Anal. Chem. 1995,67, 1132-1138
DNA Conformational Dynamics in Polymer Solutions above and below the Entanglement Limit Xuelong Shi, Richard W. Hammnd, and Michael D. Mods* Department of Chemistv, The University of Michigan, Ann Ahor, Michigan 481 09-1055
Video microscopy of nucleic acids (DNA) undergoing electrophoresis in hydroxyethyl cellulose (HEC) sieving buffers demonstrates previously unobserved shapechanging interactionsbetween DNA and HEC molecules. We provide the fkst visual demonstration of entanglement between DNA and one or several discrete HEC molecules, which has been postulatedto occur in ultradilute p o w e r solutions. Qpically, nucleic acids appear to become entangled with HEC at a single region only, in both dilute and fully entangled HEC solutions. Fluctuations of the center of mass velocity of a DNA molecule and its correlation with conformation are revealedfrom analyses of the image data. These observations account for the success of recentry reported rapid, high-resolutiondc and pulsed-field capillary electrophoretic separations of nucleic acids in ultradilute hydroxyethyl cellulose solutions and hydroxyethyl cellulose/poly(elhylene oxide) solutions. Capillary electrophoresis in buffers containing solutions of linear polymers (commonly called sieving buffers) is increasingly important for separation of both single-stranded and doublestranded DNA.' Of the various polymers used in sieving buffers, derivatized cellulose appears to be especially attractive because the low viscosities of cellulosecontainingbuffers allow high-speed separations. Recently it has been shown that good separations are possible at cellulose concentrations near2and at least an order of magnitude below the entanglement limit.3 Field inversion functions to decrease bandwidths and improve resolution even under these ultradilute buffer condition~.~,~ These fmdings are at variance with conventional theories of gel electrophoresis in sieving buffers. The conventional theories postulate networks of interlocking structures through which nucleic acids migrate either as spheres able to fit through the openings in the network (Ogston model)6or, if they are too large, then by reptati~n.~ Viovy and Duke8 have attempted to explain electrophoretic behaviors of DNA in ultradilute polymer solution by a variant of the Ogston model. They concluded that nucleic acid separations are possible in nonentangled polymer solutions as long as individual polymer chains function as obstacles around which the DNA molecules must travel. Barron et al.233abandoned the (1) Cohen, A S.; Smisek, D. L.; Keohavong, P. Trends Anal. Chem. 1993,12, 195-202. (2) Barron, A. E.; S a n e , D. S.; Blanch, H. W.J. Chromafgr. 1993,652,3-16. (3) Barron, A. E.; Blanch, H. w.; Soane, D. s. Electrophoresis 1994,15,597615. (4) Kim, Y.; Morris, M. D.Anal. Chem. 1994,66, 3081-3085. (5) Kim, Y.; Moms, M. D. Anal. Chem. 1995,67, 784-786. (6) Ogston, A G. Trans. Faraday SOC.1958,54, 1754-1757. (7) Lerman, L. S.; Frisch, H. L. Biopolymers 1982,21,995-997. (8) Viovy, J.-L.; Duke, T. Electrophoresis 1993,14,322-329.
