

INADEQUACY OF REPTATION MODELS FOR PFG |
151 |
Figure 5.19 |
Electric dichroism of DNA. An electrical field is applied in the |
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Absorption of light polarized in the |
z and |
y directions is compared. |
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tive because the molecule orients along the |
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z axis but preferentially absorbs |
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the base pairs which will be perpendicular to the |
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z axis. |
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z direction |
(E z). |
A z and |
A y |
for DNA will be nega- |
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light in |
the |
planes of |
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where |
A z is the absorbance with |
polarizers set parallel to the field, and |
A y is the ab- |
sorbance with perpendicular polarizers. This means that the net LD of oriented DNA will |
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be negative, as shown in Figure 5.19. The magnitude of the LD is a measure of the net lo- |
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cal orientation of the DNA helix axis. |
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The LD of DNA in the absence of an electrical field is zero because there is no net orien- |
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tation. When the LD of DNA in a gel is monitored during the application of a square wave |
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electrical field pulse, very surprising results are seen. What was expected is shown in Figure |
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5.20a : |
a monotonic increase in |
LD until the orientation saturates; then |
a monotonic |
Figure 5.20 Linear dichroism of DNA in a gel, as a result of a single applied electrical field pulse |
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of sufficient intensity to cause a saturating level of orientation. |
(a) Expected result. |
(b) Observed re- |
sult (from Nordén et al., 1991). |
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152 |
PRINCIPLES |
OF |
DNA |
ELECTROPHORESIS |
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decrease in |
LD soon reaching zero, after the field is removed. What is actually observed, |
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under a fairly wide range of conditions, is shown in Figure 5.20 |
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b . Upon application of the |
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field, the |
LD increases, but it overshoots above the steady state orientation value and then |
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goes through one or more oscillations before saturation occurs. When the field is turned off, |
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most |
LD is lost as expected, but a small amount takes a very long time to decay to zero. |
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Furthermore the decay kinetics depend on the original field strength, even though the decay |
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takes place in the absence of the field. This DNA behavior is very complex and difficult to |
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explain by simple models. |
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The orientation of the agarose |
molecules that make up the gel itself can |
be |
exam- |
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ined by measuring the linear birefringence, which is just |
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n z n y , where |
n is |
the refrac- |
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tive |
index |
and |
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z |
and |
y |
indicate light polarization axes, as illustrated |
in |
Figure |
5.19. |
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Birefringence must be used to examine the gel rather than LD because the gel has |
only |
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very weak near-UV absorbance. The birefringence is dominated by the gel, since it is pre- |
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sent at much higher concentrations than the DNA. Without DNA, no field-dependent bire- |
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fringence is seen at the field strengths used in these |
experiments. However, in |
the |
pres- |
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ence of DNA, the gel shows a rapid |
orientation after application of an electrical |
field |
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pulse, and a much slower disorientation after the field is removed. This indicates that the |
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DNA is interacting with the gel and remodeling its shape under the influence of the elec- |
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trical field. Clearly simplistic explanations will not be adequate to explain DNA elec- |
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trophoresis in gels. |
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When LD measurements are applied to |
monitor |
the |
effects |
of |
successive |
field |
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pulses, even |
more complications |
emerge. These |
results |
are |
illustrated |
in |
Figure |
5.21. |
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Two |
patterns of behavior are seen |
when |
pulses |
are |
applied |
spaced |
by |
an |
interval |
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t. |
When |
t |
is |
comparable |
to |
the |
pulse |
time, |
and the second |
pulse |
is |
either |
in |
the |
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same direction as the first or at 90° to the first, |
no |
overshoot |
or |
orientation |
oscillations |
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are |
seen in response to the second |
pulse. |
In |
contrast, |
when |
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t |
is comparable |
to the |
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pulse time, but the second pulse is |
oriented at 180°, or alternatively, when |
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t is very |
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long relative to the pulse time, |
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then the second pulse produces an overshoot |
and |
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oscillations comparable to those produced by the first pulse. These observations have a |
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number of profound implications. They suggest that the relaxed DNA coil is not equiva- |
