DNA Electrophoresis in Agarose Gels: Three Regimes of DNA

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J. Phys. Chem. 1994,98, 2624-2633

2624

DNA Electrophoresis in Agarose Gels: Three Regimes of DNA Migration Identified and Characterized by the Electrophoretic Orientational Behavior of DNA Soffia Magnbd6ttir, Bjorn Akerman, and Mats Jonsson' Department of Physical Chemistry, Chalmers University of Technology, S-41296 Gothenburg, Sweden Received: July 20, 1993; In Final Form: November 9, 1993'3

Linear dichroism (LD) spectroscopy has been used to follow the orientation of linear double-stranded DNA during electrophoresis in agarose gels, in order to classify the mode of migration of DNA as function of its size and the electrophoretic field strength. We have used the presence of oscillations in the LD rise profile, when applying a constant electric field, and of a component in the field-free LD decay from the steady migrative state to identify the regime where DNA migrates with the oscillatory mode of motion called geometration, which is known to hold for long DNA. We also use a vanishing steady-state LD for identifying the regime where the DNA moves without orientation, indicating Ogston type of migration (short DNA) or classical reptation (long DNA a t low fields). Between these extremes there is a regime, here termed the nongeometration regime, where the DNA moves oriented, and our results indicate that smaller DNAs migrate as anisotropic deformed coils and larger ones as reptating chains. The measurements have been performed mainly in 0.8% in gel, but similar experiments at other gel concentrations (0.7-1.4921) are in accordance with the results if the DNA coil size, described by the radius of gyration of DNA (RG),is normalized to the average pore radius of the gel (PE), indicating that RG/PEis a relevant parameter for describing DNA migration in agarose. By varying the electric field strength and the length of DNA, the borders between the three regimes have been identified, and a diagram is presented for the migration of DNA under experimental conditions normally used during electrophoresis. The orientational behavior of the DNA in the different regimes is discussed, and the measured LD response and relaxation amplitudes and times are given a molecular interpretation.

Introduction Agarose gel electrophoresis is used to fractionate DNA molecules by molecular weight. In a constant electric field, the sieving action of the porous gel matrix can be utilized to separate linear double-stranded DNA molecules of sizes up to about 30 kilobasepairs (kbp). When the DNA molecules are longer, they display essentially the same mobility and the separation becomes very poor.' In a simplified picture this is a consequence of long molecules migrating end-on through the gel-a type of motion known as reptation-and becoming orientedby the electricfield." Long DNA molecules can be separated, however, by use of pulsed field electrophoresis (PAGE) introduced by Schwartz et ai. in 1982.5 Since then, several modifications of the technique have been presented where the electric field is varied in a number of ways in time and in space. (For a review see ref 6.) The actual mechanism of the molecular weight separation in PFGE is still not fully understood but it is known from both experimental and theoretical studiesthat it is based on the reorientation the reptating chains are forced to undergo when the field changes direction.'-' A characterization of the mode of migration of the DNA on the basis of its orientational behavior is therefore important as a guide in the choice of the electrophoresis technique that gives the best separation. The first direct experimental evidence of electrophoretic orientation was obtained by using linear dichroism (LD) spectroscopy.12 Fluorescencepolarization, fluorescence-detectedLD, birefringence, and fluorescence microscopy are other techniques which have been used to study orientation1 effects.13-l8 The techniques and the literature on DNA orientation have recently been reviewed by NordCn et al.19 When a constant field is applied to a relaxed ensemble of molecules, the buildup of the orientation displays over- and undershootsbefore a steady state is observed.14.20 The oscillations were interpreted as a periodic behavior of DNA when migrating

* Abstract published in Aduance ACS Abstracts,

February 1, 1994.

0022-3654/94/2098-2624$04.50/0

through the gel, involving stretching and coiling as a result of interactions with thegel fibers. Since the molecules are all initially in their random-coil configurations, they start with their cycles in unison. But as the cycles repeat, they gradually get out of phase relative to each other and a steady state in the macroscopic orientation is observed, identical with the average orientation over a cycle. Computer simulations21*22 have confirmed this interpretation, and direct observation by fluorescence microscopy17J8.23 on long DNA has given the following scenario. The DNA chain becomes hooked on a gel fiber, and the motion of its two ends downfieldleads to formation of a U-shaped configuration with the arms pointing in the field direction. Once the tug of war between the arms has been settled, unhooking of the U leads to a collapse of the chain and the process of U-formation starts all over again. The result is a motion with oscillatory conversion between coiled and stretched states. Since the molecule for most of the time has a well-defined head which "chooses" the path through the gel in an end-on fashion, this motion can be viewed as a special case of biased reptation (seebelow), where the molecule moves end-on and oriented but without the periodic behavior of stretching and coiling. In the literature both these migration modes are frequently called reptation, althoughthe cycling motion sometimes is referred to as geometration, a term introduced by DeutschQand which also, for the sake of simplicity, will be used here to distinguish it from pure end-on migration. Most of the theoretical studies on the electrophoreticbehavior of long DNA in gels (for a recent review see ref 25) have been based on the reptation model originally introduced by de Gennesu to describe the diffusion of polymers in dense solutions, where each moleculecan be regarded as confined to a hypotheticaltube. The model was early applied to DNA electrophoresi~,2~.28 but Lumpkin et a1.2 and Slater and Noolandi3g4 were first to incorporate orientation of the DNA into the reptation theory. In these so-called biased-reptation models, the chain is assumed to move end-on and to follow rigidly the path traced by the leading segment, which lays down new tube segments preferentially in the field direction. The models account for some aspects of the Q 1994 American Chemical Society

DNA Electrophoresis in Agarose Gels

The Journal of Physical Chemistry, Vol. 98, No. 10, 1994 2625

orientational behavior but not, for example, for the oscillatory motion seen in the microscope. During the past years the reptation model has been extended, however, by removing the assumption of fixed tube length, a modification which gives a description of the motionof long DNA in better agreementwith e~periments.2~~’ Spectroscopic,microscopic, and theoretical studies have thus been able to describe the main features of the migration of long DNA in agarose gel under the action of both constant and pulsed fields. The mode of migration which leads to separation of short DNAs in constant fields is less clear but is frequentlycalled sieving. A theory for the sieving of globular proteins was outlined by Rodbart and C h r a m b a ~ hbased ~ ~ on the concept of size exclusion by the gel fibers introduced by Ogston.33 In this theory the mobility of a particle, assumed spherical and undeformable, is dependent on the fraction of the gel volume available to it. Ogston’s theory finds this fraction to have an exponential dependence of the radius of the particle, so that a plot of the logarithm of the mobility against the gel concentration (Ferguson plot) becomes linear with a slope proportional to the radius of the particle. Such plots have been observed to be approximately linear for small DNA at low electric indicating that the DNA then migrates as a globular coil through the gel. The coil size of the DNA molecule in the gel is not established, but estimates of gel pore sizes from mobilities of small DNA fragments, assuming them to be global with a radius equal to the free solution radius of gyration, RG, show fair agreement with pore sizes measured by other techniques if the mobilities are first extrapolated to zero field strength.” This suggests that the random-coil size of the DNA molecule in the gel is the same as in solution. The boundary between Ogston and reptation migration as a function of the agarose gel concentration and DNA size was estimated by Slater er al. on the basis of the Ogston model and reptation theory and mobility data at low electric fields.g6 They found that a certain proportion between the radius of gyration (RG) of DNA and the average pore radius of the gel (PE) was necessary to accomplisha reptative motion, RG> 1.4PE. However, their classification only applies at low field strengths because the analysis was based on theories for the electrophoretic mobility which are valid only in the low field limit. In this work we have classified the migration of the DNA on the basis of its electrophoretic orientational behavior measured by LD spectroscopy and have in this way been able to include field strengths that are typically used in electrophoretic separations. The smallest DNA that has been studied in the microscope with a degree of resolution which makes it possible to clarify the mode of migration is A-DNA (48 kbp), and it was found to geometrate in agarose.” The same DNA forms the lower limit in the size range (up to 600 000 kbp) where LD spectroscopy has been used to follow the dynamics of the motion and in which all investigated molecules show the typical oscillations in the orientation that indicate geometration.l4-20938 We have therefore concentrated this study to DNA of sizes smaller than A-DNA. The measurements have been performed mainly in 0.8% gel, but similar measurements at other gel concentrations (0.7-1.4%), and comparison with earlier published orientation results, are in accordance with the results obtained at 0.8% if the DNA coil size relative to the gel pore size, RG/PE, is used as the independent parameter, suggesting that this is a relevant measure of the effective size of DNA in a classification of its mode of migration in the agarose gel. From the orientation and its dynamic three regimes of DNA migration have been identified: migration as isotropic coils at small Ro/PEvalues (Ogston regime), migration either as anisotropic coils or as reptating chains oriented in the field direction, at intermediate RG/PEvalues (nongeometration regime), and migration as reptating chains oscillating between stretched and compact forms at high ROIPEvalues(geometration regime). The transition boundaries between the regimes have

