Dynamics of DNA Molecules under Gel Electrophoresis - American

Chapter 35

Dynamics of DNA Molecules under Gel Electrophoresis T. Kotaka, S. Adachi, K. Igarashi, and T. Shikata

Downloaded by CORNELL UNIV on September 6, 2016 | http://pubs.acs.org Publication Date: December 13, 1993 | doi: 10.1021/bk-1994-0548.ch035

Department of Macromolecular Science, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan

Under biased sinusoidal field gel electrophoresis (BSFGE) that utilized sinusoidal filed of strength E and frequency f superposed on steady bias field of E , large D N A fragments with size M > 20 kbp exhibit peculiar behavior, especially when E > E . A most intriguing case was what we called pin-down phenomenon in which mobility of a particular D N A became minimum at a particulae frequency (pin-down frequency) specific to M, gel concentration and field conditions. To examine the dynamics of D N A molecules under BSF conditions, we conducted frequency-domain elelctric birefringence measurements and were able to locate a few orientational relaxation modes related to the peculiar electrophoretic behavior. Direct observation via fluorescence microscopy also revealed the features of D N A molecules moving through gel network. s

b

s

b

G e l electrophoresis is currently the most important technique available to molecular geneticists for size dependent separation of chromosomal D N A fragments. The technique also provides an intriguing problem for polymer physicists in relation with molecular dynamics of uniformly charged macromolecules moving through obstacles. In fact, steady field electrophoresis i n agarose gel is a powerful tool for separating short D N A fragments according to their size M but ineffective for large fragments with M > 20 kilobasepairs (kbp) (7). For large D N A s the steady-field mobilities μ are independent of M. Thus for the separation of large fragments, various pulsedfield (PFGE) methods (2-5) were developed as motivated with an idea that alteration of the direction and/or the timing of the pulse field may activate some specific modes of motion that are dependent on M o f D N A molecules moving through the gel. W e also developed a new version which we called biased sinusoidal field gel electrophoresis ( B S F G E ) (6-8) that utilized sinusoidal filed of strength E and frequency / superposed on steady bias field of £5. The field was then defined as: 8

s

E(t)=E +E sin(2nft) h

(1)

s

and we defined the effective mobility μ in B S F G E as: 1

μ = (distance migrated A7cm)/[(time elspsed t/h)(E\/Vcm- )]

0097-6156/94/0548-0466$06.00/0 © 1994 American Chemical Society

Schmitz; Macro-ion Characterization ACS Symposium Series; American Chemical Society: Washington, DC, 1993.

(2)

35.

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KOTAKAETAL.

467

Molecules

In such studies we were able to find some interesting features o f B S F G E . A most striking case was that under a low bias condition of E > Zs (for example, E = 7.5 V / c m ; E = 2.5 V / c m ; and gel concentration C j o f 1 wt%) the mobility μ of D N A with M > 20 kbp exhibits a minimum at a particular frequency dependent on M and C ] as well as on E^. This means that D N A fragments with M either smaller or larger than this particular one move faster under these particular conditions. W e called this phenomenon, pin-down phenomenon; the frequency, p i n - d o w n frequency / ; and the minimum mobility, pin-down mobility μρ. W e then attempted to examine dynamical features of D N A molecules by conducting frequency-domain electric birefringence ( F E B ) . W e also attempted to make direct observation o f moving D N A molecules under gel electrophoresisv/α fluorescence microscopy. s

