JOURNAL
OF STRUCTURAL
BIOLOGY
107,
15-21
(1991)
Spatial Visualization of DNA in Solution ISABELLEDUSTIN,"
PATRICKFURRER,"
*Laboratoire d’Analyse Ultrastructurale, B&timent Molecular Biology Laboratory, 156 X, F-38042 University of Minnesota Medical School,
ANDRZEJ~TASIAK," JACQLJESDUBOCHET,*,~JOERGLANGOWSKI,~. EDWARDEGELMAN~:
de Biologie, Universiti de Lausanne, CM-1015 Lausanne, Switzerland; fEuropean Grenoble Cedex, France; and $Department of Cell Biology and Neuroanatomy, 4-135 Jackson Hall, 323 Church Street S.E., Minneapolis, Minnesota 55455
ReceivedMarch 27, THIS
WORK
IS DEDICATED
1991, TO
and
in revised
E. KELLENBERGER
Press, Inc.
INTRODUCTION Classical three-dimensional (3D) reconstruction methods in electron microscopy start with images of specimens, where the constrast is created by differences in electron density between the object and the surrounding media. The 3D reconstruction of both the surface and the internal structure of an object is possible, provided that many projections, spanning the complete tilt range between 0 and 90”, are available. This approach is particularly effective in the case of helical objects like tails of bacteriophages T4 (Lepault and Leonard, 1985) or RecA filaments (Egelman and Stasiak, 1986) where, due to the internal helical symmetry relating every subunit, a single image provides all the required projections (DeRosier and Klug, 1968). In the case of asymmetric objects like ribosomal subunits, correlation and classification methods applied to tilt series allow one to obtain 3D reconstructions (Radermacher, 1988). The situation is less promising when the observed correspondence
should
form
May
21, 1991
FOR
HIS
70TH
BIRTHDAY
objects are so flexible that individuals differ significantly from each other and when the whole preparation is so sensitive to beam damage that tilt series must be limited to only two pictures. A 3D reconstruction of the surface and internal structure of such objects is then impossible. More limited aims, however, are attainable. We present here a method which allows us to reconstruct the 3D path of individual flexible filamentous objects. We apply this method to trace the trajectories of individual DNA molecules embedded in a layer of vitrified solution. The method involves the determination of points along the projected filament axis in each of the two views and a simple geometric triangulation to calculate the third dimension of the path of the filament. For the purpose of visualization, the 3D path is then surrounded by the known volume of the object or by an arbitrary chosen volume suitable for the object’s graphic display. This technique fills one methodological gap in studies of the 3D structure of DNA molecules and provides information which is relevant to a better understanding of the biological activity of DNA. There is growing evidence that the total shape of a DNA molecule is essential for its function (Travers, 1989; Goodman and Nash, 1989). DNA bending can bring into close proximity distant sites along the DNA or serve as a marker for specific interactions. The subtle interaction between twist and writhe in DNA loops relates local parameters, such as the twist angle between base pairs and the local curvature of the DNA, with global features such as supercoiling and linking number (Boles et al., 1990). Until recently, the study of DNA shape relied for a large part on gel electrophoresis (Wu and Crothers, 1984) and other rather indirect physicochemical methods (Torbet and DiCapua, 1989) Electron microscopy has also contributed, in particular by characterizing lbent fragments of DNA (Laundon
An image analysis method is presented which allows for the reconstruction of the three-dimensional path of filamentous objects from two of their projections. Starting with stereo pairs, this method is used to trace the trajectory of DNA molecules embedded in vitreous ice and leads to a faithful representation of their threedimensional shape in solution. This computer-aided reconstruction is superior to the subjective threedimensional impression generated by observation of stereo pairs of micrographs because it enables one to look at the reconstructed molecules from any chosen direction and distance and allows quantitative analysis such as determination of distances, curvature, persistence length, and writhe of DNA molecules in solution. 0 1991 Academic
1 To whom
AND
be addressed.
