the pullulan fractions are in good agreement with the results obtained with other methodologies such as light scattering. Fitting the diffusion coefficients data as a function of the molecular weight allows for the determination of a calibration curve that can be applied to a wide range of mono-, oligo-, and polysaccharides. Therefore, DOSY is proposed as a versatile tool for achieving a simple estimation of the molecular weight of uncharged polysaccharides. Mixtures of homopolymers of different molecular weight can be nicely separated. An advantage of the method is that the same sample used for the NMR characterization can be used for the molecular weight determination without any further manipulation. Other water soluble polymers, such as poly(ethylene oxide) and poly(vinylpyrrolidone), can be roughly characterized using the same calibration curve.     

The permeation of organic acids through lecithin bilayers. Resemblance to diffusion in polymers.

1. The fluxes of aliphatic acids and their derivatives through black lipid membranes made of egg lecithin in decane were measured by means of a proton titration method. 2. Permeability coefficients were calculated and these were divided by the partition coefficient of the diffusing solute in different solvent systems: n-decane, olive oil, ether and octanol. The logarithms of the diffusion coefficients thus obtained were plotted against the logarithm of the molecular weight. The data could not be fitted to a single regression line in any solvent system. 3. When the logarithm of the diffusion coefficients were correlated to the logarithm of the molecular volume (equals molecular weight/ specific gravity) all the diffusants could be fitted to the same regression line, indicating that the molecular volume is a better index of molecular size and shape than the molecular weight. 4. Analysis of the experimental results assuming a model of diffusion through soft polymers (Lieb, W.R. and Stein, W. D. (1971) Current Topics in Membranes and Transport, vol. 2, pp. 1-39, Academic Press, New York) showed that decane and olive oil are not adequate model solvents for planar lecithin membranes but ether and octanol are good models. 5. The differential mass selectivity coefficient was found to be similar to that for soft polymers and biological membranes, i.e. greater than 3.0. 6. Water could be fitted by the same regression line, thus emphasizing the generality of passive transfer and implying that water crosses lipid membranes as single molecules.     

Transport characterization of hydrogel matrices for cell encapsulation

Current membrane-based bioartificial organs consist of three basic components: (1) a synthetic membrane, (2) cells that secrete the product of interest, and (3) an encapsulated matrix material. Alginate and agarose have been widely used to encapsulate cells for artificial organ applications. It is important to understand the degree of transport resistance imparted by these matrices in cell encapsulation to determine if adequate nutrient and product fluxes can be obtained. For artificial organs in xenogeneic applications, it may also be important to determine the extent of immunoprotection offered by the matrix material. In this study, diffusion coefficients were measured for relevant solutes [ranging in size from oxygen to immunoglobulin G (IgG)] into and out of agarose and alginate gels. Alginate gels were produced by an extrusion/ionic crosslinking process using calcium while agarose gels were thermally gelled. The effect of varying crosslinking condition, polymer concentration, and direction of diffusion on transport was investigated. In general, 2-4% agarose gels offered little transport resistance for solutes up to 150 kD, while 1.5-3% alginate gels offered significant transport resistance for solutes in the molecular weight range 44-155 kD-lowering their diffusion rates from 10- to 100-fold as compared to their diffusion in water. Doubling the alginate concentration had a more significant effect on hindering diffusion of larger molecular weight species than did doubling the agarose concentration. Average pore diameters of approximately 170 and 147 A for 1.5 and 3% alginate gels, respectively, and 480 and 360 A for 2 and 4% agarose gels, respectively, were estimated using a semiempirical correlation based on diffusional transport of different-size solutes. The method developed for measuring diffusion in these gels is highly reproducible and useful for gels crosslinked in the cylindrical geometry, relevant for studying transport through matrices used in cell immobilization in the hollow fiber configuration. (c) 1996 John Wiley & Sons, Inc.     