1132 Analytical Chemistry, Vol. 67, No. 6, March 75, 7995
conventional descriptions and proposed that individual nucleic acids entangle with one or more discrete cellulose molecules and drag them along. Separation occurs because the probability of entanglement between DNA and cellulose molecules increases with the length of the DNA chain. They suggested that this interaction, which they call transient entanglement coupling, represents a different mode of nucleic acid-buffer interaction than has previously been proposed or observed. The successful separation of long chain DNA by capillary electrophoresis and the beneficial effects of field inversion at HEC concentrations well below the entanglement threshold4s5 are consistent with shape- and mobility-changhg interactions. However, the electrophoretic results by themselves do not confirm or refute the view that the interactions or nucleic acid dynamics are different above and below the polymer entanglement limit. The exact mechanism of capillary electrophoresis in ultradilute polymer solutions remains unclear. Earlier workers have employed video microscopy to study nucleic acid migration and separation mechanisms during dc9J0 and pulsed-field electrophoresisll through agarose gels and fully entangled linear polyacrylamide.12 Generally, nucleic acids are found to take tortuous paths through gels. A typical motion involves movement of the chain around a fixed obstacle. Recently, Perkins and co-workers have employed video microscopy to compare nucleic acid dynamics in Newtonian fluids (Le., where the molecule interacts with no other polymer) and fully entangled DNA solution^.^^ When DNA was dragged through entangled solutions, long-lived loops and coils were formed. But isolated DNA molecules in a Newtonian fluid formed only kinks which rapidly disappeared. To our knowledge, there have been no attempts to visualize nucleic acid dynamics in dilute polymer solutions in which a nucleic acid might interact with isolated polymer molecules, or a small cluster, rather than with an extended network. In this paper, we report experiments using fluorescence microscopy to investigate nucleic acid motions under electrophoretic conditions in hydroxyethyl cellulose solutions both above and below the entanglement limit. EXPERIMENTALSECTION
The experimental apparatus was similar to that employed by Smith? An Olympus BH-2 epifluorescencemicroscope fitted with a Reichert 50x-/1.0 water immersion objective and a Photometrics Sw-1 scienti6c CCD camera was used to record the images. (9) Smith, S. B.; Aldridge, P. IC; Callis J. B. Science 1989,243,203-206. (10) Schwartz, D. C.; Koval, M. Nature 1989,338, 520-522. (11) Rampino, N. J.; Chrambach, A Biopolymers 1991,31,1297-1307. (12) Rampino, N. J.; Chrambach, A /. Chromatogr. 1992,596,141-149. (13) Perkins. T. T.; Smith, D. E.; Chu, S. Science 1994,264,819-822.
0003-2700/95/0367-1132$9.00/0 0 1995 American Chemical Society
Illumination was with 10 mW, 532 nm light from a frequencydoubled CW Nd-YAG laser, whose output was passed through a coil of optical fiber. The fiber was mechanically vibrated to break up laser coherence. The nucleic acids used were yeast chromosomes (New England Biolabs, PFG Marker, 225 kbp-1.9 Mbp). To prepare solutions, slices of the agarose plug containing 1pg of DNA were dissolved in 250 pL of 1x TBE by warming at 65 "C for 3 min. To the solutions was added 10 p L of ethidium homodimer I (0.1 pg/ pL, Molecular Probes) for fluorescence visualization at 617 nm. The electrophoresis medium was 0 . 5 ~TBE buffer containing hydroxyethyl cellulose (HEC, MW = 438 800) at concentrations of 0.03%-0.5% (w/w), depending on the experiment. This range brackets the nominal entanglement threshold, determined as 0.09% (w/w) where the plot of log specific viscosity as a function of log polymer concentration starts to deviate from slope of l.0.213HEC solutions were gently stirred for 6 h before use to ensure complete dissolution and homogeneity. Sucrose (50%-60% (w/w)) was added to the buffers to increase viscosity and slow motions for detailed observation. Neat 2-mercaptoethanol was added to make the solutionsto 4% by weighs this was used to reduce the breaking of DNA molecules due to photosensitization of the dye-DNA complex with lightell M e r addition of sucrose and 2-mercaptoethanol, solutions were stirred for 12 h. The viscosities of the TBE/HEC/sucrose solutions were measured with an Ostwald viscometer at 25 "C. The DNA solution for observation was prepared by mixing 5 pL of DNA stock solution and 95 pL of TBE/HEC/sucrose solution with final concentrations of DNA and ethidium homodimer of about 0.2 pg/mL. The combined solutions were stirred on a Vortexer for 1 min. A 5-10 p L aliquot of DNA solution was pipetted onto a microscope coverslip, over which a second coverslip (22 x 22 mm2) was placed to define a thin layer of DNA solution. Both coverslips were previously coated with linear polyacrylamide to eliminate electroosmosis, according to the procedure of Hjerten.15 The enclosed DNA sample was then placed on a microscope slide with electrodes cemented to it, which completed the electrophoresis chamber. The electrophoresis voltage was provided by a high-voltage operational amplifier (Apex 85M) configured as a 50x inverting amplifier and driven by a digital/analog converter programmed by a laboratory computer. Observations were made at 25 and 100 V/cm fields. Although no electrophoretic separations were performed, care was taken to limit observations to isolated DNA molecules which were positioned far from the surface of the slide or cover glass. Due to the limited viewing area of our microscope, it was difficult to follow the conformation dynamics of a given DNA molecule on a large spatial scale. Therefore, complete quantitative analysis of the image data was not feasible. However, some semiquantitative analysis is possible. To analyze DNA motions, quantities characterizing migration velocity and conformation of a DNA molecule are defined according to Oana et The position vector (rx,rJ of the center of mass of a DNA molecule is defined as (14) Freifelder, D.; Davison, P. F.; Geiduschek, E. P. Biofihys.1.1961, 1, 389400.
