3828
J . Phys. Chem. 1990, 94, 3828-3838
strictly as a coupled chromophore, we are able to demonstrate the presence of four low-lying electronic excited states in INDOIS calculations of the special pair of Rps. Giridis that exhibit Qv origin similar to our study here. At monomer distances much less that 3.5 A, we observe that the MGBC dimer begins to behave as supermolecule (data not shown) and the quality of a coupledchromophore model decreases. In addition, the red shift can become quite large when the chromophores have contacts less than about 3.0 The most recent X-ray coordinates for the reaction center of Rps. ciridis show that the average spacing in the BChlb special pair is about 3.3 A.4.5 The special pair appears to be a fundamental structure in most photosynthetic systems. In these cases, energy transfer is effective between antennas, and reaction centers on a picosecond time scale. For this efficiency, the lowest energy band of the reaction center must lie lower in energy than the corresponding lowest lying excited states of the antenna. Although electrochromic and geometric variations of the macrocycle may contribute to this property, formation of the dimer would be a simple and robust way to ensure that the reaction center possessed the Qv band of lowest energy.35 Furthermore, the delocalization of charge in a hydrophobic environment would be more favorable in a dimer, while intermacrocycle geometry changes could enhance not only the forward electron-transfer rate but inhibit back-reactions. The (35) Thompson, M. A.; Zerner, M. C. J . Am. Chem. So?. 1988, 110,606.
properties of BChl dimers may also be relevant to BChl-containing antenna proteins that contain BChl aggregates.20 The BChlb dimer of Rps. uiridis exhibits less symmetry than our model system here. The macrocycles are rotated and tilted with respect to one another. In addition, the macrocycles exhibit puckering, which is known to affect the electrochemical and optical properties.8 Furthermore, the BChlb dimer excited states are influenced by ligating histidines and hydrogen-bonding amino acids from the surrounding protein in addition to the other chromophores present in the reaction center. Future studies will examine these effects.36 Acknowledgment. M.A.T. is grateful for an NSF predoctoral fellowship. This work was supported in part through grants from Eastman Kodak Co. and the U S . Department of Energy, Division of Chemical Sciences, under Contract DE-AC02-76CH00016. Registry No. BChlb, 53 199-29-4. (36) We are presently examining, in addition to the actual special pair, a model of the reaction center of Rps. uiridis consisting of the six chromophores and some of the nearby amino acids. Our initial calculations employed an extensive SCF/CI with nearly 1700 singly excited configurations. The preliminary results show that the lowest excited state of the reaction center is almost purely comprised of BChlb special pair states. The concepts developed here should prove useful in an analysis of this and other low-lying states. We have designed a new program, ARGUS, which is a totally redesigned semiempirical program implemented in the programming language C and highly vectorized, (M.A.T.). These INDO/S calculations took roughly 2 CPU h to run on a Cray Model Y-MP8/864.
Reorientational Dynamics and Mobility of DNA during Pulsed-Field Agarose Gel Electrophoresis Bjorn Akerman and Mats Jonsson* Department of Physical Chemistry. Chalmers University of Technology, S-412 96 Gothenburg, Sweden (Received: July 17, 1989; In Final Form: October 18, 1989)
Reorientational dynamics of DNA and its importance for separation in pulsed gel electrophoresis have been investigated by linear dichroism (LD) and mobility measurements on DNA between 40 and 166 kilobase pairs (kbp) in 1% agarose. The time of reorientation between steady states increases linearly with the molecular weight of DNA at all investigated pulse angles. The LD measurements indicate that the reorientation, when the direction of the field is changed 90' or more, occurs via a coiled shape formed early in the transition. In crossed pulsed fields the mobility and the time-averaged DNA coil anisotropy as functions of pulse time both have a minimum at the same pulse time. The minima occur at proportionally longer pulse times as the DNA size increases, and they are deeper for a pulse angle of 120' than for 90'. The pulse time that gives the minima is considerably shorter than the time of reorientation between steady states. It is concluded that the minimum in mobility can be ascribed to the high friction coefficient of coiled shapes of reorienting DNA. Since an inverted field also forms molecules that transiently have low anisotropy, the same mechanism is suggested for pulses at 180'. Molecules smaller than 166 kbp are thus separated in present pulsed field electrophoresis techniques because different pulse times are needed to force molecules of different sizes to maintain a nearly globular conformation during migration. In the limit of long and short pulses, the DNA is shown to migrate in fields which are in effect constant and, hence, no separation occurs. For short pulses DNA only senses the effective field between the two applied fields, and it is shown that a critical pulse time of 0.1 s is required to reach this state, independent of molecular weight.
Introduction Pulsed-field gel electrophoresis (PFG) in agarose matrices has become an important tool for analysis of large D N A molecules. Unlike conventional gel electrophoresis, where the electric field is constant in time and space, PFG makes use of a field that alternates periodically between two orientations. The technique was introduced in 1983 by Schwartz et al.,' who used orthogonal, heterogeneous fields, but since then several variant^^-^ have been ( I ) Schwartz, D. C.; Saffran, W.; Welsh, J.; Haas, R.;Goldenberg, M.; Cantor, C. R. Cold Spring Harbor Symp. Quanr. B i d . 1982, 47, 189. ( 2 ) Carle. G .F.; Olson, M . W. Nucleic Acids Res. 1984, 12>5647.
0022-3654/90/2094-3828$02.50/0
described utilizing both other angles and homogeneous fields. The development of PFG has substantially improved agarose gel electrophoresis of DNA since it allows separation of much larger molecules (up to 9000 kbp6) than is possible in the conventional method by which molecules larger than about 20 kbp cannot be resolved efficiently.' (3) McPeek, Jr., F. D.; Coyle-Morris, J. F.; Gemmill, R. M. Anal. Biochem. 1986, 156, 274. (4) Chu, G.; Vollrath, D.; Davis, R. W. Science 1986, 234. 1582. (5) Smith, C. L.; Warburton, P. E.; Gaal, A,; Cantor, C. R. Genetic Engineering 8; Plenum: New York, 1986; p 45. (6) Smith, C. L.; Matsumoto. T.; Niwa, 0.; Klco, S.;Fan, J.-B.; Yanagida, M.: Cantor, C. R. Nucleic Acids Res. 1987, 15. 4481.
