Information Concerning the Mechanism of Electrophoretic DNA Separation Provided by Quantitative Video-Epif luorescence Microscopy NICHOLAS J.RAMPINO Section on Macromolecular Analysis, Laboratory of Theoretical and Physical Biology, National Institute of Child Health and H u m a n Development, National Institutes of Health, Bethesda, Maryland 20892
SYNOPSIS
Changes in conformation, length, and mobility of individual DNA molecules during agarose gel electrophoresis were measured using video micrographs obtained by epifluorescence microscopy. Globular, V-shpaed, and linear conformations of DNA are found. The mobility, upon transformation from the globular to the V-shaped conformation, decreases, suggesting a collision with a gel fiber. The duration of interaction between DNA and gel fiber is proportional to the length of DNA. Hypothetically, this proportionality underlies the size separation of DNA by agarose gel electrophoresis. DNA release from the gel fiber appears to involve the movement of the arms of the Vshaped molecule around the gel fiber. Concomitant with this movement is a length reduction the degree of which is constant for DNA of various lengths in a particular buffer milieu. The luminant densitometric profiles of DNA molecules in the V conformation show maxima a t the ends and apex of the V. The unequal distribution of nucleotides along the DNA chain appears to provide the driving force for the molecular movement around the gel fiber.
INTRODUCTION The visualization of single fluorophore-labeled DNA molecules by epifluorescence microscopy was introduced by Matsumoto et al.’ I t has been applied to agarose gel electrophoresis of DNA by Smith et al.,‘ Schwartz and Koval,3and the present a ~ t h o rPic.~ torial representations of DNA undergoing gel electrophoresis have been r e p ~ r t e d . ~However, . ~ ’ ~ no explicit size or mobility measurements quantitating the dynamics of DNA’s intramolecular geometry during electrophoresis have been reported prior to this work.” Nor has the previous work with videoepifluorescence microscopic monitoring of gel electrophoresis been used to critically assess present theories concerning the mechanism of size separation of DNA in gek7-l3 This work has aimed a t quantitating the conformational and mobility dynamics of DNA during
Hiopolyrnern. Vol 31, 1009-1016 (1991) (r 1991 .lohn Wiley & Sons, Inc
CCC 0006-3525/91/0Sl009-08$04.00
agarose gel electrophoresis. This approach can therefore be termed “quantitative video-epifluorescence microscopy” (QVEM) . QVEM promises t o displace speculative mechanisms of gel electrophoresis by those based on direct measurement of DNA molecules, to be helpful in the interpretation of electrophoretic mobility assays, and to aid in the development of gel electrophoretic media and of optimal separation conditions.
MATERIALS A N D METHODS Sample Preparation
A 0.5% solution of agarose (SeaKem GTG, FMC, Rockland, M E ) was prepared a t 65°C in either 1 X T B E buffer (89 m M Tris, 89 m M boric acid, 2 m M Naz EDTA) o r 0.5 X T B E buffer, containing 0.2 pg mL-’ of DAPI ( 4’,6’-diamidino-2-phenylindole; Molecular Probes, Eugene, OR). A 1-pL aliquot of a n agarose plug containing yeast chromosomal DNA (Pombe, 3, 5, and 6 Mb, Clontech, Palo Alto, 1009
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CA) or 1 ng of unmethylated A-DNA (Pharmacia, Uppsala, Sweden) was dissolved in 30 pL of this solution and maintained at 65°C for 3 min. The yeast chromosomal DNA was then broken through vigorous pipeting to give fragments in the range of contour length of 5-200 pm. 8-Mercaptoethanol (0.3 p L ) was added t o the mixture.’ Gel Electrophoresis
A 5-pL aliquot of the sample was pipeted on a microscope coverslip, covered with another coverslip, and allowed t o cool t o room temperature. T h e sandwich was placed as a bridge across two agarose gel blocks in a glass electrophoresis cell.I4 Electrophoresis was conducted a t regulated field strengths of 5-10 V cm-l a t 24°C across the 2.2-cm gel sandwich. During the study, the composition of the sample was kept constant except for the two changes in buffer concentration. Data Collection and Processing
Fluorescence of individual fluorophore-labeled DNA was monitored during electrophoresis by QVEM as d e ~ c r i b e d . ’An ~ 1800-fold magnification is brought about by use of a 63X microscope objective and display on a video monitor. The brightness of the image derives from a gain of up to 0.5 million achieved by a n image intensifier; this gain was adjusted to give a high-contrast image and remained constant throughout the experiment. Relative luminance of the digitized images was expressed in terms of grey levels, where black = 0 and white = 256. One greylevel unit ( G L U ) is defined as the numerical value of a pixel in terms of relative luminance. Measurements and densitometry were performed on the original video micrographs without any image enhancement. Molecular tracking employed a mouse driven cursor.
stages of the cycle can be distinguished (Figure 2 ) : ( I ) DNA in the globular conformation abruptly decelerates and changes into the V-conformation. (11) The V-shaped conformation can become symmetric; if so, the molecule is temporarily arrested. (111) Asymmetry of the V conformation progressively develops as mobility increases. At the end of this stage, DNA is linearly extended with the end of the retreating arm coincident with the apex. ( I V ) The extended DNA molecule condenses back progressively to the globular conformation, during which time the mobility becomes maximal. The cycles of a given DNA molecule are repeated but not indefinitely. In time, unless the field is appropriately pulsed, some large DNA molecules (approximately 10% of those in excess of 20-50 pm in length) become irreversibly arrested under the conditions used here.* The arrest, as well as other apparent interactions that trigger the onset of the cycle, take place a t particular locations in the field of observation. Constant locations of ”Apex Positions” and Their Distance from One Another
During stage I, the arms of the V progressively extend a t a rate of 4.5 pm/s (in 0.5 X T B E buffer) and do not appear to be impeded in their elongation. By contrast, DNA molecules in the V conformation are arrested a t constant positions within the frame of the microscope. Arrest is not observed in any but those positions. T h e minimal distance, a t a right angle to the direction of the field, between the positions of the apexes of the V conformations (“apex positions”) is approximately 3.5 pm in areas of the gel selected for absence of geometric perturbations of the V conformation. In the direction of migration, such stationary arrest points are not observed during stage 111. Therefore, no downfield arrest points are observed until V conformations are formed again. Variations in Luminant Density Along an Individual Fluorophore-Labeled D N A Molecule
RESULTS A Cycle of Conformational Changes of D N A During Agarose Gel Electrophoresis
All DNA molecules monitored by QVEM during agarose gel electrophoresis, under the conditions used, undergo a sequence of conformational changes from a globular to a V-shaped to a linearly extended form (Figure 1) . Once linear, the molecule condenses back to a globular conformation while migrating. T h i s sequence of events is termed a cycle. Four
DNA molecules in a representative video frame are selected that maintain their integrated luminant density throughout their conformational cycles.+ Under observation by QVEM, all DNA molecules exhibit nonhomogeneous luminant density along
* This 10% loss of migrating DNA due to arrest may explain the decrease of band area in the absence of pulsing in Fig. 1A of Ref. 23. This is done to distinguish perspective effects from intramolecular redistribution of luminant density.