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lent to any moving state. The initial response of this relaxed configuration leads to hyper- |
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orientation, presumably because of the nature of the way |
the DNA becomes hooked on |
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gel obstacles. Regaining the original relaxed configuration after a pulse can be very slow; |
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it can take up to 30 minutes for 100 kb DNA, which is much longer than the times in- |
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ferred for orientation and disorientation from macroscopic observations of PFG mobili- |
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ties. Apparently inverted pulses act effectively to produce a relaxed-like state. Perhaps un- |
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der these circumstances the DNA can largely retrace the paths it took when it became |
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entangled with obstacles. Perpendicular pulses do not restore a relaxed configuration. One |
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way to interpret the overshoot seen by |
LD is to postulate a phased response of the origi- |
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nal population of relaxed molecules |
to the applied field. Once the DNAs have equili- |
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brated in the field, a more complex set of orientations occurs which dephases subsequent |
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responses. |
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To mimic macroscopic PFG more |
closely, LD measurements have been performed |
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with continuous alternate pulsing. The time-averaged |
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LD was |
measured |
as |
a function |
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of pulse time for different angles, as shown in Figure 5.22. It is apparent that relatively |
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good, net local DNA orientation is |
seen with |
both long |
and |
short |
pulse |
times. |
How- |
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ever, with intermediate pulse times, |
much poorer net orientation is seen. |
This |
picture |
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fits |
very well with |
the |
earliest |
ideas |
about a |
minimum |
in |
DNA |
orientation |
at interme- |
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INADEQUACY OF REPTATION MODELS FOR PFG |
153 |
Figure 5.21 |
Dichroism of DNA in a gel produced by the second of |
two successive pulses, separated in |
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time |
by |
t. (a) |
Time course of pulses. The remaining panels show |
LD in response to |
the second pulse. |
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(b) |
Results of |
t is comparable to the pulse time with the field direction of the second pulse either paral- |
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lel to the first pulse or perpendicular to it. |
(c) Results if |
t |
is very long compared to the pulse time, or if |
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the second pulse is opposite in direction to the first pulse. (Adapted from Nordén et al., 1991.) |
diate pulse |
times. |
However, |
the mechanisms that underlie these minima appear to |
be much more |
complex |
than |
originally envisioned. Note that the minimum in orien- |
tation is much more pronounced with 120° pulses than with 90° pulses. This correlates with the much more effective ability of 120° PFG to fractionate different size DNA molecules.
Figure 5.22 Linear dichroism seen for maximally oriented bacteriophage T2 DNA produced by continually alternating electrical field directions. (Adapted from Nordén et al., 1991.)

154 PRINCIPLES OF DNA ELECTROPHORESIS
Figure 5.23 Behavior of DNA in gel electrophoresis as simulated by Monte Carlo calculations. Shown from left to right are successive time points. The black dot is an obstacle. The electrical field is vertical.
The third approach that has been used to improve our understanding of DNA electrophoresis in gels is computer simulations using Monte Carlo methods. Here the DNA is typically modeled as a set of charged masses attached by springs. The fluid is modeled by
its contribution to the kinetic energy of the DNA through brownian motion. The gel is
modeled as a set of rigid obstacles. Most early simulations were done in |
two dimensions |
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to limit the amount of computer time required. This is unlikely to allow a realistic picture |
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of either the gel or the DNA. However, more recent three-dimensional simulations are at |
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least in |
qualitative |
agreement |
with the earlier two-dimensional results. Undoubtedly |
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the |
model |
of the gel used in |
these |
simulations |
is unrealistically |
crude; |
the potential |
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used to describe the interaction |
of |
the |
DNA |
with |
the gel is hopelessly oversimplified. |
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The |
DNA model itself |
is not terribly |
accurate. |
Despite all these reservations, the |
picture |
of DNA behavior that emerges from the simulations is remarkably close to what is observed by microscopy. An example is shown in Figure 5.23. Collisions with obstacles dominate the motion of the DNA; hyperelongation of hooked structures, until they are released, apparently accounts for the overshoots seen in LD experiments.
Only a few simulations have yet been reported for PFG. These suggest that kinked structures play important roles. It seems logical that kinks should enhance the chances of
DNA hooking onto obstacles (Fig. 5.24). Thus conditions that promote kinking might lead to minima in mobility. This notion, which is not yet proved, would at least be consis-
tent with what is generally seen in macroscopic PFG experiments. The speed of most computers, and the efficiency of the algorithms used, has limited most simulations of electrophoresis to relatively short DNA chains at very dilute concentrations. Recently Yaneer Bar-Yam at Boston University has demonstrated orders of magnitude increases in simulation speed by implementing a molecular automaton approach on an intensely parallel computer architecture. This increase in the power of computer simulations should allow a wide variety of experimental conditions to be modeled much more efficiently.