0 1990 American Chemical Society
Reorientational Dynamics and Mobility of DNA In both constant- and pulsed-field electrophoresis the motion of the DNA molecules is not completely understood. According to the prevalent model, the DNA chain migrates through the gel pores in a snakelike motion called reptation, where one end leads and the rest of the molecule follows the same path. Theoriess-Io based on this model predict that long chains become extended and oriented in the electric field direction. In a constant field these effects should lead to very similar mobilities, thus accounting for the loss of resolution seen in ordinary electrophoresis. The separation produced by PFG is ascribed' to the reorientation the molecules are forced to undergo when the field changes direction. The net mobility of DNA through the gel is assumed to be modulated by the rate at which the molecule can reorient itself; a rate that in turn is expected to be dependent on the length of the molecule. Several models have been proposed, however, regarding the configuration the molecules adopt during reorientation. Schwartz et al.' assume a reorientation through a relaxed conformation whereas Southern et al." suggest that the extended configuration is retained throughout the process as one of the ends pulls the rest of the molecule into the new orientation, and Deutch12 proposes formation of kinks creating loops that have to unfold to yield a linear molecule. Carle and Olson2 (field inverted 180O) assume that the oriented molecules are wedge shaped and reorient themselves through inversion of the wedges. That DNA indeed becomes oriented during gel electrophoresis has been shown experimentally since 1985 in studies of linear dichroism of native DNAI3-lS and fluorescence anisotropy of ethidium bromide stained DNA,16 but the relevance of the orientation for the loss of separation in constant fields is still not clear.]' Recently, Smith et al.Is have been able to observe individual ethidium bromide stained DNA macromolecules in agarose gel, with the aid of a fluorescence microscope, and it was noticed that A-DNA molecules fluctuate during electrophoresis in a constant field, between compact, U-shaped, and extended states that are oriented in the field direction. This is a behavior that has also been predicted by computer simulations of DNA motion during e l e c t r o p h o r e s i ~ . Very ~ ~ ~ ~long ~ DNA chains, with contour lengths of several hundred microns, were found to be more exactly aligned by the electric field than A-DNA. When the field was suddenly rotated through an angle of 120°, the long molecules reversed their directions and the heads (which had been the tails) proceeded in the new direction, a reorientation thus resembling that predicted by Southern et al." There were also, however, indications that the leading ends of the molecules were bunched. Several g r o ~ p s lhave ~ ~ used ~ ' ~linear ~ ~ dichroism to measure the reorientation dynamics of different DNA molecules (40-680 kbp) in fields pulsed at 1 80° and found that reorientation under this condition is influenced by a kind of head-and-tail character in the DNA conformation, as suggested by Carle and Olson.2
The Journal of Physical C h e m i s t r y , Vol. 94, No. 9, 1990 3829 In the original PFG technique, inhomogeneous electric fields were thought to be required for separation.' However, homogeneous fields give good separation, providing the angle between the fields is greater than 90°.11.23 There are also indications that DNA mobility depends little on whether a field gradient is present, and it is now believed that the main role played by the inhomogeneous fields used in some PFG devices is to create field angles greater than 90°.24 A critical variable in PFG is the pulse time, since the time selected sets the limits of the DNA size range within which separation is achieved. The crossed-field techniques utilize symmetrical times, and it has been assumed that resolution is optimal for molecules with reorientation times comparable to the pulse time.' On the basis of this assumption, and from observations of the separation pattern, the reorientation time has been estimated to increase linearly with the DNA size and decrease, also linearly, with the square of the field strength.25 Optimal pulse time has been shown, however, to be inversely related to field strengths6 In the field-inversion technique,2 separation requires the use of nonsymmetrical pulse times. Mobility and linear dichroism measurements on DNAs between 40 and 680 kbp have shown that the field-reversal interval that leads to a minimum in mobility is directly correlated with the time required to reach a minimum in the orientation function upon field reversal.26 To our knowledge, no corresponding measurements have been performed on the PFG techniques utilizing crossed fields. In the present paper, linear dichroism spectroscopy has been used to follow the reorientation of linear double-stranded DNA in 1% agarose gels at various pulse angles, pulse times, and electric field strengths. The measurements have been made in homogeneous fields with the DNA molecules in zones and in native B form. Since the dichroic absorption of the DNA bases themselves has been exploited, addition of optical probes was not necessary. Mobilities measured under identical conditions are compared with the linear dichroism results.
Materials and Methods Linear Dichroism. We have used the linear dichroism (LD) of the DNA bases at 260 nm to determine the average orientation of the DNA helix axis during electrophoresis. The LD is a measure of the difference in absorption of light polarized parallel and perpendicular to a given laboratory axis through the sample: LD = Ai, - A , For random orientation of the helix axes the sample is isotropic, A l l = A, and LD is 0. If the helix axes are oriented, the orien-
tation can be characterized by the reduced linear dichroism (LD') defined as LD' = LD/Ai,,
(7) McDonell, M. W.; Simon, M. N.; Studier, F. W. J . Mol. Bioi. 1977, 110, 119. (8) Lumpkin, 0. J.; Dejardin, P.; Zimm, B. H. Biopolymers 1985, 24, 1573. (9) Slater, G. W.; Noolandi, J. Biopolymers 1986, 25, 431 (10) Adolf. D. Macromolecules 1987. 20. 116. (1 l j Southern, E. M.; Anand, R.; Brown, W.R. A,; Fletcher, D. S. Nucleic Acids Res. 1987, 15, 5925. (12) Deutsch, J. M. Phys. Rev.Left. 1987, 59, 1255. (13) Akerman, B.; Jonsson, M.; NordCn, B. J . Chem. Soc.. Chem. Commun. 1985, 422. (14) Moore, D. P.; Schellman, J. A.; Baase, W . A. Biophys. J . 1986, 49, 130a. ( 1 5 ) Baase, W.; Moore, D.; Schellman, J. A. Contribution to the Swedish
Work-Shop on Structure, Dynamics and Function of Nucleic Acids in Gothenburg, Nov 23-25, 1986. (16) Hurley, I. Biopolymers 1986, 25, 539. (17) Jonsson, M.; Akerman, B.; NordCn, B. Biopolymers 1988, 27, 381. (18) Smith, S. B.; Aldridge, P. K.; Callis, J. B. Science 1989, 243, 203. (19) Deutsch, J. M.; Madden, T. L. J . Chem. Phys. 1989, 90, 2476. Olvera de la Cruz, M. Macromolecules 1989, 22, (20) Schaffer 11, E. 0.; 1351. (21) Holzwarth, G.; McKee, C. B.; Steiger, S.; Crater, G. Nucleic Acids Res. 1987, 23, 1003 1. (22) Akerman, B.; Jonsson, M.; NordCn, B.; Lalande, M. Biopolymers 1989, 28, 1541.
where Ai, is the absorbance of the isotropic sample (absence of field). The LD' is related to the effective angle a between the transition moments of the DNA bases contributing at 260 nm and the DNA helix axis, and an orientation factor, S, describing the average orientation of this axis relative to the reference directi~n:~' LD' = 3s(3(C0s2 a ) - 1 ) / 2
(3)
Thus, LD' is made up of an orientation factor, S, and an optical factor. The orientation factor will be in the range -1 to 1 where the value 1 corresponds to perfect orientation of the DNA helix parallel to the reference direction. For double-stranded DNA in its B form, the angle a in the optical factor can be assigned equal (23) Birren, B.; Lai, E.; Clark, S. M.; Hood, L.; Simon, M. I . Nucleic Acids Res. 1988, 16, 7563. (24) Cantor, C. R.; Gaal, A.; Smith, C. L. Biochemistry 1988, 27, 9216. (25) Mathew, K. M.; Smith, C. L.; Cantor, C. R. Biochemisfry 1988, 27, 9210. (26) Baase, W. A,; Moore, D. P.; Schellman, J. A. Biophys. J . 1988, 53,
408a. (27) Schellman, J.; Jensen, H. P. Chem. Reu. 1987, 87, 1359.
