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INADEQUACY OF REPTATION MODELS FOR PFG

151

Figure 5.19

Electric dichroism of DNA. An electrical field is applied in the

Absorption of light polarized in the

z and

y directions is compared.

tive because the molecule orients along the

 

z axis but preferentially absorbs

the base pairs which will be perpendicular to the

 

z axis.

 

 

z direction

(E z).

A z and

A y

for DNA will be nega-

 

light in

the

planes of

 

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

 

be negative, as shown in Figure 5.19. The magnitude of the LD is a measure of the net lo-

 

cal orientation of the DNA helix axis.

 

 

The LD of DNA in the absence of an electrical field is zero because there is no net orien-

 

tation. When the LD of DNA in a gel is monitored during the application of a square wave

 

electrical field pulse, very surprising results are seen. What was expected is shown in Figure

 

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

 

of sufficient intensity to cause a saturating level of orientation.

(a) Expected result.

(b) Observed re-

sult (from Nordén et al., 1991).

 

 

152

PRINCIPLES

OF

DNA

ELECTROPHORESIS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

decrease in

LD soon reaching zero, after the field is removed. What is actually observed,

 

 

 

under a fairly wide range of conditions, is shown in Figure 5.20

 

 

 

 

 

 

 

b . Upon application of the

field, the

LD increases, but it overshoots above the steady state orientation value and then

 

 

 

 

goes through one or more oscillations before saturation occurs. When the field is turned off,

 

 

 

 

 

 

most

LD is lost as expected, but a small amount takes a very long time to decay to zero.

 

 

 

 

Furthermore the decay kinetics depend on the original field strength, even though the decay

 

 

 

 

 

 

takes place in the absence of the field. This DNA behavior is very complex and difficult to

 

 

 

 

 

 

explain by simple models.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The orientation of the agarose

molecules that make up the gel itself can

be

exam-

 

 

 

 

ined by measuring the linear birefringence, which is just

 

 

 

 

 

 

n z n y , where

n is

the refrac-

tive

index

and

 

z

and

y

indicate light polarization axes, as illustrated

in

Figure

5.19.

 

Birefringence must be used to examine the gel rather than LD because the gel has

only

 

 

 

 

 

very weak near-UV absorbance. The birefringence is dominated by the gel, since it is pre-

 

 

 

 

 

sent at much higher concentrations than the DNA. Without DNA, no field-dependent bire-

 

 

 

 

 

 

 

fringence is seen at the field strengths used in these

experiments. However, in

the

pres-

 

 

 

 

ence of DNA, the gel shows a rapid

orientation after application of an electrical

field

 

 

 

 

 

pulse, and a much slower disorientation after the field is removed. This indicates that the

 

 

 

 

 

 

DNA is interacting with the gel and remodeling its shape under the influence of the elec-

 

 

 

 

 

 

trical field. Clearly simplistic explanations will not be adequate to explain DNA elec-

 

 

 

 

 

trophoresis in gels.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

When LD measurements are applied to

monitor

the

effects

of

successive

field

 

 

 

 

pulses, even

more complications

emerge. These

results

are

illustrated

in

Figure

5.21.

 

 

 

 

Two

patterns of behavior are seen

when

pulses

are

applied

spaced

by

an

interval

 

 

 

 

 

t.

When

t

is

comparable

to

the

pulse

time,

and the second

pulse

is

either

in

the

 

 

 

same direction as the first or at 90° to the first,

no

overshoot

or

orientation

oscillations

 

 

 

are

seen in response to the second

pulse.

