Quantitative analysis of the three regimes of DNA electrophoresis in agarose gels

An extensive series of experiments has been performed to study the mobility of DNA fragments ranging in size from 2.0 to 48.5 kilobose pairs. By varying the agarose concentration in the gels and the electric field strength, three DNA electrophoresis regimes were clearly identified: the Ogston regime (small DNA fragments in large pores of agarose), the reptation regime without DNA chain stretching (small pores of agarose and weak electric fields), and the reptation regime with DNA chain stretching (small pores of agarose, strong electric fields, and large DNA fragments). Here we report on the experimental identification of these regimes and on the conditions governing the transition between each of them. The onset of reptation and of stretching of DNA chains in gel electrophoresis are described quantitatively for the first time, and a phase diagram for the dynamics of DNA during electrophoresis is presented.     

Electrophoretic mobility of DNA in gels. I. New biased reptation theory including fluctuations

In weak electric fields, the motion of DNA molecules undergoing gel electrophoresis may be described by biased reptation. We argue that the degree of molecular orientation induced by the field is determined by a competition between longitudinal fluctuations and drift of the molecule along the tube. A self-consistent calculation shows that the end-to-end vector of long molecules varies with the square root of the field strength, and not linearly as previously supposed. This leads to a number of new predictions about the field dependence of the molecular mobility and the size limit of resolution. We present the results of computer simulations that support the predictions of the theory of biased reptation including fluctuations. Finally, we discuss the correspondence with experimental data and the implications of our findings for the optimization of DNA electrophoresis. © 1994 John Wiley & Sons, Inc.     

Dynamics of single-stranded DNA in polyacrylamide gels during pulsed field gel electrophoresis. A birefringence study

The study of the orientation of single-stranded DNA in polyacrylamide gels in denaturing conditions has been undertaken by electric birefringence in order to determine the mechanism involved in the electrophoretic transport. The presence of an overshoot in the birefringence signal, when applying the electric field, and the study of the influences of the electric field and of the gel concentration on the dynamics show that a mechanism of reptation with elongation of the molecule occurs in polyacrylamide gels with low T values. Therefore it is suggested that the use of pulsed fields in sequencing electrophoresis is possible and can lead to a large increase of the length of the fragments that can be sequenced in one single run.     

DNA gel electrophoresis: effect of field intensity and agarose concentration on band inversion

We study the effect of electric field intensity and agarose gel concentration on the anomalous electrophoretic mobility recently predicted by the biased reptation model and experimentally observed for linear DNA fragments electrophoresed in continuous electric fields. We show that high fields and low agarose concentrations eliminate the physical mechanism responsible for anomalous DNA mobility and band inversion, in good agreement with theory, thus restoring the monotonic mobility-size relationship necessary for unambiguous interpretation of the results of DNA gel electrophoresis.     

Brownian diffusion and electrophoretic transport of double‐stranded DNA in agarose gels

The field free diffusion constant and the electric field dependence of the electrophoretic mobility and molecular orientation of DNA samples from 5 to 164 kilobase pairs in agarose gels from 0.5 to 2% have been measured by fluorescence recovery after photobleaching and birefringence. In conditions where the reptation predictions hold for the field free diffusion, they partially fail for the DNA size dependence of the low field limit of the electrophoretic mobility. The linear field dependencies of the electrophoretic mobility and orientation factor seem to favor the biased reptation model with fluctuations over the standard biased reptation model, which predicts a quadratic field dependence. The quantitative analysis of the molecular parameters shows, however, that most experiments have been carried out at values of the field where the difference between the two models may be less conclusive. The pore size dependence of the different quantities has been given a particular attention and the role of the distribution of pore sizes in the departures from the reptation predictions is discussed. © 1999 John Wiley & Sons, Inc. Biopoly 50: 45–59, 1999     

Effect of the electric field on the apparent mobility of large DNA fragments in agarose gels

The electrophoresis of a series of DNA fragments ranging in size from 0.5 to 12 kilobase pairs, has been studied as a function of agarose gel concentration and electric field strength. The apparent mobility of all fragments decreased with decreasing electric field strength and with increasing gel concentration. When extrapolated to zero electric field strength and zero agarose concentration, the apparent mobility of all DNA fragments extrapolated to a common value (2.0 ± 0.1) × 10^?4 cm²/V s. The square roots of the retardation coefficients of the various fragments were found to be linearly related to the root-mean-square radii of gyration of the fragments, as predicted by pore-size distribution theory. As predicted by reptation theory, the molecular weights of the various fragments were found to be linearly related to the reciprocal of the apparent mobilities. An equation is given for estimating the apparent pore size of agarose gels between 0.25 and 1.5% in concentration.     