3830 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 to 86°,28-30 According to eq 3, an LD' = -1.48 corresponds to a perfect orientation (S = 1). A complementary measurement to LD is LD45,which is the difference in absorption of light polarized + 4 5 O (counterclockwise) and -45' to the reference axis. Equation 3 also holds for LD4, (orientational factor S44. The average orientation relative to the reference direction is described by LD and the symmetry of this orientation by LD,?. For example, with a constant electric field as reference direction, LD4, of DNA oriented by this field is expected to be 0 in the steady state, since a homogeneous field should produce a cylindrically symmetric orientational distribution of the DNA. As can be seen from eq 3, LD' measures DNA orientation (S) and its time behavior only if the optical factor does not vary with time (aconstant), Le., only if the DNA stays in its native B form and does not change, for example, into a partly single-stranded state.31 For the B form, the value a = 86O is applicable between 250 and 300 nm;2a-30Le., the optical factor is independent of the wavelength in this range. Equations 2 and 3 then state that LD and Aisospectra should have the same shape in the given range since S is independent of wavelength. A simple test for such a proportionality is to compare the quotient between the LD time profiles at two different wavelengths with the corresponding ratio for Aiso(for DNA the Ai, spectrum is similar in agarose and free solution22). If the two quotients are equal for a number of wavelengths, this can be taken as a strong indication that DNA is in its B form during the process and that LD directly reflects DNA orientation. If they are unequal, the LD may reflect, however, not only orientation (S) but also changes in the local structure (a)of the molecule. In pulsed fields with two field directions there are two natural choices for the laboratory axis; either the direction of one of these fields or the direction of the effective field (the direction in which net migration of DNA occurs). Both have been exploited in this study. We will use the notations LD and LD,, when one of the pulsed fields is used as reference axis, and LDe" and LD$ when the effective field is used. If the pulse angle is 90°, the two alternatives are equivalent so that LD:\f = -LD and LDeff= LDd5. The orientational behavior of DNA has been investigated at four pulse angles: 60°, 90°, 120°, and 180'. In pulse experiments with one cycle of field alternation, in which reorientation is compared at the different angles, a common final field direction is used as reference axis. For the angles 60' and 120°, respectively, the first electrophoretic field is then not parallel to either of the two polarization directions of the light. Since light absorption is proportional to cos2 (3, where @ is the angle between the polarization plane of the light and the transition moment of the molecule,32the orientations in these fields will therefore give LD amplitudes that are a factor cos2 30 - cos2 60 = 1 / 2 less than corresponding orientations in the first fields at 90' and 180'. and N 4 DNA (71 kbp3,), D N A . The T 2 DNA (166 enclosed in 0.5% agarose plugs, were kindly provided by Dr. Marc Lalande, Centre National de Recherche, Montreal, Canada, and details of the sample preparation can be found in ref 20. The T7 DNA (40 k b ~ was ~ ~from ) Sigma and was used to form sample plugs of 0.5% agarose. Gel Preparation and Electrophoresis. Gels, 1% (w/v) agarose (DNA Ultrapure from Pharmacia), were cast and run in a buffer consisting of 0.05 M NaH2P04,0.05 M Tris, and 1 mM EDTA. The gel solutions, prepared by weighing buffer and agarose powder, were heated to boiling for 5 min and subsequently cor(28) Matsuoka, Y . ;Norden. B. Biopolymers 1982, 21, 2433. (29) Matsuoka, Y . ;Norden, B. Biopolymers 1983, 22, 1731. (30) Arnott, S.; Dover, S. D.: Wonacott, A. J . Acta Crystallogr., Sect B Sfrurt. Crysfallogr. Crysf. Chem. 1969, B25, 2 192. (31) NordBn, B.; Seth, S. Biopolymers 1979, 18, 2323. (32) Cantor, C. R.: Schimmel, P. R. Biophysical Chemistry; W . H . Freeman: San Francisco, 1 9 8 0 Part 11. (33) Weissman, M.; Schindler, M.; Feherm, G . Proc. Nafl. Acad. Sci. 1916, 73, 2776. (34) Zivin. R.; Malone. C.; Rothman-Denes, L. 9. Virology 1980, 104, 205. ( 3 5 ) Clark. R. W.; Wever, G.H.; Wiberg. I . S. J . Virol. 1980, 33. 438.
Akerman and Jonsson rected for evaporation by addition of water. The solution was allowed to cool to 50 'C and then poured into a casting frame of a conventional electrophoresiscell (Pharmacia-LKB Pulsaphore or Biorad Submarine cell). The gels were allowed to solidify for 2 h before the electrophoresis was started. The appropriate numbers of gel plugs (corresponding to 15-30 H g of DNA for gels to be used in LD experiments and 1 p g for mobility studies) were put in wells and covered with 0.5% gel. All gels were run at 5 V/cm and 20 'C if not otherwise stated. Mobility measurements in pulsed fields were performed in a Pulsaphore equipped with a hexagonal or rectangular electrode array, which gives homogeneous fields (*5% within the area used) alternating at 120' and 90°, respectively. In all experiments a single pulse time was used. Mobility data are presented as apparent velocities (cm/h) along the effective field direction. In the gels to be used in LD experiments (10 X I O cm2, 2 mm thick), DNA was migrated to the measuring position (center of the gel) by constant-field electrophoresis (each sample contained only one DNA size) before the gel was transferred to the electrophoresis chamber of the LD spectrophotometer. Each time a new sample preparation was used, the first run was made with pulsed fields ( 120°, 20-s pulse time); however, no sign of polydispersity was detected in the LD measurements or in the ethidium bromide staining of the gels done after completed measurements. Spectrophotometer and Electrophoresis Cell for the Optical Measurements. The design of the spectrophotometer is to be described in detail in another paper. It is constructed to measure both LD and absorbance between 250 and 600 nm by phase modulation (50 kHz) technique. The light beam is vertical so that measurements on a horizontal gel can be made. The electrophoresis cell for the spectroscopic measurements consists of a circular basin (3 cm deep and 17 cm in diameter) formed in a rectangular block of Perspex. In the central part of the cell the bottom consists of a silica plate ( I O X I O cm2) which is glued into the Perspex framework and which forms the bed for the gel. The gel is illuminated from below by the vertical light beam which has a cross section of 2 X 3 mm2. The cell is connected to two independent motor-driven scanning devices, which allow the gel to be scanned by the light beam in any direction on the horizontal plane. The electrodes of the cell are positioned in discrete positions along its periphery and are connected to a common socket via diodes, to prevent currents from flowing along inactive electrodes.' Two pairs of electrodes were used to produce pulsed electric fields at 60°, 90°, 120', or 180'. The whole electrode configuration was rigidly rotated relative to the fixed directions of the light polarizations to provide appropriately for LD or LD,, measurements. The electric field from the power supply was fed to the cell via a two-channel pulse aggregate (Pharmacia-LKB) with a rise time of less than 50 ms and with an off time between the channels of 100 ~ s Symmetric . pulse times were used in all experiments. For a given electrode pair, the field is not entirely homogeneous across the cell. However, due to the symmetry of the cell the field at the central part, where the optical measurements were made, is always of the same strength (5.0 f 0.1 V/cm in a 1 X 1 cm2 area at 100 V), and it is directed along the diameter of the cell as long as the electrodes in each pair are placed diametrically to each other. All measurements were, therefore, made with the gel placed so that the DNA zone (less than 0.5 X 0.5 cm2) was in the middle of the cell. LD Measurements. All LD measurements have been made at the concentration peak of the DNA zone, which was found by scanning the isotropic absorbance of the gel in two orthogonal directions with the field turned off. The gel UV background was corrected for by the procedure described by ref 17. Maximum DNA AiEovalues were in the range of 0.08-0.11 (path length of DNA absorbance estimated to 0.2 cm) for all the different gels, which is low enough to ensure that DNA-DNA interactions22are negligible. Since the diodic connection of the electrodes prohibits simple reversal of the electric field between each experiment, this technique to avoid migration of the zone maximum out of the
Reorientational Dynamics and Mobility of DNA
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Figure 1. LD (260 nm) of T2 D N A in 1% agarose during a 90° turn between steady-stateorientations. Electric field: 5 V/cm, E, along X followed by E, along Y. LD reference axis: E , . LD units: see text. LD = A,, - A , and LDd5 = A4S- A+. LD, calculated from L D and LD45 according to eq A2 (see Appendix). Arrows on time axis show turnon of E , , changing from E , to El, and turnoff of El.
measuring beam (as used in the foregoing LD s t u d i e ~ ~could '~~~) not be used. Instead, by scanning the gel in two directions again, but with the field turned on, the position of the maximum steady-state LD signal was found (this position coincides with that of maximum isotropic absorbance). Before each measurement, the steady-state LD was checked, and if it was smaller than this maximum, the optimal position was searched out by scanning, which was necessary for only every fifth to tenth measurement, depending on pulse duration. This procedure could in principle have been done with isotropic absorbance instead, but using the LD was found to be a more sensitive (because the gel UV background is much smaller in LD than in A,,) and faster method. There were no indications of different LD results with the DNA zone in different parts of the gel, as long as the measurements were made with the zone at the center of the cell. For the sake of comparison, all the LD data for a given DNA size are presented normalized to its steady-state-LD amplitude (at 260 nm) when the field is parallel to the reference direction (maximum steady-state LD). The buffer level in the cell was always kept high enough to cover the gel, but no circulation or external cooling of the buffer was used. Instead, manually, the whole buffer solution was replaced carefully, approximately every hour. Changes in the field distribution due to changes in the distribution of electrolyte between gel and surrounding buffer could be sensitively detected by changed orientational dynamics of DNA. When present, such effects could always be removed by equilibration between gel and surrounding buffer in the absence of the field. The increase in the average temperature in the buffer and the gel during electrophoresis was followed by the increase in current (constant voltage), and the duration of the field-off periods was always kept long enough to keep the average temperature below 25 OC.