TABLE 1: Sizes of DNA Fragments and Their Radius of Gyration Relative to the Average Pore Radius, &/&, of the 0.8%Agarose Gel Used io This Study DNA size (kbp) contour length (A) 6.6 9.4 10.9 15.0 23.1 33.5 166

22 681 32 519 31 114 51 914 19 926 115 903 514 360

ha (A)

h/Peb

1882 2278 2458 2899 3616 4361 977 1

1.83 2.21 2.39 2.81 3.51 4.24 9.48

a Radius of gyration (&) calculated from the wormlike chain models1 using 500 A for the persistence length?2 Pore radius (PE) calculated according to Slater et d . 3 6 (PE= 1030 A for 0.8% agarose).

also been estimated as functions of RG/PEand the electric field strength in the electrophoresis. At strong field (30 V/cm) the minimum DNA size for geometration, expressed as RG/PE,is 1.8 (6 kbp DNA in 0.8% gel). As the field strength is decreased, the minimum size for geometrationincreases progressively, and finally at RG/PE= 9.5 (166 kbp DNA in 0.8% gel) DNA geometrates at all fields. Ogston type of migration holds below RG/PE= 1.0 (2.2 kbp in 0.8%) at 30 V/cm, but as the field is decreased, the border shifts toward larger DNAs so that Ogston migration, or classical reptation for the longest molecules, wcurs below RG/PE = 1.7 (5.7 kbp in 0.8% agarose) at zero field.

Materials and Methods Chemicals. DNA fragments from Xho I and Hind I11 digests of A-DNA and a EcoR I digest of Col E l Amp Plasmid DNA have been used. Xho I, EcoR I, A-DNA, and the Hind I11 digest of A-DNA were purchased from Pharmacia and Col E l Plasmid DNA from Sigma. The DNAs were cleaved at 37 “C in the universal All Phor One buffer using standard methods. The A-DNA Hind 111and Xho I digests were heated to 65 “C for 10 min and quicklycooled on ice before gel loading in order to prevent linking between the 23 and 4 kbp fragments. The digests together give a series of fragments of the following sizes: 6557 (6), 9416 (9), 10 900 ( l l ) , 15 004 (15), 23 130 (23), and 33 498 (33) bp, where the numbers in parentheses are the labels used for each fragment. Bands correspondingto fragments shorter than 6 kbp contained too little material for the LD to be accurately measured. Ultrapure DNA grade agarose from BioRad was used for the agarosegels. All other chemicals were of analyticalreagent grade. Table 1 presents the sizes of the DNA fragments and the ratio between their radii of gyration and the average pore radius of 0.8% gel (RGIPE). The table shows the longest fragment has a coil radius that is approximately 4 times the average pore radius of the gel. Included in the table are also data on T2 DNA since results published earlier on this DNA will be used to supplement the results obtained in this study. Linear Dichroism. The linear dichroism (LD) of the DNA bases at 260 nm has been used to determinethe averageorientation of the DNA helix axis during electrophoresis. The LD is the difference in absorption of light polarized parallel and perpendicular to a given laboratory axis through the sample, in our case the electrophoresis direction. LD = All - A ,

(1)

Since the absorption of light is due to the interaction between the electric vector of the light and the transition dipole moments of the DNA bases, the LD signal provides information about the orientation of the helix axis, when the direction of the transition moments relative to this axis is known. If there is no macroscopicforce present to orient the molecules, Brownian motions will give them a random orientation as well as their transition moments. The sample is then isotropic, and

2626 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994

Magnbsd6ttir et al.

All = A 1 and LD is zero. However, when the electric field is present, the molecules are alignedwith the field direction resulting in orientation which can be characterized by the reduced linear dichroism (LD'), defined as LD'

1.o

= LD/A,

v1

where Ai, denotes the absorbance of the isotropic sample in absence of the field. In the case of partially oriented molecules the LD' may be described as a product of an orientation factor (S)and an optical factor (O)39 LD' = SO (3) This is possiblesincethe DNA molecule has an effectivecylindrical symmetry in terms of the transition moment directions. The aptical factor is related to the effective angle CY between the absorbing transition moments in the plane of the bases and the helix axis of the molecule. LD' = 3S((COS' a)- 1)/2

(4) The orientation factor S is equal to (3(c0s2 0) - 1)/2, where 0 denotes the angle between the helix axis and the electrophoresis direction. S will be in the range 4 . 5 to 1 where the latter value corresponds to perfect orientation along the field direction. Under the conditions prevailing in our experiments,the doublestranded DNA has been in the B-form conformation for which the effective angle CY is equal to 86OqW2 According to eq 4, an LDr = -1.48 corresponds to a perfect orientation (S = 1). To obtain the degree of orientation, the LD of migrating molecules and the isotropic absorbance ( A h )of the sample in the absenceof field have to be measured at 260 nm. The LD response deriving from DNA absorption is a direct measure of the orientation as a function of time, S(t), since there is no change in Ai, during the relatively short pulses applied and since the optical factor remains constant (DNA stays in its B-form) during the orientational process.* Electrophoresis Cell and Spectroscopic Measurements. The electrophoresis cell, the optical equipment, and the technique used for the spectroscopicmeasurements have been described in detail earlier.20143 The optical instrumentation has required a vertical electrophoresis direction, and a special electrophoresis cell for this purpose has been developed and equipped with a device for scanning both LD and isotropic absorbance along the lanes of the gel. In all experiments described here, the LD and Ahof the DNA sample were measured at the position of maximum absorbance of the DNA zone in the gel: A h with the electric field turned off, and LD with a square-formed voltage pulse of a duration that permitted determination of the dynamics of the buildup of the orientation as well as the steady-state orientation. The rise and decay times of the electric field were less than 1 ms as measured over the cell electrodes. The LD signals were recorded on a Nicolet 2090 oscilloscope. To be able to follow the rapid responses of the comparatively short DNA fragments, the response time of the LD instrument had to be set in the range 2-8 ms, which resulted in noisy signals. Each measurement was therefore repeated 6-12 times, and an average LD response was formed on which the final analysiswas made. Presented data are in turn averages of measurements in at least two gels. The LD relaxations were normalized between zero and unity and analyzed by fitting to a double-exponential decay