Transient electric birefringence of agarose gels. I. Unidirectional electric fields

The orientation of agarose gels in pulsed electric fields has been studied by the technique of transient electric birefringence. The unidirectional electric fields ranged from 2 to 20 V/cm in amplitude and 1 to 100 s in duration, values within the range typically used for pulsed field gel electrophoresis (PFGE). Agarose gels varying in concentration from 0.3 to 2.0% agarose were studied. The sign of the birefringence varied randomly from one gel to another, as described previously [J. Stellwagen & N. C. Stellwagen (1989), Nucleic Acids Research, Vol. 17, 1537–1548]. The sign and amplitude of the birefringence also varied randomly at different locations within each gel, indicating that agarose gels contain multiple subdomains that orient independently in the electric field. Three or four relaxation times of alternating sign were observed during the decay of the birefringence. The various relaxation times, which range from 1 to ～ 120 s, can be attributed to hierarchies of aggregates that orient in different directions in the applied electric field. The orienting domains range up to ～ 22 μm in size, depending on the pulsing conditions. The absolute amplitude of the birefringence of the agarose gels increased approximately as the square of the electric field strength. The measured Ker constants are ～ 5 orders of magnitude larger than those observed when short, high-voltage pulses are applied to agarose gels. The increase in the Kerr constants in the low-voltage regime parallels the increase in the relaxation times in low-voltage electric fields. Birefringence saturation saturation curves in both the low- and high-voltage regimes can be fitted by theoretical curves for permanent dipole orientation. The apparent permanent dipole moment increase approximately as the 1.6 power of fiber length, consistent with the presence of overlapping agarose helices in the large fiber bundles orienting in low-voltage electric fields, the optical factor is approximately independent of fiber length. Therefore, the marked increase in the Kerr constants observed in the low-voltage regime is due to the large increase in the electrical orientation factor, which is due in turn to the increased length of the fiber bundles and domains orienting in low-voltage electric fields. Since the size of the fiber bundles and domains approximates the size of the DNA molecules being separated by PFGE, the orientation of the agarose matrix in the applied electric field may facilitate the migration of large DNA molecules during PFGE. © 1994 John Wiley & Sons, Inc.     

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.     

Effects of supercoiling in electrophoretic trapping of circular DNA in polyacrylamide gels.

Electrophoretic velocity and orientation have been used to study the electric-field-induced trapping of supercoiled and relaxed circular DNA (2926 and 5386 bp) in polyacrylamide gels (5% T, 3.3% C) at 7.5-22.5 V/cm, using as controls linear molecules of either the same contour length or the same radius of gyration. The circle-specific trapping is reversible. From the duration of the reverse pulse needed to detrap the molecules, the average trap depth is estimated to be 90 A, which is consistent with the molecular charge and the field strengths needed to keep molecules trapped. Trapped circles exhibit a strong field alignment compared to the linear form, and there is a good correlation between the enhanced field alignment for the circles and the onset of trapping in both constant and pulsed fields. The circles do not exhibit the orientation overshoot response to a field pulse seen with linear DNA, and the rate of orientation growth scales as E(-2+/-0.1) with the field, as opposed to E(-1.1+/-0.1) for the linear form. These results show that the linear form migrates by cyclic reptation, whereas the circles most likely are trapped by impalement on gel fibers. This proposal is supported by very similar velocity and orientation behavior of circular DNA in agarose gels, where impalement has been deemed more likely because of stiffer gel fibers. The trapping efficiency is sensitive to DNA topology, as expected for impalement. In polyacrylamide the supercoiled form (superhelical density sigma = -0.05) has a two- to fourfold lower probability of trapping than the corresponding relaxed species, whereas in agarose gels the supercoiled form is not trapped at all. These results are consistent with existing data on the average holes in the plectonemic supercoiled structures and the fiber thicknesses in the two gel types. On the basis of the topology effect, it is argued that impalement during pulsed-field electrophoresis in polyacrylamide gels may be useful for the separation of more intricate DNA structures such as knots. The results also indicate that linear dichroism on field-aligned molecules can be used to measure the supercoiling angle, if relaxed DNA circles are used as controls for the global degree of orientation.     