b

b

s

g e

g e

p


Gel Electrophoresis Experimental. Experiments were conducted on commercially available D N A samples with M from 200 basepairs (bp) to 1.9 megabasepairs (Mbp) purchased from Pharmacia, L K B (Uppsala, Sweden) and Nippon Gene C o . L t d . (Tokyo, Japan). In particular we examined bacteriophage λ D N A o f 48.5 kbp and T 4 d C D N A of 166 kbp. Agarose was a D N A / R N A separation grade (Pharmacia, L K B ) . The buffer was a standard 50 m M T B E which consisted o f 50 m M [tris(hydroxymethyl)-amino]methane (tris base), 50 m M boric acid, and 1 m M ethylenediaminetetracetic acid ( E D T A ) disodium salt. Usually 0.5 mg/L ethidium bromide (EB) was added to the buffer to visualize D N A bands with a U V illuminator. A submerge type cell was used mainly at 20°C. T o generate B S F we employed a high speed, high voltage bipolar power amplifier and a conventional function generator. The details were described elsewhere (7) and will not be repeated here. Behavior in Steady Field Gel Electrophoresis. In steady field gel electro phoresis, M dependence of steady field mobility μ is known to be divided into three regimes (5,7,8): The first one is Ogston regime I for small size D N A s that do not entangle with gel strands and moves rather freely so that M dependence of μ is small; the second one is entangled-but-unstretched regime II for intermediate size D N A s for which μ M and efficient size-dependent separation is possible; and the third case is entangled-and-stretched regime III for large D N A s with M > 20 kbp for which M dependence of μ is again lost. Figure 1 illustrates an example of log μ vs log M under a steady field of strength Ε = 2.5 V / c m i n 1.0 wt% agarose gel at four different temperatures ranging from 13 to 37°C. The results show the three regimes exist as mentioned above. In these three regimes, μ increases almost uniformly with increasing temperature, and the features of their M dependences are essentially unchanged. In fact, apparent activation energy £ * estimated from the Arrhenius plot of log μ^ vs 1/T is of the same order o f 10 to 6 kJ/mol for D N A with M o f 1.35 to 166 kbp. Incidentally, E* o f water viscosity is also of the order of 8 kJ/mol. This result suggests that the friction from the medium determines the temperature dependence o f μ . Figure 1 also includes pin-down mobility μ data of 166 kbp T 4 d C phage D N A (solid symbols), on which we w i l l discuss later. 5

5

-

1

δ

δ

8

5

8

ρ

Behavior under BSF Conditions. In B S F G E we examined frequency / dependence of μ defined by equation 2 under varying £ 5 , sinusoidal field strength E and / , and found several interesting features in μ vs log / relations (7,8).

s

High to Comparable Bias Conditions. In B S F G E o f a high bias with E < Efr (for example, E = 2.5 V / c m and = 7.5 V / c m ) , μ o f D N A s o f any size were independent o f / and coincided with the steady field values μ (7). O n the other s

s

8



468

MACRO-ION CHARACTERIZATION

3

4

5

log(M/bp) Figure 1. Plot of log μ vs log M at different temperatures as indicated. Solid symbols represent μ data. 8

ρ


35.

KOTAKAETAL.

Dynamics of DNA

469

Molecules

hand, in B S F G E of a comparable bias with E = Zs (for example, E = 7.5 V / c m , E = 7.5 ~ 5.0 V/cm), each μ vs log / curve exibited a peak μ ^ at a frequency / M (around 10 H z in 1.0 wt% gel) independent of M but strongly dependent on C j , while μ in the low- and h i g h - / sides coincided with μ (7,8). A s C i was increased from 0.5 to 2.0 wt%, / rapidly shifted to the high / side and trie peak flattened out (7). The peak height Δ μ (= μ - μ^) was nearly constant for large D N A s in the regimes II and III, but increased with decreasing M for small D N A s in Ogston regime I (7). s

b

s

b

g e

5

g e

M

Μ

Μ

L o w Bias C o n d i t i o n s . In B S F G E of a low bias field with E > 2s , three interesting features emerge. Figure 2 illustrates an example in which E = 7.5 V / c m , E = 2.5 V / c m and C i = 1.0 wt%. W e see that (i) the low / values μο (= μ at / -> 0) are significantly enhanced, but (ii) the high / values μ*» (= μ at / —> «>) remain essentially the same as μ . The most striking finding is (iii) pin-down phenomenon in which μ vs log / curve of large D N A s with M > 20 kbp exhibits a minimum μρ at / p dependent on M , C i as well as on the field strengths in such a way that / p «= ' Co \ EiJE with α = 0 for E < a certain critical value (= 10 V / c m at E = 2.5 V / c m ; and α = 2 ~ 3 for E > the critical value (8). On the other hand, the pin-down mobility μ at a fixed E first decreases with increasing E and levels off at high E . When these μ data were plotted in log μ$ vs log M plots, we see that the leveled-off values of μ are found on the extrapolated portion of the steady-field regime II curve. This result implies that the particular D N A at the pin-down condition assumes an entangled-but-unstretched conformation as a result of the field reversal at a proper timing / , otherwise the D N A belonging to the regime III category assumes a stretched conformation (8). Figure 3 shows μ log / curves in E = 7.5 V / c m , E = 2.5 V / c m and C j =1.0 wt% at four different temperatures from 13 to 37°C. W e see that with increasing temperature / shifts to the high / side and μ becomes larger. These μ data are plotted in Figure 1 with the solid symbols. W e see that only 13 C data point appears close to the extrapolated portion o f the regime II curve (dotted line), and with increasing temperature μ becomes closer to the regime III value of μ$. This result means that the temperature dependence of μρ is larger than that of μ$. In fact, E* for μρ is of the order of 15 kJ/mol that is about twice as large as those of μ^ b