Results and Discussion Reorientation between Steady States. Figure 1 shows the LD signal from T 2 DNA which starts to migrate and orient in a constant electric field, the direction of which is then changed 90' when the DNA has reached its steady-state orientation. LD and LD45are given with the initial field direction as reference axis. Initially LD shows the over- and undershoot which are characteristic for T2 DNA that is in its equilibrium state in the gel when the field is turned on.22 The LD is negative since the DNA orients with its helix axis in the direction of the field. After the turn of the field, the LD decreases in magnitude, passes zero, and finally
reaches a steady positive level of the same magnitude as during the first pulse, which shows that the DNA has now reached the same degree of orientation but with the helix axis along the new field direction. During the transition between the steady states, the LD contains several discernible phases, but no overshoot is observed. The LD45is zero throughout the orientation buildup during the first pulse, evidencing the uniaxiality of the constant field orientation of DNA. However, when the field is turned a transient negative LDd5signal is observed, which becomes zero first when the LD reaches the new steady level. Corresponding courses in LD and LD45 during reorientation have also been observed by Schellman and c o - ~ o r k e r s . Since ~ ~ the new field is orthogonal to the old one and becomes constant and uniaxial within milliseconds, the broken symmetry during reorientation indicates that there existed an asymmetry with regard to the new field in the DNA conformation prevailing before the field change. That DNA, during steady migration in a constant field, has a head-to-tail character has earlier been observed in field-reversal experiment^.'^*^',^^ The negative sign shows that during the reorientation there is a preference for orientation of the helix axis along the direction between the two fields, before D N A becomes uniaxial along the new field. Since the DNA LD' spectrum contains information about the local conformation in the helix (see Materials and Methods), the LD during the experiment shown in Figure 1 was followed at different wavelengths. The result (Figure 2) is that the profiles obtained at 260, 270, and 285 nm are very similar in shape. The quotient between the signals at 260 and 270 nm (top curve) is constant (1.17) and equal to the corresponding Ai, ratios during the whole pulse cycle, except when the field is switched, or turned on and off, when transients can be seen. Similar results are obtained for 260/285 (quotient 2.50) and 260/250 (1.17; 250-nm spectrum not shown). The DNA is thus in its B form except possibly during the transients, which suggests temporary changes in its local structure when the field is changed. Such changes have been suggested as an explanation to the higher temperature sensitivity in DNA mobility in pulsed fields compared with constant fields3' However, the low LD amplitudes after the field switch make the LD ratios uncertain. Furthermore, LD is an average of all base pairs and it is highly unlikely that so many of these are perturbed that it would affect LD' to the degree seen in the transients. We will therefore assume that the main part of LD during the turnaround of the molecule really reflects axis orientation and not local structure changes. Degree of Anisotropy during Reorientation between Steady States. In a steady field, the LD measured with the field direction as reference direction shows the maximum orientation of the molecule since the orientation has a cylindrical symmetry relative to the field direction (LD45is 0) and, therefore, cannot be larger in any other direction. During reorientation in the pulsed fields, ~~~~~~
~
~
(36) Schellman, J. A,; Baase, W. A,; Moore, D. P. Private communication. (37) Mathew, M. K.; Smith, C. L.; Cantor, C. R. Biochemistry 1988, 27, 9204
3832 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
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(s) Figure 3. Regrowth LD of T 2 DNA after partial reorientation at 90' or field-free decay (symbol E2 = 0) for 4.3 (a) and 2.3 s (b). Field directions indicated at top in part a. Experimental conditions as in Figure I , except pulse durations. Time
this symmetry is broken as evidenced by the simultaneous signals in both LD and LD,, (Figure 1). In the Appendix it is shown, however, that LD and LDls can be combined to give, at each moment during reorientation, the maximum LD (LD,) of the DNA sample. Their combination also gives the angle x (the isoclinic angle) between the direction of LD, and the reference direction in the LD measurements. The time course of LD, from such an analysis of the 90' turn in Figure 1 is shown in the lower panel of the figure. The orientation shown by LD, is, as expected, the same as that shown by the LD during the buildup and the steady-state phases. When the field changes direction LD, decreases and passes through a deep minimum before it goes up to the steady level again. The anisotropy in the DNA conformation is, thus, much lower during the reorientation than during steady migration in the fields. The isoclinic angle x (not shown) swings from 0" to 90" during reorientation and is 45' when LD, reaches its minimum. Molecular Shape during Reorientation between Steady States. The low degree of anisotropy in the molecule under reorientation could be due to canceling between one positive and one negative contribution originating from the leading and trailing part, respectively, of a stretched molecule that reorients according to Southern's model." We will now show, however, that a more likely explanation is a reorientation through a coillike conformation. I n Figure 3 the conformation during a 90" turn is probed by reapplying the original field at different times after it was changed by 90'. The way the LD falls off and is restored for molecules that are partly reoriented by the orthogonal field is compared with the behavior of molecules that are instead allowed to relax in the absence of a field for the same amount of time. Figure 3a shows that the initial fall in LD is equal in the two cases until 7 5 % of steady-state LD has disappeared. During the subsequent regrowth phase, it is seen that molecules which are allowed to relax field free respond with a (reduced) overshoot to the reapplied field. Molecules that have instead been reorienting for the same amount of time show no overshoot but have a slower buildup. If the original field is turned on before the reorientation and the field-
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Figure 4. Resolved reorientation at 90° obtained by subtraction of a field-free decay (from steady state) from the reorientation LD at 90° (Figure 6 ) . The buildup from equilibrium (eq)is shown (displaced along the vertical axis) for the sake of comparison. Experimental conditions as in Figure 6 .
free-relaxation curves have diverged (Figure 3b), the initial regrowth is equal in the two cases, but later the reoriented molecules again respond more slowly than those which have been relaxed in the absence of a field. These results show that the second field does affect the molecules, but in a way that initially cannot be seen in the LD relaxation. The conclusion is that the reorientation consists of two phases, relaxation in the old direct and buildup in the new direction, and that these processes occur in different parts of the molecule. The initial LD relaxation is located in a region that carries the major part of the LD, and hence must be rather extended, while the buildup is in a region of low orientation, which must have a shape resembling that of the equilibrium state of the molecule. The latter state is most likely coiled molecules, as indicated both by simulation^^^^^^ and by direct observation using microscopy of labeled DNA.I8 That DNA during steady migration has a head-to-tail character has been shown by field-inversion experiments in mobility2 and in LD'5921322 and by the LD15 experiments (Figure 1) of this study. On the basis of the LD results it has been suggested22that the tail is similar to the equilibrium state of the molecule, Le., most likely coiled. Molecules that are partly stretched and partly coiled have also been observed in simulations of D N A migration in gels.19s20Together with these observations the results indicate that reorientation occurs through a relaxation of the stretched part in the old field direction, a process that occurs in parallel with (but, at least initially, almost independently of) a buildup in the new direction guided by a coiled part. The lines of argument given above led us to try to resolve the reorientation LD into a field-free-relaxation curve and a buildup LD process. Subtracting an experimental field-free-relaxation LD from the reorientation LD leaves a buildup delay of 2.5 s (Figure 4) which should be compared with the total reorientation time, t,, (defined as the time between when the field is switched and the LD has reached within 5% of the new steady level), of 15 s. The minimum in LD, during reorientation appears 2.5 s after the field is switched (Figure I ) , and its low value (0.05) indicates a low anisotropy in the shape of the molecule and, thus, a conformation close to that in the equilibrium state. That such a state is reached early after the field switch is also supported by the fact that t , depends on electric field (Figure 5) in a way very similar to the time t,, to reach steady-state orientation from equilibrium.22 The absence of overshoot before the new steady level is reached is surprising, however, since the buildup should be similar to that from equilibrium. We think the most likely explanation for the absence is the following. Simulations of migration of DNA in gelsI9 and direct observation'* strongly indicate that DNA of the sizes used in this study oscillates between stretched and compact conformations during "steady-state" migration. Since in equilibrium the molecules are all more or less coillike, in startup from this state the molecules will initially perform these oscillations in concert and will stretch (as observed in startup simulations20)and relax coherently, giving
The Journal of Physical Chemistry, Vol. 94, No. 9, I990 3833
Reorientational Dynamics and Mobility of DNA treo
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Figure 5. Field strength dependence in reorientation time
(t,,, see text) for T2 D N A at 60°, 90°, and 120° reorientation between steady states. Inset: log (2,) vs log (E). Least-squares fits (lines) give power-law exponent 1.4 f 0.1 at all angles. In 1% agarose.