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MECHANISM OF ELECTROPHORETIC DNA SEPARATION
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Distance (pm) Figure 1. Cycle of conformational changes of a representative DNA molecule during agarose gel electrophoresis: DNA was sheared S. pornbe chromosome. Agarose gel electrophoresis ( 1 X TBE buffer, 24"C, 5 V / c m ) . Left panel: video micrograph. Right panel: Luminant density profiles of the DNA chain. A: globular DNA. B: Asymmetric V conformation. T h e shorter ( t o p ) arm has the highest luminant density a n d leads in the direction of migration. C: DNA molecule slipping around the apex, the position of which is stationary. Nucleotide concentration is elevated a t the apex, presumably due t o a n interaction with a gel fiber. D: Linearly extended conformation; retreating arm coincident with the former apex position. T h e nonhomogeneous distribution of luminant density is maintained throughout the cycle. Bar = 10 fim. Panel designations B, C, and D refer t o both the images a n d the density profiles. T h e two arms of DNA in t h e V conformation shown in image B correspond to the two uppermost luminant density profiles. Likewise, the density profiles aligned horizontally with image C correspond t o the upper a n d lower arms. Distances in the density profiles are measured from the apex position.
their length. One representative DNA molecule exhihiting such a nonhomogeneous distribution of luminant density a t various stages of the cycle is
shown in Figure 1. T h e ends of the molecule are the most luminous; the apex of the V-shaped conformation is also elevated. T h e integrated luminant
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Stage of Cycle
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under the luminant density profiles presented in Figure 1B were 780 GLU for the leading (upper) arm and 735 GLU for the retreating (lower) arm. T h e retreating arm, while maintaining a maximum at the tail end, diminishes in luminant density (560 GLU) a s the leading arm increases (950 GLU) in relative luminant density (Figure 1C). Surprisingly, the luminant density a t the apex of the V conformation appears to remain constant (26 GLU, S E = 0.7, n = 9 ) during stage I11 of the cycle.
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Contour Length Changes upon Transition from the Symmetric V to the Linear Conformation During Stage 111
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Figure 2. Length and displacement rate of the luminant densitometric centroid of DNA during the cycle of conformational changes: Conditions as in Figure 1 except different molecule, 0.5 X TBE buffer. Stage I designates the formation of a symmetric V conformation, stage I1 a lag period, during which the molecule remains stationary, stage I11 the progressive asymmetry of the V conformation coincident with a fixed degree and rate of length reduction, and stage IV the condensation of the linear conformation to the original globular form.
density of the conformational forms shown in Figure 1is conserved: In the example shown, the integrated luminant density of the molecule is 1500 GLU,irrespective of conformation. It is assumed that the relative luminant density is proportional to the concentration of intercalated fluorophore and, consequently, is a measure of the nucleotide density along the DNA molecule. The Redistribution of Luminant Density During the Cycle
During the cyclic conformational change from a globular t o a V-shaped to a n extended DNA molecule, a maximum of luminant density a t the end of both arms of the molecule is preserved. The arm with the higher total luminant density leads in the direction toward the anode. For example, the areas
DNA molecules varying in contour length in the symmetric V conformation from 18 to 64 pm were monitored for contour length ratio between the symmetric V conformation (Figure lB,C ) and the linear conformation (Figure 1 D ) . Independent of their size, the length reduction in going from the V shaped to the linear conformation is 41% ( S E = 3%, n = 4 ) , in 1 X TBE buffer, and 22% ( S E = 1.196,n = 1 2 ) in 0.5% T B E buffer. This decrease in size proceeds a t a constant rate of 4.4 and 2.2 pm/s in the representative cases shown in Figure 3A and B, respectively. T h e condensation rate is higher (7.0 p m / s ) in 1 X T B E than in 0.5 X T B E buffer (compare Figure 3C with Figure 3B ) . The degree of length reduction was independent of field strength within the narrow range used. Length measurements in TBE buffer were compared to ideal values, using A-DNA as a standard. T h e A-DNA in the I3 form of 48.5 kilobases has a calculated contour length of 16.4 pm.I5 In 0.5 X T B E buffer, its measured length in the V conformation is 12.8 pm, or 78% of the calculated value; in the linear conformation, it is 10.0 pm, or 60% of the calculated length. T o interpret the results of this study in terms of base-pair numbers, these factors need to be applied. Dynamics Related to the Angle Between the Arms of the V-Shaped Conformation
The “apex angle” between the arms of V-shaped DNA was measured for selected molecules in the size range of 10-30-pm contour length. Selection is made for molecules presenting maximal apex angles. Presumably, these are molecules oriented parallel t o the stage of the microscope. They represent approximately 1%of those visible on a representative frame. T h e apex angle is larger (29.7”, S E = 0.7, n = 28) for 0.5 X T B E than for 1 X T B E (22”, S E
MECHANISM OF ELECTROPHORETIC DNA SEPARATION
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= 1.0, n = 4) buffer. The orientation of the leading arm, with respect to the axis of the electric field, appears conserved initially when the V conformation changes to the linear conformation (Figure 1) .
The Duration of the Conformational Cycle as a Function of the Length of DNA
The time it takes for DNA to pass through the conformational cycle appears proportional to its effective length (Figure 3A, B ) . This effective length depends on the degree of internal condensation and therefore on buffer concentration. The longer duration of the cycle for longer molecules can be accounted for by the longer dwell-time in the V-shaped conformation (Figures 2 and 3 ) . The increased dwell-time in the V conformation for larger DNA presumably underlies electrophoretic size separation. Average Migration Rates of DNA of Different Sizes Measured on Individual Molecules as a Function of Field Strength and Cycles/ Path Length
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Figure 3. Length of the arms of DNA in the V conformation as a function of time: Leading arm: diamonds; retreating arm: squares. Conditions as in Figure 1, except A: 0.5 X T B E buffer; contour length of DNA was 64 pm in the symmetric V conformation ( t = 0 s) a n d 50 pm in the linear conformation ( t = 6.7 s ) . B: 0.5 X TBE buffer; contour length of DNA was 30 pm in the symmetric V conformation ( t = 0 s ) a n d 23.5 pm in t h e linear conformation ( t = 3.3 s ) . C: 1.0 X T B E buffer; contour length of DNA was 25 pm in the symmetric V-conformation ( t = 0 s ) and 14.5 pm in the linear conformation ( t = 1.45 s ) . T h e time of release from t h e gel fiber is double for a molecule of twice the length, as shown by comparison of A t o H. T h e lag period (stage 11, Figure 2 ) is lengthened for the longer molecule. In 0.5 X TBE buffer ( A a n d B ) , t h e molecules internally condense during their movement around the apex position t o a degree which is independent of their length: T h e ratio between t h e linear extended molecule ( t = 6.6 s in A, 3.2 s in B ) a n d t h e symmetric V conformation ( t = 0 s ) is 22%. I n 1.0 X T B E buffer ( C ) , the molecule is shorter, the degree of length reduction is 41% between the linear extended molecule ( t = 1.45 s ) , a n d the symmetric V conformation ( t = 0 s ) .