15 1047-8477191
$3.00
Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
16
DUSTIN
and Griffith, 1988) and by measuring the topological properties of knots and catenanes (Spengler et al., 1985). However, the necessity of adsorbing the molecules onto a supporting film in conventional electron microscopy forces an inherently 3D system to be transformed into a 2D one, thus losing or modifying information. This limitation can be overcome by cryo-electron microscopy. It allows direct visualization of biological particles in their aqueous environment by the vitrification of a thin layer of solution (Adrian et al., 1984; Dubochet et al., 1988). DNA is observed by this method without any chemical modification or stain. This was shown recently for plasmid DNA molecules, which can be precisely visualized in relaxed and supercoiled form, under different salt conditions (Adrian et al., 1990). We now show that the 3D path of vitrified DNA molecules can be faithfully reconstructed from two tilt images, even when a poor signal-to-noise ratio of the pictures makes it very difficult to get a direct stereo impression by looking at the stereo pair of micrographs. MATERIALS Preparation
AND
METHODS
of the DNA
Naturally supercoiled pUC 9 DNA was prepared following the standard plasmid isolation procedure (Sambrook et al., 1989), which includes lysis by alkali, CsClLethidium bromide equilibrium gradients, and isoamyl alcohol extraction to remove ethidium bromide from DNA. In some preparations, holoenzyme of Escherichia coli RNA polymerase was bound to naturally supercoiled pUC 9 DNA according to the procedure of Klaus et al. (1983). Electron
ET AI,. The direction of the tilt axis of the stereo pairs is determined by finding the direction along which the distance between corresponding points does not change on both micrographs. Image
Processing
The computer processing is performed on a Silicon Graphics 4D20 Workstation. An Eikonix 1412 CCD camera is used to digitize images from magnified electron microscopy prints. Images are stored and manipulated using the SEMPER software (Synoptics). The magnification and sampling are chosen so that the filaments are typically around 5 pixels wide. The background density of the selected region can be flattened with a linear gradient correction, and the contrast of the molecule adjusted for optimal visualization on the display. The two micrographs of a stereo pair are oriented with the tilt axis (Oy axis) placed vertically on the display. They are aligned along the Oy direction on the basis of a reference point, which is a precisely defined feature, clearly visible on both micrographs. This can be, for example, a conspicuous contamination mark or an RNA polymerase molecule bound to the DNA molecule. Coordinate axes are chosen to bring the photographic plane perpendicular to the Oz axis. The reference point mentioned above is taken as the origin for the 3c, y, and z coordinates. The coordinate of a point i in space, (x, yi, zJ, projected on the first image plane, is (xi’, yi’), and on the second projected plane it becomes LX,“, y,“). Provided that Oy is parallel to the tilt axis, yi’ = yi”. A simple calculation then gives the z coordinate for this point: zi = (x”, cos 0 - r’J/sin 0, where 0 is the tilt angle between the two micrographs. The determination of the path of the DNA molecules is made by clicking with the mouse along the center of the filaments displayed on the screen. Clicking of individual points on the first image defines their coordinates (xi’, y,‘). This also defines the yi” coordinate for the corresponding points on the second image. The movement of the pointer is then restricted to the x direction at yL = yZ’ = Ye”. The distance between successive points typically corresponds to 6 nm on the molecule. Bicubic spline interpolation based on these chosen points results in a smooth path overlapping each displayed projection of the molecule.
Microscopy
Specimens were prepared as described previously (Dubochet et al., 1988; Adrian et al., 1990). A 3-pl drop of DNA solution (-200 pgiml) in Tris-EDTA (pH 7.51, 10 mM MgCl, was put on hydrophobic-perforated carbon film (Fukami et al., 1972). In the case of the DNA with bound RNA polymerase, the specimen buffer was 30 mM triethanolamine-Cl (pH 7.9), 10 mM MgCl,, and 0.1% glutaraldehyde. An automatic system (Cyrklaff et al., 1990) is used for blotting most of the drop in ca. l-2 set and immediately releasing the plunger. After a O.l-set free fall, the specimen is immersed into liquid ethane cooled close to its freezing point. The thin liquid layer of solution, spanning the holes of the supporting film, is then vitrified in ca. 10m4 sec. The vitrified specimen is transferred, without rewarming, into a Gatan 626 cryo-specimen holder and introduced into a Philips CM 12 electron microscope, equipped with a special blade-type anticontaminator (Homo et al., 1984) and an eucentric goniometer. Stereo pairs of micrographs were performed with a tilt angle of 220”. This large angular difference increases precision of 3D reconstructions but makes it difficult to obtain direct 3D impressions by viewing stereo pairs. Micrographs are recorded at ca. 2 p,m underfocus, at a temperature of - 172°C (nominal), at a magnification of x 60 000, and with minimum beam exposure on SO 163 Kodak film, and developed for 12-22 min in D 19, full strength. Under these conditions, the speed of the film is 2 pm2 per electron per optical density unit, and the dose per micrograph is ca. 2 x lo3 electrons/rim’. The total dose for stereo recording is double. Magnification is determined by a cross-grating replica.