0
rise to an oscillating LD. Sooner or later, however, the coherence will be lost and only the average degree of orientation during a cycle will be observed, and a virtual steady-state orientation will be reached. At a given instant some molecules are coiled up and others are partially stretched out, together forming an average head-and-tail conformation similar to the one indicated by the reorientational LD results as discussed above. In the pulsed-field experiments of Figure 1 the molecules are in this noncoherent steady state when the field is switched and therefore will respond with different overshoot amplitudes and time constants, because individual molecules have different-sized heads to drive the buildup in the new direction. The resulting buildup will be smeared out, in analogy with the monotonous LD growth observed for a mixture of A-oligomers starting from equilibrium (result not shown) notwithstanding that each component shows a distinct (but size-dependent) overshoot.2' The reorientation is not completed until the largest coils have turned around; hence t,,, should be close to but not larger than t,,, which is indeed the case (Figure 6a, 90'). If the picture of the reorientation given above is correct, the major part (about 75%) of the initial decrease toward zero LD magnitude (Figure 1) occurs mainly through field-free-like relaxation of the noncoiled part of the molecule. The low LD, early during the transition would then reflect an average conformation of the molecules resembling that of the equilibrium coils. Influence of Pulse Angle on Reorientation between Steady States. Figure 6a shows the LD of transitions of T2 DNA between steady states at different pulse angles, with a common final electric field as reference direction. During the first pulse the LD along the different directions differs in magnitude, being 0.58 for 60" and 120' (compared to 1 for 90'). This is close, however, to the theoretical value 1/2 (see Materials and Methods), which shows that the fields are indeed close to 60" and 120' (the deviation being less than 3'). For the angles investigated the reorientation time, ,t increases in the order 120°, 60°, 90°,and 180' (Figure 6a, inset; the switch time between the electrode pairs is so short that at 0' there is no decay of orientation and hence t,,, = 0). It is also seen that at all angles except at 180' the transition between the steady states is faster than the buildup of the steady state from equilibrium (see inset). While no overshoot is seen at 60' and 90°,a weak one is observed at 120" and an overshoot similar to that in the buildup from the equilibrium is observed at 180'. In Figure 3 it was shown that the initial falloff in LD during the transition at 90' is the same as the relaxation without the field. That this does not hold at other pulse angles is demonstrated in Figure 6b. During the initial reorientation, the magnitude of the LD decreases faster at 120' and 180°, equally fast at 90°,and slower at 60°, compared to the field-free relaxation. A faster
1 0'
120
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Time (s) Figure 6. Reorientation LD of T2 D N A for 60°, 90°,and 120' pulse
angles compared with buildup from equilibrium (eq). Experimental conditions as in Figure 1, except LD reference direction: E2. E , is applied at t = 40 s and has the same direction at all angles. Arrows show the direction of the first field E , . (a) Full reorientation process. Inset: f, (see text) vs pulse angle. The 180° response is not shown but is given in ref 22. (b) Initial part. L D during E , scaled to 1 for the sake of comparison. Pulse angles indicated. Dashed curve: field-free decay.
decrease at 180' has also been reported by Moore et al.38 Both the initial LD relaxation and t,, are thus strongly dependent on the pulse angle, however in different ways. The different dependencies may be explained on the basis of the conclusions about the molecular shape during reorientation at 90' (see above). It is reasonable to assume that the stretched part of the molecule, if not hooked, has lower friction than the coiled part and will take the lead. The faster relaxation at 180' than at 90°,where the initial relaxation is equal to the field-free relaxation (Figure 6b), may then be interpreted in the following way. When the field is inverted, the molecules begin to move backward and the more mobile stretched part catches up with the coil (or if the stretched part is a hooked tail the coiled part eats up the tail) and the coil grows in size, until eventually the whole molecule becomes coiled. The process is driven by the field and becomes, therefore, faster than field-free relaxation. Initially the migrating molecules have different degrees of coil-and-tail character but the forward migration that led to this situation is now reversed, which leads to a leveling out of the distribution and formation of full coils more or less simultaneously. The buildup of the orientation in the new direction then occurs from a state resembling the equilibrium state, and the total reorientation time, t,, should therefore be longer than the time it takes to build up the orientation from equilibrium, which also is the case (Figure 6a). At 120' a similar process may occur but, since the migration is not directly backward, some of the uneven distribution may be maintained during the reorientation. The average intermediate coil becomes smaller which leads to a much faster buildup of the (38) Moore, D.P.;Schellman, J. A,; Baase, W. A. Biophys. J 1987, 51, 509a.
3834 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
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DNA size (kbp) Figure 7. 1, between steady states vs molecular weight at different pulse angles (indicated). At 5 V/cm; 1% agarose. Each point is an average of three measurements.
orientation in the new direction, Le., a short t,. At 60" the initial relaxation is very slow, which is understandable since the moderate change in migration direction compared with the other angles should mean that in the main the molecules retain their headand-tail character throughout the reorientation. The tails cause the molecules to have high friction (the reasm why they are tails) during the whole reorientation, which explains why t , is longer than at 120O. The lack of overshoot during transitions between steady stales at 60" and 90° can be explained by a lack of coherence in the steady state. The only way to obtain a marked overshoot from the steady state is to invert the field,** which supports the mechanism for the 180" reorientation proposed above. A pulse angle of 120" combines the mechanism at 90" with the field-driven coiling at 1 80°,which explains why there is a weak overshoot in the buildup of orientation in the new direction. Effect of Molecular Size on Reorientation between Steady States. The observations presented so far were made on T2 DNA, but similar results have also been obtained for T7 and N 4 DNA. The differences are mainly that the steady-state orientation is lower (LD' values at 5 V/cm and 1% agarose are 0.04, 0.06, and 0.12 for T7, N4, and T2, respectively) and the reorientation is faster, the shorter the DNA. Figure 7 shows that the reorientation time, t,,, between steady states decreases approximately linearly with molecular size ( L ) at three different pulse angles. This means that the reorientation process can explain, in principle, the separation in PFG if it can be shown that the mobility during reorientation is lower than during migration in a steady field. According to the figure, the separation should be equally good at all angles since the relative reorientation times are independent of pulse angle. This is in disagreement with the finding that optimal separation in PFG is obtained at pulse angles aroud 120°.4923However, in the figure t,,, is for reorientations between steady states in a single pulse cycle, while separation in PFG occurs during repeated pulses for which the pulse time may be too short to allow the molecules to reach a fully extended conformation during each pulse. We therefore decided to study the reorientation also in repeated pulses and at different pulse times. Reorientation in Pulsed Fields. Figure 8 presents LD responses from T2 DNA in pulse sequences at 90' pulse angle and at different pulse times Tp. The effective field is used as the reference direction, and all responses start with DNA in equilibrium. Only results at T p < t,,, are shown in the figure. For Tp > tree the steady-state orientation is always reached within each field and the LD responses are, as expected, similar to those shown in Figure 1 (single pulse cycle also starting with DNA in equilibrium) in the first pulse cycle, with a repetition of the reorientation time profile of this in the following cycles. For Tp< t,, the steady-state orientation is not reached within each field but LD$ (the analogue to LD in Figure 1) becomes a series of interchanging positive and negative peaks (Figure 8a). The peak to peak value decreases steadily with decreasing Tp and is reduced below the noise level for Tp between 0.2 and 0.1 s. Beginning at Tp = O.ls, LD'" (the analogue to LD45in Figure 1) is, as can be seen from Figure 8b, very similar to an LD response
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Figure 8. LD$ (a) and LDCN (b) of T2 DNA during a sequence of field pulses at 90'. Pulse times indicated. LD reference direction: effective field. The curves are displaced along the LD axis for the sake of clarity. All responses start off from DNA in equilibrium. Note change of vertical and horizontal scales in lower section of part 8a. At 5 V/cm; 1% agarose.