In

contrast,

when

 

 

 

 

 

 

 

 

t

is comparable

to the

pulse time, but the second pulse is

oriented at 180°, or alternatively, when

 

 

 

 

 

 

t is very

long relative to the pulse time,

 

then the second pulse produces an overshoot

and

 

 

 

 

oscillations comparable to those produced by the first pulse. These observations have a

 

 

 

 

 

 

number of profound implications. They suggest that the relaxed DNA coil is not equiva-

 

 

 

 

 

 

lent to any moving state. The initial response of this relaxed configuration leads to hyper-

 

 

 

 

 

orientation, presumably because of the nature of the way

the DNA becomes hooked on

 

 

 

 

 

 

 

gel obstacles. Regaining the original relaxed configuration after a pulse can be very slow;

 

 

 

 

it can take up to 30 minutes for 100 kb DNA, which is much longer than the times in-

 

 

 

ferred for orientation and disorientation from macroscopic observations of PFG mobili-

 

 

 

 

 

 

ties. Apparently inverted pulses act effectively to produce a relaxed-like state. Perhaps un-

 

 

 

 

 

der these circumstances the DNA can largely retrace the paths it took when it became

 

 

 

 

 

entangled with obstacles. Perpendicular pulses do not restore a relaxed configuration. One

 

 

 

 

 

 

way to interpret the overshoot seen by

LD is to postulate a phased response of the origi-

 

 

 

 

 

nal population of relaxed molecules

to the applied field. Once the DNAs have equili-

 

 

 

 

 

brated in the field, a more complex set of orientations occurs which dephases subsequent

 

 

 

 

 

 

 

responses.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To mimic macroscopic PFG more

closely, LD measurements have been performed

 

 

 

 

 

 

 

with continuous alternate pulsing. The time-averaged

 

 

 

 

 

 

LD was

measured

as

a function

 

of pulse time for different angles, as shown in Figure 5.22. It is apparent that relatively

 

 

 

 

good, net local DNA orientation is

seen with

both long

and

short

pulse

times.

How-

 

 

 

 

 

ever, with intermediate pulse times,

much poorer net orientation is seen.

This

picture

 

 

 

 

 

fits

very well with

the

earliest

ideas

about a

minimum

in

DNA

orientation

at interme-

 

 

 

 

 

 

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

time

by

t. (a)

Time course of pulses. The remaining panels show

LD in response to

the second pulse.

(b)

Results of

t is comparable to the pulse time with the field direction of the second pulse either paral-

lel to the first pulse or perpendicular to it.

(c) Results if

t

is very long compared to the pulse time, or if

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

to limit the amount of computer time required. This is unlikely to allow a realistic picture

of either the gel or the DNA. However, more recent three-dimensional simulations are at

least in

qualitative

agreement

with the earlier two-dimensional results. Undoubtedly

the

model

of the gel used in

these

simulations

is unrealistically

crude;

the potential

used to describe the interaction

of

the

DNA

with

the gel is hopelessly oversimplified.

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.

 

 

 

 

 

 

 

 

 

DNA

TRAPPING ELECTROPHORESIS

155

Such

increases

in

computation

speed are needed because two additional

variations

of

 

PFG show considerable promise for enhanced size resolution, but

each

of

these intro-

 

duces additional complications into both the experiments and any attempts

to simulate

 

them.

 

 

 

 

 

 

 

 

 

 

 

 

DNA TRAPPING ELECTROPHORESIS

 

 

 

 

 

 

 

 

 

The technique of DNA trapping

electrophoresis

was

devised by

Levi

Ulanovsky

and

 

Walter

Gilbert

as

an approach

to improving

the

resolution

of

DNA

sequencing

gels.

 

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

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

of the streptavidin.

 

 

 

 

 

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.

 

 

If the picture just described is

accurate, one can make the further prediction that

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

three different FIGE conditions with

DNAs tethered to streptavidin. Very slow FIGE

leads to a reappearance of the limiting mobility. Apparently under these conditions all

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.)

 

 

 

 

 

 

 

 

SECONDARY PULSED FIELD GEL ELECTROPHORESIS (SPFG)

157

Apparently

these pulses are too short

to allow the trapped molecules to escape.

