J. Mot. Biol. (1990) 213, 931-951
Structure of Plectonemically Supercoiled D N A T. Christian Bolest Department of Molecular Biology University of California, Berkeley Berkeley, CA 94720 U.S.A.
James H. White Department of Mathematics University of California Los Angeles, CA 90024 U.S.A.
and Nicholas R. Cozzarelli Department of Molecular and Cell Biology Division of Biochemistry and Molecular Biology University of California Berkeley, CA 94720 U.S.A. (Received 29 August 1989; accepted 11 December 1989) Using electron microscopy and topological methods, we have deduced an average structure for negatively supercoiled circular DNA in solution. Our data suggest that DNA has a branched plectonemic (interwound) form over the range of supercoiling tested. The length of the superhelix axis is constant at 41 ~/o of the DNA length, whereas the superhelix radius decreases essentially hyperbolically as supercoiling increases. The number of supercoils is 89 ~o of the linking deficit. Both writhe and twist change with supercoiling, but the ratio of the change in writhe to the change in twist is fixed at 2"6 : 1. The extent of branching of the superhelix axis is proportional to the length of the plasmid, but is insensitive to superhelix density. The relationship between DNA flexibility constants for twisting and bending calculated using our structural data is similar to that deduced from previous studies. The extended thin form of plectonemically supercoiled DNA offers little compaction for cellular packaging, but promotes interaction between cis-acting sequence elements that may be distant in primary structure. We discuss additional biological implications of our structural data.
The number of times the two strands of the DNA double helix are intertwined, i.e. the linking number of the DNA (Lk), is a constant that can be changed only by breaking the DNA backbone. Although Lk is a topological property, it is the sum of two geometric parameters that describe the shape of the DNA, writhe (Wr) and twist (Tw) (White, 1969):
1. I n t r o d u c t i o n
DNA supercoiling, the coiling of the axis of the double helix, is ubiquitous in biological systems. It arises in two ways. It can result from winding around proteins, as in eukaryotic nucleosomes. Supercoiling can also result from the topological constraint imposed upon underwound or overwound closed molecules free in solution. Both sources of supercoiling are important in ~vo. The topological properties of closed circular DNA provide a conceptual framework for understanding supercoi]ing (for a review, see Cozzarelli et al., 1990).
Lk = Wr+Tw.
Wr is a measure of the coiling of the DNA axis, and Tw reflects the helical winding of the DNA strands around each other. For circular DNAs isolated from natural sources, supercoiling is a geometric compensation for a deficiency in linking number. There is an unfavorable free energy associated with decreasing Lk from the preferred value of the
t Present address: Graduate Department of Biochemistry, Brandeis University, Waltham MA 02254, U.S.A. 0022-2836/90/120931-21 $03.00/0
(1)
931
© 1990 Academic Press Limited
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T . C . Boles et al.
relaxed state (Depew & Wang, 1975; Pulleyblank et al., 1975; Frank-Kamenetskii, 1990), operationally defined as the equilibrium value after nicking and religation. To minimize this free energy change, the DNA adopts a supercoiled shape, thereby changing the values of Wr and Tw. Negative supercoiling is important for a wide variety of biological processes. First, the free energy of negative supercoiling assists processes that require untwisting or denaturation of DNA, such as DNA replication and transcription. Thus, negative supercoiling helps polymerases, helicases, singlestrand binding proteins, and other accessory proteins to force apart the two strands of the DNA double helix, allowing freer access to the genetic information stored in the base sequence (Funnell et a/., 1986; McClure, 1985). Negative supercoiling also promotes a variety of structural alterations that lead to DNA unwinding. Examples include Z-DNA, cruciforms and H-DNA {for a review, see Wells, 1988). Second, because supercoiled DNA is bent, processes that bend DNA are frequently promoted by, or even require, negative supercoiling. Nucleoprotein complexes that bend DNA are important in the cellular packaging of DNA, transcriptional regulation, replication, transposition and recombination {Better et al., 1982; Dodson et al., 1985; Fried & Crothers, 1983; Friedman, 1988; Richmond et al., 1984; Salvo & Grindley, 1988). A particularly important example is the compaction of DNA afforded by the tight solenoidal winding around histones in eukaryotic nucleosomes. Third, recent results on site-specific recombination and transposition suggest that supercoiled DNA structure plays a direct role in bringing together and aligning distant cis-acting DNA sequences and their associated protein-binding factors (Benjamin & Cozzarelli, 1989; Craigie & Mizuuchi, 1986; DrSge & Cozzarelli, 1989; Kanaar et al., 1989). This