Evaluation of agar and agarose gels for studying mechanical impedance in rice roots

Agar and agarose gels were evaluated as systems to mechanically impede roots of rice (Oryza sativa L.). Two-layer gels were used so that seedlings established in a layer of weak gel (0.35% weight/volume) and then grew downwards to encounter a treatment gel of up to 5.0% (w/v). Agarose gels were stronger than agar gels of the same concentration, reaching a maximum penetrometer resistance of 1.2 MPa at a concentration of 5.0%, compared to 0.3 MPa with agar. The 5.0% agar gel stimulated elongation of the seminal axis by 40% in seedlings of variety TN1 (compared with elongation in the 0.2% gel), but decreased it by 15% in the variety Lac 23. Although increasing agarose concentration decreased seminal axis elongation in both varieties, the seminal axis did not reach the lower layer of treatment gel when the concentration of the treatment gel was greater than 2.0%. The decreased root elongation was therefore a non-mechanical inhibition. In experiments conducted using a different batch of agarose, these inhibitory effects were not seen and strong agarose gels stimulated seminal axis elongation. It was concluded that the agar and agarose gel systems studied were unsuitable for studying the effect of mechanical impedance on the elongation of rice roots and that great care should be taken in interpreting the results of experiments using gels as a growth medium. This revised version was published online in June 2006 with corrections to the Cover Date.     

Characterization of sugar diffusion coefficients in alginate membranes

The diffusivity of several monosaccharides and disaccharides in calcium alginate gels was determined using a specially designed diaphragm cell. The diffusion coefficients of the tested sugars are 4 to 18% smaller in alginate gel than in water and, with the exception of fructose, this difference increases with increasing sugar molecular weight. Also the position of the carbonyl group seems to be determined in the value of the diffusion coefficient - ketoses have lower diffusion coefficients than aldoses.     

Comparative study of the pullulans synthesized by Pollularia (Aureobasidium) pullulans strains of different ploidies

Pullularia pullulans strains of different ploidy synthesize pullulans similar in their characteristics to those described in literature. These are glucans whose glucose residues are linked with alpha(1 leads to 4) and alpha(1 leads to 6) bonds in the proportion of 2.2:1. The pullulans differ from one another in their water solubility, molecular mass and in the ability to be cleaved by alpha-amylase and dextranase. The minor structural modifications of pullulan molecules in the polyploid strains as compared to the pullulan synthesized by the parent haploid culture are caused, apparently, by mutations induced with mitotic poisons.     

Production of high molecular weight pullulan by Aureobasidium pullulans HP-2001 with soybean pomace as a nitrogen source

The production of pullulan by Aureobasidium pullulans HP-2001 was enhanced by yeast extract as a nitrogen source as well as soybean pomace. The highest production of pullulan by A. pullulans HP-2001 with yeast extract was 5.5 g/l whereas that of pullulan with soybean pomace was 7.5 g/l. The gas chromatogram of pullulan produced by A. pullulans HP-2001 with soybean pomace as a nitrogen source showed that the major and minor components were glucose and mannose. The FTIR spectra of pullulans produced with yeast extract, a mixture of yeast extract and soybean pomace, and soybean pomace alone exhibited similar features. The increase in content of reducing sugars after pullulanase treatment of pullulans produced with different nitrogen sources indicated that all the pullulans had alpha-(1,6) glucosidic linkages of alpha-(1,4) linked maltotriose units. The average molecular weights of pullulans produced with various concentrations of yeast extract and soybean pomace ranged from 0.17 to 1.32x10(6) and from 1.32 to 5.66x10(6), respectively. All pullulans produced by A. pullulans HP-2001 in this study had the same basic structures, but their ratios of monomeric components were a little different, which might result in the production of pullulans with different molecular weights.     