Integrating the velocities of DNA over all stages of the conformational cycle and over several cycles, one can formulate a n average velocity. This average velocity increases in proportion to field strength (Figure 4) and in inverse proportion to buffer concentration. When DNA in its globular conformation passes through the gel, without apparent interaction, its mobility [for 0.5 T B E buffer, 2.1 p m 2 / s / V X (SE = 0.08, n = 20); for 1 X TBE, 1.0 pm2/s/V X (SE = 0.04, n = l o ) ] is high, identical for DNA of various sizes, and constant a t a value that agrees with that reported for sucrose density gradient electrophoresis.16 These mobilities refer to the migration between apparent collisions with the gel fibers. Without such a n interaction, there is no significant change in molecular length or velocity, so that the curves in Figure 2A and B during the time between gel interactions would be plotted as horizontal lines. The persistence of the globular conformations was 1-2 s.
DISCUSSION This report deals with the migration of DNA through agarose gel under commonly used conditions of electroph~resis.'~ The possibility of taking measurements of DNA length, of luminant density, and
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Figure 4. Proportionality between DNA length and migration rate, due to increased cycle time for larger molecules: Field strengths: 10 V / c m (circles); 6.5 V/cm (crosses). Other parameters as in Figure 3A, B. Migration rates were measured across a 100-pmpath. Average number of the conformational transition cycles was 3 for each molecule. In view of the proportionality between time spent undergoing conformational changes ( “cycle time” ) and DNA length (Figure 3A, B ) the abscissa in this figure also denotes the inverse cycle time. Size separation is then seen to be a function of cycle time, e.g., the time not spent migrating at the free mobility. Migration rates are in agreement with those obtained macroscopically by measurement of band displacement in gel electrophoresis.
of angles as a function of time has provided new insights into the mechanisms underlying gel electrophoretic separations. The Molecular Mechanisms Underlying Separation of DNA in Agarose Gels Collision Between DNA and Gel Fiber. The most
important finding is that DNA passing through the gel can be slowed in its migration rate and ultimately arrested. T h e points of arrest in the frame of the video microscope appear stationary in space and time, and hence the same for different molecules passing by. We interpret this deceleration and arrest as a collision with a gel fiber. T h e duration of the interaction with the gel fiber, consisting of the unraveling of the globular molecule into a V-shaped one, of the time spent arrested in a symmetric V conformation, and of the time spent in slipping around the fiber was found to be proportional to the length of DNA. It is hypothesized that this is the prime mechanism underlying size separation of DNA in agarose gels. The Nature of the Interaction Between DNA and Gel Fiber. It is the interaction with the gel fiber
that appears t o cause the observed conformational change from a globular molecule, migrating a t con-
stant and size-independent velocity, to a V-shaped one. T h e V shape is commonly asymmetric but symmetric molecules are found, presumably depending on the locus of the collision along the globular DNA surface. While the position of the apex of the V remains stationary, the length of one arm of the V becomes greater while the other one shortens. This is interpreted as the movement of the DNA molecule around the stationary gel fiber. T h e movement of DNA around the fiber appears to involve a n interaction as evidence by the persistence of a luminant density maximum a t the apex during stage 111, indicative of an accumulation of nucleotides a t this point. This interaction between DNA and fiber after a variable number of cycles, is thought to lead to the observed complete and final arrest of large DNA. If the field is inverted, DNA arrested in the V conformation exhibits inversion of the arms, with the apex often remaining anchored in its original position. Collision and Reptation During Migration. T h e observed dynamics of DNA migration in agarose gels involves elements of collision and elements of reptation.’ Collisions with stationary fibers are evidenced by the persistence of DNA a t particular points. T h e elongation of the arms in forming the V-shaped conformation does not appear t o lead to a pileup of polynucleotide chain, as it is not detectable as a stationary fluorescent spots in the direction of migration, analogous to those spots detected orthogonally. Therefore, it is assumed that the elongated arms are displaced through the gel fiber network by a reptating motion. Properties of the DNA Molecule
T h e properties of DNA reported in this section refer to DNA in an agarose medium. Among present media, agarose appears unique in allowing for the preparation and storage of large DNA. While it is a medium supportive of the native state of DNA, it provides a t the same time a network of gel fibers with which DNA can interact and be conformationally altered in ways detectable by QVEM. The length of DNA. T h e contour length of DNA appears inversely proportional to buffer concentration. At the concentrations used in this study, the DNA population consists of all of the conformational forms t o differing degrees. Furthermore, it is shown by QVEM that individual DNA molecules exhibit variable contour lengths during migration ( Figure 2A). We interpret this variability in length as evi-
MECHANISM OF E L E C T R O P H O R E T I C DNA SEPARATION
dence f‘or the molecular elasticity of DNA. By definition, “a body is said to be elastic if it suffers a deformation when a stretching or compressing force is applied to it.”” The stretching referred to in that definition comes about by having the arms of the V conformation being pulled forward on either side of the fixed gel fiber. The compressing force tending to condense DNA appears entropic in origin: The globular conformation is that which is least disruptive of hydrogen-bonded water structure around the molecule. However, the elasticity of DNA comprises nonideal features unlike a rubber band or a spring, as shown by the nonhomogeneous luminant density profiles (Figure 1) . Measuring the length of the arms of the symmetric V conformation of DNA, the contour length can he considered the summed length of the arms. This sum has been compared to the contour length of the linearly extended conformation. Independent of‘the summed length of the arms of V-shaped molecule ( 18-64 pm), the ratio of the length of the linear DNA t o that of the V-shaped conformation is, surprisingly, a constant for a particular buffer concentration (Figure 3 ) . This result implies that longer DNA condenses more rapidly than shorter DNA during stage 111 of the cycle. For example (Figure 3 1 , the linear rate of length reduction for molecules of 64- and 30.5-pm length was measured as 4.4 and 2.2 pm/s, respectively. T h e corresponding rates of length reduction in more highly concentrated buffer are higher (Figure 3 C ) . Intramolecular Nucleotide Distribution. T h e distribution of nucleotide density appears to be nonuniform along the DNA length (Figure 1). In particular, the ends of the molecule appear to have a relatively high nucleotide concentration. The maximal nucleotide concentration appears to be in the end leading in the direction of migration. Also, the leading arm contains more nucleotide than the trailing arm. T h e higher nucleotide content of the leading arm of the V conformation suggests that this arm exerts the greater electrostatic force and thus pulls the trailing arm around the gel fiber. However, this model by itself seems insufficient since it would predict a minimum of nucleotide concentration a t the apex of the V conformation, which is not found. T h e accumulation of nucleotide a t the apex suggests some physical or chemical interaction between DNA and gel fiber that acts to impede the movement of the DNA across the fiber. The observation that large DNA ( > 20 pm) is arrested after a period of time can possibly also be explained in terms of this DNAgel fiber interaction.