effect appears to result from the specific geometry of negative supercoiling. Finally, supercoiling causes changes in the repeat of the DNA double helix (White et al., 1988). Such changes could alter the binding of proteins and other ligands to DNA, and also affect the phasing between adjacent cis-acting sequences. A description of the structure of supercoiled circular DNA in solution should greatly increase our understanding of the role of supercoiling in these diverse processes. Very little is known on this subject. For example, the relationship between linking deficit and the number of supercoils is unknown. Similarly, Wr and T w have not been determined for the extensively supercoiled DNA isolated from cells. One problem has been that hydrodynamic techniques traditionally used to study macromolecules in solution, such as sedimentation, gel electrophoresis and light-scattering, give information only about gross average properties of the population of molecules. Extraction of shape information from the data is indirect and requires many model-dependent assumptions. For this reason, much of our present knowledge about super-
(b)
Figure 1. Comparison of the shape of plectonemically and solenoidally supereoiled DNA. (a) A diagram of a 4-6 kb plectonemically supercoiled DNA molecule with a a of -0"060. The DNA is wound as a regular right-handed superhelix except for the deviations at the ends of the superhelix axis and the branch points. The line representing the DNA double helix in (a) has a width of 22 A in the scale of the Figure. To compare the geometry of plectonemie supercoils with a model for the supercoiling found in nueleosomes, in (b), the same 4"6 kb DNA is wound into a smooth left-handed solenoidal superhelix with a radius of 43 A and a pitch of 28 A (Richmond et al., 1984). This structure has 57 solenoidal supercoils. Assuming a nucleosomal helical repeat of 10"0bp/turn, the solenoidal model will have a a of -0"079 (Cozzarelli et al., 1989). The scale used in (b) is the same as in (a), except that the diameter of the double helix in the closed solenoidal superhelix has been reduced by 50%, for clarity, and a blowup of the supercoils is shown. coiled DNA structure has come from electron microscopy. These studies suggested that supercoiled circular DNA has a branched plectonemic {interwound) form (Upholt et al., 1971; Vinograd et al., 1965). An interwound form for circular DNA in solution was also deduced from the structure of products of the site-specific Int recombination system of bacteriophage lambda (Spengler et al., 1985). This study also demonstrated that the interwound structure was right-handed. Here, we present a systematic study of the structure of negatively supercoiled circular DNA as a function of linking number deficit. We use a model for the average structure of interwound DNA in solution, illustrated by Figure l(a), in which the DNA is a regular right-handed interwound superhelix whose axis is branched. This model is mathematically well-defined and allows the expression of important geometric properties that cannot be measured directly, in terms of those that can. We use a site-specific recombination assay and electron microscopy to measure the number of supercoils about the superhelix axis, and electron microscopy to measure the length and branching of the axis. From these measurements, we calculate the variation in superhelix radius, superhelix pitch angle, Wr and T w , with increasing linking deficit. We find that the structure is entirely different from the supercoiling observed in nucleosomal DNA, which is depicted in Figure l(b). We discuss the energetic and biological implications of our measurements.
Plectonemically Supercoiled D N A
2. E x p e r i m e n t a l
Procedures
933
deficits will usually be expressed independent descriptor, o', where:
(a) D N A For electron microscopy, 2 plasmids, differing in size by a factor of 2, were studied. Both are derivatives of pBR322 (Bolivar et al., 1977; Sutcliffe, 1979). pAB7.0d is 6978 bpt in length (Wasserman et al., 1988), and pJB3.5d is 3480 bp in length (Bliska & Cozzarelli, 1987). For experiments using site-specific recombination catalyzed by the lambda integrase system (Int), 2 additional plasmids were used, pJB3.5i (3459 bp: Bliska, 1988) and pBNW3.8d (3800(+50) bp: Wasserman el al., 1988). All 4 plasmids contain the aUP and allB recombination sites of the Int system. In pJB3.5d and pBNW3.8d, the recombination sites are oriented as direct repeats. With these substrates, Int recombination produces dimeric catenanes, pJB3.5i is a derivative of pJB3.5d in which the recombination sites are oriented as inverted repeats; recombination of this substrate gives knotted products. For pJB3.5d, pJB3.5i and pBN~V3.8d, the distances between the recombination sites are 574, 515 and 900(_+50) bp, respectively (BIiska, 1988; Bliska & Cozzarelli, 1987; Wasserman el at., 1988). Large-scale plasmid purification was performed using the alkaline lysis method, followed by 2 cycles ofethidium bromide/CsCl equilibrium density-gradient centrifugation (Maniatis el al., 1982). (b) Topoisomerase reactions and measurement of ALk To prepare plasmid samples with defined levels of supercoiling, DNA (100/~g]ml) was relaxed in the presence of 0 to 8 pg ethidium bromide/ml and with a 5-fold excess of wheat germ topoisomerase I (Dynan et al., 1981) over that necessary for full relaxation. In early experiments using electron microscopy, relaxation was carried out in Topo I buffer (50mM-Tris'HCl (pH 8-0), 50 mM-NaCl, 1 mm-dithiothreitol, l mM-EDTA) for 30 min at 37°C. For later electron microscopy experiments, reactions were performed in TE buffer (I0 mM-Tris'HCI (pH 8"0), 1 mm-EDTA) for 30 rain at 25°C. For experiments using Int site-specific recombination, relaxations were performed at 25°C in Int buffer (20 mM-Tris" HC1 (pH 8"0), 50 mm-NaC1, 10 mM-MgCl2). Reactions were terminated by addition of sodium dodecyi sulfate to I °/o (w/v) final concentration. Protein and ethidium bromide were removed by 3 extractions with phenol, and the DNA was precipitated with ethanol. Linking number difference was measured by the band counting method (Keller, 1975; Shure & Vinograd, 1976). A series of 0"8% (w/v) agarose gels (40 mM-Tris-acetate (pH 7"8), 5 mM-sodium acetate, 2 mm-EDTA) containing from 0 to 40 #g chloroquine phosphate/ml were run at 1"3 V]cm for 24 h with buffer recirculation to resolve sample topoisomer distributions. Gels were stained with ethidium bromide and photographed under short-wave ultraviolet light. Photographic negatives were scanned with a Zeineh soft laser densitometer. The linking difference, ALk, is the difference between the average Lk of a sample and the average Lb after relaxation, Lk o. Relaxation is obtained by topoisomerase treatment under temperature and buffer conditions identical to those used to analyze the sample. To facilitate comparisons between plasmids of different size, linking
t Abbreviations used: bp, base-pair(s); IHF, 3 integrative host factor; kb, l0 bases or base-pairs.
a =
using the
(Lk-Lbo) ALk = Lk o Lk o '
size-
(2)
For most of the electron microscopy, DNA samples that were relaxed in Tope I buffer at 370C were spread for electron microscopy in TE buffer at 25°C. In some experiments, the same samples were spread in Int reaction buffer at 25°C. To correct for changes in a caused by differences in temperature and solution conditions, we compared the Lk values for samples relaxed under these 3 conditions. The change in a was -0.003 for transfer from Tope I buffer at 37°C to TE at 25°C+ For transfer from Topo I buffer at 37°C to Int buffer at 25°C, the change in a was -0.007. All reported a values have been corrected using these conversion factors and refer to the superhelical density under the buffer and temperature conditions used for spreading. (e) Electron microscopy Electron microscopy was performed using the polylysine adsorption method of Williams (1977). Samples were prepared at room temperature (25°C). Briefly, carbon-coated formvar grids were exposed to high-voltage glow discharge at 70 to 100 mTorr (1 Torr ~ 133.322 Pa) for 20 s and then coated with poly-L-lysine (Sigma Chemical Co.) by adding 8 #l o f a 1 #g]ml solution for 1 rain. The grids were drained and air-dried by aspiration with a drawn-out Pasteur pipette. An 8-#1 drop of DNA solution (0-5 to 5/~g DNA/ml) was added to the grid and allowed to adsorb for 1 rain. This was followed by a 20 s wash in 0-1 M-ammonium acetate, staining in 5% (w]v) uranyl acetate for 20s, and a 5s wash in 0-01 M-ammonium acetate. The grids were rapidly air-dried by aspiration and rotary shadowed with tungsten. Micrographs were taken at a primary magnification of 33,000 x using a JEOL100CX electron microscope. (d) Measurement of electron micrographs Most of the measurements were performed on photographic prints (final magnification 82,500x) using an electronic digitizer (Numonics). To measure the number of DNA crossings/DNA molecule, also called nodes, negatives were projected onto paper (final magnification 330,000 x ), the path of the DNA was traced, and the nodes were counted from the tracings. The variation introduced by using different grids for each DNA sample was estimated by comparing the average lengths of nicked molecules on each grid. The grid-to-grid variation in these measurements was, at most, 5°/o of the average total length. To minimize the effect of this variation, we normalized all data from a grid using the average length of nicked molecules on the same grid. We assume this length to be the number of basepairs in the plasmid multiplied by 3"35 A per base-pair, or 23,380A for pAB7.0d and 11,660A for pJB3.5d (1 A = 0"1 nm}. These values are within 5 % of the lengths measured using the nominal magnification of the microscope. The superhelix axis is defined as the line that passes through the nodes and bisects the area enclosed by the DNA between adjacent nodes. Because of the regular shape of the supercoils, the path of this line could be determined unambiguously and, therefore, it was drawn freehand. Fig. 2 shows a typical electron micrograph of a
934
T . C . Boles et al.
