Volume 15 Number 23 1987
Nucleic Acids Research
Transient orientation of linear DNA molecules during pulsed-fleld gel electrophoresis
G.Holzwarth, Chad B.McKee, Susan Steiger and Glenn Crater
Department of Physics, Wake Forest University, Winston-Salem, NC 27109, USA
Received July 17, 1987; Revised and Accepted October 1, 1987
ABSTRACT
The transient orientation of lambda DNA and lambda-DNA oligomers has
been measured during pulsed field gel electrophoresis. The DNA becomes
substantially aligned parallel to the electric field E. In response to a
single rectangular pulse, orientation shows an overshoot with a peak at 1
second, then a small undershoot, and finally a plateau.
When the field is
turned off, the orientation dissipates in two distinct exponential phases.
Field inversion leads to periods of orientation with intervening periods of
reduced orientation as the chains reverse direction. Field inversion pulses
applied to linear oligomers of lambda-DNA show that orientation responses
slow down but increase in amplitude as molecular weight increases, for a
given field. Because DNA stretching and alignment parallel to E are
expected to correlate with DNA velocity, the velocity in response to a
pulsed field is also expected to exhibit an overshoot.
INTRODUCTION
Pulsed electrophoretic fields are being widely used to separate linear
DNA chains containing 30 Kbp or more, such as the chromosomal DNA of
yeast(l-3) or parasitic protozoans(4,5) and even large restriction fragments
of human chromosomal DNA(6).
A particularly simple embodiment of the
method, field-inversion gel electrophoresis, or FIGE, uses a single field
which reverses direction every 1 to 30 seconds(7).
Our goal here is to
understand the novel molecular motions which occur during FIGE and which
give FIGE the ability to separate DNA molecules according to their molecular
weight M.
DNA chains containing 30 Kbp exist in solution as random coils whose
root-mean-square radius of gyration is 0.5 micron.
By contrast, the pore
radius in the II agarose gels used in FIGE is only 0.1 micron(8,9).
Nevertheless, when subjected to electric fields of around 10 V/cra, the DNA
molecules are able to move through the gel at a substantial velocity.
This
has been ascribed(lO) to a novel class of polymer motions termed reptation,
in which a polymer moves end-first along a "tube" of constraints fixed by
the gel fibers, like a snake through the grass.
Several recent theoretical
studies of the gel electrophoresis of DNA are based upon the reptation
i IRL Press Limited, Oxford, England.
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= O
Figure 1. Schematic diagram of a randomly coiled DNA molecule in a
gel(dots) and three possible stretched conformations which the DNA molecule
might adopt in response to an electric field. The orientation function f is
zero for the randomly coiled molecule but is positive for the three
stretched structures.
model(11-13); they are able to explain many features of the steady state
electrophoresis.
One prediction of these theories is that the DNA molecules
become stretched out with their long axes parallel to the electric field E
at relatively moderate field strengths, such as 10 V/cm.
A schematic
diagram of this stretching and orientation process is given in Figure 1.
One useful measure of the extent of alignment of the DNA with respect
to the electric field is the orientation function f, which is defined by the
relation
f = [3<cos29> - l]/3
(Eq.l)
where 6 is the angle between E and the local DNA helix axis, as shown in
Figure 2.
For random orientation of the local helix axis, <cos 8> = 1/3 and
f = 0; for molecules with their helix axes fully parallel to E, <cos28> = 1
and f = +1.
High values of the orientation function for DNA in gels have
recently been observed experimentally at low but constant values of
E(14,1S).
Our goal here is to measure the dynamics of the orientation
function of DNA when the DNA is subjected to a pulsed field.
The method chosen to measure the dynamics is fluorescence-detected
linear dichroism.
We first carry out a normal FIGE experiment to separate
the DNA into distinct bands of known molecular weight.
The gel is then
stained with ethidium bromide(EB), which intercalates into the DNA with its
plane perpendicular to the DNA helix axis(16).
A beam of linearly
polarized, 488 nm light is then directed at a particular band.
The
direction of polarization of this exciting light is modulated so that it is
alternately parallel and perpendicular to E.
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If the DNA is preferentially
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Figure 2. The angle 6 used to describe the orientation of the DNA chain
with respect to the direction of the electric field.
oriented with its helix axis parallel to E, there will be more fluorescence
whenever the exciting 488 nra light is linearly polarized perpendicular to E
than when the exciting light is polarized parallel to E, because the EB
absorbs 488 nra light only when the light is polarized parallel to the EE
plane.