at constant field (Figure l ) , although the buildup is slower and the (apparent) steady-state magnitude is about half of that. When Tp is increased, the LDeffdecreases in amplitude, but the time profile is kept intact, at least below Tp = 2 s. At Tp = 5 s the oscillatory profile is now modulated by the pulsing itself, which in turn dominates at 10-s pulse time. When Tpbecomes larger than t,,, (not shown), LDe* is nonzero only transiently after the field is switched (cf. LDls in Figure 1 ) . The corresponding measurements at a pulse angle of 120" (not shown) exhibit a DNA behavior very similar to that at 90", except for an even slower buildup of the orientation along the effective field at short pulse times. The results clearly show that the DNA at short pulse times cannot follow each component of the pulsed field (LD:: is zero throughout the pulse sequence), but is only sensitive to the effective
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3835
Reorientational Dynamics and Mobility of DNA
Pulse time
(SI
Pulse time
(s)
0.1
Figure 9. Pulsed electrophoretic LD in the limit of short pulses. (a) Steady levels in LD'" (Figure 8a) and (b) peak to peak values in LDiy (Figure 8b) vs Tp. Pulse angle: 90' (filled symbols); 120' (open symbols). DNA sizes: T2 (0),N4 (0),T7 (A). Encircled stars are constant field LD at the effective field; see Figure IO.
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Time (s) Figure 10. LDC" response ( 5 V/cm) of T2 D N A for Tp = 0.1 s at 90' (Figure 8a), 120°, and 60' compared with constant field LD response (as during E l in Figure 1) at the applied field, E = 5 V/cm, (0') and effective fields ( 120°, E/2; 90°,E/2'l2; 60°, E-3]/*/2). Pulsed responses are indicated by P.
field (LDeffhas initially the shape of a constant-field response and then becomes constant). In order to determine the limiting conformation and the pulse time when it is reached, the maximum amplitudes in LD;;' and the steady-state levels in LDCff(from Figure 8a and Figure 8b, respectively, at 90') were plotted against Tp(Figure 9). At both 90' and 120°, LD$' becomes zero at Tp = 0.1 s, and LDeffapproaches a limiting value which is close to the steady-state value in a constant field of the same field strength as the effective field at the pulse angle in question. That the T2 DNA in a pulsed field at this Tpis sensitive only to the effective field is further supported by the result shown in Figure IO, where responses at Tp = 0.1 s for different pulse angles are compared with responses to a constant field of a strength corresponding to the effective field for those angles. The LDCffresponses are very close to the constant field responses; the differences for 60' and 120' are within experimental error, while at 90' the orientation is somewhat lower with a pulsed than with a constant field. For N4 and T7, the LD responses at different pulse times and pulse angles (not shown) are very similar to those observed for T2, except that the LD pattern is scaled to shorter values of Tp due to the faster reorientation for the shorter DNA molecules. There is, however, no corresponding shift in the limiting pulse time for which the investigated DNA is only sensitive to the effective field as shown by the extrapolation toward short Tp (Figure 9). For all three lengths of DNA this occurs for Tpbetween 0.2 and 0.1 s, and it is confirmed by the experiment shown in Figure 10, when repeated for N4 and T7 DNA (not shown). The conclusion is that the electrophoretic reorientational dynamics of DNA at Tp= 0.1 s is independent of molecular weight, at least within the DNA size range investigated in this study (40-166 kbp). The LD measurements in pulsed crossed fields thus show that a transition takes place from orientation along each field direction
1
10 100 1000
Pulse time (s)
Figure 11. Electrophoretic velocity vs pulse time (T,) in fields pulsed at 90' (filled symbols) or 120' (open symbols). D N A size: T2 (O), N 4 (m), T7 (A). uaw is the apparent velocity in the direction of net migration. Stars are constant-field mobility (Figure 12) corrected for the difference
in actual and apparent path. Encircled stars are constant-fieldmobility at the effective field. At 5 V/cm; 1% agarose. Inset: pulse times that give minimum in velocity vs molecular weight.
to an orientation along the effective field as the pulse duration is decreased. Our aim below is to look for correlations between this orientational behavior and the electrophoretic mobility measured under similar conditions. Mobility in Pulsed Fields. Figure 11 shows the apparent velocity, uaPp,of T2, N4, and T7 DNA in fields pulsed at 90' and 120' at various pulse times, Tp. For 1 20' and short pulses uaPp approaches a common value for the three lengths of DNA. For increased pulse times the mobility passes through a minimum that is deeper and clearly shifted to longer pulse times the larger the DNA. Further increase in pulse time leads to a secondary minimum around Tp = 100 s for T7 and N4 but not for T2. Finally, a common limiting mobility for long Tpis reached by T7 and N4 DNA and approached by T2 DNA. When the mobility is measured with a pulse angle of 90°, there is still a principal minimum but it is shallower and its position less sensitive to molecular weight than at 120' (see Figure 11, inset). For T2 the minima are at about Tp = 5 s at both angles, but N 4 and T7 show a much weaker shift toward shorter Tp.at 90' than at 120'. Hence, for a given pulse time the separation is better at 120' than at 90' (the optimal relative mobilities are for N 4 and T2, 2.7 (120') and 1.4 (90'); for T7 and T2, 3.2 (120') and 1.6 (90')). With decreasing Tpthe three lengths of DNA converge toward a common value although at Tp = 0.1 s, T2 still migrates somewhat slower than N4 and T7. If Tp is increased, a secondary minimum is observed for N 4 and T7, the same as for 120°, but it is broader and occurs at longer Tp. Therefore, none of the three DNA molecules reaches a true plateau mobility (for the pulse times used) when Tpis increased, but all cleary approach a value that is close to the mobility for T7 at T = 3000 s. The rate of this approach is slower, however, at 90t than at 120°, even if the secondary minimum is disregarded. Figure 11 shows that the efficient separation of DNA (in the 40-1 66-kbp range) in pulsed-field gel electrophoresis is due to a deep minimum in apparent mobility at a pulse time that is different for different sizes of DNA. A minimum in mobility as a function of pulse time has earlier been reported, by Schellman and c o - w o r k e r ~for , ~ ~field-inversion gel electrophoresis, but to our knowledge it has not been observed for pulse angles other than 180'. It should be mentioned that the mobility still decreases monotonously with molecular weight at all values of Tpin spite of this minimum. While the deep mobility minimum occurs at pulse times that correspond to typical reorientation times for the DNA molecules (Figure 7), the additional small minimum for T7 and N4 at a pulse time of about 100 s is hard to interpret in terms of orientational effects since these DNA sizes have typical orientation times on the order of 15 s or less. Changes in the gel structure caused by electroosmotic flows induced by DNA in zones1' may be an explanation since they occur over a time scale of minutes and,
3836
The Journal of Physical Chemistry. Vol. 94, No. 9, 1990
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Figure 12. Steady-statemobility of T2 ( 0 )and T7 (A)DNA; 1 % agarose.