perhelix axis points
Figure 2. Measurement strategy for electron microscopy. At the left is a micrograph of a 7 kb plasmid DNA molecule (pAB7.0d) with a specific linking deficit of -0"027. At the right is a tracing that illustrates how some of the measurements of the DNA were performed. Nodes are points at which 2 DNA helices cross in projection. We define the superhelix axis as the curve that passes through the superhelical nodes and bisects the area enclosed by the DNA between the nodes. Almost all supercoiled molecules observed in our study display a branched structure. Branch points are defined as points where the superhelix axes from three or more plectonemic segments intersect. To measure the total axis length for branched molecules, we determined the length of the axis for each plectonemie segment and summed them to obtain the total. The molecule shown has 2 branch points, 5 plectonemic segments and 25 nodes. supercoiled molecule and a tracing that illustrates the axis. This molecule is branched, as were almost all the molecules examined in this study. As shown in Fig. 2, we define branch points as places where 3 or more interwound regions intersect. Segments are defined as the interwound regions between neighboring branch points, or between branch points and the ends of the superhelix axis. To measure the length of the superhelix axis in branched molecules, an axis length was measured for each individual segment in the molecule, and these lengths were summed. The area of the grid surface enclosed by the DNA supercoils as viewed in the micrographs was measured using the area mode of the digitizer. Many molecules were not measurable because they overlapped other molecules, or because the DNA path could not be traced unambiguously. The fraction of observed molecules that were measurable varied between 10 and 33% and was 15 to 18% for most grids. There was no systematic decrease in the fraction of measurable molecules with increasing linking deficit. (e) Recombination assays Int-mediated recombination of pJB3.5d, pJB3.5i and pBNW3.8d and analyses of the product catenane or knot
complexity were performed as described (Bliska, 1988; Bliska & Cozzarelli, 1987). Briefly, substrate DNA (25 #g/ml) was incubated with phage lambda I n t and Escheriehia coli integrative host factor (IHF and Int both at 6/~g/ml) in I n t buffer for 30rain at 25°C. DNA products were purified by extraction with phenol and precipitation with ethanol, singly nicked with DNase I in the presence of excess ethidium bromide, and resolved according to catenane or knot complexity by agarose gel electrophoresis (Sundin & Varshavsky, 1981). Product bands were identified by comparison with reference knot ladders generated by treating the substrate plasmid with bacteriophage T4 DNA topoisomerase (Spengler et al., 1985). The average catenane or knot complexity was determined from densitometric analyses of these gels. (f) Mathematical model and measurement strategy We use an idealized, average model for plectonemically supercoiled DNA in solution that is characterized by a regular, right-handed, interwound helical geometry (Fig. l(a)). The superhelix axis is branched, and therefore we consider each molecule to be composed of a series of individual interwound segments that are joined at the branch points. To introduce the mathematics, we consider a simplified, unbranched molecule where the DNA winds
Plectonemically Supercoiled DN A
935
join the 2 helical segments. To extend this simple case to our branched model, we imagine that segment ends lack hemispherical caps where they meet at branch points. Thus, in molecules with a single branch point, each interwound segment will have a single hemispherical cap on the end away from the branch point. In multiply branched molecules, there will be some interwound segments that extend between 2 branch points and lack both caps. Because this model is mathematically welldefined, the interrelationships between geometric parameters are easily determined. Our strategy is to measure directly experimentally convenient parameters, such as the length of the DNA (L), the length of the superhelix axis (1), and the number of supercoils (n). With these data, we use the properties of the model to calculate the parameters that are difficult or impossible to measure directly: the superhelix radius (r), the superhelix pitch angle (6), Wr and Tw. The length of the DNA, L, is the sum of 2 components, the length on the caps, L~aps, and the length in the helically interwound regions, L~,l~r:
f~fL
Structure of Plectonemically Supercoiled D N A T. Christian Bolest Department of Molecular Biology University of California, Berkeley Berkeley, CA 94720 U.S.A.