Spatial
Visualization
The Wavefront Personal Visualizer, running on the graphic workstation, was used for rendering of three-dimensional objects. The reconstruction algorithm generates a curved line, corresponding to the axis of the DNA filament, in a 3D space. The reconstructed molecules are most conveniently visualized as flexible cylinders, obtained by attributing an arbitrary thickness to the 1D curve. This is achieved by surrounding the median axis of the filaments with polygonal surfaces. Octagons are positioned centered on the curve and orthogonal to the local tangent. These primitives are used to define parametric bicubic spline surfaces using the intrinsic geometric functions of the workstation. The ends of the tubular filaments are then closed by hemispherical surfaces. RESULTS
Test of the Reconstruction
Procedure
To check our reconstruction program, we applied it to two different projections of a wire model, mimicking an interwound DNA molecule. The test is shown in Fig. 1, where two projections (A,B) of the wire model (obtained by forming the object’s shadow with a parallel illumination of a photographic enlarger) are presented, together with the real (C) and reconstructed (D) object. Projection B is related to
SPATIAL
VISUALIZATION
OF DNA
17
F ‘IG 1.1. A model for testing reconstruction. (A, B) Two projection views of the ca. E-cm aluminium wire shaped to mimic the trajectory ofa Sl lpercoiled DNA molecule. The projections were obtained by using the nearly parallel illumination from a photographic enlarger in ordl er to expose the printing paper placed underneath the model. Tilt angle, + 40”. The end of the shorter aluminium wire f is used as a refe !re !nce point. After another 1-90” rotation, comparison is made between C, the picture of the wire and D, its computer-aided 3D recc m struction (C and D are seen from the same viewpoint). The parts of the wire perpendicular to the tilt axis (vertical) are imperfectly rect ml strutted because of insufficient information. The digitization of the curve was made with 57 points.
18
DUSTIN
projection A by a 40”-clockwise rotation of the object around the Oy vertical axis. (These two projections are presented as a stereo pair to enable the reader to create his or her own impression of the 3D shape of the object.) The surface view of the real object and of the reconstruction correspond to a further 90”clockwise rotation around the same axis from the position corresponding to B. The end of the wire f is used as reference point. The similarity between the real object (C) and its reconstruction (D) in this and other orientations provides a qualitative validation of the procedure. For noise-free projection images like those shown in Figs. 1A and lB, digitalization procedure is rather unambiguous and repeated digitalizations performed by the same or a different person lead to very similar, almost overlapping reconstructions. However, with very noisy images, the digitalization procedure becomes prone to misrepresentation and each reconstruction might differ. It is discussed later how the knowledge about stiffness and total length of the observed molecules can help to choose the proper digitalization path. Reconstruction of the 30 Trajectory of Tightly Supercoiled DNA Molecules Suspended in a Vitrified Film
The reconstruction procedure is applied to DNA molecules suspended in a buffer containing 10 mM MgCl,. It was demonstrated previously that in the presence of 10 n&f MgCl,, supercoiled DNA molecules adopt the form of a tight superhelix in which two opposing segments of interwound DNA molecules approach each other, except at the end loops (Adrian et al., 1990). The DNA regions, where two double-stranded segments are aligned together, show better contrast in vitrified specimens (due to the doubling of the mass per unit length of the filament) and therefore serve as a convenient object for study. Figure 2 (top) shows a stereo pair of micrographs of a tightly supercoiled pUC 9 DNA molecule. The end loops are hardly visible on these micrographs and have not been considered. The reconstructed object is presented in the same orientation as the visual stereo impression obtained from the stereo pair. Another stereo pair of a tightly supercoiled DNA filament is presented on top of Fig. 3. The center of one E. coli RNA polymerase bound to this DNA molecule has been used as a fixed reference point for the calculation. The reconstructed filament is shown from a different direction. Reconstructed images are based on the full set of 3D coordinates obtained after digitalization of the stereo pairs of molecules. Therefore, we are able to measure curvilinear and direct distances between points of interest on the observed DNA molecules.
ET AL.
For the reconstructed segments of molecules shown in Figs. 2 and 3 the curvilinear lengths are respectively 380 and 440 nm, while the corresponding endto-end distances are 210 and 170 nm. Such measurements are obviously impossible on the stereo impression obtained by conventional viewing of stereo micrographs. DISCUSSION
The method we present here for the computeraided reconstruction of filamentous nonplanar objects from two projections allows one to obtain 3D coordinates for the path of such objects. These data and the resulting reconstruction have several advantages over the subjective stereo impression obtained by viewing a stereo pair of electron micrographs. The stereo impression does not allow for the rotation of the representation, whereas the computer reconstruction enables one to observe it from any viewpoint. Since 3D coordinates are calculated, the quantitative analysis of such path-related parameters as the distance between points of interest measured along the filament or across space can be performed. In the case of DNA molecules observed in vitrified films, this method offers a way to directly measure the persistence length and the writhe of the molecules in solution. In addition, the method allows a representation of the 3D path of filamentous objects independent of the observer’s ability to obtain a 3D impression by viewing stereo pairs of micrographs. We show that two projections, related by a 40” tilt, are sufficient to obtain adequate reconstructions of filamentous objects. It is obvious that the higher the angular difference between the two projections (up to go”), the more precise the reconstruction can be. However, obtaining projections with tilt angles higher than 40” is frequently difficult, due to mechanical obstacles or specimen’s vibrations. Two projections alone do not provide sufficient information to define those regions of the filaments which are perpendicular (or close to perpendicular) to the tilt axis. Unsurprisingly, closer inspection of the differences between the reconstructed and real objects in Fig. 1 shows that these regions are most prone to be misrepresented in the reconstruction. In these regions, only a third projection, tilted around a different axis, would enable one to resolve all the indetermination. The reconstruction procedure presented here depends, of course, on having adequate micrographs, where the filamentous object can be traced and digitized along its path. However, in some short regions of low contrast, where it is difficult to pinpoint exactly the position of the axis of the filament, prior knowledge about continuity and flexural rigidity of the filament can help to make an educated choice.