Transient electric birefringence of agarose gels. II. Reversing electric fields and comparison with other polymer gels

The transient electric birefringence of low electroendosmosis (LE) agarose gels oriented by pulsed unidirectional electric fields was described in detail in Part I [J. Stellwagen and N. C. Stellwagen (1994), Biopolymers, Vol. 34, p. 187]. Here, the birefringence of LE agarose gels in rapidly reversing electric fields, similar in amplitude and duration to those used for field inversion gel electrophoresis, is reported. Symmetric reversing electric fields cause the sign of the birefringence of LE agarose gels, and hence the direction of orientation of the agarose fibers, to Oscillate in phase with the applied electric field. Because of long-lasting memory effects, the alternating sign of the birefringence appears to be due to metastable changes in gel structure induced by the electric field. If the reversing field pulses are equal in amplitude but different in duration, the orientation behavior depends critically on the applied voltage. If E < 7 V/cm, the amplitude of the birefringence gradually decreases with increasing pulse number and becomes unmeasurably small. However, if E > 7 V/cm, the amplitude of the birefringence increase more than 10-fold after ～ 20 pulses have been applied to the gel, suggesting that a cooperative change in gel structure has occurred. Because there is no concomitant change birefringence must be due to an increase in the number of agarose fibers and /or fiber bundles orienting in the lectric field, which in turn indicates a cooperatice breakdown of the noncovalent “junction zones” that corss-link the fibers in to the fgel matrix. The sign of the birefringence of LE agarose gels is always positive after extensive junction zone breakdown, indicating that the agarose fibers and fiber bundles preferentially orient parallel to the lectric field when they are freed from the constraints of the gel matrix. Three other gel-forming polymers, high electroendosmosis (HEEO) agarose (a more highly changed agarose), β-carrageenan (a stereoisomer of agarose), and polyacrylamide (a chemically corss-linked polymer) were alos studied in unidirectional and rapidly reversing electric fields. The birefringence of HEEO agarose backbone chain. The β-carrageenan gels exhibit variable orientation behavior in reversing electric fields, suggesting that its internal gel structure is not as tightly interconnected as that of agaroise gels. Both HEEO agarose and β-carrageenan gels exhibit a large increase in the amplitude of the birefringence with increasing pulse number when asymmetric reversing pulses > 7 V/cm are applied to the gels, suggesting that junction zone breakdown in a common feature of polysaccharide gels. Chemically cross-linked polyacrylamide gels exhibit very small birefringence signals, indicating that very little orientation occurs in pulsed lectric fields. The sign of the birefringence is independent of the polarity of the lectric field, as expected from the Kerr law, and normal orientation behavior is observed in reversing electric fields. Hence, the anomalous change in sign of the birefringence observed for agarose gels in reversing electric fields must be due to the metastable junction zones in the agarose gel matrix, which allow gel fiber rearrangements to occur. © 1994 John Wiley & Sons, Inc.     

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.     