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Structural Persistence of the V Conformation. The arrested DNA in the V conformation can be expected to be randomly oriented in the field of‘ the microscope since the gel fiber with which it interacts should be also randomly oriented in the gel. Therefore, of the thousands of DNA molecules monitored, only relatively few exhibit an orientation parallel to the plane of microscope stage. A maximal apex angle is found and is a constant for a particular buffer concentration, e.g., 29.7” in 0.5 X TBE. Furthermore, the average apex angle a t higher buffer concentration (1.0 X T B E ) decreases to 22’. From the constancy of the apex angle we deduce that the arms of DNA are oriented in space. Moreover, the angle of the leading arm of DNA with respect to the electric field appears to be maintained while the molecule moves around the fiber. T h e linearly extended DNA once formed can maintain that angle with respect to the field for some duration of time. Ultimately, it reorients to migrate in the direction of the field. This observation supports the notion of a molecular refractoriness to conformational change. Hypothetical Answers to Three Questions
1. Why Is the Rate of Length Reduction During the Transformation from the V to the Linear Conformation Higher for Longer DNA? It has been stated
above that it appears that the nucleotide density in the arms of the V conformation of DNA governs the force acting on each arm. The opposing forces of the two arms in that conformation create a tension in the molecule. This tension is maximal in the symmetric V conformation and zero at a first approximation in the linearly extended DNA. Since DNA in the V conformation is longer than in the linear conformation, it appears that the tension in the molecule is proportional to its length. Since as stated above DNA acts as a n elastic body, the higher the tension (in the V conformation) the greater must be the compressing force, and the greater the rate of condensation. 2. Why Is the Ratio Between the Chain Lengths of the Linear and V Conformations a Constant Dependent on Buffer Concentration! DNA can be elongated in one of two ways: by lowering of the buffer concentration’ or by stretching the DNA across a gel fiber. When it is elongated, the surface charge density and therefore the density of the counterion shell should decrease. Elongation therefore implies that counterions are released into the bulk phase. T h e release of counterions involves a gain in entropy and therefore in free energy of dil ~ t i o n . As ’ ~ the length of DNA decreases progres-
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sively as the tension decreases, the density of the counterion shell should increase, causing the DNA t o condense. T h e constant length ratio of the extended and V conformations for DNA of various sizes then derives from the proportionality between tension (stretching force) and compressing force (free energy of counterion dilution) in different lengths of DNA. 3. Why Is There an Apex Angle, Why Does It Persist, and Why Is It Dependent on Buffer Concentration? Polyions become stiff a t low ionic strength
through high intramolecular electrostatic repulsion.*'Such a relatively stiff polyion, placed into a n electric field, will exhibit a large dipole moment.2' The induced dipole may cause the two arms of the V conformation to repel each other electrostatically a t the apex. This electrostatic repulsion could potentially form and stabilize the V conformation. The degree of repulsion should be inversely proportional to buffer concentration and thus the apex angle can be expected t o increase with decreasing buffer concentration as shown in this study. The spreading of the arms of the V may also be related to electroendosmotic back flow, since such flow is inversely related to buffer concentration, a s is the apex angle. An induced dipole on DNA surrounded by its counterion shell 22 may also explain the observed minimum of luminant density a t the center of the arms of DNA in the V conformation (Figure lB, C ) . The minimum may be due to the bidirectional pull of the field on such a n induced dipole. This work was supported in part by a Biotechnology Associateship from the National Research Council. I want to thank A. Chrambach for editorial assistance and most valuable discussions. R. K. Mortimer, H. Bremermann, H. Morrison (all UC Berkeley), J. R. Sellers, K. R. Spring, J. Zimmerberg, D. Rodbard, and D. Rau (all NIH) provided either parts of the instrumentation and/or valuable discussions.
REFERENCES 1. Matsumoto, S., Morikawa, K. & Yanagida, M. (1981)
J . Mol. Biol. 152, 501-516.
2. Smith, S. B., Aldridge, P. K. & Callis, J. B. (1989) Science 243, 203-206. 3. Schwartz, D. C. & Koval, M. (1989) Nature 338,520522. 4. Rampino, N. J. ( 1989) doctoral thesis, University of California a t Berkeley. 5. Gurrieri, S., Rizzarelli, E., Beach, D. & Bustamante, C. (1990) Biochemistry 29, 3399-3401. 6. Khurana, A. (1990) Phys. Today 43, 20-22. 7. Ogston, A. G. (1958) Trans. Faraday Soc. 54, 17541757. 8. De Gennes, P. G. (1971) J . Chem. Phys. 55, 572579. 9. Smisek, D. L. & Hoagland, D. A. ( 1990) Science 248, 1221-1223. 10. Lumpkin, 0. J., Dejardin, P. & Zimm, B. H. (1985) Biopolymers 24, 1573-1593. 11. Noolandi, J., Rousseau, J., Slater, G. W., Turmel, C. & Lalande, M. (1987) Phys. Rev. Lett. 58, 2428-2431. 12. Zimm, B. H. (1988) Phys. Rev. Lett. 6 1 , 2965-2968. 13. Deutsch, J. M. (1988) Science 240,922-924. 14. Rampino, N. & Chrambach, A. (1990) Anal. Biochem., submitted. 15. Lewin, B. (1990) Genes ZV, Oxford University Press, Oxford, UK, pp. 83 and 307. 16. Olivera, B. M., Baine, P. & Davidson, N. (1964) Biopolymers 2, 245-257. 17. Maniatis, T., Fritsch, E. F. & Sambrook, J. (1982) Molecular Cloning, Cold Spring Harbor Laboratories, Cold Spring Harbor, NY, p. 150. 18. Ohanian, H. C. (1985) Physics, W. W. Norton, New York, p. 135. 19. Anderson, C. F. & Record, M. T . (1990) A n n . Rev. Biophys. Biophys. Chem. 19, 423-465. 20. Hagerman, P. J. (1988) Ann. Rev. Biophys. Biophys. Chem. 17, 265-286. 21. Mandel, M. & Odijk, T. (1984) Ann. Rev. Phys. Chem. 35, 75-108. 22. Doi, M. & Edwards, S. F. (1988) The Theory of Polymer Dynamics, Oxford University Press, Oxford, UK, pp. 125 and 303. 23. Carle, G. F., Frank, M. & Olson, M. V. ( 1986) Science 232, 65-68. Received December 3, 1990 Accepted April 3, 1991
SYNOPSIS
Changes in conformation, length, and mobility of individual DNA molecules during agarose gel electrophoresis were measured using video micrographs obtained by epifluorescence microscopy. Globular, V-shpaed, and linear conformations of DNA are found. The mobility, upon transformation from the globular to the V-shaped conformation, decreases, suggesting a collision with a gel fiber. The duration of interaction between DNA and gel fiber is proportional to the length of DNA. Hypothetically, this proportionality underlies the size separation of DNA by agarose gel electrophoresis. DNA release from the gel fiber appears to involve the movement of the arms of the Vshaped molecule around the gel fiber. Concomitant with this movement is a length reduction the degree of which is constant for DNA of various lengths in a particular buffer milieu. The luminant densitometric profiles of DNA molecules in the V conformation show maxima a t the ends and apex of the V. The unequal distribution of nucleotides along the DNA chain appears to provide the driving force for the molecular movement around the gel fiber.