SPATIAL
VISUALIZATION
OF DNA
FIG . 2. Stereo pair of tightly supercoiled DNA and corresponding reconstruction. put c 1 vitrified in a solution containing 10 mM Mgz+ (see Materials and Methods). for 501ne observers since the angular difference between right and left micrograph stereo pairs. Only “4-stranded” tightly supercoiled regions of DNA are considered. 45 poi nts, is presented from the same viewpoint as the stereo view.
Top right and left are stereo images of superc Obtaining direct stereo impression might be dil amounts to 40” instead of 20” or even less in star The reconstructed part of this molecule, digitized
19
:oiled gicu1t ldard with
DUSTIN
FI( digiti RNA visib
ET AL.
;. 3. Spatial visualization of a tightly supercoiled DNA molecule. Another supercoiled DNA molecule (same preparation), vvith 35 lzed points. Top views form a stereo pair on which the reconstruction is based. Reference point for the reconstruction is the E. ,wli polymerase that can be observed on both micrographs (arrow). Axis of the tightly supercoiled part follows a helical path. This isv veil le after the reconstructed molecule is rotated by + go”, + go”, and - 30” around the Ox, Oy, and Oz axes, respectively.
SPATIAL VISUALIZATION OF DNA
Such controls as the measurement of the total length of the reconstructed filament can help to check if the guess was a sensible one. Therefore it is sometimes possible to obtain an adequate reconstruction of the object from its two projections, even when it is not possible to obtain a 3D impression by direct viewing of a stereo pair. We thank Mr. M. Adrian for providing us with stereo micrographs, Mrs. B. ten Heggeler-Bordier for providing a sample of DNA with bound RNA polymerases, Ms. C. Cottier for photographic service,and Dr. D. Cangemi for fruitful discussions.This work was supported in part by Swiss National Fund Grants 3125694.88 and 31-27146.89 (to J. Dubochet and A. Stasiak) and Grant INT-9096163 from the United States National Science Foundation (to E. H. Egelman). REFERENCES ADRIAN,M.,DUBOCHET,J.,LEPAULT,J.,ANDMCDOWALL,A.W. (1984) Nature 308, 3236. ADRIAN,M., TEN HEGGELER-BORDIER, B., WAHLI, W., STASIAK, A.Z.,STASIAK,A.,ANDDUBOCHET,J.(~~~O)EMBOJ.~,~~~~4554.
21
BOLE&T. C.,WHITE,J.H.,AND COZZARELLI,N.R.U~~O)J.Mol. Biol. 213, 931-951. CYRKLA~,M., ADRIAN,M., ANDDUBOCHET,J.(1990) J.Electron Microsc. Tech. 16, 351-355. DEROSIER, D.J., ANDKLUG, A. (1968) Nature 217, 130-134. DUBOCHET,J., ADRIAN,M., CHANG,J., HOMO,J., LEPAULT,J., MCDOWALL,A.W., ANDSCHULTZ,P. (1988) Q.Rev.Biophys. 21, 129-228. EGELMAN,E.H., AND STASIAK,A. (1986) J. Mol.Biol. 191, 677697. FUKAMI,A., ADACHI,K., ANDKATOH,M. (1972) J.EZectron Microsc. 21, 99. GOODMAN,S. D., ANDNASH,H. A. (1989) Nature 341, 251-254. KLAUS,S.,VOGEL,F.,GAUTSCHI,J.,ST~LHAMMAR-CARLEMALM, M., ANDMEYER,J. (1983) Mol. Gen. Genet. 189, 21-26. LAUNDON,C.H., ANDGRIFFITH,J.(1988) Cell 52, 545-549. LEPAULT,J.,ANDLEONARD,K.(1985)J. MoZ.Biol. 182,431441. SPENGLER,S.J.,STASIAK,A.,ANDCOZZARELLI,N.R.(~~~~)C~Z~ 42, 325-334. RADERMACHER, M. (1988) J. Electron Microsc. Tech. 9, 359-394. TORBET,J.,ANDDICAPUA,E. (1989) EMBOJ.8,43514356. TRAVERS, A. (1989) Nature 341, 184-185. W&H.-K., ANDCROTHERS,D.M.(1984) Nature 308, 509-513.