James H. White Department of Mathematics University of California Los Angeles, CA 90024 U.S.A.
and Nicholas R. Cozzarelli Department of Molecular and Cell Biology Division of Biochemistry and Molecular Biology University of California Berkeley, CA 94720 U.S.A. (Received 29 August 1989; accepted 11 December 1989) Using electron microscopy and topological methods, we have deduced an average structure for negatively supercoiled circular DNA in solution. Our data suggest that DNA has a branched plectonemic (interwound) form over the range of supercoiling tested. The length of the superhelix axis is constant at 41 ~/o of the DNA length, whereas the superhelix radius decreases essentially hyperbolically as supercoiling increases. The number of supercoils is 89 ~o of the linking deficit. Both writhe and twist change with supercoiling, but the ratio of the change in writhe to the change in twist is fixed at 2"6 : 1. The extent of branching of the superhelix axis is proportional to the length of the plasmid, but is insensitive to superhelix density. The relationship between DNA flexibility constants for twisting and bending calculated using our structural data is similar to that deduced from previous studies. The extended thin form of plectonemically supercoiled DNA offers little compaction for cellular packaging, but promotes interaction between cis-acting sequence elements that may be distant in primary structure. We discuss additional biological implications of our structural data.
The number of times the two strands of the DNA double helix are intertwined, i.e. the linking number of the DNA (Lk), is a constant that can be changed only by breaking the DNA backbone. Although Lk is a topological property, it is the sum of two geometric parameters that describe the shape of the DNA, writhe (Wr) and twist (Tw) (White, 1969):
1. I n t r o d u c t i o n
DNA supercoiling, the coiling of the axis of the double helix, is ubiquitous in biological systems. It arises in two ways. It can result from winding around proteins, as in eukaryotic nucleosomes. Supercoiling can also result from the topological constraint imposed upon underwound or overwound closed molecules free in solution. Both sources of supercoiling are important in ~vo. The topological properties of closed circular DNA provide a conceptual framework for understanding supercoi]ing (for a review, see Cozzarelli et al., 1990).
Lk = Wr+Tw.
Wr is a measure of the coiling of the DNA axis, and Tw reflects the helical winding of the DNA strands around each other. For circular DNAs isolated from natural sources, supercoiling is a geometric compensation for a deficiency in linking number. There is an unfavorable free energy associated with decreasing Lk from the preferred value of the
t Present address: Graduate Department of Biochemistry, Brandeis University, Waltham MA 02254, U.S.A. 0022-2836/90/120931-21 $03.00/0
(1)
931
© 1990 Academic Press Limited
932
T . C . Boles et al.
relaxed state (Depew & Wang, 1975; Pulleyblank et al., 1975; Frank-Kamenetskii, 1990), operationally defined as the equilibrium value after nicking and religation. To minimize this free energy change, the DNA adopts a supercoiled shape, thereby changing the values of Wr and Tw. Negative supercoiling is important for a wide variety of biological processes. First, the free energy of negative supercoiling assists processes that require untwisting or denaturation of DNA, such as DNA replication and transcription. Thus, negative supercoiling helps polymerases, helicases, singlestrand binding proteins, and other accessory proteins to force apart the two strands of the DNA double helix, allowing freer access to the genetic information stored in the base sequence (Funnell et a/., 1986; McClure, 1985). Negative supercoiling also promotes a variety of structural alterations that lead to DNA unwinding. Examples include Z-DNA, cruciforms and H-DNA {for a review, see Wells, 1988). Second, because supercoiled DNA is bent, processes that bend DNA are frequently promoted by, or even require, negative supercoiling. Nucleoprotein complexes that bend DNA are important in the cellular packaging of DNA, transcriptional regulation, replication, transposition and recombination {Better et al., 1982; Dodson et al., 1985; Fried & Crothers, 1983; Friedman, 1988; Richmond et al., 1984; Salvo & Grindley, 1988). A particularly important example is the compaction of DNA afforded by the tight solenoidal winding around histones in eukaryotic nucleosomes. Third, recent results on site-specific recombination and transposition suggest that supercoiled DNA structure plays a direct role in bringing together and aligning distant cis-acting DNA sequences and their associated protein-binding factors (Benjamin & Cozzarelli, 1989; Craigie & Mizuuchi, 1986; DrSge & Cozzarelli, 1989; Kanaar et al., 1989). This effect appears to result from the specific geometry of negative