(15)Hjerten, S. J.J. Chromafogr. 1985, 347, 191-198. (16)Oana, H.; Masubuchi, Y.; Matsumoto, M.; Doi, M.; Matsuzawa,Y.; Yoshikawa, K Macromolecules 1994, 27,6061-6067.
X
Y
where
(3)
and ZCv,y,t.) is the image intensity at point (XJ) and time t. From the series of data 7(t),the center of mass velocity v&) along the applied field is computed according to eq 4.
v,(t> =
r,[t
+ (1/2At>l- r,[t
- (1/2At)l
At
(4)
To correlate the center of mass velocity with the conformation of DNA, radii Rl and R, (R1>R$, which are along the two principal axes, respectively, are calculated as
Physically, RI and R, represent the dimensions of the DNA molecule along the two principal axes. In eqs 5 and 6, MLI,Myy, and Mxy are the components of the two-dimensional radius of gyration tensor, defined as (7)
X
Y
The time development of V,,RI,and R, reveals the characteristics of DNA motions. The data processing was performed using IPLab (Signal Analytics Corp., Vienna, VA). RESULTS AND DISCUSSION
In order to use our scientific CCD camera for studies of nucleic acid dynamics, it was necessary to slow DNA motions so that detailed observations could be made at one frame every 2-4 s. By capillary electrophoresis we confumed that addition of glycerol or sucrose to the sieving buffer solution reduced mobilities, as expected, but had no other effects on electrophoresis. In particular, there was no electrophoretic separation for restriction enzyme fragment mixtures in TBE buffers containing varying amounts of glycerol or sucrose but no sieving polymers. Thus, we concluded, as did Perkins et al.,I3that viscosity modification can be used in dynamics experiments to make the time scale consistent with the camera frame rate. Analytical Chemistry, Vol. 67, No. 6, March 75, 7995
1133
4-
-0.8
3-
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. s 0
5
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2-
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,
, 4
,
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8
,
, 12
,
, 16
,
, 20
,
, 24
,
,
,
28
32
,
, ‘ o 36
time, sec
Figure 1. Time sequence of yeast chromosomal DNA electrophoresis in 0.5% HEC, 50% sucrose, and 0 . 5 ~ TBE solution at 25 V/cm field, showing conformational transformation. The frames were taken at 4.0 s intervals (left column, followed by right column). Contrast is inverted (fluorescent regions black) for clarity. The migration direction is indicated by an arrow, and the scale bar represents 10 pm.