OF STRUCTURAL
BIOLOGY
107,
15-21
(1991)
Spatial Visualization of DNA in Solution ISABELLEDUSTIN,"
PATRICKFURRER,"
*Laboratoire d’Analyse Ultrastructurale, B&timent Molecular Biology Laboratory, 156 X, F-38042 University of Minnesota Medical School,
ANDRZEJ~TASIAK," JACQLJESDUBOCHET,*,~JOERGLANGOWSKI,~. EDWARDEGELMAN~:
de Biologie, Universiti de Lausanne, CM-1015 Lausanne, Switzerland; fEuropean Grenoble Cedex, France; and $Department of Cell Biology and Neuroanatomy, 4-135 Jackson Hall, 323 Church Street S.E., Minneapolis, Minnesota 55455
ReceivedMarch 27, THIS
WORK
IS DEDICATED
1991, TO
and
in revised
E. KELLENBERGER
Press, Inc.
INTRODUCTION Classical three-dimensional (3D) reconstruction methods in electron microscopy start with images of specimens, where the constrast is created by differences in electron density between the object and the surrounding media. The 3D reconstruction of both the surface and the internal structure of an object is possible, provided that many projections, spanning the complete tilt range between 0 and 90”, are available. This approach is particularly effective in the case of helical objects like tails of bacteriophages T4 (Lepault and Leonard, 1985) or RecA filaments (Egelman and Stasiak, 1986) where, due to the internal helical symmetry relating every subunit, a single image provides all the required projections (DeRosier and Klug, 1968). In the case of asymmetric objects like ribosomal subunits, correlation and classification methods applied to tilt series allow one to obtain 3D reconstructions (Radermacher, 1988). The situation is less promising when the observed correspondence
should
form
May
21, 1991
FOR
HIS
70TH
BIRTHDAY
objects are so flexible that individuals differ significantly from each other and when the whole preparation is so sensitive to beam damage that tilt series must be limited to only two pictures. A 3D reconstruction of the surface and internal structure of such objects is then impossible. More limited aims, however, are attainable. We present here a method which allows us to reconstruct the 3D path of individual flexible filamentous objects. We apply this method to trace the trajectories of individual DNA molecules embedded in a layer of vitrified solution. The method involves the determination of points along the projected filament axis in each of the two views and a simple geometric triangulation to calculate the third dimension of the path of the filament. For the purpose of visualization, the 3D path is then surrounded by the known volume of the object or by an arbitrary chosen volume suitable for the object’s graphic display. This technique fills one methodological gap in studies of the 3D structure of DNA molecules and provides information which is relevant to a better understanding of the biological activity of DNA. There is growing evidence that the total shape of a DNA molecule is essential for its function (Travers, 1989; Goodman and Nash, 1989). DNA bending can bring into close proximity distant sites along the DNA or serve as a marker for specific interactions. The subtle interaction between twist and writhe in DNA loops relates local parameters, such as the twist angle between base pairs and the local curvature of the DNA, with global features such as supercoiling and linking number (Boles et al., 1990). Until recently, the study of DNA shape relied for a large part on gel electrophoresis (Wu and Crothers, 1984) and other rather indirect physicochemical methods (Torbet and DiCapua, 1989) Electron microscopy has also contributed, in particular by characterizing lbent fragments of DNA (Laundon
An image analysis method is presented which allows for the reconstruction of the three-dimensional path of filamentous objects from two of their projections. Starting with stereo pairs, this method is used to trace the trajectory of DNA molecules embedded in vitreous ice and leads to a faithful representation of their threedimensional shape in solution. This computer-aided reconstruction is superior to the subjective threedimensional impression generated by observation of stereo pairs of micrographs because it enables one to look at the reconstructed molecules from any chosen direction and distance and allows quantitative analysis such as determination of distances, curvature, persistence length, and writhe of DNA molecules in solution. 0 1991 Academic
1 To whom
AND
be addressed.