supercoiling. Finally, supercoiling causes changes in the repeat of the DNA double helix (White et al., 1988). Such changes could alter the binding of proteins and other ligands to DNA, and also affect the phasing between adjacent cis-acting sequences. A description of the structure of supercoiled circular DNA in solution should greatly increase our understanding of the role of supercoiling in these diverse processes. Very little is known on this subject. For example, the relationship between linking deficit and the number of supercoils is unknown. Similarly, Wr and T w have not been determined for the extensively supercoiled DNA isolated from cells. One problem has been that hydrodynamic techniques traditionally used to study macromolecules in solution, such as sedimentation, gel electrophoresis and light-scattering, give information only about gross average properties of the population of molecules. Extraction of shape information from the data is indirect and requires many model-dependent assumptions. For this reason, much of our present knowledge about super-
(b)
Figure 1. Comparison of the shape of plectonemically and solenoidally supereoiled DNA. (a) A diagram of a 4-6 kb plectonemically supercoiled DNA molecule with a a of -0"060. The DNA is wound as a regular right-handed superhelix except for the deviations at the ends of the superhelix axis and the branch points. The line representing the DNA double helix in (a) has a width of 22 A in the scale of the Figure. To compare the geometry of plectonemie supercoils with a model for the supercoiling found in nueleosomes, in (b), the same 4"6 kb DNA is wound into a smooth left-handed solenoidal superhelix with a radius of 43 A and a pitch of 28 A (Richmond et al., 1984). This structure has 57 solenoidal supercoils. Assuming a nucleosomal helical repeat of 10"0bp/turn, the solenoidal model will have a a of -0"079 (Cozzarelli et al., 1989). The scale used in (b) is the same as in (a), except that the diameter of the double helix in the closed solenoidal superhelix has been reduced by 50%, for clarity, and a blowup of the supercoils is shown. coiled DNA structure has come from electron microscopy. These studies suggested that supercoiled circular DNA has a branched plectonemic {interwound) form (Upholt et al., 1971; Vinograd et al., 1965). An interwound form for circular DNA in solution was also deduced from the structure of products of the site-specific Int recombination system of bacteriophage lambda (Spengler et al., 1985). This study also demonstrated that the interwound structure was right-handed. Here, we present a systematic study of the structure of negatively supercoiled circular DNA as a function of linking number deficit. We use a model for the average structure of interwound DNA in solution, illustrated by Figure l(a), in which the DNA is a regular right-handed interwound superhelix whose axis is branched. This model is mathematically well-defined and allows the expression of important geometric properties that cannot be measured directly, in terms of those that can. We use a site-specific recombination assay and electron microscopy to measure the number of supercoils about the superhelix axis, and electron microscopy to measure the length and branching of the axis. From these measurements, we calculate the variation in superhelix radius, superhelix pitch angle, Wr and T w , with increasing linking deficit. We find that the structure is entirely different from the supercoiling observed in nucleosomal DNA, which is depicted in Figure l(b). We discuss the energetic and biological implications of our measurements.
Plectonemically Supercoiled D N A
2. E x p e r i m e n t a l
Procedures
933
deficits will usually be expressed independent descriptor, o', where:
(a) D N A For electron microscopy, 2 plasmids, differing in size by a factor of 2, were studied. Both are derivatives of pBR322 (Bolivar et al., 1977; Sutcliffe, 1979). pAB7.0d is 6978 bpt in length (Wasserman et al., 1988), and pJB3.5d is 3480 bp in length (Bliska & Cozzarelli, 1987). For experiments using site-specific recombination catalyzed by the lambda integrase system (Int), 2 additional plasmids were used, pJB3.5i (3459 bp: Bliska, 1988) and pBNW3.8d (3800(+50) bp: Wasserman el al., 1988). All 4 plasmids contain the aUP and allB recombination sites of the Int system. In pJB3.5d and pBNW3.8d, the recombination sites are oriented as direct repeats. With these substrates, Int recombination produces dimeric catenanes, pJB3.5i is a derivative of pJB3.5d in which the recombination sites are oriented as inverted repeats; recombination of this substrate gives knotted products. For pJB3.5d, pJB3.5i and pBN~V3.8d, the distances between the recombination sites are 574, 515 and 900(_+50) bp, respectively (BIiska, 1988; Bliska & Cozzarelli, 1987; Wasserman el at., 1988). Large-scale plasmid purification was performed using the