INTRODUCTION The visualization of single fluorophore-labeled DNA molecules by epifluorescence microscopy was introduced by Matsumoto et al.’ I t has been applied to agarose gel electrophoresis of DNA by Smith et al.,‘ Schwartz and Koval,3and the present a ~ t h o rPic.~ torial representations of DNA undergoing gel electrophoresis have been r e p ~ r t e d . ~However, . ~ ’ ~ no explicit size or mobility measurements quantitating the dynamics of DNA’s intramolecular geometry during electrophoresis have been reported prior to this work.” Nor has the previous work with videoepifluorescence microscopic monitoring of gel electrophoresis been used to critically assess present theories concerning the mechanism of size separation of DNA in gek7-l3 This work has aimed a t quantitating the conformational and mobility dynamics of DNA during
Hiopolyrnern. Vol 31, 1009-1016 (1991) (r 1991 .lohn Wiley & Sons, Inc
CCC 0006-3525/91/0Sl009-08$04.00
agarose gel electrophoresis. This approach can therefore be termed “quantitative video-epifluorescence microscopy” (QVEM) . QVEM promises t o displace speculative mechanisms of gel electrophoresis by those based on direct measurement of DNA molecules, to be helpful in the interpretation of electrophoretic mobility assays, and to aid in the development of gel electrophoretic media and of optimal separation conditions.
MATERIALS A N D METHODS Sample Preparation
A 0.5% solution of agarose (SeaKem GTG, FMC, Rockland, M E ) was prepared a t 65°C in either 1 X T B E buffer (89 m M Tris, 89 m M boric acid, 2 m M Naz EDTA) o r 0.5 X T B E buffer, containing 0.2 pg mL-’ of DAPI ( 4’,6’-diamidino-2-phenylindole; Molecular Probes, Eugene, OR). A 1-pL aliquot of a n agarose plug containing yeast chromosomal DNA (Pombe, 3, 5, and 6 Mb, Clontech, Palo Alto, 1009
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CA) or 1 ng of unmethylated A-DNA (Pharmacia, Uppsala, Sweden) was dissolved in 30 pL of this solution and maintained at 65°C for 3 min. The yeast chromosomal DNA was then broken through vigorous pipeting to give fragments in the range of contour length of 5-200 pm. 8-Mercaptoethanol (0.3 p L ) was added t o the mixture.’ Gel Electrophoresis
A 5-pL aliquot of the sample was pipeted on a microscope coverslip, covered with another coverslip, and allowed t o cool t o room temperature. T h e sandwich was placed as a bridge across two agarose gel blocks in a glass electrophoresis cell.I4 Electrophoresis was conducted a t regulated field strengths of 5-10 V cm-l a t 24°C across the 2.2-cm gel sandwich. During the study, the composition of the sample was kept constant except for the two changes in buffer concentration. Data Collection and Processing
Fluorescence of individual fluorophore-labeled DNA was monitored during electrophoresis by QVEM as d e ~ c r i b e d . ’An ~ 1800-fold magnification is brought about by use of a 63X microscope objective and display on a video monitor. The brightness of the image derives from a gain of up to 0.5 million achieved by a n image intensifier; this gain was adjusted to give a high-contrast image and remained constant throughout the experiment. Relative luminance of the digitized images was expressed in terms of grey levels, where black = 0 and white = 256. One greylevel unit ( G L U ) is defined as the numerical value of a pixel in terms of relative luminance. Measurements and densitometry were performed on the original video micrographs without any image enhancement. Molecular tracking employed a mouse driven cursor.
stages of the cycle can be distinguished (Figure 2 ) : ( I ) DNA in the globular conformation abruptly decelerates and changes into the V-conformation. (11) The V-shaped conformation can become symmetric; if so, the molecule is temporarily arrested. (111) Asymmetry of the V conformation progressively develops as mobility increases. At the end of this stage, DNA is linearly extended with the end of the retreating arm coincident with the apex. ( I V ) The extended DNA molecule condenses back progressively to the globular conformation, during which time the mobility becomes maximal. The cycles of a given DNA molecule are repeated but not indefinitely. In time, unless the field is appropriately pulsed, some large DNA molecules (approximately 10% of those in excess of 20-50 pm in length) become irreversibly arrested under the conditions used here.* The arrest, as well as other apparent interactions that trigger the onset of the cycle, take place a t particular locations in the field of observation. Constant locations of ”Apex Positions” and Their Distance from One Another
During stage I, the arms of the V progressively extend a t a rate of 4.5 pm/s (in 0.5 X T B E buffer) and do not appear to be impeded in their elongation. By contrast, DNA molecules in the V conformation are arrested a t constant positions within the frame of the microscope. Arrest is not observed in any but those positions. T h e minimal distance, a t a right angle to the direction of the field, between the positions of the apexes of the V conformations (“apex positions”) is approximately 3.5 pm in areas of the gel selected for absence of geometric perturbations of the V conformation. In the direction of migration, such stationary arrest points are not observed during stage 111. Therefore, no downfield arrest points are observed until V conformations are formed again. Variations in Luminant Density Along an Individual Fluorophore-Labeled D N A Molecule
RESULTS A Cycle of Conformational Changes of D N A During Agarose Gel Electrophoresis
All DNA molecules monitored by QVEM during agarose gel electrophoresis, under the conditions used, undergo a sequence of conformational changes from a globular to a V-shaped to a linearly extended form (Figure 1) . Once linear, the molecule condenses back to a globular conformation while migrating. T h i s sequence of events is termed a cycle. Four
DNA molecules in a representative video frame are selected that maintain their integrated luminant density throughout their conformational cycles.+ Under observation by QVEM, all DNA molecules exhibit nonhomogeneous luminant density along
* This 10% loss of migrating DNA due to arrest may explain the decrease of band area in the absence of pulsing in Fig. 1A of Ref. 23. This is done to distinguish perspective effects from intramolecular redistribution of luminant density.