furthermore, have been observed to tend to decrease in intensity with increasing molecular weight of the D N A (unpublished results). However, the secondary minimum should clearly be studied further, so in this paper which concentrates on the connection between mobility and orientational effects of DNA, we will disregard it. Orientation and Mobility in the Limit of Long and Short Pulses. The limiting mobilities in Figure 1 1 can be understood in terms of corresponding LD data (Figures 1 and 8) and mobilities in constant fields of different strengths as given for T7 and T2 DNA in Figure 12. In the limit of long pulse times, the DNA will effectively migrate in a constant electric field, since the time needed for reorientation will be negligible compared with the time available for migration in the directions of the applied field (Figure 1) and, consequently, the mobility should approach that measured in constant-field electrophoresis. The limiting apparent velocities at long Tp(Figure 1 1 ) are indeed close to the constant-field velocities (stars) when these are calculated from the steady-state mobilities (Figure 12) by taking into account the fact that the actual path traveled by the DNA in the limit of long Tpis 2Il2 and 2 times the apparent distance at pulse angles of 90' and 120', respectively. That all three D N A molecules approach the same limiting velocity is expected since the steady-state mobility is independent of D N A size (Figure 12). It is also seen (Figure 11) that the shorter the DNA, the faster the limiting mobility is approached, and this is expected since the reorientation time between steady states, which is the relevant process in the case of long Tp, decreases with decreasing molecular weight (Figure 7). Even if the secondary minima are disregarded, the approach is slower at 90' than at 120', which is understandable since t,, is longer at 90' than at 120" (Figure 7 ) . The mobility did not become constant in the limit of short pulses (Figure 11) at the pulse times (Tp I 0.1 s) then available to us. The mobility and LD measurements together, however, show that DNA reaches a limiting conformation for a Tpof about 0.1 s, and that the limiting behavior is that of a DNA molecule in a constant electric field equal in strength and direction to the effective field between the two field directions. From LD this is clearly shown by the results in Figures 8-10. In the mobility (Figure 1 1 ) an effective field behavior at Tp = 0.1 s is indicated by the approximate agreement between the pulsed velocity at this Tpand the corresponding constant field velocity (encircled star). At 90°, but not at 120", the pulsed velocity of T2 for Tp = 0.1 s is a little lower than for the other DNA molecules. In a constant field they should be equal (Figure 12), and the LD profiles in Figure 10 (T2) do indeed indicate that at Tp = 0.1 s the apparent field at 90' (but not at 120') is not quite equal to the effective field. The effective field behavior of DNA at short pulse times is not surprising. As suggested by Schwartz et aL,I sooner or later the direction of the electric field will change so quickly that no part of the DNA will be able to follow each component, but the molecule will only respond to the effective field. The mobility and LD (orientation) thus agree as to the limiting pulse times that give an apparent constant field behavior to the DNA. This observation implies that orientation is an important factor in determining DNA mobility in gels, at least as long as the field is sensed as constant by the DNA. That orientation
Akerman and Jonsson should affect the migration has been discussed for several years, but direct evidence has been lacking. In the case of DNA smaller than 23 kbp, it has been questioned whether the small orientational effects that were observed (constant field) could explain effects ascribed to orientation, e.g., field-dependent mob the orientation is much stronger for the longer DNA molecules used in this study. The strong field dependence of their constant-field mobilities (Figure 12) also has an analogue in orientation since the steady-state orientation of long DNA is known to increase strongly with the field strength.22 Orientation and Mobility at Intermediate Pulse Times. At intermediate pulse times the DNA molecules are subjected to continuous reorientations where the steady-state orientation is never reached within each pulse (see the pulse sequences in Figure 8). Since the LD measurements indicate that the reorientation between steady states occurs via a coillike intermediate, it is reasonable to assume that the D N A molecules at intermediate pulse times also behave as coils that become partly stretched and for which the LD is a measure of the average degree of anisotropy. In a constant field a large LD (a high degree of stretching) in the migration direction corresponds to a high velocity (low friction) and vice versa. In crossed pulsed fields an upper limit for the DNA anisotropy is given by LD, (see Appendix), and by comparing this with uappan idea of the importance of the orientation d y i n g pulsing can be obtained. However, since uappis the average velocity over a pulse cycle, a time average of LD, during one pulse cycle had to be evaluated. To that end, time-averaged LDeffand LD;: amplitudes were calculated from the part of the recorded sequences (Figure 8) where the signals had reached a strictly periodic behavior. These amplitudes were then used to calculate average x and LD, values according to eq A2 in the Appendix. The average LD and LDls values, and the LD, constructed from them, are shown as functions of the pulse time ( Tp) for T2 at 90' pulse angle in Figure 13a. The so calculated LD, values of T2 at both 90" and 120' are shown in Figure 13b and for all three DNAs at 90' in Figure 13c. A comparison of the LD, curves in Figure 13 with the corresponding apparent velocity curves in Figure 11 shows that the pulse times that give the minima in LD, agree well with those that give the principal minima in velocity. At 90' they are consistenly shorter for LD, but the linear dependence on molecular weight (Figure 1 1, inset) is reproduced (Figure 13, inset). This clearly indicates a connection between average velocity and degree of anisotropy. uapp is the average velocity along the effective field direction, while LD, is the degree of anisotropy along the isoclinic direction, x. As the pulse time is increased, the average x amplitude varies between 0' for short Tpand 45' and 60' for long Tp,at the 90' and 120' pulse angles, respectively (not shown). This variation in x reflects the transition from migration along the effective field to migration along each field as the pulse time increases. The migrative path for intermediate pulse times is hard to ascertain. Parts of the molecules will respond by stretching out along each field component and the resulting center-of-mass path will be complex. A crude but reasonable assumption is that for any Tp the migration of the center-of-mass during each pulse occurs in the direction of largest anisotropy of the molecule (least friction), Le., the isoclinic direction (by analogy with the behavior in a constant field where the direction of migration and the direction of maximum orientation always coincide). The angle x will then give the average direction of migration relative to the effective field in each pulse, and LD, is a measure of the average resistance along this direction. Under this assumption LD, reflects friction for migration along the actual path while uaPpis the velocity along the net path. In the limit of short pulses they are identical, but as the pulse time increases the actual path becomes proportionally longer. If the LD, curves were corrected for this effect, to correspond to apparent velocities, they would be shifted downward (except at T = 0.1 s) and more so the longer the Tp. Indeed, for long pulses the LD, coincides at 90' and 120° (Figure 13b), which indicates that the velocities along the real path are equal and that the difference
Reorientational Dynamics and Mobility of DNA T2 9 oo
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Figure 13. Average of LD for one pulse cycle vs pulse time. (a) Timeaverage LDC" and LDiy for T2 DNA at 90' calculated from the curves shown in Figure 8 where the transients have decayed. Average LD, was calculated according to eq A2 in the Appendix. (b) Average LD, vs T, for T2 DNA pulsed at 9O0 and 120O. (c) Average LD, vs Tp for T2, N4, and T7 pulsed at 90'. Inset shows the pulse times that give minima in LD, vs DNA size L. All figures are restricted to pulse times smaller than t,. For longer pulse times average LD, increases as 1 - 1 / T , toward I.