alkaline lysis method, followed by 2 cycles ofethidium bromide/CsCl equilibrium density-gradient centrifugation (Maniatis el al., 1982). (b) Topoisomerase reactions and measurement of ALk To prepare plasmid samples with defined levels of supercoiling, DNA (100/~g]ml) was relaxed in the presence of 0 to 8 pg ethidium bromide/ml and with a 5-fold excess of wheat germ topoisomerase I (Dynan et al., 1981) over that necessary for full relaxation. In early experiments using electron microscopy, relaxation was carried out in Topo I buffer (50mM-Tris'HCl (pH 8-0), 50 mM-NaCl, 1 mm-dithiothreitol, l mM-EDTA) for 30 min at 37°C. For later electron microscopy experiments, reactions were performed in TE buffer (I0 mM-Tris'HCI (pH 8"0), 1 mm-EDTA) for 30 rain at 25°C. For experiments using Int site-specific recombination, relaxations were performed at 25°C in Int buffer (20 mM-Tris" HC1 (pH 8"0), 50 mm-NaC1, 10 mM-MgCl2). Reactions were terminated by addition of sodium dodecyi sulfate to I °/o (w/v) final concentration. Protein and ethidium bromide were removed by 3 extractions with phenol, and the DNA was precipitated with ethanol. Linking number difference was measured by the band counting method (Keller, 1975; Shure & Vinograd, 1976). A series of 0"8% (w/v) agarose gels (40 mM-Tris-acetate (pH 7"8), 5 mM-sodium acetate, 2 mm-EDTA) containing from 0 to 40 #g chloroquine phosphate/ml were run at 1"3 V]cm for 24 h with buffer recirculation to resolve sample topoisomer distributions. Gels were stained with ethidium bromide and photographed under short-wave ultraviolet light. Photographic negatives were scanned with a Zeineh soft laser densitometer. The linking difference, ALk, is the difference between the average Lk of a sample and the average Lb after relaxation, Lk o. Relaxation is obtained by topoisomerase treatment under temperature and buffer conditions identical to those used to analyze the sample. To facilitate comparisons between plasmids of different size, linking
t Abbreviations used: bp, base-pair(s); IHF, 3 integrative host factor; kb, l0 bases or base-pairs.
a =
using the
(Lk-Lbo) ALk = Lk o Lk o '
size-
(2)
For most of the electron microscopy, DNA samples that were relaxed in Tope I buffer at 370C were spread for electron microscopy in TE buffer at 25°C. In some experiments, the same samples were spread in Int reaction buffer at 25°C. To correct for changes in a caused by differences in temperature and solution conditions, we compared the Lk values for samples relaxed under these 3 conditions. The change in a was -0.003 for transfer from Tope I buffer at 37°C to TE at 25°C+ For transfer from Topo I buffer at 37°C to Int buffer at 25°C, the change in a was -0.007. All reported a values have been corrected using these conversion factors and refer to the superhelical density under the buffer and temperature conditions used for spreading. (e) Electron microscopy Electron microscopy was performed using the polylysine adsorption method of Williams (1977). Samples were prepared at room temperature (25°C). Briefly, carbon-coated formvar grids were exposed to high-voltage glow discharge at 70 to 100 mTorr (1 Torr ~ 133.322 Pa) for 20 s and then coated with poly-L-lysine (Sigma Chemical Co.) by adding 8 #l o f a 1 #g]ml solution for 1 rain. The grids were drained and air-dried by aspiration with a drawn-out Pasteur pipette. An 8-#1 drop of DNA solution (0-5 to 5/~g DNA/ml) was added to the grid and allowed to adsorb for 1 rain. This was followed by a 20 s wash in 0-1 M-ammonium acetate, staining in 5% (w]v) uranyl acetate for 20s, and a 5s wash in 0-01 M-ammonium acetate. The grids were rapidly air-dried by aspiration and rotary shadowed with tungsten. Micrographs were taken at a primary magnification of 33,000 x using a JEOL100CX electron microscope. (d) Measurement of electron micrographs Most of the measurements were performed on photographic prints (final magnification 82,500x) using an electronic digitizer (Numonics). To measure the number of DNA crossings/DNA molecule, also called nodes, negatives were projected onto paper (final magnification 330,000 x ), the path of the DNA was traced, and the nodes were counted from the tracings. The variation introduced by using different grids for each DNA sample was estimated by comparing the average lengths of nicked molecules on each grid. The grid-to-grid variation in these measurements was, at most, 5°/o of the average total length. To minimize the effect of this variation, we normalized all data from a grid using the average length of nicked molecules on the same grid. We assume this length to be the number of basepairs in the plasmid multiplied by 3"35 A per base-pair, or 23,380A for pAB7.0d and 11,660A for pJB3.5d (1 A = 0"1 nm}. These values are within 5 % of the lengths measured using the nominal magnification of the microscope. The superhelix axis is defined as the line that passes through the nodes and bisects the area enclosed by the DNA between adjacent nodes. Because of the regular shape of the supercoils, the path of this line could be determined unambiguously and, therefore, it was drawn freehand. Fig. 2 shows a typical electron micrograph of a