’
101 1
MECHANISM OF ELECTROPHORETIC DNA SEPARATION
'
\
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Distance (pm) Figure 1. Cycle of conformational changes of a representative DNA molecule during agarose gel electrophoresis: DNA was sheared S. pornbe chromosome. Agarose gel electrophoresis ( 1 X TBE buffer, 24"C, 5 V / c m ) . Left panel: video micrograph. Right panel: Luminant density profiles of the DNA chain. A: globular DNA. B: Asymmetric V conformation. T h e shorter ( t o p ) arm has the highest luminant density a n d leads in the direction of migration. C: DNA molecule slipping around the apex, the position of which is stationary. Nucleotide concentration is elevated a t the apex, presumably due t o a n interaction with a gel fiber. D: Linearly extended conformation; retreating arm coincident with the former apex position. T h e nonhomogeneous distribution of luminant density is maintained throughout the cycle. Bar = 10 fim. Panel designations B, C, and D refer t o both the images a n d the density profiles. T h e two arms of DNA in t h e V conformation shown in image B correspond to the two uppermost luminant density profiles. Likewise, the density profiles aligned horizontally with image C correspond t o the upper a n d lower arms. Distances in the density profiles are measured from the apex position.
their length. One representative DNA molecule exhihiting such a nonhomogeneous distribution of luminant density a t various stages of the cycle is
shown in Figure 1. T h e ends of the molecule are the most luminous; the apex of the V-shaped conformation is also elevated. T h e integrated luminant
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Stage of Cycle
I
I1
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IV
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under the luminant density profiles presented in Figure 1B were 780 GLU for the leading (upper) arm and 735 GLU for the retreating (lower) arm. T h e retreating arm, while maintaining a maximum at the tail end, diminishes in luminant density (560 GLU) a s the leading arm increases (950 GLU) in relative luminant density (Figure 1C). Surprisingly, the luminant density a t the apex of the V conformation appears to remain constant (26 GLU, S E = 0.7, n = 9 ) during stage I11 of the cycle.
111 IV
Contour Length Changes upon Transition from the Symmetric V to the Linear Conformation During Stage 111
0
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Time (s)
Figure 2. Length and displacement rate of the luminant densitometric centroid of DNA during the cycle of conformational changes: Conditions as in Figure 1 except different molecule, 0.5 X TBE buffer. Stage I designates the formation of a symmetric V conformation, stage I1 a lag period, during which the molecule remains stationary, stage I11 the progressive asymmetry of the V conformation coincident with a fixed degree and rate of length reduction, and stage IV the condensation of the linear conformation to the original globular form.
density of the conformational forms shown in Figure 1is conserved: In the example shown, the integrated luminant density of the molecule is 1500 GLU,irrespective of conformation. It is assumed that the relative luminant density is proportional to the concentration of intercalated fluorophore and, consequently, is a measure of the nucleotide density along the DNA molecule. The Redistribution of Luminant Density During the Cycle
During the cyclic conformational change from a globular t o a V-shaped to a n extended DNA molecule, a maximum of luminant density a t the end of both arms of the molecule is preserved. The arm with the higher total luminant density leads in the direction toward the anode. For example, the areas
DNA molecules varying in contour length in the symmetric V conformation from 18 to 64 pm were monitored for contour length ratio between the symmetric V conformation (Figure lB,C ) and the linear conformation (Figure 1 D ) . Independent of their size, the length reduction in going from the V shaped to the linear conformation is 41% ( S E = 3%, n = 4 ) , in 1 X TBE buffer, and 22% ( S E = 1.196,n = 1 2 ) in 0.5% T B E buffer. This decrease in size proceeds a t a constant rate of 4.4 and 2.2 pm/s in the representative cases shown in Figure 3A and B, respectively. T h e condensation rate is higher (7.0 p m / s ) in 1 X T B E than in 0.5 X T B E buffer (compare Figure 3C with Figure 3B ) . The degree of length reduction was independent of field strength within the narrow range used. Length measurements in TBE buffer were compared to ideal values, using A-DNA as a standard. T h e A-DNA in the I3 form of 48.5 kilobases has a calculated contour length of 16.4 pm.I5 In 0.5 X T B E buffer, its measured length in the V conformation is 12.8 pm, or 78% of the calculated value; in the linear conformation, it is 10.0 pm, or 60% of the calculated length. T o interpret the results of this study in terms of base-pair numbers, these factors need to be applied. Dynamics Related to the Angle Between the Arms of the V-Shaped Conformation
The “apex angle” between the arms of V-shaped DNA was measured for selected molecules in the size range of 10-30-pm contour length. Selection is made for molecules presenting maximal apex angles. Presumably, these are molecules oriented parallel t o the stage of the microscope. They represent approximately 1%of those visible on a representative frame. T h e apex angle is larger (29.7”, S E = 0.7, n = 28) for 0.5 X T B E than for 1 X T B E (22”, S E
MECHANISM OF ELECTROPHORETIC DNA SEPARATION
60 50
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= 1.0, n = 4) buffer. The orientation of the leading arm, with respect to the axis of the electric field, appears conserved initially when the V conformation changes to the linear conformation (Figure 1) .
The Duration of the Conformational Cycle as a Function of the Length of DNA
The time it takes for DNA to pass through the conformational cycle appears proportional to its effective length (Figure 3A, B ) . This effective length depends on the degree of internal condensation and therefore on buffer concentration. The longer duration of the cycle for longer molecules can be accounted for by the longer dwell-time in the V-shaped conformation (Figures 2 and 3 ) . The increased dwell-time in the V conformation for larger DNA presumably underlies electrophoretic size separation. Average Migration Rates of DNA of Different Sizes Measured on Individual Molecules as a Function of Field Strength and Cycles/ Path Length
1
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Figure 3. Length of the arms of DNA in the V conformation as a function of time: Leading arm: diamonds; retreating arm: squares. Conditions as in Figure 1, except A: 0.5 X T B E buffer; contour length of DNA was 64 pm in the symmetric V conformation ( t = 0 s) a n d 50 pm in the linear conformation ( t = 6.7 s ) . B: 0.5 X TBE buffer; contour length of DNA was 30 pm in the symmetric V conformation ( t = 0 s ) a n d 23.5 pm in t h e linear conformation ( t = 3.3 s ) . C: 1.0 X T B E buffer; contour length of DNA was 25 pm in the symmetric V-conformation ( t = 0 s ) and 14.5 pm in the linear conformation ( t = 1.45 s ) . T h e time of release from t h e gel fiber is double for a molecule of twice the length, as shown by comparison of A t o H. T h e lag period (stage 11, Figure 2 ) is lengthened for the longer molecule. In 0.5 X TBE buffer ( A a n d B ) , t h e molecules internally condense during their movement around the apex position t o a degree which is independent of their length: T h e ratio between t h e linear extended molecule ( t = 6.6 s in A, 3.2 s in B ) a n d t h e symmetric V conformation ( t = 0 s ) is 22%. I n 1.0 X T B E buffer ( C ) , the molecule is shorter, the degree of length reduction is 41% between the linear extended molecule ( t = 1.45 s ) , a n d the symmetric V conformation ( t = 0 s ) .