15 1047-8477191
$3.00
Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
16
DUSTIN
and Griffith, 1988) and by measuring the topological properties of knots and catenanes (Spengler et al., 1985). However, the necessity of adsorbing the molecules onto a supporting film in conventional electron microscopy forces an inherently 3D system to be transformed into a 2D one, thus losing or modifying information. This limitation can be overcome by cryo-electron microscopy. It allows direct visualization of biological particles in their aqueous environment by the vitrification of a thin layer of solution (Adrian et al., 1984; Dubochet et al., 1988). DNA is observed by this method without any chemical modification or stain. This was shown recently for plasmid DNA molecules, which can be precisely visualized in relaxed and supercoiled form, under different salt conditions (Adrian et al., 1990). We now show that the 3D path of vitrified DNA molecules can be faithfully reconstructed from two tilt images, even when a poor signal-to-noise ratio of the pictures makes it very difficult to get a direct stereo impression by looking at the stereo pair of micrographs. MATERIALS Preparation
AND
METHODS
of the DNA
Naturally supercoiled pUC 9 DNA was prepared following the standard plasmid isolation procedure (Sambrook et al., 1989), which includes lysis by alkali, CsClLethidium bromide equilibrium gradients, and isoamyl alcohol extraction to remove ethidium bromide from DNA. In some preparations, holoenzyme of Escherichia coli RNA polymerase was bound to naturally supercoiled pUC 9 DNA according to the procedure of Klaus et al. (1983). Electron
ET AI,. The direction of the tilt axis of the stereo pairs is determined by finding the direction along which the distance between corresponding points does not change on both micrographs. Image
Processing
The computer processing is performed on a Silicon Graphics 4D20 Workstation. An Eikonix 1412 CCD camera is used to digitize images from magnified electron microscopy prints. Images are stored and manipulated using the SEMPER software (Synoptics). The magnification and sampling are chosen so that the filaments are typically around 5 pixels wide. The background density of the selected region can be flattened with a linear gradient correction, and the contrast of the molecule adjusted for optimal visualization on the display. The two micrographs of a stereo pair are oriented with the tilt axis (Oy axis) placed vertically on the display. They are aligned along the Oy direction on the basis of a reference point, which is a precisely defined feature, clearly visible on both micrographs. This can be, for example, a conspicuous contamination mark or an RNA polymerase molecule bound to the DNA molecule. Coordinate axes are chosen to bring the photographic plane perpendicular to the Oz axis. The reference point mentioned above is taken as the origin for the 3c, y, and z coordinates. The coordinate of a point i in space, (x, yi, zJ, projected on the first image plane, is (xi’, yi’), and on the second projected plane it becomes LX,“, y,“). Provided that Oy is parallel to the tilt axis, yi’ = yi”. A simple calculation then gives the z coordinate for this point: zi = (x”, cos 0 - r’J/sin 0, where 0 is the tilt angle between the two micrographs. The determination of the path of the DNA molecules is made by clicking with the mouse along the center of the filaments displayed on the screen. Clicking of individual points on the first image defines their coordinates (xi’, y,‘). This also defines the yi” coordinate for the corresponding points on the second image. The movement of the pointer is then restricted to the x direction at yL = yZ’ = Ye”. The distance between successive points typically corresponds to 6 nm on the molecule. Bicubic spline interpolation based on these chosen points results in a smooth path overlapping each displayed projection of the molecule.
Microscopy
Specimens were prepared as described previously (Dubochet et al., 1988; Adrian et al., 1990). A 3-pl drop of DNA solution (-200 pgiml) in Tris-EDTA (pH 7.51, 10 mM MgCl, was put on hydrophobic-perforated carbon film (Fukami et al., 1972). In the case of the DNA with bound RNA polymerase, the specimen buffer was 30 mM triethanolamine-Cl (pH 7.9), 10 mM MgCl,, and 0.1% glutaraldehyde. An automatic system (Cyrklaff et al., 1990) is used for blotting most of the drop in ca. l-2 set and immediately releasing the plunger. After a O.l-set free fall, the specimen is immersed into liquid ethane cooled close to its freezing point. The thin liquid layer of solution, spanning the holes of the supporting film, is then vitrified in ca. 10m4 sec. The vitrified specimen is transferred, without rewarming, into a Gatan 626 cryo-specimen holder and introduced into a Philips CM 12 electron microscope, equipped with a special blade-type anticontaminator (Homo et al., 1984) and an eucentric goniometer. Stereo pairs of micrographs were performed with a tilt angle of 220”. This large angular difference increases precision of 3D reconstructions but makes it difficult to obtain direct 3D impressions by viewing stereo pairs. Micrographs are recorded at ca. 2 p,m underfocus, at a temperature of - 172°C (nominal), at a magnification of x 60 000, and with minimum beam exposure on SO 163 Kodak film, and developed for 12-22 min in D 19, full strength. Under these conditions, the speed of the film is 2 pm2 per electron per optical density unit, and the dose per micrograph is ca. 2 x lo3 electrons/rim’. The total dose for stereo recording is double. Magnification is determined by a cross-grating replica.