That portion of the fluorescence signal which is modulated at the
same frequency and phase as the polarization of the exciting light is
extracted with a lock-in amplifier.
This provides a direct measure of the
extent to which the DNA is preferentially oriented in the direcction of the
electrophoretic field E.
The method is sensitive, requires very little
DNA, and can give dynamic information when the DNA is suddenly stretched and
oriented by an electric field.
MATERIALS AND METHODS
Samples.
Lambda DNA was purchased from Bethesda Research Laboratories.
Agarose was Sea-Kern LE grade from FMC Co. IX agarose gels were cast in
buffer containing 45 mM Tris base, 45 raM boric acid, 1.25 mM EDTA, pH
8.2(0.5xTBE).
Samples were briefly preheated at 65 C to convert oligomers
to lambda monomer and were applied to the gel in standard IX "dye mix"(7).
T4 DNA was prepared by briefly heating intact T4 bacteriophage(Carolina
Biological Supply) in standard "dye mix" containing 5% sodium lauryl
sulphate.
Electrophoresis•
FIGE was carried out in 0.5xTBE in a BRL model H3
horizontal electrophoresis chamber, following Ref 7 in most details.
Buffer
was circulated through a chiller to maintain an operating temperature of
13-14 C. The initial electrophoretic separation by FIGE was at + and - 10
V/cm with 3.0 sec forward and 1.0 second backward pulse times; the net
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Figure 3. Schematic diagram of apparatus.
L-laserj M=photoelastic
modulator; G=gel containing DNA bands stained with EB; BS=beam stop;
F=long-pass glass filters; PMT=photomultiplier tube; O-oscilloscope;
C=computer; S-floppy disc storage; PS=programmable power supply. A lockin
amplifier should appear in the drawing between the photoraultiplier and the
oscilloscope.
velocity of lambda DNA was 1.1 cm/h under these conditions.
The gel was
then stained with EB for 1 h at 0.15 microgram/ml, destained with 0.5xTBE
and photographed on a 300 nm Fotodyne transilluminator.
For preheated
samples, a single sharp band corresponding to the lambda monomer was
obtained.
If samples were not preheated, 9 or more bands were observed,
corresponding to catamers of the lambda monomer.
The electrophoretic field was generated through ASYST software, an IBM
XT computer, a Kepco SN488 converter, and a Kepco BOP-500 programmable
bipolar power supply.
This power supply was capable of switching
between
+500 and -500V in 0.2 ras and could be set to any intermediate voltage by the
computer.
Fluorescence-detected Linear Dichroism(FDLD). After initial
electrophoresis, the stained gel was returned to the electrophoresis chamber
for observation in laser light during electrophoresis.
of the apparatus is shown in Figure 3.
The overall layout
The gel was illuminated from below
by a 2 mW ribbon-shaped beam of 488 nm light from a Siemens Ar laser.
All
fluorescent light at 580-680 nm within a 40° cone angle was collected by a
photomultiplier tube placed just above the gel; a beam stop and glass
long-pass filters placed between the gel and the photomultiplier tube
blocked the direct laser beam and 488 nm light scattered by the gel.
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The
Nucleic Acids Research
E
r\
U
f
10.0 V/cm
0.10 —
-
8.3
rs
6.6
4.9
uW
32
-
00
8
t(s)
10
12
14
16
Figure 4. Orientation of lambda DNA by a 5 sec unidirectional pulse of
strength E=3.2 to 10.0 V/cm.
laser beam was scanned from the sample well along the path or lane of the
DNA until the DNA band of interest was detected and the peak fluorescence
intensity I of the band was recorded.
The polarization of the laser beam was then modulated at 100 KHz by a
Hinds photoelastic modulator between directions parallel and perpendicular
to the direction of the electrophoretic field.
The photomultiplier signal
was sent to a PAR 5207 lock-in amplifier for detection of the difference in
fluorescence intensity between excitation light polarized parallel to and
that polarized perpendicular to the electrophoretic field; we call this 100
KHz difference signal the response R, after it has been integrated with a
time constant of 30 or 100 ms.
The time course of the electrophoretic field
E, together with the time course of the response, were recorded on a storage
oscilloscope(Tektronix 5223) and saved on a floppy disc for subsequent
analysis.