Figure 5.24 Expected behavior of kinked DNA in electrophoresis.

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DNA |
TRAPPING ELECTROPHORESIS |
155 |
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Such |
increases |
in |
computation |
speed are needed because two additional |
variations |
of |
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PFG show considerable promise for enhanced size resolution, but |
each |
of |
these intro- |
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duces additional complications into both the experiments and any attempts |
to simulate |
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them. |
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DNA TRAPPING ELECTROPHORESIS |
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The technique of DNA trapping |
electrophoresis |
was |
devised by |
Levi |
Ulanovsky |
and |
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Walter |
Gilbert |
as |
an approach |
to improving |
the |
resolution |
of |
DNA |
sequencing |
gels. |
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These gels examine single-stranded DNA in crosslinked polyacrylamide under the denaturing conditions of 7 M urea and elevated temperatures. Typical behavior of DNA under such conditions is shown in Figure 5.25. A monotonic decrease in mobility with increas-
ing DNA size is seen until at some threshold, usually around 1 kb, a limiting mobility is reached, and all larger molecules move through the gel at the same velocity. This presumably reflects complete orientation, just as we have argued for double-stranded DNA in agarose. To circumvent the loss in resolution at large DNA sizes, a globular protein was attached to one end of the DNA, as shown schematically in Figure 5.26. The actual protein used was streptavidin because of the ease of placing it specifically on the end-bi-
otinylated target DNA. Streptavidin is a 50 kDa tetramer that can have a diameter of 40Å. This is considerably fatter than the 25-Å diameter of the DNA double helix. Note that streptavidin has such a stable tertiary and quaternary structure that it remains as a folded globular tetramer even under the harsh, denaturing conditions of DNA sequencing gel electrophoresis.
The larger size of the streptavidin, and its lack of charge under the electrophoretic conditions used, should ensure that the tagged end exists predominantly as the DNA tail. Periodically the head of the DNA chain will enter gel pores too large for the bulky tail to penetrate. This will lead to enhanced trapping, since the entire DNA will have to back out
of the pore in order for |
net motion to occur. Above a certain DNA size, thermal |
energies |
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may be insufficient to |
allow |
such |
backtracking, |
and once |
trapped, |
the |
tethered DNA |
might remain so indefinitely. |
A |
typical experimental |
result |
is shown |
in |
Figure 5.25. |
Figure 5.25 DNA trapping electrophoresis. Shown is the dependence of the electrophoretic mobility of single-stranded DNA on size for ordinary DNA and DNA end-labeled with streptavidin
(see Fig. 5.26). (Adapted from Ulanovsky et al., 1990.)

156 PRINCIPLES OF DNA ELECTROPHORESIS
Figure 5.26 |
Effect of a bulky end label on |
DNA mobility |
in gels. |
(a) |
Comparison of DNA with |
DNA terminally labeled with streptavidin. |
(b) |
Trapping |
of DNA in a pore because of the |
bulkiness |
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of the streptavidin. |
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Instead of a limiting mobility, tagged DNA shows a zone of super high resolution until, at a key size, the mobility drops to zero. This is all in accord with the simple view illustrated
in Figure 5.23. |
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If the picture just described is |
accurate, one can make the further prediction that |
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FIGE will assist the escape of the |
trapped DNA. These results are shown |
in Figure |
5.27. The three curves in this figure |
show the size dependence of DNA mobility under |
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three different FIGE conditions with |
DNAs tethered to streptavidin. Very slow FIGE |
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leads to a reappearance of the limiting mobility. Apparently under these conditions all |
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trapped molecules can be rescued. Very rapid FIGE fails to remove any trapping |
effects. |
Figure 5.27 DNA trapping electrophoresis under FIGE conditions. Shown is FIGE mobility for
three different sets of conditions, Forward/reverse (ms): 800/200 (long dashed line), 80/20 (solid line), 8/2 (short dashed line). In each case the sample was a single-stranded DNA terminally labeled
with a streptavidin. (Adapted from Ulanovsky et al., 1990.)