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perhelix axis points
Figure 2. Measurement strategy for electron microscopy. At the left is a micrograph of a 7 kb plasmid DNA molecule (pAB7.0d) with a specific linking deficit of -0"027. At the right is a tracing that illustrates how some of the measurements of the DNA were performed. Nodes are points at which 2 DNA helices cross in projection. We define the superhelix axis as the curve that passes through the superhelical nodes and bisects the area enclosed by the DNA between the nodes. Almost all supercoiled molecules observed in our study display a branched structure. Branch points are defined as points where the superhelix axes from three or more plectonemic segments intersect. To measure the total axis length for branched molecules, we determined the length of the axis for each plectonemie segment and summed them to obtain the total. The molecule shown has 2 branch points, 5 plectonemic segments and 25 nodes. supercoiled molecule and a tracing that illustrates the axis. This molecule is branched, as were almost all the molecules examined in this study. As shown in Fig. 2, we define branch points as places where 3 or more interwound regions intersect. Segments are defined as the interwound regions between neighboring branch points, or between branch points and the ends of the superhelix axis. To measure the length of the superhelix axis in branched molecules, an axis length was measured for each individual segment in the molecule, and these lengths were summed. The area of the grid surface enclosed by the DNA supercoils as viewed in the micrographs was measured using the area mode of the digitizer. Many molecules were not measurable because they overlapped other molecules, or because the DNA path could not be traced unambiguously. The fraction of observed molecules that were measurable varied between 10 and 33% and was 15 to 18% for most grids. There was no systematic decrease in the fraction of measurable molecules with increasing linking deficit. (e) Recombination assays Int-mediated recombination of pJB3.5d, pJB3.5i and pBNW3.8d and analyses of the product catenane or knot
complexity were performed as described (Bliska, 1988; Bliska & Cozzarelli, 1987). Briefly, substrate DNA (25 #g/ml) was incubated with phage lambda I n t and Escheriehia coli integrative host factor (IHF and Int both at 6/~g/ml) in I n t buffer for 30rain at 25°C. DNA products were purified by extraction with phenol and precipitation with ethanol, singly nicked with DNase I in the presence of excess ethidium bromide, and resolved according to catenane or knot complexity by agarose gel electrophoresis (Sundin & Varshavsky, 1981). Product bands were identified by comparison with reference knot ladders generated by treating the substrate plasmid with bacteriophage T4 DNA topoisomerase (Spengler et al., 1985). The average catenane or knot complexity was determined from densitometric analyses of these gels. (f) Mathematical model and measurement strategy We use an idealized, average model for plectonemically supercoiled DNA in solution that is characterized by a regular, right-handed, interwound helical geometry (Fig. l(a)). The superhelix axis is branched, and therefore we consider each molecule to be composed of a series of individual interwound segments that are joined at the branch points. To introduce the mathematics, we consider a simplified, unbranched molecule where the DNA winds
Plectonemically Supercoiled DN A
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join the 2 helical segments. To extend this simple case to our branched model, we imagine that segment ends lack hemispherical caps where they meet at branch points. Thus, in molecules with a single branch point, each interwound segment will have a single hemispherical cap on the end away from the branch point. In multiply branched molecules, there will be some interwound segments that extend between 2 branch points and lack both caps. Because this model is mathematically welldefined, the interrelationships between geometric parameters are easily determined. Our strategy is to measure directly experimentally convenient parameters, such as the length of the DNA (L), the length of the superhelix axis (1), and the number of supercoils (n). With these data, we use the properties of the model to calculate the parameters that are difficult or impossible to measure directly: the superhelix radius (r), the superhelix pitch angle (6), Wr and Tw. The length of the DNA, L, is the sum of 2 components, the length on the caps, L~aps, and the length in the helically interwound regions, L~,l~r:
f~fL