Spatial
Visualization
The Wavefront Personal Visualizer, running on the graphic workstation, was used for rendering of three-dimensional objects. The reconstruction algorithm generates a curved line, corresponding to the axis of the DNA filament, in a 3D space. The reconstructed molecules are most conveniently visualized as flexible cylinders, obtained by attributing an arbitrary thickness to the 1D curve. This is achieved by surrounding the median axis of the filaments with polygonal surfaces. Octagons are positioned centered on the curve and orthogonal to the local tangent. These primitives are used to define parametric bicubic spline surfaces using the intrinsic geometric functions of the workstation. The ends of the tubular filaments are then closed by hemispherical surfaces. RESULTS
Test of the Reconstruction
Procedure
To check our reconstruction program, we applied it to two different projections of a wire model, mimicking an interwound DNA molecule. The test is shown in Fig. 1, where two projections (A,B) of the wire model (obtained by forming the object’s shadow with a parallel illumination of a photographic enlarger) are presented, together with the real (C) and reconstructed (D) object. Projection B is related to
SPATIAL
VISUALIZATION
OF DNA
17
F ‘IG 1.1. A model for testing reconstruction. (A, B) Two projection views of the ca. E-cm aluminium wire shaped to mimic the trajectory ofa Sl lpercoiled DNA molecule. The projections were obtained by using the nearly parallel illumination from a photographic enlarger in ordl er to expose the printing paper placed underneath the model. Tilt angle, + 40”. The end of the shorter aluminium wire f is used as a refe !re !nce point. After another 1-90” rotation, comparison is made between C, the picture of the wire and D, its computer-aided 3D recc m struction (C and D are seen from the same viewpoint). The parts of the wire perpendicular to the tilt axis (vertical) are imperfectly rect ml strutted because of insufficient information. The digitization of the curve was made with 57 points.
18
DUSTIN
projection A by a 40”-clockwise rotation of the object around the Oy vertical axis. (These two projections are presented as a stereo pair to enable the reader to create his or her own impression of the 3D shape of the object.) The surface view of the real object and of the reconstruction correspond to a further 90”clockwise rotation around the same axis from the position corresponding to B. The end of the wire f is used as reference point. The similarity between the real object (C) and its reconstruction (D) in this and other orientations provides a qualitative validation of the procedure. For noise-free projection images like those shown in Figs. 1A and lB, digitalization procedure is rather unambiguous and repeated digitalizations performed by the same or a different person lead to very similar, almost overlapping reconstructions. However, with very noisy images, the digitalization procedure becomes prone to misrepresentation and each reconstruction might differ. It is discussed later how the knowledge about stiffness and total length of the observed molecules can help to choose the proper digitalization path. Reconstruction of the 30 Trajectory of Tightly Supercoiled DNA Molecules Suspended in a Vitrified Film
The reconstruction procedure is applied to DNA molecules suspended in a buffer containing 10 mM MgCl,. It was demonstrated previously that in the presence of 10 n&f MgCl,, supercoiled DNA molecules adopt the form of a tight superhelix in which two opposing segments of interwound DNA molecules approach each other, except at the end loops (Adrian et al., 1990). The DNA regions, where two double-stranded segments are aligned together, show better contrast in vitrified specimens (due to the doubling of the mass per unit length of the filament) and therefore serve as a convenient object for study. Figure 2 (top) shows a stereo pair of micrographs of a tightly supercoiled pUC 9 DNA molecule. The end loops are hardly visible on these micrographs and have not been considered. The reconstructed object is presented in the same orientation as the visual stereo impression obtained from the stereo pair. Another stereo pair of a tightly supercoiled DNA filament is presented on top of Fig. 3. The center of one E. coli RNA polymerase bound to this DNA molecule has been used as a fixed reference point for the calculation. The reconstructed filament is shown from a different direction. Reconstructed images are based on the full set of 3D coordinates obtained after digitalization of the stereo pairs of molecules. Therefore, we are able to measure curvilinear and direct distances between points of interest on the observed DNA molecules.
ET AL.
For the reconstructed segments of molecules shown in Figs. 2 and 3 the curvilinear lengths are respectively 380 and 440 nm, while the corresponding endto-end distances are 210 and 170 nm. Such measurements are obviously impossible on the stereo impression obtained by conventional viewing of stereo micrographs. DISCUSSION
The method we present here for the computeraided reconstruction of filamentous nonplanar objects from two projections allows one to obtain 3D coordinates for the path of such objects. These data and the resulting reconstruction have several advantages over the subjective stereo impression obtained by viewing a stereo pair of electron micrographs. The stereo impression does not allow for the rotation of the representation, whereas the computer reconstruction enables one to observe it from any viewpoint. Since 3D coordinates are calculated, the quantitative analysis of such path-related parameters as the distance between points of interest measured along the filament or across space can be performed. In the case of DNA molecules observed in vitrified films, this method offers a way to directly measure the persistence length and the writhe of the molecules in solution. In addition, the method allows a representation of the 3D path of filamentous objects independent of the observer’s ability to obtain a 3D impression by viewing stereo pairs of micrographs. We show that two projections, related by a 40” tilt, are sufficient to obtain adequate reconstructions of filamentous objects. It is obvious that the higher the angular difference between the two projections (up to go”), the more precise the reconstruction can be. However, obtaining projections with tilt angles higher than 40” is frequently difficult, due to mechanical obstacles or specimen’s vibrations. Two projections alone do not provide sufficient information to define those regions of the filaments which are perpendicular (or close to perpendicular) to the tilt axis. Unsurprisingly, closer inspection of the differences between the reconstructed and real objects in Fig. 1 shows that these regions are most prone to be misrepresented in the reconstruction. In these regions, only a third projection, tilted around a different axis, would enable one to resolve all the indetermination. The reconstruction procedure presented here depends, of course, on having adequate micrographs, where the filamentous object can be traced and digitized along its path. However, in some short regions of low contrast, where it is difficult to pinpoint exactly the position of the axis of the filament, prior knowledge about continuity and flexural rigidity of the filament can help to make an educated choice.