Standardization gels contained 1% LE agarose, 0.003 mg/ml EB and
0.5xTBE and 0.15 mg/ml calf-thymus DNA.
Conversion of measured data to orientation values.
In order to convert
observed response voltages R and band intensity measurements I to absolute
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df/dt
0.01 r
10
E(V/cm)
Fipure 5. Dependence of the slope of the attack phase of orientation by a
unidirectional.pulse upon the strength of the electric field. The units of
df/dt are sec .
values of the orientation function f, two auxiliary numbers, R Q and I o , were
determined with the normal gel replaced by a linear polarizer and the
standardization gel.
The polarizer axis was oriented perpendicular to E.
With the modulator off, the fluorescence intensity was recorded as I Q .
Then, with the modulator on, the peak lock-in signal was recorded as RQ.
The observed ratio R o /I 0 obtained with the standard gel and polarizer
corresponded to an orientation function f = 1.0 and thus provided the scale
factor for converting observed values of R and I for the any band in a gel
to absolute f numbers:
f - RIO/IRO
(Eq.2)
There is an assumption in the above analysis that the value of f obtained
from experiment through equation 2 corresponds to the value of f defined by
equation 1.
This would be exactly correct if all the fluorescent light were
collected, rather than that in a 40° cone.
Because some of the light is not
collected, there may be a small additional term in <cos 8> in Equation 1.
RESULTS
Figure 4 shows the dynamic response of the orientation parameter f of
lambda DHA subjected to a single pulse of 5 sec duration.
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The amplitude of
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.10-
f
.05-
Figure 6. Fractional orientation in the plateau region for lambda DNA,
plotted versus field strength in V/cm. The theoretical values are taken from
Lumpkin, Dejardin and Zimralll).
the electric pulse varies from 3.15 to 10.0 V/cm.
immediately apparent.
Several features are
First, the sign of f is always positive, which means
that the DNA helix becomes aligned parallel to E.
Second, although a simple
rectangular pulse ii. applied, the response of the DMA is complex.
In
particular, at high voltages, f shows a pronounced overshoot, followed by an
undershoot, before a plateau is reached.
At 10 V/cm, the value of f at the
peak is 30% greater than its plateau value, and the time to reach the peak
is 1.0 sec.
This time increases as E decreases.
plateau is also field-dependent.
The time to reach the
As the voltage decreases to 3.15 V/cm, the
overshoot disappears and the plateau amplitude drops sharply.
At the end of
the 5-second pulse, when E goes to zero, f decreases gradually toward zero.
Inspection of Figure 4 shows that the initial rate of change of
orientation(the "attack" period) is markedly voltage-dependentj Figure 5
shows a log-log plot of the initial slope plotted against E. The slope of
the log-log plot is 2.7, indicating a very strong dependence on E.
The steady-state orientation is measured by the height of the plateaus
in Figure 4;
the observed data can be compared to predictions of the
steady-state theory of Lumpkin, Dejardin and Zimm(LDZ)(11).
is shown in Figure 6.
This comparison
Although the agreement is not exact, it is certainly
"in the ball park". The curvature is remarkably well predicted by the
theory.
A recent computer simulation of DNA reptation in a gel corrects an
error in the LDZ theory and yields somewhat smaller values of the chain
stretching at equilibrium(12).
In contrast to the attack response and plateau orientation, the decay of
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Figure 7. Orientation response of lambda DNA by a short field-inversion
sequence, for pulse times of 5, 2, 1, and 0.5 second. The upper trace shows
E with 5 sec forward and reverse times. The uppermost response trace(second
curve from top) shows the response of the DNA to the 5-second pulses. The
third, fourth, and fifth curves show the response when the field on and off
times were 2.0, 1.0, and 0.50 sec. The magnitude of E was 10 V/cra for all
traces.
the orientation is largely independent of the orienting field. The decay
cannot be fitted to a single exponential, but a double exponential is
adequate.
The curves for decay from various starting orientations are
surprisingly similar when normalized to the plateau orientation.
The
initial decrease has a time-constant of 0.18 for the 10 v/cm orientation.
second time-constant, 3.3 sec, applies at longer times.
A
For orientation at
only 1.44 V/cm, the longer process appears to have a somewhat longer time
constant, 6 s e c , but these data are only approximate because the degree of
orientation is so low.
Although the above data are useful for defining the response to a
rectangular pulse, the practical procedure used to separate large DNA
molecules employs inverting fields.