Protein sorption and recovery by hydrogels using principles of aqueous two-phase extraction

Use of the thermodynamic principles of aqueous two-phase extraction (ATPE) to drive protein into a crosslinked gel is developed as a protein isolation and separation technique, and as a protein loading technique for drug delivery applications. A PEG/dextran gel system was chosen as a model system because PEG/dextran systems are widely used in aqueous two-phase extraction and dextran gels (Sephadex(R)) are common chromatographic media. The effects of polymer concentrations and molecular weights, salts, and pH on the partitioning of ovalbumin matched ATPE heuristics and data trends. Gel partition coefficients (Cgel/Csolution) increased with increasing PEG molecular weight and concentration and decreasing dextran concentration (increased gel swelling). The addition of PEG to the buffer solution yielded partition coefficients more than an order of magnitude greater than those obtained in systems with buffer alone, or added salt. A combined salt/PEG system yielded an additional order of magnitude increase. For example, when ovalbumin solution (2.3 mg/mL) was equilibrated with Sephadex(R) G-50 at pH 6.75, the partition coefficients were 0.13 in buffer, 0.11 in buffer with 0.22M KI, 2.3 in 12 wt% PEG-10,000 and 32.0 in 12 wt% PEG-10, 000 with 0.22M KI. The effect of anions and cations as well as ionic strength and pH on the partitioning of ovalbumin also matched ATPE heuristics. Using the heuristics established above, partition coefficients as high as 80 for bovine serum albumin and protein recoveries over 90% were achieved. In addition, the wide range of partition coefficients that were obtained for different proteins suggests the potential of the technique for separating proteins. Also, ovalbumin sorption capacities in dextran were as high as 450 mg/g dry polymer, and the sorption isotherms were linear over a broad protein concentration range.     

Separation of the DNA molecules beyond conventional size limits by gel electrophoresis with sodium dodecyl sulfate.

Electrophoretic mobility of DNA through polyacrylamide as well as agarose gels is greatly increased by sodium dodecyl sulfate (SDS). DNA molecules well beyond the conventionally separable size limits are separated readily and rapidly by gel electrophoresis with SDS in a conventional static electric field. Furthermore in optimal concentration gels DNA molecules of similar molecular sizes are separated better from one another in the presence of SDS than without it. Evidence is presented that SDS may act at least in part by altering conformation of DNA. This simple and readily available means for high resolution separation of hitherto impossible sizes of DNA molecules in polyacrylamide and agarose gels in an ordinary static electric field should find general use in molecular genetic analyses. Structural analyses of DNA-protein complexes are also facilitated by virtue of the simultaneous separation of the DNA and protein components on the same gel lane.     

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.     

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.     

A laser light scattering study of gellan gels

A study of gellan has been made using the technique of photon correlation spectroscopy. It has been confirmed that gellan gels are largely stationary at a molecular level like other polysaccharide gels and quite unlike the gels of flexible polymers such as polyacrylamide. Solution-gel transitions of deacetylated gellan in 0.025MNaCl have been studied both as a function of concentration and temperature, and the results compared with those of a parallel investigation of agarose. The interstitial spaces within gellan gels have also been studied by measuring the diffusion coefficients of dextran fractions within the gels. Since all gels are nonergodic systems, the theory of dynamic light scattering from such systems is discussed insofar as it affects the present work. It has been shown that the gellan and agarose aqueous systems are fundamentally different, in that agarose does not from a solution at very low concentrations, but splits up into macroscopic gel particles. At very low concentrations, gellan forms a solution in the presence of both gelleing and nongelling ions, the molecules of which shows little change in hydrodynamic diameter with temperature in the range 20–80°C. At higher concentrations where gels are formed, both gellan and agarose exhibit hystersis in their tempertature transitions from gel to solution and solution to gel, the solution being of large molecular aggregates. The transitions are sharp, but in both cases ther is a continous rearrangement in the structural morphology over the entire temperature range on heating, rendering the system more homogeneous prior to dissociation. In the case of gellan, however, there are two distincit phases in these structural changes—this is not true of agarose. The mean mass per unit length of the gellan fibre in the presence of 0.025M NaCl is 19 k daltons/nm at 0.7% concentration and varies with concentration to the power 0.15. The mass per unit length of the agarose fibre is much larger (ca. 110 k Daltons/nm), this difference being consistent with the difference in properties at very low concentrations. © 1994 John Wiley & Sons, Inc.     