When samples were placed between cover slips, there was frequently some DNA movement as the system came to mechanical equilibrium. The direction varied with the details of assembly, and the sample took as much as 1 h to come to mechanical equilibrium. No experiments were performed until the system came to rest. When a field was applied, DNA motion was always in the direction of electrophoretictransport, and opposite to the expected direction of electroosmosis, if it were present. Because the surfaces of the coverslips were coated with neutral molecules, these observations confirm that electroosmsois was absent or very slight. While care was taken to keep mixing gentle to avoid shearing DNA, it is possible that some shearing might have occurred. Because the molecules were never fully extended, the apparent lengths of partially extended molecules were consistent with the existence of intact DNA, whose contour lengths were in the expected range of 75-650 pm. In any event, our observations were on mixed length nucleic acids. Of necessity, interpretations of their dynamic behavior can only be qualitative and not dependent upon exact knowledge of chain length. Figure 1shows an example of the timeresolved electrophoretic behavior of an isolated DNA molecule in 0.5% HEC solution (viscosity, 1950 cp; average mesh sue, 226 A). This HEC concentrationwas chosen to be well above the HEC entanglement threshold, 0.09%.3 Although viscosity is a useful parameter to characterize.thepolymer solution, we have to keep in mind that the DNA electrophoretic mobility cannot be simply scaled with the inverse of viscosity of the polymer solutions, as evidenced in the results of Barron et al.? because of the continuous conformation change of DNA during migration. At 25 V/cm, a DNA molecule frequently underwent conformational transformation from a compact irregular mass to a U-shaped form, as shown in the first few frames of Figure 1. The transformation usually began at a single region of the molecule, from which two arms of the extending DNA molecule emerged and grew. It was frequently observed that one arm finished stretching earlier than the other, to give an asymmetric configuration. As soon as one of the arms completed its stretching, it started to retreat back along the stretchingpath until the molecule slipped off the vertex. The final stage of this process is visible in the last frame of Figure 1. In almost all of our observations, the 1134 Analytical Chemistry, Vol. 67, No. 6, March 15, 1995
Figure 2. Example of time development of V,, 6, and Rs of yeast chromosomal DNA during electrophoresisin 0.5% HEC, 50% sucrose, and 0 . 5 ~TBE solution. The field strength is 25 V/cm.
conformation of entangled DNA was a U or V, not a W, suggesting a single region where the DNA was entangled with the HEC network. The center of mass velocity of a DNA molecule was found to change during migration, as shown in Figure 2. A nucleic acid slowed down when it encountered an obstacle. It speeded up immediately after it broke free of the obstacle because of the quick release of the stored elastic energy. The correlation between conformation and center of mass velocity was demonstrated by the correlation between R1 and 6. Both RIand 6 fluctuated when the DNA molecule went through a conformation change, while Rsremained relatively constant. These observations were consistent with what has been observed in gel electrophoresis.16 Among the observed U-shaped DNA molecules, some DNA molecules (about 30%)went through conformation change with their apexes moving slowly in the migration direction (-0.08 pm/ s) and the curvatures of the U-shaped DNA molecules around the apexes remaining nearly constant (-1 pm-l), while others changed with their apexes moving relatively faster (-0.2 pm/s). The slow motion of the apex for some DNA molecules was not due to adhesion of DNA to the glass surface. If it were, one would not be able to see the DNA molecule sliding around the apex while it slipped off the obstacle. Clearly, the apex was the region where the DNA was entangled with the HEC network. The difference in apex migration velocities between DNA molecules may imply the inhomogeneity the of polymer network. Regardless of the apex velocity, the heads always moved faster than the apex. For a DNA molecule with a slowly moving apex, one or both of the heads could move as fast as 0.4 pm/s. For a DNA molecule with a relatively faster moving apex, the heads also moved at a velocity of about 0.4 pmls. This velocity difference between the faster moving head and the apex reflected the large resistance force at the apex, suggesting that the polymer network in 0.5% HEC solution was semirigid. Semirigidity is expected in polymer solutions at concentrations well above the entanglement limit, since the number of entanglement points available for each HEC molecule is large. The observed dynamic behavior of DNA under electrophoresis is similar to that seen in an agarose matrix:-11 which has been modeled as a random array of rigid posts.17 When the field was increased to 100 V/cm, DNA molecules became more fully aligned in the field direction and more elongated (Figure 3), as predicted by Deutsch for the rigid (17) Deutsch, J. M.Science 1988,240,922-924.
Figure 3. Time sequence of yeast chromosomal DNA electrophore~ solution at 100 V/cm sis in 0.5% HEC, 50% sucrose, and 0 . 5 TBE field. The image series shows the movement of apex and the change of the apex angle of the U- or V-shaped molecule. The frames were taken at 3.0 s intervals. Contrast, migration direction, and scale bar as in Figure 1.