Integrating the velocities of DNA over all stages of the conformational cycle and over several cycles, one can formulate a n average velocity. This average velocity increases in proportion to field strength (Figure 4) and in inverse proportion to buffer concentration. When DNA in its globular conformation passes through the gel, without apparent interaction, its mobility [for 0.5 T B E buffer, 2.1 p m 2 / s / V X (SE = 0.08, n = 20); for 1 X TBE, 1.0 pm2/s/V X (SE = 0.04, n = l o ) ] is high, identical for DNA of various sizes, and constant a t a value that agrees with that reported for sucrose density gradient electrophoresis.16 These mobilities refer to the migration between apparent collisions with the gel fibers. Without such a n interaction, there is no significant change in molecular length or velocity, so that the curves in Figure 2A and B during the time between gel interactions would be plotted as horizontal lines. The persistence of the globular conformations was 1-2 s.
DISCUSSION This report deals with the migration of DNA through agarose gel under commonly used conditions of electroph~resis.'~ The possibility of taking measurements of DNA length, of luminant density, and
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U
._ 6 10c
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Figure 4. Proportionality between DNA length and migration rate, due to increased cycle time for larger molecules: Field strengths: 10 V / c m (circles); 6.5 V/cm (crosses). Other parameters as in Figure 3A, B. Migration rates were measured across a 100-pmpath. Average number of the conformational transition cycles was 3 for each molecule. In view of the proportionality between time spent undergoing conformational changes ( “cycle time” ) and DNA length (Figure 3A, B ) the abscissa in this figure also denotes the inverse cycle time. Size separation is then seen to be a function of cycle time, e.g., the time not spent migrating at the free mobility. Migration rates are in agreement with those obtained macroscopically by measurement of band displacement in gel electrophoresis.
of angles as a function of time has provided new insights into the mechanisms underlying gel electrophoretic separations. The Molecular Mechanisms Underlying Separation of DNA in Agarose Gels Collision Between DNA and Gel Fiber. The most
important finding is that DNA passing through the gel can be slowed in its migration rate and ultimately arrested. T h e points of arrest in the frame of the video microscope appear stationary in space and time, and hence the same for different molecules passing by. We interpret this deceleration and arrest as a collision with a gel fiber. T h e duration of the interaction with the gel fiber, consisting of the unraveling of the globular molecule into a V-shaped one, of the time spent arrested in a symmetric V conformation, and of the time spent in slipping around the fiber was found to be proportional to the length of DNA. It is hypothesized that this is the prime mechanism underlying size separation of DNA in agarose gels. The Nature of the Interaction Between DNA and Gel Fiber. It is the interaction with the gel fiber
that appears t o cause the observed conformational change from a globular molecule, migrating a t con-
stant and size-independent velocity, to a V-shaped one. T h e V shape is commonly asymmetric but symmetric molecules are found, presumably depending on the locus of the collision along the globular DNA surface. While the position of the apex of the V remains stationary, the length of one arm of the V becomes greater while the other one shortens. This is interpreted as the movement of the DNA molecule around the stationary gel fiber. T h e movement of DNA around the fiber appears to involve a n interaction as evidence by the persistence of a luminant density maximum a t the apex during stage 111, indicative of an accumulation of nucleotides a t this point. This interaction between DNA and fiber after a variable number of cycles, is thought to lead to the observed complete and final arrest of large DNA. If the field is inverted, DNA arrested in the V conformation exhibits inversion of the arms, with the apex often remaining anchored in its original position. Collision and Reptation During Migration. T h e observed dynamics of DNA migration in agarose gels involves elements of collision and elements of reptation.’ Collisions with stationary fibers are evidenced by the persistence of DNA a t particular points. T h e elongation of the arms in forming the V-shaped conformation does not appear t o lead to a pileup of polynucleotide chain, as it is not detectable as a stationary fluorescent spots in the direction of migration, analogous to those spots detected orthogonally. Therefore, it is assumed that the elongated arms are displaced through the gel fiber network by a reptating motion. Properties of the DNA Molecule
T h e properties of DNA reported in this section refer to DNA in an agarose medium. Among present media, agarose appears unique in allowing for the preparation and storage of large DNA. While it is a medium supportive of the native state of DNA, it provides a t the same time a network of gel fibers with which DNA can interact and be conformationally altered in ways detectable by QVEM. The length of DNA. T h e contour length of DNA appears inversely proportional to buffer concentration. At the concentrations used in this study, the DNA population consists of all of the conformational forms t o differing degrees. Furthermore, it is shown by QVEM that individual DNA molecules exhibit variable contour lengths during migration ( Figure 2A). We interpret this variability in length as evi-
MECHANISM OF E L E C T R O P H O R E T I C DNA SEPARATION
dence f‘or the molecular elasticity of DNA. By definition, “a body is said to be elastic if it suffers a deformation when a stretching or compressing force is applied to it.”” The stretching referred to in that definition comes about by having the arms of the V conformation being pulled forward on either side of the fixed gel fiber. The compressing force tending to condense DNA appears entropic in origin: The globular conformation is that which is least disruptive of hydrogen-bonded water structure around the molecule. However, the elasticity of DNA comprises nonideal features unlike a rubber band or a spring, as shown by the nonhomogeneous luminant density profiles (Figure 1) . Measuring the length of the arms of the symmetric V conformation of DNA, the contour length can he considered the summed length of the arms. This sum has been compared to the contour length of the linearly extended conformation. Independent of‘the summed length of the arms of V-shaped molecule ( 18-64 pm), the ratio of the length of the linear DNA t o that of the V-shaped conformation is, surprisingly, a constant for a particular buffer concentration (Figure 3 ) . This result implies that longer DNA condenses more rapidly than shorter DNA during stage 111 of the cycle. For example (Figure 3 1 , the linear rate of length reduction for molecules of 64- and 30.5-pm length was measured as 4.4 and 2.2 pm/s, respectively. T h e corresponding rates of length reduction in more highly concentrated buffer are higher (Figure 3 C ) . Intramolecular Nucleotide Distribution. T h e distribution of nucleotide density appears to be nonuniform along the DNA length (Figure 1). In particular, the ends of the molecule appear to have a relatively high nucleotide concentration. The maximal nucleotide concentration appears to be in the end leading in the direction of migration. Also, the leading arm contains more nucleotide than the trailing arm. T h e higher nucleotide content of the leading arm of the V conformation suggests that this arm exerts the greater electrostatic force and thus pulls the trailing arm around the gel fiber. However, this model by itself seems insufficient since it would predict a minimum of nucleotide concentration a t the apex of the V conformation, which is not found. T h e accumulation of nucleotide a t the apex suggests some physical or chemical interaction between DNA and gel fiber that acts to impede the movement of the DNA across the fiber. The observation that large DNA ( > 20 pm) is arrested after a period of time can possibly also be explained in terms of this DNAgel fiber interaction.