SPATIAL
VISUALIZATION
OF DNA
FIG . 2. Stereo pair of tightly supercoiled DNA and corresponding reconstruction. put c 1 vitrified in a solution containing 10 mM Mgz+ (see Materials and Methods). for 501ne observers since the angular difference between right and left micrograph stereo pairs. Only “4-stranded” tightly supercoiled regions of DNA are considered. 45 poi nts, is presented from the same viewpoint as the stereo view.
Top right and left are stereo images of superc Obtaining direct stereo impression might be dil amounts to 40” instead of 20” or even less in star The reconstructed part of this molecule, digitized
19
:oiled gicu1t ldard with
DUSTIN
FI( digiti RNA visib
ET AL.
;. 3. Spatial visualization of a tightly supercoiled DNA molecule. Another supercoiled DNA molecule (same preparation), vvith 35 lzed points. Top views form a stereo pair on which the reconstruction is based. Reference point for the reconstruction is the E. ,wli polymerase that can be observed on both micrographs (arrow). Axis of the tightly supercoiled part follows a helical path. This isv veil le after the reconstructed molecule is rotated by + go”, + go”, and - 30” around the Ox, Oy, and Oz axes, respectively.
SPATIAL VISUALIZATION OF DNA
Such controls as the measurement of the total length of the reconstructed filament can help to check if the guess was a sensible one. Therefore it is sometimes possible to obtain an adequate reconstruction of the object from its two projections, even when it is not possible to obtain a 3D impression by direct viewing of a stereo pair. We thank Mr. M. Adrian for providing us with stereo micrographs, Mrs. B. ten Heggeler-Bordier for providing a sample of DNA with bound RNA polymerases, Ms. C. Cottier for photographic service,and Dr. D. Cangemi for fruitful discussions.This work was supported in part by Swiss National Fund Grants 3125694.88 and 31-27146.89 (to J. Dubochet and A. Stasiak) and Grant INT-9096163 from the United States National Science Foundation (to E. H. Egelman). REFERENCES ADRIAN,M.,DUBOCHET,J.,LEPAULT,J.,ANDMCDOWALL,A.W. (1984) Nature 308, 3236. ADRIAN,M., TEN HEGGELER-BORDIER, B., WAHLI, W., STASIAK, A.Z.,STASIAK,A.,ANDDUBOCHET,J.(~~~O)EMBOJ.~,~~~~4554.
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BOLE&T. C.,WHITE,J.H.,AND COZZARELLI,N.R.U~~O)J.Mol. Biol. 213, 931-951. CYRKLA~,M., ADRIAN,M., ANDDUBOCHET,J.(1990) J.Electron Microsc. Tech. 16, 351-355. DEROSIER, D.J., ANDKLUG, A. (1968) Nature 217, 130-134. DUBOCHET,J., ADRIAN,M., CHANG,J., HOMO,J., LEPAULT,J., MCDOWALL,A.W., ANDSCHULTZ,P. (1988) Q.Rev.Biophys. 21, 129-228. EGELMAN,E.H., AND STASIAK,A. (1986) J. Mol.Biol. 191, 677697. FUKAMI,A., ADACHI,K., ANDKATOH,M. (1972) J.EZectron Microsc. 21, 99. GOODMAN,S. D., ANDNASH,H. A. (1989) Nature 341, 251-254. KLAUS,S.,VOGEL,F.,GAUTSCHI,J.,ST~LHAMMAR-CARLEMALM, M., ANDMEYER,J. (1983) Mol. Gen. Genet. 189, 21-26. LAUNDON,C.H., ANDGRIFFITH,J.(1988) Cell 52, 545-549. LEPAULT,J.,ANDLEONARD,K.(1985)J. MoZ.Biol. 182,431441. SPENGLER,S.J.,STASIAK,A.,ANDCOZZARELLI,N.R.(~~~~)C~Z~ 42, 325-334. RADERMACHER, M. (1988) J. Electron Microsc. Tech. 9, 359-394. TORBET,J.,ANDDICAPUA,E. (1989) EMBOJ.8,43514356. TRAVERS, A. (1989) Nature 341, 184-185. W&H.-K., ANDCROTHERS,D.M.(1984) Nature 308, 509-513.