+

T

+

LD(t) = Ae-'/'/'l BeJ/'z C (5) The quality of the fits was estimated from the residual between the fitted and the measured curve. To obtain good fits, a constant term had to be added, which never accounted for more than 9% of the total LD amplitude. It did not reflect a shift in the base line, since the LD always returned to the original base line after a time period much longer (about 10 s) than T I and 7 2 . As discussed later, the behavior of the constant term suggests that

t 5, ALD

$ 0.5

t

I

LDss

11 kbp 9 kbp ~~

180

_ _ _ _ ~

360

TIMEhns

Figure 1. LD buildup responses from four DNAs of different lengths (indicated) in agarose gel to a constant electrophoreticfield turned on at time zero. Gel concentrationis 0.8%, field strength is 15 V/cm, ALD is the sum of the amplitudes of the over- and undershoot, and LD, is the steady-state LD. The responses are normalized with regard to LD,.

it reflects a physical process, but of such slow rate and low amplitude that the noise level in our LD measurements does not allow this process to be measured accurately enough in the same time window used to follow the much faster main components. Fitting to three exponentials never gave a better fit than eq 1. In the cases where the amplitude for the longer time constant, B, in a double-exponentialfit was below 4% of the total amplitude (our experimental uncertainty), a trial fit to a single-exponential decay always gave a time constant within 5% of the short one from a doubleexponential fit. Taking into consideration the small difference between the residual plots for these two fits and the low proportion of the slower process, a single-exponential fit was considered sufficient to describe these decays. Gel Preparation, DNA Loading, and Electropboresis. If not otherwise stated, the agarose gels were 0.8% (w/w) in 50 mM Tris, 50 mM boric acid, and 1.25 mM EDTA buffer (pH 8.5). The gel solution was prepared by heating the buffer with the agarose powder to 100 "C until the agarose powder was fully dissolved. After the evaporated water was compensated for, the solution was cooled to approximately 80 OC and poured into the vertical quartz cell, which had been preheated to the same temperature, and the gel was then allowed to form by cooling at room temperature. It was held in place by a nylon net with a mesh size 0.1 X 0.1 mmz glued to the bottom of the cell. The DNA was loaded into the sample well that had been cast at the top of the gel. Each fragment was studied in at least two gels, which in some cases contained different amounts of DNA. However, the DNA concentration has been kept below 0.2 mM to avoid effects due to DNA-DNA interactions.20 The variations between different gels (typically 4% in the dynamic parameters) can therefore be ascribed to differences in gel structure. During theelectrophoresis,fresh buffer solution was continuouslysupplied to the electrode compartments to compensate for the buffer ion losses due to electrophoretic transport. The electrophoresis as well as the subsequent LD measurements were made at room temperature (20-22 "C).After the LD measurements the gel was stained with ethidium bromide and photographed in order to confirm that the DNA had migrated into the gel as a zone. ResUlts

Buildup of Orientation. Figure 1 shows LD responses (260 nm) from four DNA fragments of different sizes in the agarose gel when a constant field is turned on at time zero. All responses start off from the DNA system in the gel in relaxed state (taken as the state of the system giving a LD response that does not change with increasing waiting time before the field is appIied20). The LD isnormalizedwithrespect to the steady-statevalue(LD,),

DNA Electrophoresis in Agarose Gels

The Journal of Physical Chemistry, Val. 98, No. 10, 1994 2627

kbP 0.5

r

!

5 20 15v/cmI o 3OVlcm

40

80

18

I 31

""'i c!

0.1

p8

P

1

80

TIME Ims

Figure 2. ALD as function of DNA size (&) normalized to gel pore size (Pe).Gel concentrationis 0.81,field strengthsare indicated, and ALD is normalized with regard to LD,.

which depends on the size of the DNA (see below), to better illustrate the DNA size dependence in the LD buildup. The responses can be considered as originating entirely from DNA since contributions to the LD from orientation effects in the gel structure were found to be negligible (as measured at 320 nm).43 The response functions thus directly reflect the rise kinetics of theDNA helixorientations. Thenegativesign oftheLDconfinns earlier reports of preferential orientation of the helix axis in the direction of the electric field. It is seen that the various DNA sizes respond differently to the electric field. The smallest fragment shows a monotonic rise profile in the buildup of the orientation whereas the larger ones exhibit a clear over- and undershoot(peak-to-troughvalue ALD), with amplitudes that grow with the DNA size, before reaching the steady-state orientation. Such oscillations have been reported earlier for larger DNA,14Jo*38 but not in the present size range. The time to reach the overshoot increases with increasing DNA size, again in agreement with observations on longer DNA.14J0 However, it is the observation that the presence of oscillations in the orientational buildup, and their amplitudes, depends on the size of the DNA that is of special importance for the purpose of this papor. This dependence is shown in Figure 2 for the whole investigated DNA size range at two field strengths. It is seen that ALD is zero (absence of oscillations) for DNA fragments up to about 9 kbp (&/PE = 2.2) at 15 V/cm, and up to 6 kbp (&/PE = 1.8) at 30 V/cm, and that it then rises rapidly with increasing DNA size but reaches an apparent saturation for long DNA. The buildup of the orientation is also affected by the field strength, as exemplified by the responses at different fields for the 9 kbp fragment shown in Figure 3. For the sake of comparison, the responses are also here normalized with regard to the steadystate LDvalue (LD,), since this, as shown below, depends on the field strength. While the buildup has a simple monotonous rise kinetics at 15 V/cm, oscillations are observed at higher fields with a ALD value relative to LD, that goes through a maximum at 22.5 V/cm, then decreases, and virtually disappears again at 37.5 V/cm. As shown in Figure 4, such a maximum is observed for all fragment sizes that show oscillations, although for the longer fragments ALD does not return to zero in the field range investigated. It should be noted that the positions of the maxima occur at a field strength that is nearly independent of DNA size. This indicates that the 6 kbp fragment never exhibits oscillations since ALD for this fragment, as shown by the figure, is zero throughout the field range where a potential maximum should have occurred. Extrapolation to zero ALD of the low field branch of the curves for the other fragments (Figure 4, dashed part of the curves) gives the field strength which must be reached for respective fragment before oscillations appear in the buildup of

Figure 3. LD buildup responses from 9 kbp DNA at four different field

strengths (indicated). Gel concentrationis 0.81,and the responees are normalized with regard to LD,,. 0.5

I

-

0.4

A A

$ 1

9kbp ISkbp 23 kbp 33kbp

0.3

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0

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ENcm-' Figure4. Field strengthdependencein ALD. DNA lengths are indicated. Gel concentration is 0.81,and ALD is normalized with regard to LD,. Note that ALD is zero for 6 kbp at all the fields studied. *

0.3

v)

0.2

6 c;l I

0.1

0.0 I

Figure 5. Degree of steady-state Orientation (LP") as a function of DNA size (&) normalized to the gel pore size (&). Field strengthsare indicated. Gel concentration is 0.8%.

its orientation. These results can be used, as will be shown in the Discussion section, to create a border between two regimes of different modes of DNA migration. Steady-State Orientation. Figure 5 shows that the degree of orientation (LD') correspondingto the steady-state level (LD',) increaseswith increasing DNA size and increasing field strength, in agreement with the results of an earlier studP3of steady-state orientation of DNA in the same size range. For all fields the orientation increases linearly with increasing RG/PEwithin the DNA size range investigated here, but comparison with earlier

Magnhd6ttir et al.