Stretching and overstretching of DNA in pulsed field gel electrophoresis. I. A quantitative study from the steady state birefringence decay

Using a sensitive birefringence instrument, the birefringence arising from the orientation of the DNA chain during electrophoretic transport has been recorded. This birefringence is shown to proceed both from the alignment (stretching) of the molecule in the direction of the electric field and from the extension of the length of its primitive path (overstretching). The contribution of these two processes can be separated in the decay of the birefringence after the end of the application of the electric field. The fast relaxation of the overstretching occurs first and is demonstrated to be the main contribution to the birefringence. The orientation factor of the remaining stretched state and its decay can be quantitatively understood using the biased reptation model. It provides, in addition, a high value for the tube diameter or gel pore size a (4500 ± 450 Å for a 0.7% agarose gel with a c^?0.6_g dependence in the agarose concentration c_g) and a low value for the effective charge per base pair (0.2e as compared to 0.5e using the condensation hypothesis). The contribution of overstretching to the birefringence is also quantitatively interpreted in term of the change in the mean length l of DNA inside a pore size a. The dynamics of decay of this overstretching is well represented by a stretched exponential with a stretching exponent α = 0.44. The mean decay time decreases slightly with increasing fields and scales with the overall DNA length close to N²₀. © 1993 John Wiley & Sons, Inc.     

Electrophoretic mobility of lambda phage HIND III and HAE III DNA fragments in agarose gels: a detailed study

The electrophoretic mobility (μ) of DNA fragments from λ phage and ΦX 174, split by restriction enzyme to molecular lengths from 3 × 10² to 2.36 × 10⁴ base pairs, has been investigated in 0.6–4% agarose gels at various field strengths, ionic strengths, and temperatures. As already observed, μ is seen to be very sensitive to the field, increasing with field strength. The sensitivity increases with the molecular length of the DNA and decreases at high gel concentration. Our data are in qualitative agreement with recent theoretical predictions that concern the influence of the electric field on electrophoretic mobility. Mobility data have been extrapolated to zero field. This enables a comparison of our experimental results with theoretical predictions on the dependence of μ on the molecular weight of the DNA fragments. Our data fit, quite closely, a reptation model, where the tube path is described as a semiflexible entity with a persistence length equal to the pore diameter. The influence of the agarose concentration and the ionic strength of the buffer on the two parameters of the model—intrinsic electrophoretic mobility (μ₀) and the number of base pairs per element of the tube (g)—are well described by the model. The temperature dependence of the electrophoretic mobility, together with the influence of the agarose concentration on μ₀, indicate that the hydrodynamic drag is the leading frictional force on the DNA molecules in the gel.     

Dynamics of DNA molecules in gel studied by fluorescence microscopy

The dynamics of individual DNA molecules in a thin gel were studied with fluorescence microscopy. Driven by an electric field, molecules hooked around isolated obstacles and became extended. By analyzing molecular images, we identified the reptation tube and primitive chain. When the field was turned off, the molecules relaxed. The relaxation time tau1 and primitive chain length at equilibrium depend on N, the size of the molecule in base pairs, consistently with reptation theory. Using five yeast chromosomal DNAs ranging in size from 245 kb to 980 kb, we found that: These results constitute a way of sizing individual DNA molecules by imaging rather than by gel electrophoresis.     

Orientation of DNA in agarose gels.

An orientation of the lambda DNA during the electrophoresis in agarose gels was measured by a microscopic linear dichroism technique. The method involved staining the DNA with the dye ethidium bromide and measuring under the microscope the polarization properties of the fluorescence field around the electrophoretic band containing the nucleic acid. It was first established that the fluorescence properties of the ethidium bromide-DNA complex were the same in agarose gel and in a solution. Then the linear dichroism method was used to measure the dichroism of the absorption dipole of EB dye bound to lambda DNA. In a typical experiment the orientation of two-tenth of a picogram (2 x 10(-13)g) of DNA was measured. When the electric field was turned on, the dichroism developed rapidly and assumed a steady state value which increased with the strength of the field and with the size of DNA. A linear dichroism equation related the measured dichroism of fluorescence to the mean orientation of the absorption dipole of ethidium bromide and to an extent to which the orientation of this dipole deviated from the mean. The observed development of dichroism in the presence of an electric field was interpreted as an alignment of DNA along the direction of the field. The increase in the steady state value of dichroism with the rise in the strength of the field and with the increase of the size of DNA was interpreted as a better alignment of DNA along the direction of the field and as a smaller deviation from its mean orientation.     