s

s

b

g e


§

g e

M l

l

t

a

s

s

b

s

ρ

s

b

s

ρ

ρ

_ 1

p

s

p

b

g e

ρ

ρ

e

ρ

Frequency-Domain Electric Birefringence. To examine the features of moving D N A molecules under B S F conditions, we conducted frequency-domain electric birefringence ( F E B ) measurements with a home-made F E B apparatus. The apparatus consisted of a semiconductor laser with 670 nm wavelength, a polarizer, a 3 mm or 1 mm optical path-length quartz Kerr cell of 50 mm length and 5 mm width, a quarter-wave (λ/4) plate, an analyzer and a photodiode connected to a fast Fourier transform (FFT) analyzer (Hitachi, VC2420). In each run the Kerr cell was filled with agarose gel of a desired concentration, and both ends of the cell were filled with the T B E buffer and connected with salt bridges to electrode baths. A D N A solution was applied on the top of the Kerr cell, and a small steady field was applied to bring the D N A band to the center o f the cell illuminated with laser beam. Then the steady field was shut off (E = 0), and a sinusoidal field of desired E and / was applied with the same bipolar power amplifier used in B S F G E experiments. Birefringence An induced by a sufficiently weak sinusoidal field of strength E and frequency / ( ω = 2nf) consists of a direct current (dc) component An^ and an alternating current (ac) component An of 2 ω with a phase lag of δ (9,10). The dynamic Kerr coefficient Κ is then given as b

s

s

c

âC


470



-

3

-

2

-

1

0

1

2

3 Steady

log(//Hz) Figure 2. Plot of μ vs log / under a low-bias B S F condition for D N A s of different M as indicated. Solid symbols represent μ data. δ


35.

Dynamics of DNA

KOTAKAETAL.

2

K = 2An/\E \

=K

s

ac

2

with K

= An /\E \ ;

dc

dc

+ ATsin(2œt) + / Γ cos(2cût)

(3)

2

fC= 2An

s

471

Molecules

ac

s i n 6 / | t f | , andK" = 2 A r t c o s 5 / | £ | s

a c

2

s

The birefringence is proportional to the orientation function of D N A molecules and the dynamic Kerr coefficients represent the orientation function related to rotational diffusion of the D N A molecules in agarose gel. We measured An as a function of 2 / and determined Κ and K" by equation 3 for 21 kbp fragment, 48.5 kbp λ D N A and 166 kbp T 4 d C D N A . W e plotted l o g ( - / T ) vs log(2/) for the three samples. In the plots we found a small mode always appearing at the same highest frequency / independent of M of all the samples. Thus we shifted the curves for 21 kbp and 48.5 kbp D N A s vertically so that the small modes (marked as / ) appearing around f = 10 H z were superposed onto the / mode of 166 kbp D N A . The results are shown in Figure 4. In Figure 4, we see three relaxation modes for 21 and 48.5 kbp D N A s , but only two modes for 166 kbp D N A . The first mode at the highest frequency / is independent of M as mentioned above but dependent on C i in such a way that / C g e f - This result means that this first mode is presumably related to vibrational motion of D N A segments between entanglement points of D N A molecules with gel strands or the motion of D N A molecules induced by the motion of gl strands. Thus we may call this mode gel mode. (However the signals cannot be from gel strands alone, because the signals from the gel strands themselves are very weak as compared to those from D N A molecules.) The second mode appearing at a frequency / « ' close to / p of each D N A shifts to the low / side with increasing Cgei as well as with M in such a way that / C f W , which is the same as that of / . This second mode seems to be related to the pin-down phenomenon, and we call this mode pin-down mode. The third mode appearing at the lowest frequency / R also rapidly shifts to the low / side with increasing C g i and M in such a way that / R «= C f M - 3 . Thus we could not locate the f mode for 166 kbp T 4 d C D N A i n 1.0 wt% gel. Figure 5 shows double logarithmic plots of the characteristic times τ (= 1/2π/: defined as the reciprocal angular frequency of each mode) vs M relation determined from F E B experiments. Figure 5 also shows the relaxation time data (solid symbols) obtained by Strum and W e i l (77) via time-domain electric birefringence (TEB) in 0.7 wt% agarose gel. First we notice that T of the gel mode is independent of M . For this gel mode, /e was close to / at which we saw an enhancement i n μ i n B S F G E under comparable bias conditions (7). The enhancement appears for all D N A s even those belonging to the Ogston I regime that cannot entangle with the gel strands. Thus the gel mode is presumably related to the motion of the gel strands. For the pin-down mode, τ is proprtional to C„Q\M that is equivalent to the behavior of / ( C g e f M ) . When a sinusoidal field of / is applied, the stretching o f D N A molecules (of a particular size) along the field can be effectively suppressed due to the field alteration at the proper timing of / j f . Thus at this pin-down mode the particular D N A molecules may assume rather tightly coiled-conformation so that their μ sharply reduces to exhibit pin-down phenomenon at this particular / . O n the other hand, T R corresponding to the / R mode exhibits M dependence that was predicted by de Gennes for diffusion of long chain molecules through fixed obstacles and called reptation (72). Thus this mode may be called repatation mode. e