2628 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994

m

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.

O

P

A

o

0

A

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125

250

TIME /ms Figure 6. Field-free decays for three DNA lengths (indicated) when relaxing from steady-stateorientations in 0.8% gel at 30 V/cm. LD is normalized with respect to thesteady-statevalue. Fittedcurvesaredrawn through the decays; a double-exponentialfit for 23 and 33 kbp; a singleexponential fit for 6 kbp DNA.

i3

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1

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40

50

60

80

70

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Figure 8. Variationsof the relative amplitudes A and B (corresponding to the relaxation times 71 and 72, respectively) and C (an offset with a very long relaxation time compared to 71 and T Z ) with the field strength for two DNA lengths (indicated). Gel concentration is 0.8%.

400

T, 23kbp

A 23kbp B 23kbp C 23kbp A 33kbp B 33kbp C 33kbp

T

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E / Vcm-' Figure 7. Variations of the relaxation times 71 and 7 2 with the electric

field for two DNA lengths (indicated). Gel concentration is 0.8%. measurements on T2 DNA (166 kbp, RG/PE = 9.5) shows that the orientation levels off for longer DNA. There is no sign of deviation from linearity, however, when going toward shorter DNA, and the extrapolated intersections with the Ro/PE axis should give a fairly good estimation of the effective DNA coil size that forms the border, a t the field strength in question, where a transition occurs from motion with orientation to motion without orientation. Relaxation of Orientation. In addition to the buildup of the steady-state orientation, we will also use the field-free relaxation of this orientation to characterize the motion of DNA in the gel. Figure 6 shows the LD relaxations of three DNA sizes when the field (30 V/cm) is turned off a t time zero. (LD in the figure is normalized to LD,.) The decay of the 6 kbp fragment is well described by a single exponential whereas the 23 and 33 kbp fragments required double exponentials. Figure 7 shows how the two LD relaxation time constants, 71 and 7 2 , depend on the field strength for two of the fragments. The relative amplitudes, A and E, corresponding to the time constants 71 and 7 2 , respectively, are shown as functions of field strength in Figure 8, together with the offset term C (see Materials and Methods section). Amplitude A tends to increase a t the cost of E as the field becomes stronger, whereas the offset term is independent of the field within the experimental uncertainty. As will be discussed in detail later, our interpretation is that the amplitudevariations reflect a shift of the orientation distribution to faster relaxing modes as the field strength, and thus the degree of orientation (see Figure 5 ) , increases. The way the two time constants are affected by the size of the DNA is shown in Figure 9 at two field strengths. The relaxation

3

Figure 9. Time constants 71 and

4

5

E

as a function of DNA size (&) normalized to gel pore size (PE)at two field strengths (indicated). Gel concentration is 0.8%. 72

time corresponding to the fast process (71) is more or less constant at 25 ms for all DNA sizes that has been investigated, whereas the time corresponding to the slow process ( 7 2 ) is considerably longer for the larger DNA molecules. However, with decreasing molecular size 72 approaches 71 with a trend a t the respective field which indicates that it merges with 71 a t a RG/PE ratio of approximately 2 at both 15 and 30 V/cm. This transition from two relaxation processes into one is also seen in the decay amplitudes in Figure 10 where E (the amplitude of the slow process) for the two fields becomes zero at the corresponding RGIPE ratio. Oscillation Recovery. The relaxation of the LD orientation does not lead to a complete equilibration of long DNA molecules as shown by Akerman et a1.20 in a work on T2 DNA (166 kbp). It was found that the over- and undershoot in a pulse applied after a long time of field-free condition in the gel were much more pronounced than in a second pulse of the same polarity and field strength applied shortly after the LD in the first pulse had relaxed. The time to recover 90% of the full amplitudes of the over- and undershoot was typically 20 min, whereas the time to relax 90%of the LD only was about 10 s. The major part of the over- and undershoot recovery is thus a reorganization of a DNA which is already randomly oriented. The kinetics of this process is shown for the 23 and 33 kbp fragments in Figure 11, where the oscillation magnitude, ALD, observed in a second pulse is plotted against the time delay between the pulses. The semilogarithmic plots in Figure 12 show that the oscillation recovery for these fragments is well represented by single-exponential

The Journal of Physical Chemistry, Vol. 98, No. 10, 1994 2629

DNA Electrophoresis in Agarose Gels

kbP 1.o

1-1

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0.5

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B 15V/cm A c 1 5 V h n A 30V/cm o B 30V/cm A C 30V/cm

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20

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5

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:

30

40

1

Figure 10. Relative amplitudes A, B, and C as a function of DNA size (&) normalized to gel pore size (PB) at two field strengths (indicated). Gel concentration is 0.8%.

0.4

0.0

Time/s Figure 11. Kinetics of over- and undershoot (ALD) recovery for two DNA lengths (indicated). ALD in the second pulse is normalized to its maximum value, ALD, (see text), vs field-free diffusion time between two DU~SCSof the same wlaritv. Gel concentration is 0.8% and field streigth is 30 V/cm. 6 n

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Time/s Figure 12. Semilogarithmicplot of the ALD recovery (from Figure 11, where experimental conditions are given). The slopes correspond to time constants 0.9 and 2.2 s for 23 and 33 kbp, respectively.

kinetics. The time constants are 0.9 s for 23 kbp and 2.2 s for 33 kbp and are thus seen to be long compared to the LD decay times.

Discussion Border betweeen Ceometration and Nongeometration. Zdentification from the Dynamics of the Buildup ofthe Orientation. Figures 1-4clearly show that the absence (ALD = 0) or presence (ALD > 0) of oscillations in the buildup of the orientation is

dependent on the coil size and the field strength in the electrophoresis. Oscillationsin the LD haveearlier been observed only for long DNA (>50 kbp)14JO*38where both computer simulation^^.^^ and microscopic s t u d i e ~ ~ ~ demonstrate J~J3 that they reflect ongoing osciIlatory motion (geometration) and not an effect that occurs only initially when the molecules start From their relaxed coils. They will be observed initially only, because only when starting from relatively similar equilibrium conformations will the molecules perform the oscillations concertedly enough to show up in a spectroscopic average. Sooner or later the molecules are bound to get out of phase, and only an average orientation over the migration cycle is measured. However, it cannot be concluded from these studies that presence of LD wcillatipns in the buildup of the orientation always implies that the steady-state motion is geometration. For the small DNA fragments studied in this paper the probability of forming U-shaped conformations,which seems to be a necessary condition for geometration, may be high initially when the molecules start from their relaxed coilforms, but low for the conformationstaken by the molecules after the first cycle, which may be small anisotropic coils or short oriented chains. Nor is the absence of oscillations automatically an indication of a nonoscillatory migration. If the DNA molecules are short enough,an alternative explanation could be that they are too small compared to the length scale of the gel heterogeneities to be able to respond coherently. However, it will be shown below that the LD relaxation data speak against these explanations and that we can use the presence of initial oscillations as evidence of ongoing geometration and the absence as evidence of a mode of migration we will call nongeometration for the present. From Figure 2 it is clear that the magnitude of the oscillations (ALD) is sensitively dependent on DNA size. The apparent saturation in the 50-100 kbp range shows that the interesting size range to use the oscillations for characterization is primarily between 6 kbp, where oscillations are absent, and 20-30 kbp. In this region the steep decline in ALD for smaller and smaller molecules means low uncertainty in determiningthecritical DNA size where oscillations disappear, and the mode of migration changes from geometration to nongeometration. This occurs between 6 and 9 kbp at both 15 and 30 V/cm. In Figure 4, which shows how ALD for the investigated fragments varies with the field strength, the extrapolated intersection with the field axis decreases consistently with increasing DNA size and provides, for each fragment, the field for which the oscillations start to appear, i.e., the field when that DNA size starts to geometrate. In a diagram where the critical field is plotted against the ratio Ro/Pe (Figure 13, filled circles), the curve can be viewed as the border between nongeometration and geometration. The field required for T2 DNA (&/PE = 9.5) to show oscillations is lower than 0.1 V/cm in both 0.5% and 1% agarose” and is therefore included in Figure 15 as a limiting case for long DNA, which always geometrates. When going toward shorter DNA, we expect an asymptote for the border close to 6 kbp (RoIPE = 1.8) since no oscillations are observed for this fragment at any of the studied fields (Figure 4). As stated above, the border is between 6 and 9 kbp at both 15 and 30 V/cm. The trends in Figure 2 and a close inspection of the LD response profiles, indicate, however, that there is a weak shift of the border toward smaller molecules as the field is increased. This means that the border is nearly, but not perfectly, vertical for the strong fields in this size range, in agreement with such an asymptote. Below we will present somemore data that support the location of this border and that it is also valid at other gel concentrations than 0.8%. Identification from Orientation-Relaxation Data. As was discussed above, the presence or absence of oscillations in the buildup of the orientation does not in itself provide evidence that the molecules continue to geometrate, or are nongeometrating,