1015
Structural Persistence of the V Conformation. The arrested DNA in the V conformation can be expected to be randomly oriented in the field of‘ the microscope since the gel fiber with which it interacts should be also randomly oriented in the gel. Therefore, of the thousands of DNA molecules monitored, only relatively few exhibit an orientation parallel to the plane of microscope stage. A maximal apex angle is found and is a constant for a particular buffer concentration, e.g., 29.7” in 0.5 X TBE. Furthermore, the average apex angle a t higher buffer concentration (1.0 X T B E ) decreases to 22’. From the constancy of the apex angle we deduce that the arms of DNA are oriented in space. Moreover, the angle of the leading arm of DNA with respect to the electric field appears to be maintained while the molecule moves around the fiber. T h e linearly extended DNA once formed can maintain that angle with respect to the field for some duration of time. Ultimately, it reorients to migrate in the direction of the field. This observation supports the notion of a molecular refractoriness to conformational change. Hypothetical Answers to Three Questions
1. Why Is the Rate of Length Reduction During the Transformation from the V to the Linear Conformation Higher for Longer DNA? It has been stated
above that it appears that the nucleotide density in the arms of the V conformation of DNA governs the force acting on each arm. The opposing forces of the two arms in that conformation create a tension in the molecule. This tension is maximal in the symmetric V conformation and zero at a first approximation in the linearly extended DNA. Since DNA in the V conformation is longer than in the linear conformation, it appears that the tension in the molecule is proportional to its length. Since as stated above DNA acts as a n elastic body, the higher the tension (in the V conformation) the greater must be the compressing force, and the greater the rate of condensation. 2. Why Is the Ratio Between the Chain Lengths of the Linear and V Conformations a Constant Dependent on Buffer Concentration! DNA can be elongated in one of two ways: by lowering of the buffer concentration’ or by stretching the DNA across a gel fiber. When it is elongated, the surface charge density and therefore the density of the counterion shell should decrease. Elongation therefore implies that counterions are released into the bulk phase. T h e release of counterions involves a gain in entropy and therefore in free energy of dil ~ t i o n . As ’ ~ the length of DNA decreases progres-
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sively as the tension decreases, the density of the counterion shell should increase, causing the DNA t o condense. T h e constant length ratio of the extended and V conformations for DNA of various sizes then derives from the proportionality between tension (stretching force) and compressing force (free energy of counterion dilution) in different lengths of DNA. 3. Why Is There an Apex Angle, Why Does It Persist, and Why Is It Dependent on Buffer Concentration? Polyions become stiff a t low ionic strength
through high intramolecular electrostatic repulsion.*'Such a relatively stiff polyion, placed into a n electric field, will exhibit a large dipole moment.2' The induced dipole may cause the two arms of the V conformation to repel each other electrostatically a t the apex. This electrostatic repulsion could potentially form and stabilize the V conformation. The degree of repulsion should be inversely proportional to buffer concentration and thus the apex angle can be expected t o increase with decreasing buffer concentration as shown in this study. The spreading of the arms of the V may also be related to electroendosmotic back flow, since such flow is inversely related to buffer concentration, a s is the apex angle. An induced dipole on DNA surrounded by its counterion shell 22 may also explain the observed minimum of luminant density a t the center of the arms of DNA in the V conformation (Figure lB, C ) . The minimum may be due to the bidirectional pull of the field on such a n induced dipole. This work was supported in part by a Biotechnology Associateship from the National Research Council. I want to thank A. Chrambach for editorial assistance and most valuable discussions. R. K. Mortimer, H. Bremermann, H. Morrison (all UC Berkeley), J. R. Sellers, K. R. Spring, J. Zimmerberg, D. Rodbard, and D. Rau (all NIH) provided either parts of the instrumentation and/or valuable discussions.
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J . Mol. Biol. 152, 501-516.
2. Smith, S. B., Aldridge, P. K. & Callis, J. B. (1989) Science 243, 203-206. 3. Schwartz, D. C. & Koval, M. (1989) Nature 338,520522. 4. Rampino, N. J. ( 1989) doctoral thesis, University of California a t Berkeley. 5. Gurrieri, S., Rizzarelli, E., Beach, D. & Bustamante, C. (1990) Biochemistry 29, 3399-3401. 6. Khurana, A. (1990) Phys. Today 43, 20-22. 7. Ogston, A. G. (1958) Trans. Faraday Soc. 54, 17541757. 8. De Gennes, P. G. (1971) J . Chem. Phys. 55, 572579. 9. Smisek, D. L. & Hoagland, D. A. ( 1990) Science 248, 1221-1223. 10. Lumpkin, 0. J., Dejardin, P. & Zimm, B. H. (1985) Biopolymers 24, 1573-1593. 11. Noolandi, J., Rousseau, J., Slater, G. W., Turmel, C. & Lalande, M. (1987) Phys. Rev. Lett. 58, 2428-2431. 12. Zimm, B. H. (1988) Phys. Rev. Lett. 6 1 , 2965-2968. 13. Deutsch, J. M. (1988) Science 240,922-924. 14. Rampino, N. & Chrambach, A. (1990) Anal. Biochem., submitted. 15. Lewin, B. (1990) Genes ZV, Oxford University Press, Oxford, UK, pp. 83 and 307. 16. Olivera, B. M., Baine, P. & Davidson, N. (1964) Biopolymers 2, 245-257. 17. Maniatis, T., Fritsch, E. F. & Sambrook, J. (1982) Molecular Cloning, Cold Spring Harbor Laboratories, Cold Spring Harbor, NY, p. 150. 18. Ohanian, H. C. (1985) Physics, W. W. Norton, New York, p. 135. 19. Anderson, C. F. & Record, M. T . (1990) A n n . Rev. Biophys. Biophys. Chem. 19, 423-465. 20. Hagerman, P. J. (1988) Ann. Rev. Biophys. Biophys. Chem. 17, 265-286. 21. Mandel, M. & Odijk, T. (1984) Ann. Rev. Phys. Chem. 35, 75-108. 22. Doi, M. & Edwards, S. F. (1988) The Theory of Polymer Dynamics, Oxford University Press, Oxford, UK, pp. 125 and 303. 23. Carle, G. F., Frank, M. & Olson, M. V. ( 1986) Science 232, 65-68. Received December 3, 1990 Accepted April 3, 1991