 

Intermediate FIGE conditions produce a very impressive increase in the useful separation

 

 

range of the gel. Overall, DNA trapping electrophoresis appears to be a very interesting

 

idea

worth

further elaboration and pursuit. It

underscores

the

fact

that

trapping,

and

 

not sieving, appears to be the dominant effect underlying DNA electrophoretic size sepa-

 

 

rations.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SECONDARY PULSED

FIELD

GEL

ELECTROPHORESIS

(SPFG)

 

 

 

 

 

 

 

 

 

 

The

 

history

of

SPFG

is

amusing.

Tai

Yong

Zhang,

a technician then working with

 

us

in the

early 1990s, was instructed to perform the experiment shown schematically

 

in

Figure

5.28. The

notion

was

to

use

a series

of

rapid field

alternations to

perturb

 

the

 

motion

of the head of an oriented DNA chain moving

in

response

to

a

slowly

 

 

varying field. The result should be to

fold

the chain into a zigzag pattern, which ought

 

to

affect

its subsequent orientation kinetics markedly

when

the

primary

field

direc-

 

tion is switched. Zhang, whose English

was quite imperfect at the time, misunderstood

 

the

original

instructions and

did

the

experiment

shown

schematically in

Figure 5.29

a .

He

applied

periodic, short

intense

pulses,

along the direction of net

 

DNA

motion. At

 

 

about

the

same time Jan Noolandi’s group

did a similar experiment, shown in Figure

 

5.29 b .

They

applied short, intense pulses opposite

to

the

direction of net DNA motion.

 

The

results

of both experiments, now called SPFG, are quite similar. The overall rate of

 

DNA motion is dramatically increased. In addition, under some SPFG conditions, greatly

 

 

improved resolution is seen, and larger molecules can be handled than is possible with

 

 

conventional PFG alone under comparable field strengths and primary pulse times. Some

 

 

examples are shown in Figure 5.30.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

While the actual mechanism for the success of SPFG is unknown, one suggested

 

mechanism shown in Figure 5.31 seems quite reasonable. DNA in PFG spends most of its

 

 

time

trapped

on

obstacles. As long

as

the

field

direction

remains constant,

the

applied

 

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.

 

 

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

 

 

S

INTO GELS

 

 

 

 

 

 

 

 

An additional,

surprising

aspect

of SPFG

was

revealed when the

behavior of

molecules

 

as large as (presumably) intact human DNAs was observed. It was found that the condi-

 

tions

required for

gel

entry

were

far

more

stringent

than

the

conditions

needed

to

move DNA, once the DNA was inside the running gel matrix. This may reflect a trivial ar-

 

tifact, that the DNA must be broken in order to enter the matrix, or it could be revealing an

 

intriguing

aspect

of

DNA behavior.

Note

that DNA

samples

for

PFG

or

SPFG

are all made in situ in agarose, as shown schematically in Figure 5.32. The sample agarose

 

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

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-

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-

 

 

somal DNA molecules in the size range between 50 kb and 5.8 Mb by SPFG. Samples are (lane 1)

 

 

S. pombe,

(lane 2) Pichia 1A which consists of a mixture of

P. scolyti

and P. mississipiensis,

(lane

3)P. scolyti,

(lane 4)P. mississippiensis,

(lane 5)S. cerevisiae,

and (lane 6) lambda concatemers.

 

Separation on a 1% agarose gel using

(a) a pulse program as follows: (i) 4800 s, 2.2 volts/cm pri-

 

mary pulses with 1 : 15 s (1 second pulse every 15 seconds), 6 volts/cm secondary pulses for 12 h,

 

 

(ii) 2400 s, 2.8 volts/cm primary pulses with 1 : 15 s, 6 volts, cm secondary pulses for 12 h, (iii) 240

 

s, 6 volts/cm primary pulses with 1 : 15 s; 10 volts/cm secondary pulses for 21 h, and (iv) 120 s, 6

 

volts/cm primary pulses with 1 : 15 s, 10 volts/cm secondary pulses for 10 h.

 

(b) The same primary

 

pulse program shown in

(a) but without secondary pulses. (From Zhang et al., 1991.)

 

 

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.

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