2630 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994

during steady-state migration. No clear conclusions regarding this question can be drawn from the steady-state LD either, since it can only reflect the average of the oscillations. However, the dynamics in the relaxation of the molecules back to their equilibrium states in the gel, when the field is turned off, should be sensitive for the conformations the molecules start to relax from. We have therefore analyzed the field-free LD decay from the steady-state LD, when the molecules are in sready migrative states, to see whether there is a parallel indication in this decay of a change in mode of migration in the size and field ranges where the oscillations disappear. First, the relevance of the twoexponential fitting model is discussed in terms of the field dependence in the fitted time constants and amplitudes. Figure 8 shows that for a given DNA size there is a shift from amplitude B to amplitude A as the field increases. This shows that as the molecules become more aligned by a stronger field (Figure 5), the orientation resides more and more in the rapidly decayingcomponent. Similar trends have been observed on long DNA and have been interpreted as a shift toward more efficient stretching of the molecules along the path of the molecule (the tube) at higher fields.20v44In addition, especially the 7 2 relaxation time decreases with increasing field (Figure 7), an effect which suggests that the two-exponential representation is not fully adequate: if the decay consisted of two pure relaxation modes characteristic for the DNA in the gel, only the amplitudes would shift and the decay rates should remain constant. Heterogeneity effects due to DNA polydispersity seem unlikely as a cause to the decreasing relaxation times because we have used restriction fragments from monodisperse mother molecules. A possible explanationto the decreasecould be that increased field strength, which leadsto a more oriented DNA molecule (Figure 5), initiates modes in the molecule characterized by shorter relaxation times which tend to dominate the relaxation, since such modes may be expected to be more populated the more deformed the molecule. The variations in 71 and 72 with E are small, however, compared to the difference between them at any given field. Furthermore, Figure 9 shows that whereas the fast decay process has a rate which is essentially the same for all DNA sizes studied, the slow component is clearly slower the longer the DNA. This supports that the two decay components are really distinct processes. For T2 DNA LD decays in gels of different concentrations have also strongly indicated two distinct components in the orientation relaxation, with the rapid part being much less sensitive to pore size than the slower contribution.20 We therefore conclude that the two-process description of the LD decay is sufficient for our purpose of identifying changes in mode of migration. Whether the offset term C in the fitting really reflects a third process or not is more uncertain. Figure 14 shows that there is a long tail in the LD decay with a relaxation time much longer than the fast A and B components. In a fit of the decay limited to a few tenths of a second, such a tail will indeed be reasonably described by a low offset term, and we therefore believe that C correspondsto a very slow process with little significancefor the faster LD decays. Mayer et al." have reported a similar slow and low-amplitudethird contribution to the birefringence signal from disorienting DNA in agarose gels, which they ascribe to tube renewal by reptation. Under conditions similar to ours the amplitude of this component for 33 kbp is 0.08 and the time constant about 5 s, in fair agreement with our data (Figure 14). Our data on the influence of DNA size and field strength on C are too uncertain, however, to allow quantitative comparison with the trends observed by Mayer efal. for their slow decay component. When discussing molecular interpretations, we will return to results on the oscillation recovery which suggest that a thud process indeed is present, but regarding the classification of the migration we will concentrate on the main amplitudes A and B. Figure 10 presents, at fields 15 and 30 V/cm, the relative contributions of A, B, and C in the LD relaxation as functions

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Figure 13. Diagram showing how the orientational behavior of linear double-stranded DNA during agarose gel electrophoresis depends on electric field strength and DNA size. The diagram is based on LD measurements (see text) on DNA in 0.8% agarose. Molecular sizes of DNA (in kbp) and their corresponding radii of gyration, RG,relative to the average pore size of the gel, PE,are given on the upper and lower x axes, respectively. Three regimes are identified: oscillations in the orientation (ALD > 0) at high RG/PEvalues indicating migration as reptating chains oscillating between stretched and compact forms (geometration regime); steady orientation (ALD = 0) at intermediate RG/PEvalues indicatingmigrationas anisotropiccoilsor reptatingchains oriented in the field direction (nongeometration regime); absence of orientation(LD = 0) at low &/PEvalues indicatingmigrationas isotropic coils (Ogston regime) or for long DNA in the limit of zero field (transition point RG/PE= 1.4 according to Slater et a1.36) as classically reptating chains. Results at other gel concentrations(0.7-1.4%) (not shown),and derived from data of Holzwarth et al.,I4were found to fit into the diagram provided RGwas normalized with PEindicating that RG/PEis the relevant parameter for characterizing the DNA migration in agarose.

of the DNA size. It can be seen that for the longest molecules in our study about 25% of the LD decay occurs through the slow channel (B). As the molecules become shorter, a larger and larger fraction of the orientation resides in the fast decaying component A so that B becomes in effect zero (transition from doubleexponential to monoexponential decay) for a DNA size between 6 and 9 kbp. As can be seen from Figure 2 the oscillations in the buildup of the orientation show a similar course at these field strengths; their magnitude (ALD) decreases with decreasing length of DNA and disappears also for a critical size between 6 and 9 kbp. It can also be noted from the respective figure that the disappearance of both Band the oscillations is slightly shifted toward a smaller DNA when the field is changed from 15 to 30 V/cm. The results clearly show that the B component reflects the same DNA behavior as the oscillations, Le., geometration. The behavior of the relaxation amplitudes thus supports the position of the boundary curve for the strong fields in Figure 13. We have not measured LD decays for longer DNA to check whether Bdisappearswhen the nongeometration regime is entered, because the transition fields for those sizes were too low to allow the LD decay data to be quantitatively analyzed. However, there is no reason to believe that the longer DNAs behave differently from the smaller ones, where B is present only when oscillations also are present. This result also shows that it is sufficient to look for oscillations in the LD buildup to be able decide whether the molecules geometrate during the steady-state migration. There is a clear advantage in that a single experimental parameter can be used to characterize the motion, as compared to the extensive measurements (e.g., Ferguson plots) that are needed to classify the migration on the basis of mobility. Some measurements at other gel concentrations than 0.8% (between 0.7 and 1.4%) show that if RG is scaled with PE,the presence or absence of overshoot fits into the border diagram also in these cases (not shown). Furthermore, we could use the data