seen in apparent velocities (Figure 11) is a pure geometrical effect, as is suggested also by the good agreement between the apparent velocities and the velocities (stars) calculated, with regard to this effect, from the steady-state mobilities. At intermediate pulse times the geometrical effect is in principle calculable from the average value of x (if the assumption that this coincides with the true average direction of migration is correct). At the LD, minima of T2 at 90° and 120°, the average values of x are 20° and 40°, respectively, which give velocities along the actual path (x)which are 6% and 30% higher than uaPp. As the calculations of the averages of both LD, and x are rather crude, no effort has been made to correct the LD, curves. We simply note that such a correction moves the LD, minima toward longer pulse times, more so at 120° than at 90°,which makes their positions even closer to those observed for the velocity minima. There is also a second effect that may distort the LD, curves compared to the velocity curves, namely, the unknown relation between LD and frictional coefficient, which is an average of the complex orientational distribution indicated for reorienting DNA. A crude estimate of the velocity that corresponds to a certain LD during pulsing can be made in the following manner. The minimum LD, values for T2 DNA at 120' and 90' were used to calculate the equivalent field strengths needed to produce the same LDs in steady-state migration.22 The steady-state mobilities (Figure 12) in these fields were in turn used as an approximation for the mobilities of the DNA conformation at these minima. The minimum in the velocities derived from LD in this way is deeper at 120' than at 90°,in agreement with measured velocities, but both are lower than the measured velocities by a factor of ap-
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3837 proximately 2. A direction of migration other than x cannot account for the discrepancy since this should lead to even lower LD-derived velocities. The differences, then, most likely lie in differences in orientational distribution (for a given LD) in DNA during migration in steady and pulsed fields. The unavoidable coupling during pulsing, between relaxation in one direction and buildup in the other, probably produces a distribution of molecular shapes different from that in steady-state migration. For example, the occasional U-shaped conformation, seen during steady migration,ls which contributes strongly to the LD but has low mobility, may never have a chance to develop during pulsing. It should also be pointed out that the relative magnitudes of LD, for the different DNA molecules cannot be expected to be the same as for velocity since the field dependence in LD, but not in mobility (Figure 12), is different for different sizes of DNA. This is clearly seen in Figure 13c for T p = 0.1 s where the LD, values of the three D N A molecules are different in spite of the fact that they only sense the effective field (constant) where their mobilities are equal (Figure 12). Kind of Motion. If it is assumed that the critical pulse time (0.1 s), when the DNA senses the effective field, is determined by the orientation time of an "effective orienting element" (the smallest part that is able to affect the orientation of the whole molecule), then an estimate of the size of the smallest part can be obtained from comparison with electric orientation of short DNA in gels.39,40 From these studies, a response time of 0.1 s in a 1% agarose gel at 5 V/cm can be expected for a fragment of about 4000 bp. This is in fair agreement with the 2000 bp estimated in a 1% gel for the leading ~egment,~' the head, in biased reptation theorys-IO of DNA gel electrophoresis. According to this theory, the size of the head is assumed to be independent of molecular weight, as is indeed observed for the critical pulse time (between 40 and 166 kbp, Figure 9). In order to be transferred to the whole molecule, the orientation of the leading part in a new direction must be locked by the matrix which probably requires a translation over a distance corresponding to one pore diameter. From the velocity range 0.2-0.4 cm/h at T p = 0.1 s (Figure 1 l ) , the DNA is calculated to travel 0.5-1 .O average pore diameter (1000 8, at 1% gel) in 0.1 s, depending on the pulse angle. The possibility that the critical pulse time is governed by translation rather than by the reorientation of the head cannot, therefore, be excluded. Neither can it be excluded that the DNA molecules used in this study are too short to be in the reptation regime and that they move instead in a nonentangled way through the gel pores. Concluding Remarks. The fair agreement in crossed pulsed fields between LD predicted velocities (based on intermediate coils) and measured ones supports the existence of a relaxed coil as the dominating intermediate step during pulsing, for the DNA sizes used in this study (a coiled intermediate shape is probably not true for much longer DNAIs). In such a case, the minimum in mobility is obtained by shifting the direction of the electric field fast enough to avoid large extensions in any direction, but slowly enough to avoid migration occurring only along the effective field. The optimum pulse time is then determined by a trade-off between the times for the fast relaxation of the orientation in the old direction and the comparatively slow growth in the new one (see Molecular Shape during Reorientation between Steady States). A relation between minima in orientation and mobility has also been found in field inversion gel electrophoresis for DNA between 40 and 680 kbp26which points to the possibility that separation of intermediate-sized DNA molecules in both crossed-field and field-inversion techniques is based on the same basic principle, namely, that the pulsing keeps the molecules coiled. In the section Influence of Pulse Angle on Reorientation between Steady States it was suggested, on the basis of the result in Figure 6, that a pulse angle of 120' combines the mechanism at 90' (a coiling nearly (39) Stellwagen, N. C. J . Biol. Struct. Dyn. 1985, 2, 299. (40) Parus, S. J.; Schick, R. A.; Matsumura, M.; Morris, M. D. Anal. Chem. 1988,60, 1632. (41) Hervet, H.; Bean, C. P. Biopolymers 1987, 26, 727.
3838 The Journal of Physical Chemistry, Vol. 94. No. 9, I990 unaffected by the field) with that at 180' (a coiling driven by the field). The result should then be a more efficient coiling at 120' than at 90°, which may explain why the minimum in mobility in Figure 1 1 is deeper at 120' than at 90'. The better separation at 120" than at 90' is due to the depth and position in the minimum in mobility being much more sensitive to molecular weight at the larger angle (Figure 11). A comparison of this aspect of the velocity with LD requires measurements of LD and LD4, at 120' for N 4 and T7 which, with present DNA concentrations, give very low signals at this angle. When loads are increased even more than in this study, DNA-DNA interactions may become important, and these experiments are, therefore, left to a forthcoming paper. Acknowledgment. We thank Professor Bengt Nordin for his never-failing interest in this work and the design of the dichrometer, Professor Schellman and co-workers for helpful discussions and suggestions, Mr. Tore Eriksson for constructional work and technical assistance, and Dr. Marc Lalande for providing the DNA. We are also grateful to Pharmacia LKB Biotechnology Co. for generous gifts of equipment and chemicals. The work has been supported in part by the National Swedish Board of Technical Development.
Appendix In general terms the absorption of a sample is described by the dipole strength matrix D:*' Dxx
DXY
Dxz
in that the absorption A, of light with polarization vector v is given by A , = KvDv (AI) where K is a constant for a given wavelength. The laboratory fixed coordinate system is X,Y,Z. The geometric representation of the dipole matrix is known as the absorption ellipsoid, which describes the absorption properties of the sample by its dimensions and orientation. For example, the maximum absorption and the polarization direction for which it occurs are given by the length and orientation of the longest axis of the ellipsoid. In this appendix we will show how, with some simplifying assumptions, the measurements of LD and LD,, can be combined to give dimensions and orientations of the absorption ellipsoid relevant for the interpretation of pulsed electrophoresis of DNA. The absorption ellipsoid is analogous to the ellipsoid of the refractive index,42and this formal analogy in the mathematical structure allows us to draw on the paper by Oriel and S ~ h e l l m a n on , ~ ~the case of (42) Norden, B. Appl. Specrrosc. Reo. 1978, 14, 157.
Akerman and Jonsson (nonuniaxial) flow birefringence. Since all forces that influence the DNA molecules have a horizontal mirror plane (gel surface and gravitation effects omitted), one main axis of the absorption ellipsoid must be along the vertical ( 2 )axis, which reduces D to the form43 Dxx
DXY
0
D = [ F
o"yy
;zz]
where X is the chosen reference direction and Y is orthogonal to X and 2. Furthermore, D will be diagonalized in a coordinate system ( x y Z ) obtained by rotating the XYZ system an angle x (the isoclinic angle) around the Z axis (in the plane of the gel) Dxx 0
0
.=[: ODY izz1 where the absorption properties are now characterized by the dimensions of the ellipsoid (Dxx,DyyrDzz) and by its orientation in space ( x , Z ) . To fully determine the absorption ellipsoid for a system with this symmetry, four absorption measurements (which may include isotropic absorption) are needed (cf. the full determination of the refractive index ellipsoid for the nonuniaxial flow orientation in a cylindrical For this it is necessary to propagate light in two directions through the sample, which is not possible in our case since the slab gels used in this study do not allow light to be propagated horizontally through the gel. With only a vertical beam, the projection of the ellipsoid in the gel plane, Le., its orientation ( x ) relative to the X direction and its principal LD, LD, = D , - Dyyrcan be determined from measurements of LD (=D, - Dw) and LD45(=2Dxy).27 The appropriate equations have been derived by Oriel and S ~ h e l l m a n : ~ ~ tan 2 x = LD,5/LD LD, = LD cos 2%
+ LD,,
(A2a) sin 2 x
(A2b)
From eq 3 and A2 it follows that LD, factorizes in the same way as LD and LD4, and with the same optical factor: LD, = 3S,((3C0s2 a ) - 1 ) / 2
('43)
S , describes the average orientation of the helix axis relative to the x direction, and eq A2 also gives the simple result that SX2 = S2 S452.The maximum LD is used as a measure of the effective friction coefficient (see main text) of a given state. Therefore, LD, is the interesting parameter as long as the orientation in the Z direction is less than in the x direction. This can be expected since all forces in the vertical direction are negligible.
+
(43) Oriel, P.;Schellman, J. A. Biopolymers 1966, 4 , 469.