network case.17 Interestingly, the apex of a V- or a U-shaped molecule always moved more rapidly (-0.7 pmls), and the apex angle could change appreciably at higher fields, from 5" to 60" for example. The displacement of the apex could be as much as 12 pm before the molecule slipped off the obstacle, as shown in the last frame of Figure 3. The elasticity of the network cannot possibly account for this large displacement or the change in the apex angle, because the contour length of HEC is only -0.8 pm. If this large apex displacement were due to a collective effect involving many HEC molecules, the apex velocity would be expected to decrease with time because of the increased force required to extend the network further. Instead, our measurements showed relatively constant velocity of the apex. We attribute the apex displacement and angle change to partial rupture of the network, caused by the strong force exerted by a DNA molecule on the entangled HEC molecules with which it is in direct contact. This disruption would lead to changes in the entanglement of a nucleic acid with HEC and can be thought as another kind of "constraint release" through direct interaction between DNA and the network instead of the conventional constraint release due to spontaneous fluctuations of the network structure, as originally proposed by de Gennes.18 At 0.16%HEC (viscosity, 161 cp; average mesh size, 531 A), slightly above the entanglement limit, DNA molecules migrated in two distinct conformations at 25 V/cm (Figure 4). One was the U- or V-shaped conformation, idenaed by the left vertical arrow in F i r e 4A The other was a slightly elongated conformation (right vertical arrow, Figure 4A) in which most of the molecule remained in a compact ball. The curvature of the U-shaped molecule at the apex was around 0.9 pm-l, while the apex angle of a V-shaped molecule could vary in the range between 30" and 70". The apex of a U- or V-shaped molecule moved more rapidly (about 0.7 pmls) in 0.16% than in 0.5% solutions. The apex velocity increase could be partly attributed to the decreased viscosity of the polymer solution. However, an (18) De Gennes, P. G. J. Chem. Phys. 1971,55,572-579.
important quantity, the velocity difference between the apex and the head, could reflect the network differences between polymer solutions of different concentration. In 0.16%HEC solution, the velocity of the head is only 10%-15%greater than that of the apex, indicating a smaller resistance force at the apex and a weaker network compared to those in 0.5%HEC solution. As in the more concentrated solutions, the motion of a DNA molecule in the Uor V-shaped conformation was similar to conventional reptation motion through a matrix of fixed obstacles or openings. The center of mass velocity for the U- or V-shaped DNA molecule also fluctuated during migration as in the more rigid 0.5% HEC solutions. When the DNA molecule migrated in the slightly elongated form, it often had a slim leading head followed by a massive globular tail (Figure 4A). A DNA could migrate in this form for tens of micrometers before it was transformed into a U- or V-shaped conformation. This observation suggests that not every encounter between a HEC molecule and a DNA results in formation of a U-shaped complex. Some parts of the network can be very weak because of loose entanglement between HEC molecules, even though it is possible to form a complete polymer network at 0.16%HEC. At 100 V/cm, more elongated shapes were observed (not shown), and migration of the apex was faster, much as in the more concentrated HEC solution. We observed DNA motion in 0.032%HEC solution (viscosity, 65 cp), which is a concentration well below the 0.09% HEC entanglement limit (Figure 5). At 25 V/cm, most of the DNA molecules were slightly deformed globes or nascent U-shapes, with short arms, as shown in Figure 5, but some were V-shaped with appreciable size. On average the DNA chains were less extended and the V-shaped DNA molecule had shorter lietimes than those in higher concentration polymer solutions. The existence of those extended conformations demonstrates interaction between DNA and some relatively large obstacle. At 100 V/cm, the deformed globular molecules became highly elongated. These elongated DNA molecules in 0.032%HEC solution had an inhomogeneous fluorescence distribution along the molecule, suggesting that some coiled regions remain. In this dilute HEC solution, it is impossible to form an extended entangled HEC network. However, there may exist some HEC clusters which could act as a local network. An individual HEC molecule, or if it exists, an HEC cluster, can be considered to be a floating obstacle, with which DNA becomes entangled, as Our observations are consistent with suggested by Barron et al.2~~ the hypotheses that the DNA/HEC aggregates are labile3and that not all collisions lead to formation of an aggregate. However, our measurements are not sufficiently detailed to allow estimation of lifetimes or lifetime extrapolation to low-viscosity sugar-free solutions. The deformed globular conformations in Figure 5 also arose from the interaction between DNA and HEC molecules, because no such conformationscould be found in 0% HEC solution. These shapechange interactions can be important for DNA separations in the dilute polymer solutions. Shapechange interactions are also suggested by the improved separation of DNA fragments using pulsed-field capillary ele~trophoresis.4~~ Simple transient entanglement between DNA and HEC molecules, without changing DNA shape and breaking its nearly spherical symmetry, should not be effective in introducing size dependence of elecAnalytical Chemistry, Vol. 67, No. 6, March 15, 1995
1135
&-
‘
.