DNA Electrophoresis in Agarose Gels of Holzwarth et al.I4 on the overshoot for 48 kbp DNA in 1% agarose to extrapolate a critical field for absence of overshoot under these conditions, in the same way as was done in Figure 4. This point fits very well with our data as can be seen in Figure 13. In addition, Smith et aZ.17have shown by microscopy that 48 kbp indeed migratesoscillatory under conditionscorresponding to the geometration regime in Figure 13. In conclusion, the available data support our boundary diagram to an extent that makes us believe it is essentially correct. More data at different gel concentrations are necessary, however, to firmly establish that RG/PEindeed is the relevant parameter in a characterization of the mode of migration of the DNA. Border between NongeometrationandOgstonMigration. When the extrapolated intersections with the RG/PEaxis (LDI, = 0, no orientation) in Figure 5 and the electric fields they correspond to are introduced in Figure 13 (open circles), the resulting points form a nearly vertical line, which thus represents the border between regimes where the DNA migrates with and without orientation. The absence of orientation in the regime to the left of the border indicates that the DNA molecules there migrate in conformationswith randomly distributed segments. For short DNAs isotropic coils (Ogston migration) and for longer ones reptating chains that retain their random-walk conformations (classical reptation) are possible conformations. However, the theories based on the Ogston and the classical reptation models give predictions which are in strict agreement with DNA electrophoresis experiments only when these are performed at very low electric field ~trengths.*~,2*J~ Slater et aZ.have estimated, on the basis of these theories and mobility data, that the transition from Ogston migration to random-walk reptation occurs at a RG/PEvalue of 1.4 when the field is close to zero.36 The extrapolation of our border to zero field (Figure 13) gives a RG/ PEvalue of 1.7. According to the results of Slater et al., this suggeststhat at low fields the longest molecules to the left of our border migrate according to the random-walk reptation mechanism and shorter ones according to the Ogston mechanism. From Figure 13 it can be seen that as the field is increased the border shifts toward shorter DNA, but so slowly that at 30 V/cm migration without orientation still holds for a RG/PEvalue of 1. For the molecules nearest to the left of the border reptation is therefore a possibility also at higher fields, but reptation at finite fields should lead to orientation.24 However, it is also hard to believe that molecules with RG > PEshould be able to move as undisturbed coils, especially at high fields where the electric force can be expected to induce a deformation of the coils by forcing them to pass also through pores of the gel that would normally be too small. That DNAs of these sizes also are affected by the field is indicatedby the fact that their mobilities inagaroseincrease with increasing Isotropic compression of the coils could retain a random distribution of orientations of their segments, but this is unrealistic in view of the fact that the electric field is uniaxial. However, the measured LD is an average over all molecules in the sample, and zero LD (no net orientation) could thereforebe a result of a cancellation between negativeand positive contributionsfrom segmentsthat are oriented, for instance, along the field when the coils are squeezed through small pores and perpendicular to the field when the coils collide with gel fibers and their segments are piled up against these. Their average conformations during the migration may still be isotropic coils of size that depends on the molecular weight and which are sieved and separated by the gel using a mechanism similar to the Ogston mechanism for undeformed spherical objects. The element of pure Ogston migration is likely to increase with decreasing RG/ PE and far to the left of the border, where RG is much less than PE;it is probably the dominating mode of migration also at higher fields. Our conclusion is therefore that the absenceof orientation in the regime to the left of the border is due to Ogston or Ogstontype migration, except for the very largest molecules in the zero-

The Journal of Physical Chemistry, Vol. 98, No. 10, 1994 2631 field limit which probably migrate according to the random-walk reptation mechanism. An interesting observation in itself is that the plots of LDr, versus RG/PEin Figure 4 are linear as opposed to the case when plotted simply against molecular weight (results not shown). This fact too supports that Ro/Pe indeed is a relevant parameter for characterization of migration of DNA in gels. Mode of Migration in the Nongeometration Regime between the Ogston and the Ceometration Regime. The fact that 6 kbp (RG/PE= 1.8) constitutes an asymptotic value for the geometration border in Figure 13 means that the coil must be larger than the average pore of the gel in order to geometrate. This makes sense since the molecule must be big enough to divide itself between at least two cavities in the gel to become hooked by a gel fiber and form U-shapes. It is also easy to imagine that a somewhat smaller DNA coil can enter the nongeometration regime, where LD oscillations are absent (no U-formations) but where there still is a fmitedegreeof orientation, by simply adopting its shape to the pores and migrating from cavity to cavity as a deformed anisotropic coil. Is it reasonable to believe that this picture holds everywhere to the left of the geometration border? At 3 V/cm, e.g., the transition occurs for RG/Pe = 4; Le., a DNA molecule with a radius as large as 4 times the average pore radius is still not geometrating. It is difficult to believe that such a large molecule is able to migrate through the gel as a coil without having the steric possibility to form U-configurations, so the nongeometration character of the migration most likely is due to another factor that prevents the molecules from forming these configurations. In fact, the work of Slater et aZ.36 clearly indicates that in weak fields the migration of molecules in this size range is by biased reptation; i.e., the motion is end-on with the molecules oriented but without cycling between stretched and coiled forms. A plausible reason why increasing the field will lead to that these DNA start to geometrate (Figure 13) could be the following. Increasing the field speeds up the migration of the molecules, and the thermal motion needed to disentangle the molecules from the gel fibers will have shorter time to do that before the field-driven motion has locked the molecules into U-shapes. If this hypothesis is correct, the absenceor presence of oscillationsis not determined by steric factors only but by the dynamical competition between thermally and electrically driven motions: as the field increases, the molecules will be locked up in U-shapes because there is not time enough to unravel the entanglement before the arms are overstretched by the field. The transition of course is not abrupt, but instead there will be a gradual increase of this effect with increasing field which also can be seen in Figure 4 where the oscillation amplituderelative to thesteady-state orientation, ALD/ LD, (the degree of overstretching), is zero at low fields but increases gradually with increasing field. It then reaches a maximum, and an explanation for this can be found by looking at the field dependence in the constituents ALD and LD,: the maximum occurs because the oscillation amplitude saturates earlier with the field than does the steady-state level (results not shown). This is understandable since a given DNA size can only reach a certain degree of maximum orientation with increasing field (which has to occur in the U-conformation of the oscillatory cycle), and thus the peak LD saturates. Thesteady-state average, LD,, however, can continue to grow because there is still the possibility that as the field increases the molecules spend a larger and larger fraction of their cyclic life in that high-orientation state. In conclusion the possibility that the nongeometration regime may contain several regions cannot be excluded. There may be at least two modes of migration where the DNA is oriented but show no oscillations: migration as deformed coils for short DNA and reptation according to the biased reptation model for longer DNA.

2632 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994 0.3 A

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Figure 14. Details of ALD recovery (from Figure 11,where experimental conditions are given). Theremaining LD from the fist pulse when the second pulse is applied, LD(O), normalized to LD,, as a function of the elapsing time between the two pulses.

Figure IS. ALD, normalized to ALD, in the second pulse (from Figure 11) as a function of the remaining LD from the first pulse, LD(0) (from Figure 14). DNA length is 33 kbp and experimentalconditions are as

in Figure 11.