Two protocols, variable fields forward
and back, or variable time forward and back, have served to separate
particular molecules(7).
Figure 7 shows the response of lambda DNA to four
different field inversion sequences.
10 V/cm.
In each case the field amplitude is +
However, the pulse lengths are 5, 2, 1, and 0.5 seconds in the
different experiments.
During the first 5-sec pulse, the orientation
function f increases rapidly to an overshoot followed by a plateau, as in
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Figure 8. Orientation response of rungs of the lambda ladder to a short
field inversion sequence with 5 sec on and off times and 10 V/cm amplitude
in each instance. Upper trace shows E. Curves 2 through 6 show the
response for the first 5 catamers of the lambda ladder. The data were noisy
because the bands in the gel were faint.
Figure 4.
Upon field inversion, there is a marked decrease in f to 30% of
the plateau value.
This decrease in f takes only 0.3 sec.
The orientation
function f then rises at a rate comparable to that seen in the initial rise
or in Figure 4.
This increase culminates in a smaller overshoot as f
returns to the same plateau, but in response to the opposite field.
The
presence of a strong dip in f between the two plateaus suggests that the
molecule is not simply like a worm in its burrow, which could as easily go
forward as backward.
Rather, it suggests that the leading portion of the
electrically driven DNA chain, which may be an end or a bend, as in a
hairpin, differs from the trailing portion of the chain.
A wedge-like
structure, as suggested by Carle et al.(7), has the necessary property of
requiring rearrangement upon reversing direction.
The lower traces of Figure 7 show the response of the molecules to a set
of field-inversion pulses of constant amplitude, 10 V/cm, but variable
duration.
For pulses of 2 sec. duration, the overshoot is still apparent,
but the plateau is largely gone.
At 1 sec, there is no sign of a plateau.
Note that the amplitude of the overshoot remains large, and that the fall in
orientation upon field reversal is rapid when compared to the subsequent
rise in orientation, leading to a response which resembles a sawtooth.
Finally, when the pulse segments are reduced to 0.5 sec, the amplitude of
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0.1
Figure 9. Plateau orientation of DNA plotted against its molecular weight,
for the first 4 rungs of the lambda ladder. The value of E was 10 V/cm.
the response at overshoot is diminished;
the molecule has not had time to
reach the full extent of overshoot, and the subsequent peaks in the sawtooth
are diminished.
Figure 8 shows the effect of chain length on the orientation function
of a brief field-inversion sequence.
the "lambda ladder";
The data were taken for 5 "rungs" of
the ladder is prepared by allowing lambda DNA to form
linear oligomers with itself by basepairing at its sticky ends(7).
For 1 to
5 units of lambda DNA in the catamer, one obtains 48.5, 97, 146, 194, and
243 Kbp. There are two changes in f as Kbp increases.
increases.
First, the amplitude
Second, the overshoot moves to longer times.
The period of
reduced orientation after field reversal becomes more pronounced as M
increases.
Surprisingly, the rate at which f relaxes back to zero, when the
field is turned off, is essentially independent of M.
Figure 9 is a log-log plot of the value of f at the plateau for the
first 4 oligomers. The plateau value increases as [Kbp]
.
Extrapolation
to the range of the DNA in the largest chromosomes of yeast suggests that
these molecules would be almost fully oriented during gel electrophoresis at
E - 10 V/cm.
Figure 10 shows t , the time required to reach the peak in f, for
various molecular weights, at a fixed field of 10 V/cm.
This time increases
steadily with M, for the range 48.5Kbp < M < 243Kbp studied here, according
to the relation
tp - (.020 ± .001)M - (0.23 ± .01)
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Eq. 3
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<p(s>
5-
321-
100
200
Kbp
Figure 10. Time to reach the overshoot peak for the first 5 rungs of the
lambda ladder(O) and for T4 DNA( ) . The value of E was 10 V/cm.
for t
in seconds and M in Kbp.
The overshoot peak times are very similar
to the times found to be useful when DNAs of particular sizes are being
separated(l-6).
DISCUSSION
The FDLD method for measuring transient DNA orientation has three
strengths.
First, it permits the study of individual bands in a standard
gel, thus ensuring that each molecule studied has a unique M.
use of EB allows one to detect very small amounts of DNA.
concentration can be kept very low;
this prevents
Second, the
Third, the DNA
intermolecular
interactions.
The use of EB is not without its costs, however.
mobility of the DNA.
been reported(9).