e

e

e

g e

e

1>3

- 1

p

g e

p

e

lA

g e

R

E

M

}

ρ

x

1

p

_ 1

p

1

p

3

Fluorescence Microscopy of Moving DNA Molecules To observe dynamical structure of moving D N A molecules in gel electrophoresis, we utilized fluoresence microscopy proposed by Yanagida et al. (13), developed by Schwartz and K o v a l (14) and by Yoshikawa et al (15). In fact, experiments were



472

MACRO-ION

-

2

-

1

0

1

2

CHARACTERIZATION

3 Steady

log(//Hz) Figure 3. Plot of μ vs log / for 166 kbp T 4 d C D N A at different temperatures as indicated. 1

1

1

1

1

Cgel =1 0wt% 50 mM TBE -25 °C EsrIOVcrrr

Ε

X

fp

1

A \

166kbp

21kbp

il

ι1.

L

-2

3

..

ι

1

-1

ι

ι

I

0 1 log(2f/Hz)

iι

2

3

Figure 4. Plot of log(-/T') vs log (2/) in F E B experiments.


Dynamics of DNA Molecules


35. KOTAKAETAL.


473

474


conducted in Prof. Yoshikawa's laboratory at Nagoya University according to their routine (8,15,16). Observation was made primarily on T4 dC-DNA in 0.5 wt% agarose gel containing 50 mM TBE buffer, 4 %(v/v) 2-mercapto-ethanol and a fluoresent dye, ethidium bromide (EB). Nikon TMD microscope was used with a high sensitivity SIT TV camera (Hamamatsu Photonics, Hamamatsu, Japan). EB complexed T4 dC-DNA (DNArEB) were illuminated with 520 nm light and emitted fluorescence of 580 to 620 nm were observed The images were recorded on a video tape from which hard copies were made. Figure 6 shows traces of video images of T4dC-DNA:EB moving under (a) a steady field of Ε = 10.5 V/cm, a BSF field of E = 7.5 V/cm and E = 2.5 V/cm at (b) the pin-down frequency / (= 0.215 Hz) and at (c) low / (= 0.0316 Hz < /-) together with the field conditions. The figures are self-explanatory: Under a steady field, a DNA molecule initially in coiled-up conformation forms an U-shaped hook structure with elongated arms around an (invisible) obstacle. The arms are pulled by the field but the molecule stays at the same position for some time until the balance between the arms is broken. Once the balance is broken and the molecule becomes J-shaped conformation, then the longer arm pulls the shoter one quickly to pass around the obstacle and the molecule resumes the initial coiled-up conformation, as seen in Figure 5(a) (76). The process is highly nonuniform: Under a given steady field a short chain (but long enough to entangle with gel strands) rapidly repeats stretching-and-contracting motions but migrates a shorter distance per step, whereas a large fragment does it slowly but jumps a larger distance in one step. In effect, they migrate on an average with the same rate. Under a BSF pin-down condition the particular DNA molecule with initially coiled-up conformation begins to being stretched out, but coils up again as the field is reversed at the timing of / resonant to the characteristic time τ ' of the molecule. Thus, as seen in Figure 5 (b) the DNA molecule almost always assumes a coiled conformation. Under such a situation only the bias field contributes to its forward migration and the coiled molecule moves very slowly. This explains why μ is comparable to the value of μ extraporated from the regime II curve, where the DNA molecule is believed to be assuming entangled-butunstretched, coiled conformation. However, at low / (< / ) a DNA molecule spends a sufficient time under a strong effective field for repeating measuring worm like (stretching-and-contracting) motion before the field is reversed. Thus it exhibits an enhanced mobility. This observation nicely fits to the picture deduced from the results of steady field and BSFGE experiments as well as from FEB experiments described above. s