Molecular Mechanisms in the Orientation Relaxation. It is clear that the slower of the LD decays is associated with the formation of U-shapes, since its amplitude B is nonzero only in the presence of oscillations (ALD > 0), and both B and ALD grow in parallel with increasing size (Figures 2 and 10). What is the mechanisticconnection between the slow LD decay and the formation of a U? A plot of ALD in a second electric field pulse (from Figure 11) versus the remaining LD from the first pulse when the second pulse is applied, LD(0) (from Figure 14), is shown for 33 kbp DNA in Figure 15. Extrapolation to ALD = 0 shows that the oscillations start to show up when about 60% of the LD has disappeared. According to the LD decay data, this occurs after about 35 ms, at which point 75% of the A component has disappearedwhereas almost 90%of the B component remains. This observation indicates that the fast LD decay has little influence on the oscillation since such a large fraction of that process can occur without any sign of oscillation. Second, the good correlation between ALD growth and the decay of the last 40% of the LD (Figure 15) suggestsa coupling between oscillation recovery and the slow LD decay component since it dominates this phase of the LD relaxation. Such a correlation was observed also for T2 DNA in weak fields: an oscillation was observed in a second pulse only if the slow LD decay in the first pulse was entered, and then the oscillation amplitude grew with decreasing LD in the first just as seen here in Figure 15. The fact that the curve shows two different slopes will be returned to below, but it is clear from the time scale for the oscillation recovery process (Figure 1 1) and the time constant in the B-decay process (Figure 9) that the coupling between the two processes is reflected in the part of the curve which has the lowest slope.

Magntisddttir et al. A molecular interpretation of the coupling between LD decay and oscillation can be based on the effect of DNA size on the various relaxation rates. The time constant of the fast LD decay (71) is essentially independent of DNA size in the 5-fold size range investigated here (Figure 9). This suggests that the orientation that relaxes with T~ is on a local level compared to the extension of the molecules. Reorientation effects*and effects of field spikes on the mobility in PFGEMon the same time scale have been interpreted to occur on the pore size level and involve the amount of DNA that can be housed in an average cavity. This is often referred to as a blob and contains 1-2 kbp.19 The orientation on the blob level could involve short loops of DNA that are stretched by the field, as simulations and analysis of LD amplitudes indicate.19 In contrast, the slow LD decay time constant increasesinitially with size but tend to level out at about 30 kbp (Figure 9). This suggeststhat the slow LD decay involves larger pieces of the DNA molecules, approximatelyup to 30 kbp. What kind of gel structures, larger than the pore size, can provide such a length scale? Electron micrographs indicate that gel inhomogeneitiesin terms of variations in cavity sizes occur over thousands of angstroms?’ which could provide a driving force for a second LD relaxation mechanism involving typically tens of kbp: a gain in entropy will drive the redistribution of segments from small to large cavities because the latter allow for more degrees of freedom. In this picture, the driving force will be weak between domains of the molecule large enough to sample an average gel, and hence the timeconstant for this process should level out when the DNA coils reach this size. The radius of gyration of a 30 kbp fragment is 4300 A (and in field-aligned state may occur an even longer distance), in fair agreement with the length scale for the inhomogeneities. The entropy force invoked above is the basis for Zimm’s Lakes-andStraits model.*% This model has proven successful in describing the dynamics of DNA migration in inverted fields but has not yet been applied to the relaxation as the field has been turned off. It is interesting to note that diffusion of bright domains, or “beads”, of relaxed DNA along the contour of aligned but partially relaxed molecules have been observed in the fluorescencem i ~ r o s c o p e .The ~ ~ beads diffusedrapidlyona timescaleof seconds,and theaveragedistance between the beads was on the order of 1 pm, which is in fair agreement with 72 and its DNA size dependence. These observations suggest that such a ‘bead” diffusion mechanism may be involved in theslow LD decay. The decrease in 7 2 so that it finally coincides with 71 as the DNA becomes smaller (Figure 9) agrees with this picture. The diffusive redistribution of segments along thecontour takes shorter and shorter time as the molecular domain decreases in size, and finally,when the blob size is reached, only the intrablob relaxation responsible for the fast decay component remains and then 71 = 7 2 and B becomes zero. Finally, there is the third process which has been studied for T2 and other long DNAs by following the slow oscillation recovery20 and a tail of low amplitude in birefringence.1s Its rate constant and amplitude vary with DNA size, gel concentration, and field strength in very good agreementwith a classical reptation process and hence are ascribed to a diffusion out of the fieldinduced tube conformation. In this study the observed relaxation times, 0.9 s for 23 kbp and 2.2 s for 33 kbp (Figure 12), are somewhat larger than the results, 0.5 and 1.8 s, respectively, of the two above studies when their results are converted to our conditions. Our values are in fair agreement with an L3 dependence, and the oscillation recovery process thus likely reflects a reptation-like diffusion process. Slow relaxation of oriented gel fibers4353 could affect this process, but there are no indications in our LD measurements that the short field pulses used in this work produce orientation effects in the gel structure (see Buildup of Orientation in the Result section). In Figure 15 the return of the first 50% of the oscillation, reflected in the branch of the curve showing the lowest slope, was above interpreted as being

DNA Electrophoresis in Agarose Gels mechanistically coupled to theslow LD decay (the Bcomponent). The return of the last half of the oscillation is accompanied, as can be seen in the figure, by the decay of the remaining 5% of the original LD. Interestingly enough, these 5% corresponds to the offset term C (see Figure 10) which relaxes very slowly compared to the B component. We will tentatively ascribe the C component to tube orientation, since the oscillation recovery kinetics is in good agreement with a reptation process for renewal of the tube. The reason why the first 50% of the oscillation recovery, seen as the low-slope part in Figure 14, is not seen in the monoexponential oscillation growth kinetics (Figure 12) is that this part returns so fast that it only corresponds to the first 4-5 points in Figure 12, which is too few to give a reliable second slope.

Concluding Remarks DNA agarose gel electrophoresisis still much of a trial-anderror technique in the sense that optimal running conditions are difficult to predict a priori. The analysis made in this work, of how DNA of different lengths move through the gel under circumstances normally used in the separations, will make a systematic search for such conditions easier. The fact that we have used orientationaldata insteadof mobility data in the analysis of the motion may seem irrelevant since in the end it is the velocity difference that causcsthe desired separation. However, all current theories of electrophoresisare based on simplified models which cannot provide criteria from mobility data for a quantitative characterization of the mode of motion, except at very low electric field.36 Electrophoretic orientation is known to be intimately connected to the velocity,19 and thus will reflect the same interactions, but has the advantage that it directly quantifies effects that reflects the state of the migrating molecule and which are of importance for the separation. Comparison with actual separation experimentscan therefore also be made. For instance, in conventional electrophoresis, where a constant field is used, the most conspicuous effect is the gradual disappearance of the resolution in the separation in the DNA size range 5-30 kbp and how an increased field makes this problem more severe.' According to our classification scheme, this occurs in the geometrationregime, where the DNA oscillates between stretched and coiled states during the migration and where the LD displays an overshoot (the stretched state) and undershoot (the coiled state). The decrease in the resolution is at least qualitatively paralleled by the behavior of the LD overshoot amplitude: the separation decreasesand disappears in the same DNA size region where the overshoot (see Figure 2) grows and saturates. In addition, the decreased separation efficiency that follows from an increased field strength is paralleledby an increasein overshoot amplitude (Figure 4). This suggests that it is the part of the oscillatory motion that is coupled to the overshoot in the LD; Le., the stretched state of the DNA, that leads to a more sizeindependent velocity. It is probably so that the uncoiling and transition to the stretched state that follows from hooking on a gel fiber removes the incentive for sieving, which is based on differences in coil sizes. A larger fraction of the cycle time will be spent in the stretched state the longer the molecule and the stronger the field. Field inversion gel electrophoresis(FIGE) is on the other hand thought to utilize the inherently oscillatory character of DNA migration in gels by an antiresonance effect: pulsing the field at a frequency which is optimal for a certain DNA size holds the molecule in a state where it is more coiled and thereby better sieved than in a steady field. This mechanism requires geometration-like conditions and should thus work only within the geometration regime. Studies on short DNA indeed show that FIGE improves separation down to 5 kbp,S4in rough agreement with our data. Crossed field electrophoresis,on the other hand, probably does not always rely on internal dynamics in the DNA