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SECONDARY PULSED FIELD GEL ELECTROPHORESIS (SPFG) |
157 |
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Apparently |
these pulses are too short |
to allow the trapped molecules to escape. |
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Intermediate FIGE conditions produce a very impressive increase in the useful separation |
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range of the gel. Overall, DNA trapping electrophoresis appears to be a very interesting |
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idea |
worth |
further elaboration and pursuit. It |
underscores |
the |
fact |
that |
trapping, |
and |
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not sieving, appears to be the dominant effect underlying DNA electrophoretic size sepa- |
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rations. |
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SECONDARY PULSED |
FIELD |
GEL |
ELECTROPHORESIS |
(SPFG) |
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The |
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history |
of |
SPFG |
is |
amusing. |
Tai |
Yong |
Zhang, |
a technician then working with |
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us |
in the |
early 1990s, was instructed to perform the experiment shown schematically |
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in |
Figure |
5.28. The |
notion |
was |
to |
use |
a series |
of |
rapid field |
alternations to |
perturb |
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the |
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motion |
of the head of an oriented DNA chain moving |
in |
response |
to |
a |
slowly |
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varying field. The result should be to |
fold |
the chain into a zigzag pattern, which ought |
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to |
affect |
its subsequent orientation kinetics markedly |
when |
the |
primary |
field |
direc- |
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tion is switched. Zhang, whose English |
was quite imperfect at the time, misunderstood |
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the |
original |
instructions and |
did |
the |
experiment |
shown |
schematically in |
Figure 5.29 |
a . |
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He |
applied |
periodic, short |
intense |
pulses, |
along the direction of net |
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DNA |
motion. At |
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about |
the |
same time Jan Noolandi’s group |
did a similar experiment, shown in Figure |
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5.29 b . |
They |
applied short, intense pulses opposite |
to |
the |
direction of net DNA motion. |
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The |
results |
of both experiments, now called SPFG, are quite similar. The overall rate of |
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DNA motion is dramatically increased. In addition, under some SPFG conditions, greatly |
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improved resolution is seen, and larger molecules can be handled than is possible with |
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conventional PFG alone under comparable field strengths and primary pulse times. Some |
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examples are shown in Figure 5.30. |
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While the actual mechanism for the success of SPFG is unknown, one suggested |
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mechanism shown in Figure 5.31 seems quite reasonable. DNA in PFG spends most of its |
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time |
trapped |
on |
obstacles. As long |
as |
the |
field |
direction |
remains constant, |
the |
applied |
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field will tend to keep the DNA trapped, as illustrated directly in trapping electrophoresis.
Figure 5.28 Untried experiment on the effect of short perpendicular pulses on PFG mobility.

158 PRINCIPLES OF DNA ELECTROPHORESIS
Figure 5.29 Electrical field configurations actually used in SPFG. |
(a) In our own work, |
(b) in the |
work of Jan Noolandi and collaborators. |
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Any tangential field, such as applied in either implementation of SPFG, will tend to bias the configuration of the trapped DNA, making it easier to slip off the obstacle in response to the primary field. At present it is difficult to find optimal SPFG conditions because of the large number of experimental variables involved, and the fact that these variables are highly interactive (Table 5.1). Perhaps the vastly improved rates of simulations of DNA electrophoresis will soon be applied to increase our understanding of SPFG.
ENTRY |
OF DNA |
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S |
INTO GELS |
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An additional, |
surprising |
aspect |
of SPFG |
was |
revealed when the |
behavior of |
molecules |
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as large as (presumably) intact human DNAs was observed. It was found that the condi- |
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tions |
required for |
gel |
entry |
were |
far |
more |
stringent |
than |
the |
conditions |
needed |
to |
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move DNA, once the DNA was inside the running gel matrix. This may reflect a trivial ar- |
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tifact, that the DNA must be broken in order to enter the matrix, or it could be revealing an |
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intriguing |
aspect |
of |
DNA behavior. |
Note |
that DNA |
samples |
for |
PFG |
or |
SPFG |
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are all made in situ in agarose, as shown schematically in Figure 5.32. The sample agarose |
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is a |
low-gelling |
temperature |
variety |
that |
has |
different |
pore sizes than the running |
gel. |
In addition the sample gel (0.5%) usually has half the agarose concentration of the running gel (1.0 to 1.1%). However, what is probably more significant is that once the sample cells are lysed, and the chromosomal DNAs freed of bound protein and any other cel-
lular constituents, they find themselves |
in free solution inside a chamber much bigger |
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than |
the |
gel pores. When the electrical |
field is turned on, the DNA coils in free solution |
are |
swept |
to one side of the chamber where they may encounter the gel in quite a differ- |
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ent |
state |
than they experience once they |
have threaded its way into the first series of gel |
pores.