--
,
Figure 4. Time sequence (A-F) of yeast chromosomal DNA electrophoresis in 0.16% HEC, 55% sucrose, and 0 . 5 TBE ~ solution at 25 V/cm field. Frames at 4.0 s intervals; contrast, migration direction, and scale bar as in Figure 1. The downward arrows identify the apex,or starting positions of two molecules. The movement of the apex of the U-shaped molecules is visible. .. ..
Figure 5. Time sequence (A-D) showing the existence of both small U-shaped molecules and deformed global conformations for yeast chromosomal DNA molecules undergoing electrophoresisin 0.032% HEC, 60% sucrose, and 0 . 5 TBE ~ solution at 25 V/cm field. Frames at 4.0 s intervals; contrast, migration direction, and scale bar as in Figure 1.
trophoretic mobilities. For such a case, both the electric force and the frictional force experienced by a randomly coiled DNA molecule are still proportional to DNA size as it is in free solution, resulting in sizeindependence of electrophoretic mobility. Although the conformation change of a DNA molecule in 0.032%HEC solutions was not as dramatic as those in higher concentration polymer solutions, fluctuations of VX and R1 as well as the correlation between these two quantities were still prominent enough to be observed, as shown in Figure 6. These fluctuations are probably characteristic of DNA motions in polymer solutions, even in dilute polymer solutions. The small but observable conformationfluctuations which were reflected in fluctuationsof Rl(t) must originate from the interaction between DNA and HEC molecules. Initially, it seems surprising that interaction of DNA with a single HEC molecule or even a small cluster should be sufficient to cause readily visible extension of DNA. Yet a simple calculation of the frictional force exerted 1136 Analytical Chemistry, Vol. 67, No. 6, March 15, 1995
by HEC on the DNA suggests that some extension of DNA should occur. The drag force Ff needed to pull one HEC molecule along with a DNA molecule can be estimated using hydrodynamic theories.
F,=
5%
(10)
The friction coefficient 6 of a non-freedraining polymer molecule can be calcidated according to the following equation:19
9n3’2
5 =T o r
(11)
where r is the radius of gyration of HEC molecule and 70is the (19) Yamakawa, H.Modem Theory of Polymer Solutions; Harper & Row: New York, 1971.
1
0.8
0.6
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0.4
1 0
0.2
4
~
1
2
1
B
Z
Q
Z
4
2
8
3
2
3
6
4
0
4
4
4
6
D ~ U
time, sec
Figure 6. Example of time development of V,, 9, and Rs of yeast chromosomal DNA during electrophoresis in 0.032% HEC, 60% sucrose, and 0 . 5 TBE ~ solution. The field strength is 25 V/cm.
solution viscosity. If the HEC molecule is assumed to be spherical, its radius of gyration can be estimated to be around 115 nm using the Porod-Kratky m ~ d e l . Assuming ~ , ~ ~ that the HEC molecule is dragged with a velocity of 1pmls in a solution with viscosity of 50 cp, then the frictional force can be calculated to be around 0.07 pN according to eqs 10 and 11. This force is large enough to extend the entangled DNA about 16 pm, from the measurements of the force-extension curve of Smith et al.21 In an aqueous solution which is usually used in DNA electrophoretic separation experiments, a similar drag force would be expected because the decrease of the solution viscosity will be compensated by an increase in the migration velocity of DNA as long as the electric field remains the same. One should be careful in estimating the DNA extension during electrophoresis using the force-extension data of Smith et al., which were obtained under very different conditions. In their experiment, one end of the DNA is stationary (a boundary with zero velocity) and the other end is pulled (external force acting on single point); therefore, the force-extension curve was obtained under static conditions. In other words, the extension is only dependent on the magnitude of the force, regardless of how fast each part of the DNA responds to the force applied at the end. In contrast, every part of the DNA molecule can move in response to an external force in dilute polymer solutions under electrophoresis conditions. In this case, the extension is dependent not only on the magnitude of the force but also on how fast each part of the DNA responds to the force. In other words, it is essentially a dynamic problem. In a dynamic situation, the extension of DNA is always less than that found in a static situation under the same force. Although our estimation shows too great an effect, the force introduced by entanglement of even a single HEC with DNA is probably large enough to cause some DNA conformation change. Of course, if the obstacle is an HEC cluster, the DNA conformation change would be greater. In 0% HEC at 25 V/cm, no elongation of DNA could be observed. The molecules remained compact, essentially circular masses. Surprisingly,DNA molecules became slightly but visibly elongated along the field direction at 100 V/cm, although they had relatively homogeneous fluorescence distribution, suggesting (20) Cantor, C. R; Schimmel, P. R Biophysical Chemistry, Part 111: n e Behavior of Biological Macromolecules; W. H. Freeman: New York, 1980. (21) Smith, S. B.; Finzi, L.; Bustamante, C. Science 1992,258, 1122-1126.