The Journal of Physical Chemistry, Vol. 98, No. 10, 1994 2633

coil but exploits the global orientation of the chain. According to our data, crossed fields then should have an effect on the separationalso in the nongeometration regime, Le., toeven smaller DNAs.

Acknowledgment. This work is supported by the Swedish Research Council for Engineering Sciences. References and Notes (1) McDonald, M. W.; Simon, M. N.;Studier, F. W. J. Mol. Biol. 1977, 110, 119. (2) Lumpkin, 0. J.; DeJardin, P.; Zimm,B. H. Biopolymers 1985,24, 1573. (3) Slater, G. W.; Noolandi, J. Biopolymers 1985, 24, 2181. (4) Slater, G. W.; Noolandi, J. Biopolymers 1986, 25, 431. (5) Schwartz, D. C.; Saffran, W.; Welch, J.; Haas, R.; Goldenbcrg, M.; Cantor, C. R. Cold Spring Harbor Symp Quant. Biol. 1982, 47, 189. (6) Kramer, K. S.;Jolly, J. F. In Gene Technology;J a c o h n , G. K., Jolly, S.O., Eds.; VCH Publishers: New York, 1989; Vol. 7b, p 555. (7) Platt, K. J.; Holzwarth, G. Phys. Rev. A 1989, 40, 7292. (8) Akerman, B.; Jonsson, M. J. Phys. Chem. 1990,94, 3828. (9) Deutsch, J. M. J . Chem. Phys. 1989, 90,7436. (10) Madden, T. L.; Deutsch, J. M. J. Chem. Phys. 1991,94, 1584. (1 1) Duke, T. A. J. In Proceedings of the First International Conference on Electrophoresis,Supercomputingand the Human Genome;Cantor, C. R., Lim, H. A., Us.; World Scientific: Teaneck, NJ, 1991; p 75. ( 12) Akerman, B.; Jonapon, M.; Nordtn, B. J . Chem.Soc.,Chem.Commun. 1985, 422. (13) Hurley, I. Biopolymers 1986, 25, 539. (14) Holzwarth, G.; McKee, C. B.; Steiger, S.;Crater, G.Nucl. Acids Res. 1987, 15, 10031. (15) Sturm, J.; Weill, G. Phys. Rev. Lett. 1989, 62, 1484. (16) Stellwagen, N. C. J. Biomol. Stmet: Dyn. 1985, 3, 299. (17) Smith, S. B.; Aldridge, K.; Callis, J. B. Science (Washington, DC) 1989, 243, 203. (18) Schwartz, D.; Koval, M. Nature (London) 1989,383,520. (19) Nordtn, B.; Elvingson, C.; Jonsson, M.; Akerman, B. Q.Rev. Biophys. 1991, 24, 103. (20) Akerman, B.; Jonsson, M.; Nordtn, B.; Lalande, M. Bfopolymers 1989, 28, 1541. (21) Deutsch, J. M. Science (Washington, DC) 1988, 240,922. (22) Duke, T. A. J. J. Chem. Phys. 1990, 93, 9055. (23) Gurrieri, S.;Rizzarelli, E.; Beach, G.; Bustamente, C. Biochemistry 1990. 29. 3396. (24) Cantor, R. C.; Smith, C. L.; Mathew, M. K. Annu. Rea Biophys. Chem. 1988, 17, 287. (251 Zimm, B. H.; Levene, S . D. 0. Rev. BioDhvs. 1992.. 25. 171. (26) de Gennes, P. G. J. Chem. Pxys. 1971, j5,-575. (27) Lerman, L. S.;Frisch, H. L. Biopolymers 1982, 21, 995. (28) Lumpkin, 0. J.; Zimm, B. H. Biopolymers 1982, 21, 2315. (29) Viovy, J. L. Phys. Rev. Lett. 1988, 60, 855. (30) Noolandi, J.; Slatcr, G. W.; Lim, H. A,; Viovy, J. L. Science (Washington, DC) 1989, 243, 1456. (31) Smith,S. B.; Heller,C.;Bustamcnte,C.Biochemistry1990,30,5264. (32) Rodbard, D.; Crambach, A. Proc. Nutl. Acad. Sci. U.S.A. 1970,65, 970. (33) Ogston, A. G. Trans. Faraday Soc. 1958,54, 1754. (34) Sewer, P.; Allen, J. L. Biochemistry 1984, 23, 922. (35) Stellwagen, N. C. Biopolymers 1985, 24, 2243. (36) Slater, G.W.; Rousseau, J.; Noolandi, J.; Turmel, C.; Lalande, M. Biopolymers 1988, 27, 509. (37) Holmes, D. L.; Stellwagen, N. C. Electrophoresis 1990, 11, 5. (38) Moore, D. B.A. Thcais, University of Oregon, Eugene, 1986. (39) Nordtn, B.; Kubista, M.; Kurucsev, T. Q. Rev. Biophys. 1992, 25, 51. (40) Matsuoka, Y.; NordCn, B. Biopolymers 1982, 21, 2433. (41) Matsuoka, Y.; Nordtn, B. Biopolymers 1982, 22, 1731. (42) Arnott, S.;Dover, S.D.; Wonacott, A. J. Acta Crystallogr.,Sect. B Struct. Crystallogr. Crysr. Chem. B 1969, 25, 2192. (43) Jonsson, M.; Merman, B.; Nordtn, B. Biopolymers 1988, 27,381. (44) Mayer, P.;Sturm, J.; Weill,G. C. R. Acad.Sci. Paris 1991,312,587. (45) Hervet, H.; Bean, C. P. Biopolymers 1987, 26, 727. (46) Turmel, C.; Brassard, E.;Slater, G.W.;Noolandi, J. Nucl. Acids. Res. 1990, 18, 569. (47) Attwood, T. K.; Nelmes, B. J.; Sellen, D. B.Biopolymers 1988,27, 201. (48) Zimm, B. H. Phys. Rev. Lcrr. 1988,61,2965. (49) Zimm, B. H. J. Chem. Phys. 1991, 91,2187. (50) Zimm, B. H. J. Chem. Phys. 1991,95, 3026. (51) Bloomfield, V. A,; Crothers, D. M.; Tinoco, I. Physical Chemistry of Nucleic Acids; Harper & Row: New York, 1974. (52) Hagerman, P. J. Annu. Rev. Biophys. Chem. 1988, 17, 265. (53) Stellwagen, J.; Stellwagen, N. C. Nucleic Acids Res. 1989,17,1537. (54) Birren, B. W.; h i , E.;Hood, L.; Simon, M. I. Anal. Biochem. 1989, 177, 282.