Figure 5.30 Examples of the effect of secondary pulses on PFG behavior. Separation of chromo- |
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somal DNA molecules in the size range between 50 kb and 5.8 Mb by SPFG. Samples are (lane 1) |
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S. pombe, |
(lane 2) Pichia 1A which consists of a mixture of |
P. scolyti |
and P. mississipiensis, |
(lane |
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3)P. scolyti, |
(lane 4)P. mississippiensis, |
(lane 5)S. cerevisiae, |
and (lane 6) lambda concatemers. |
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Separation on a 1% agarose gel using |
(a) a pulse program as follows: (i) 4800 s, 2.2 volts/cm pri- |
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mary pulses with 1 : 15 s (1 second pulse every 15 seconds), 6 volts/cm secondary pulses for 12 h, |
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(ii) 2400 s, 2.8 volts/cm primary pulses with 1 : 15 s, 6 volts, cm secondary pulses for 12 h, (iii) 240 |
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s, 6 volts/cm primary pulses with 1 : 15 s; 10 volts/cm secondary pulses for 21 h, and (iv) 120 s, 6 |
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volts/cm primary pulses with 1 : 15 s, 10 volts/cm secondary pulses for 10 h. |
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(b) The same primary |
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pulse program shown in |
(a) but without secondary pulses. (From Zhang et al., 1991.) |
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Figure 5.31 Schematic picture of how secondary pulses may accelerate PFG by releasing DNAs from obstacles.
159

160 PRINCIPLES OF DNA ELECTROPHORESIS
TABLE 5.1 Interactive Parameters in Secondary Pulsed Field Electrophoresis (SPFG).
Electrical Parameters |
Other Parameters |
a
Primary field strength |
Agarose gel concentration |
Primary pulse time |
Particular type of agarose (low melting, high |
Angle of alternation of primary fields |
endoosmosis, etc.) |
Secondary field strength |
Ionic strength |
Direction of secondary field |
Temperature |
Secondary pulse time |
Specific ions present (e.g., acetate versus borate) |
Phase between secondary and primary fields |
|
Homogeneity of primary field |
|
Homogeneity of secondary field |
|
a Known to affect PFG and thus assumed to affect SPFG as well.
|
One |
possible |
consequence of the way in which |
large |
DNA is |
made and |
the |
||||||
obstacles it must overcome to enter a gel |
is shown |
schematically |
in |
Figure |
5.33. |
||||||||
Vaughan Jones, |
a |
mathematical topologist at |
the University of California, Berkeley, |
||||||||||
in |
thinking |
about large |
DNA |
molecules, |
suggested |
in |
1989 |
that |
above |
a critical |
|||
DNA |
size |
the |
conformation |
of |
these chains |
would |
always |
contain |
at |
least |
one |
potential knot. Much earlier, Maxim Frank-Kamenetskii, in thinking about DNA cyclization reactions, had very similar thoughts (Frank-Kamenetskii, 1997). Knot for-
mation |
poses |
no problems inside cells where topoisomerases exist in abundance that |
can tie |
and |
untie knots at will. Similarly it is no problem for an isolated DNA mole- |
cule in solution. However, as DNA enters a gel, any knots it contains are prime targets for entanglement on obstacles. Despite the fact that this has occurred, the remainder of the DNA molecule will tend to be pulled further into the gel by the influence of the
electrical field. This will result in tightening the knot, and it may lead to permanent trapping of the DNA at the site of entry into the gel. Secondary pulses could help to alleviate this problem by continually untrapping the knotted DNA from the obstacle
until it has, by chance, assumed an unknotted configuration that allows it to fully enter the gel and move unimpeded. This idea has been explored recently by Jean Viovy who
has demonstrated, using a clever multidimensional version of PFG, that DNA molecules do become irreversibly trapped when they are forced to run in agarose above a
certain field strength (Viovy et al., 1992). Viovy argues from considerations of the forces involved that the effect of secondary pulses may be to prevent knots from tight-
ening rather than to untie them once formed. What is needed is a clever way to test this intriguing but unproved suggestion.
Figure 5.32 Preparation of large DNA molecules by in-gel cell lysis and deproteinization.