First, it affects the
Under steady fields, a 102 decrease in mobility has
During field inversion, we have found that the presence
of EB causes a somewhat larger decrease, 172, in the mobility of lambda DNA.
On the other hand, photonicking of the EB-stained DNA, which is a well-known
problem during irradiation at 265 nra, did not occur during irradiation with
the 488 nm light used in our experiments, as judged by the absence of
detectable changes in DNA dynamics or mobility after deliberately
lengthy
irradiation.
One of the most striking results of our experiments is the very large
extent of orientation of the DNA parallel to E, even under comparatively
modest fields such as 10 V/cm.
Similar observations have been made
previously for steady fields using two very different techniques, linear
dichroism of unstained DNA(14), and fluorescence polarization of EB-stained
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DNA(15).
It is noteworthy that the average mobility of large DNA molecules
during gel electrophoresis in steady fields is also strongly
field-dependent(9).
This observation supports the view that even small
values of E force the DNA into a stretched conformation which can then move
more rapidly through the gel.
Once the field is turned off, the orientation function f of the DNA
decays to zero with a double-exponential decay.
Similar double-exponential
decays have been seen previously with short DNA fragments, following
orientation by 10,000 volts/cm pulses(17).
However, no overshoots or
undershoots were reported for these small molecules when the field was first
applied.
The data reported here show that the orientation process in gels
depends on electric field, molecular mass M and pulse time in a complex
manner.
The overshoot only appears at sufficiently high field strengths.
In this connection, it is notable that both FIGE, and the companion
technique in which the electric field alternates in two orthogonal
directions in the gel(l,2), are effective as separation tools at field
strengths similar to those which give the overshoot.
In the equilibrium reptation theory for DNA gel electrophoresis(ll,12),
the orientation f and velocity v are intimately linked through the parameter
<h
>.
The quantity h
is the component of the end-to-end vector h in the
direction of the electric field;
<h
> is its mean-square value. If f and v
are also linked in dynamic experiments, then the instantaneous velocity in
response to a pulsed field will also exhibit an overshoot.
As the pulse
time increases, the average velocity, which is what is usually measured in
electrophoresis, will exhibit an abrupt increase for values of pulse time
which preferentially sample the overshoot peak(18).
There is some evidence
for this in FIGE experiments (Ref. 7, Fig. 1 ) .
We have carried out preliminary measurements of the instantaneous
velocity of lambda DNA in response to a pulsed field in IX agarose.
The
data show that the center of mass of the molecules moves 5.8 ± 0.3 microns
in the first second after a 10 V/cm pulse is applied.
Thus, after one
second, the molecule has moved far beyond the gel pores originally occupied,
which probably have a random-coil radius of gyration of only 0.5 microns.
It takes only 3 seconds for f to reach a plateau(Figure 4 ) .
the center of mass has moved 2 0 + 1
microns, a distance
By that time
almost
identical
to the contour length of this DNA, 18 microns.
The orientation function f of lambda DNA in response to field
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inversion(Figure 7) shows a rapid reduction when the field changes sign. A
similar result has been briefly reported for T4, T7, and G bacterophage
DNA(19).
The end-first reptation models developed so far appear to predict
a constant orientation upon field reversal, since the trailing end of the
molecule has, in these models, the same average value of the orientation
function as the initial segment.
This suggests that one area in need of
theoretical development is the possibility that the trailing segments of the
chain can have a different extent of orientation than the leading segments.
Some possible arrangements, such as hairpin bends, are shown in Figure 1.
Such arrangments are considered in computer simulations presented in
Reference 13, but the time interval in the simulation is too short to be
tested against the data presented here.
Reptation theory and experiments on solid polymers such as polyethylene
show that the time constant for the relaxation of a stretched polymer chain
back to random coil dimensions increases as M (ref.20).
suggested that an M
It has been
dependence of relaxation time plays an important role
in pulsed-field gel electrophoresis of large DNA molecules.
Our
observations do not support such a strong dependence of the field-free
relaxation on M.
This suggests caution in applying reptation concepts
developed for solid polymers to agarose gels which are, after all, very open
structures.
ACKNOWLEDGEMENTS
The National Science Foundation, the North Carolina Biotechnology
Center, Chevron Research Corporation, Research Corporation, and the Archie
Fund of Wake Forest University all provided funds for which we are most
grateful.
We thank Exxon Research and Engineering Company for equipment
donations, and William A. Thomas for comments on the manuscript.
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