a uniform coiled configuration. This elongation could be caused by the shear force acting on the relatively rapidly moving polymers. In polymer solutions at all concentrations we have investigated, DNA molecules take either U- or V-shaped conformations or deformed globular conformations in the course of time during electrophoresis. In a highconcentration polymer solution, a DNA molecule spends more time in U-or V-shaped conformations. In a lowconcentration polymer solution, a DNA molecule spends more time in the deformed globular conformations. It seems that the time fraction of each type of conformation varies continuously with the concentration of the polymer. No abrupt change in the DNA behavior was found in polymer solutions around the entanglement limit. These observations are consistent with electrophoretic results of Barron and co-~orkers.~ CONCLUSIONS
DNA electrophoretic motions in concentrated polymer solutions are qualitatively similar to those in agarose gels. As the polymer solution becomes more dilute, segmental motion is still observed, even below the entanglement threshold, as evidenced by the revealed fluctuations of the center of mass velocity of DNA molecule and its correlation with conformations. The small but observable conformation changes of DNA molecules in dilute polymer solutions are most likely due to entanglement of an HEC molecule or an HEC cluster with a DNA molecule. However, neither electrophoresis nor microscopy provides any direct evidence to sustain either the view that the complexes are just mechanically bound or that they are held together in whole or in part by hydrogen bonds. Our observations suggest that the subentanglement complexes are special cases of the same family of DNA conformationchanging complexes, in a broad sense, which are observed in concentrated HEC solutions and even in agarose gels. We do agree with Barron et al.233in describing DNA motions in dilute polymer solutions as caused by formation of entities composed of discrete DNA and HEC chains. While the kinds of motions observed are similar at all HEC concentrations, the probability of a DNA/HEC encounter is a function of HEC concentration, and the lifetime of the resulting complex appears to be concentrationdependent as well. It follows that the same general experimental tactics, such as field inversion, should be useful under a wide range of conditions. In particular, field inversion has been shown to improve resolution of CGE in media as different as cross-linked polya~rylamide,2~~23 linear p~lyacrylamide,~~~~~ and derivatized cellulo~es.~~5 A further implication is that a general theory of DNA electrophoresis covering the entire usable range of sieving buffer concentrations and DNA chain lengths should exist, although the classical Ogston and reptation models may not be the most useful ones even for entangled matrices. (22) Demana, T.; Lanan, M.; Moms, M. D.Anal. Chem. 1991,63,2795-2797. (23) Heiger, D. N.; Cohen, A. S.; Karger, B. L.]. Chromatogr. 1990,516, 3348. (24) Sudor, J.; Novotny, M. V. Anal. Chem. 1994,66,2446-2450.
Analytical Chemistty, Vol. 67, No. 6, March 15, 1995
1137
ACKNOWLEDQMENT
We would like to thank the referees for their thoughtful suggestions and acknowledge the generous assistance of the National Institutes of Health through Grant GM-37006 to M.D.M.
1138 Analytical Chemistry, Vol. 67,No. 6, March 75, 7995
Received for review October 24, 1994. Accepted January 17, 1995.@ AC940978C @Abstractpublished in Adoance ACS Abstracts, February 15, 1995.