Physical properties and gel electrophoresis behavior of R12-derived plasmid DNAs.

A series of closed circular (I) plasmid DNAs has been derived from drug resistance factor R12, and the nicked circular (II) and linear (III) derivatives of these molecules prepared by irradiation in the presence of ethidium bromide and by treatment with restriction enzyme EcoRI, respectively. These DNAs encompass the molecular weight range 3.6 to 61 megadaltons. The base compositions range from 45% to 51% (GC) as estimated by buoyant density determinations. The smaller plasmids are significantly less supercoiled (9-10%) than are the larger (12-13%). The gel electrophoretic behavior of the three DNA structural forms was determined as a function of molecular weight in agarose gels of concentrations ranging from 0.7% to 1.6% and at electrophoresis salt concentrations from 0.02 M to 0.08 M sodium acetate. The mobilities of DNAs I and III undergo a reversal relative to each other at a molecular weight which decreases with increasing agarose gel concentration. The molecular weight at which DNA II fails to enter a gel depends upon the ionic strength during electrophoresis but not upon the gel concentration.     

Further studies on the contribution of electrostatic and hydrophobic interactions to protein adsorption on dye-ligand adsorbents.

The adsorption equilibria of bovine serum albumin (BSA), gamma-globulin, and lysozyme to three kinds of Cibacron blue 3GA (CB)-modified agarose gels, 6% agarose gel-coated steel heads (6AS), Sepharose CL-6B, and a home-made 4% agarose gel (4AB), were studied. We show that ionic strength has irregular effects on BSA adsorption to the CB-modified affinity gels by affecting the interactions between the negatively charged protein and CB as well as CB and the support matrix. At low salt concentrations, the increase in ionic strength decreases the electrostatic repulsion between negatively charged BSA and the negatively charged gel surfaces, thus resulting in the increase of BSA adsorption. This tendency depends on the pore size of the solid matrix, CB coupling density, and the net negative charges of proteins (or aqueous - phase pH value). Sepharose gel has larger average pore size, so the electrostatic repulsion-effected protein exclusion from the small gel pores is observed only for the affinity adsorbent with high CB coupling density (15.4 micromol/mL) at very low ionic strength (NaCl concentration below 0.05 M in 10 mM Tris-HCl buffer, pH 7.5). However, because CB-6AS and CB-4AB have a smaller pore size, the electrostatic exclusion effect can be found at NaCl concentrations of up to 0.2 M. The electrostatic exclusion effect is even found for CB-6AS with a CB density as low as 2.38 micromol/mL. Moreover, the electrostatic exclusion effect decreases with decreasing aqueous-phase pH due to the decrease of the net negative charges of the protein. For gamma-globulin and lysozyme with higher isoelectric points than BSA, the electrostatic exclusion effect is not observed. At higher ionic strength, protein adsorption to the CB-modified adsorbents decreases with increasing ionic strength. It is concluded that the hydrophobic interaction between CB molecules and the support matrix increases with increasing ionic strength, leading to the decrease of ligand density accessible to proteins, and then the decrease of protein adsorption. Thus, due to the hybrid effect of electrostatic and hydrophobic interactions, in most cases studied there exists a salt concentration to maximize BSA adsorption.     

Orientation of DNA molecules in agarose gels by pulsed electric fields

The electric birefringence of DNA restriction fragments of three different sizes, 622, 1426, and 2936 base pairs, imbedded in agarose gels of different concentrations, was measured. The birefringence relaxation times observed in the gels are equal to the values observed in free solution, if the median pore diameter of the gel is larger than the effective hydrodynamic length of the DNA molecule in solution. However, if the median pore diameter is smaller than the apparent hydrodynamic length, the birefringence relaxation times increase markedly, becoming equal to the values expected for the birefringence relaxation of fully stretched DNA molecules. This apparent elongation indicates that end-on migration, or reptation is a likely mechanism for the electrophoresis of large DNA molecules in agarose gels. The relaxation times of the stretched DNA molecules scale with molecular weight (or contour length) as N2.8, in reasonable agreement with reptation theories.