b


p

_ 1

p

ρ

δ

p

Concluding

Remarks

Under steady fierld GE, large DNA molecules migrate virtually at the same rate independent of M (> 20 kbp) and cannot be properly separated. By superposing a sinusoidal field of adequate frequency and strength onto the steady field, we can activate certain internal modes of motion of the DNA molecules. Especially in a DNAfragmentof a particular size M at the pin-down condition the stretching-andcontracting mode of the DNA molecule is resonant to the timing of the field alteration. Thus the DNA molecule assumes an unstretched, coiled conformation and migrates slower than those either of the larger or smaller sizes. Near BSF pin-down conditions μ becomes sensitive to M and size dependent separation of large DNA fragments becomes possible. The pin-down frequency / varies as / ρ ~ M~*Cg \ Eb E as long as E is not too large (7,8). This feature allows us to design BSF conditions appropriate for separating giant DNA fragments. p

l

C

Q

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35.

KOTAKAETAL.

a) Steady field behavior

5

1 Q

t/s


475


1 5 £ / ν α ΐ Γ ΐ

—π—r I

2.53

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12.14

h 15.11

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Figure 6. Traces of T4dC D N A : E B moving under (a) a steady field of Ε = 10 V / c m ; a B S F field of E = 7.5 V / c m and E = 2.5 V / c m at (b) the pin-down frequency / (= 0.215 H z ) and at (c) low / (= 0.0316 H z < / ) . Continued on next page s

b

p


p


476


b) BSF at pin-down condition

10

Jim

Figure 6. Continued.


KOTAKAETAL.



35.


477

478


W e thank the Ministry of Education, Science and Culture (Mombusho), Japan for financial support through a Grant 01470107.


Acknowledgement.

Literature Cited. (1) McDonnel, M.W.; Simon, M.N.; Studier, F. W. J. Mol. Biol. 1977, 110, pp. 114-146. (2) Schwartz, D.C.; Cantor, C.R. Cell 1984, pp 77-84. (3) Carle, G.F.; Frank, M.; Olson, M. V. Science 1986, 232, pp 65-68. (4) Lalande, M.; Noolandi,J.;Turnmell, C.; Rousseau,J.,Slater, G.W. Proc. Natl Acad. Sci. USA 1987, 84, pp 8011-8015. (5) Slater, G.W.; Rousseau, J.; Noolandi,J.;Turnmel, G.; Lalande, M. Biopolymers 1988, 27, pp 509-524. (6) Shikata, T.; Kotaka, T. Bioplymers 1991, 31, pp 253-254. (7) Shikata, T.; Kotaka, T. Macromolecules 1991, 24, pp 4868-4873. (8) Kotaka, T.; Adachi, S.; Shikata, T. Electrophoresis 1993, 14, pp 313-321. (9) Parus, S.J.; Shick, R.A.; Matsumura, M.; Morris, M.D. Analytical Chemistry 1988, 60, pp 1932-1635. (10) Ookubo, N.; Hirai, Y.; Ito, K.; Hayakawa, R. Macromolecues 1989, 22, pp 1359-1366. (11) Strum, J.; Weil, G. Phys. Rev. Lett. 1989, 62, pp 1484-1486. (12) De Gennes, P.-G. J. Chem. Phys. 1971, 55, pp 572-579. (13) Yanagida, M.; Hiraoka, Y.; Katsura, I. Cold Spring Harbor Symp. Quant. Biol. 1983, 47, pp 117-187. (14) Schwartz, D.C.; Koval, M. Nature 1989, 338, pp 520-522. (15) Matsuzawa, Y.; Ninagawa, K.; Yoshikawa, K.; Doi, M. Nucleic Acids Res. Symp. 1990, ser. 22, pp 77-78. (16) Kotaka, T.; Adachi, S.; Matsuzawa, Y.; Yoshikawa, K. Rep. Progr. Polym. Phys., Jpn 1992, 35, pp 687-688. RECEIVED September 7, 1993


Dynamics of DNA Molecules under Gel Electrophoresis - American

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