Field inversion gel electrophoresis in denaturing polyacrylamide gels.

The velocities of single stranded DNA molecules in denaturing polyacrylamide gels during symmetric and asymmetric field inversion were measured at different pulse times and gel concentrations. Under the conditions chosen in our study, pulse times as short as a few milliseconds lead to a retardation of DNA molecules larger than 400 bases. We found that a field inversion with an electric field in the forward direction of about double the strength of that applied in the backward direction is a good compromise between the degree of retardation, the temperature control requirements and the run time of the gel.     

On the theory of gel electrophoresis of DNA: extension and evaluation of the Lumpkin-DèJardin-Zimm model

Using fundamental concepts of hydrodynamics in porous media, we have rederived the Lumpkin-DèJardin-Zimm (LDZ) model for the gel electrophoresis of reptating, infinitely long, worm-like chains, such as DNA. The force balance provides a constraint for evaluating the correlation among the segment-to-field angles of a given molecular conformation. We have used an approximate analytical expression to account for this correlation in order to apply the present derivation to finite chain lengths. The resulting extended LDZ model predicts a nonlinear variation of electrophoretic mobility (mu) with reciprocal chain length (1/Lc) at low electric field strengths, similar to the one observed. The present derivation is valid only at low electric field strengths, and the predictions of the extended LDZ model fit data for a dimensionless electric field strength, E1*, of less than 1.23. An empirically useful criterion for determining the onset of reptation is also described. The present treatment shows how size-exclusion effects can be included in future theories. Models based on reptation alone are shown to predict a discontinuity in the molecular chain length dependence of mobility at a critical molecular size. Such discontinuities are not observed experimentally.     

Model and computer simulations of the motion of DNA molecules during pulse field gel electrophoresis

A model is presented for the motion of individual molecules of DNA undergoing pulse field gel electrophoresis (PFGE). The molecule is represented by a chain of charged beads connected by entropic springs, and the gel is represented by a segmented tube surrounding the beads. This model differs from earlier reptation/tube models in that the tube is allowed to leak in certain places and the chain can double over and flow out of the side of the tube in kinks. It is found that these kinks often lead to the formation of U shapes, which are a major source of retardation in PFGE. The results of computer simulations using this model are compared with real DNA experimental results for the following cases: steady field motion as seen in fluorescence microscopy, mobility in steady fields, mobility in transverse field alternation gel electrophoresis (TFAGE), mobility in field inversion gel electrophoresis (FIGE), and linear dichroism (LD) of DNA in agarose gels during PFGE. Good agreement between the simulations and the experimental results is obtained.     

Study of large DNA fragments in agarose gels by transient electric birefringence

The pulsed-field gel electrophoresis (PFG) is a newly developing technique used in the fractionation of large DNA fragments. Advances in PFG demand a better understanding in the corresponding mechanisms of DNA dynamics in the gel network. Detailed experiments are needed to verify and to extend existing theoretical predictions as well as to find optimum conditions for efficient separation of large DNA fragments. In the present study, deformation of large DNA fragments (40-70 kilobase pairs) imbedded in agarose gels were investigated by using the transient electric birefringence (TEB) technique under both singular polarity and bipolarity electric pulses at low applied electric field strengths (E less than or equal to 5 V/cm). The steady-state optical retardation (delta s) of DNA molecules is linearly proportional to E2. At a given E, the amplitude of optical retardation [delta(t)] increases monotonically with the pulse width (PW) and then reaches a plateau value [delta(t = 0) = delta s] where t = 0 denotes the time when the applied field is turned off or reversed. The field-free decay time (tau-a few minutes) is several orders of magnitudes slower than that from previous TEB observations using high electric field strengths (E-kV/cm) and short pulse widths (PW-ms). The degree of deformation (stretching and orientation) and the time of restoration to the equilibrium conformation of overall DNA chains have been related to delta and tau. In field inversion measurements, exponentially rising and linearly falling of birefringence signals in the presence of forward/inverse applied fields were observed. The rising and falling of birefringence signals were reproducible under a sequence of alternating pulses. Comparison of our results with literature findings and discussions with theories are presented.