Structure of helical RecA-DNA complexes

J. Mol. Riol. (I 986) 191. 677-697

Structure of Helical RecA-DNA

Complexes

Complexes Formed in the Presence of ATP-Gamma-S or ATP Edward H. Egelman Department of Molecular Biophysics and Biochemistry Yale University, New Haven, CT 06511, U.S.A.

Andrzej Stasiak Institute E.T.H.-Honggerberg, (Received 21 March

for Cell Biology 8093-Zurich, Switzerland

1986, and in revised form 3 June 1986)

Electron micrographs of RecA-DNA filaments, formed under several different conditions, have been analyzed and the filament images reconstructed in three dimensions. In the presence of ATP and a non-hydrolyzable ATP analog, ATP-gamma-S, the RecA protein forms with DNA a right-handed helical complex with a pitch of approximately 95 A. The most detailed view of the filament was obtained from analysis of RecA filaments on doublestranded DNA in the presence of ATP-gamma-S. There are approximately six subunits of RecA per turn of the helix, but both this number and the pitch are variable. From the examination of single filaments and filament-filament interactions, a picture of an extremely flexible protein structure emerges. The subunits of RecA protein are seen to be arranged in such a manner that the bound DNA must be partially exposed and able to come into contact with external DNA molecules. The RecA structure determined in the presence of ATP-gamma-S appears to be the same as the “pre-synaptic” state that occurs with ATP, in which there is recognition and pairing between homologous DNA molecules.

general is: how can RecA, a molecule of J& 38,000, perform all these functions? Although there has been a great deal of biochemical analvsis of RecA, there is still no model for t’he mechanism by which the protein functions. Structural studies of RecA and its interactions with its substrates can contribute significantly towards answering this question. RecA polymerizes on DNA (Fig. 1(c)) in the presence of adenosine 5’-O-(3-thiotriphosphate) (ATP-gamma-S), a non-hydrolyzable analog of ATP (West et al., 1980; McEntee et al., 1981; Stasiak et al., 1981), to form helical filaments approximately 110 A in diameter, with a pitch of about 95 A (DiCapua et aE., 1982). The stoichiometry of the complex has been determined by mass per unit length measurements to be one RecA monomer per three base-pairs (DiCapua et al., 1982). The same value (1 RecA per 3 base-pairs) was also obtained by fluorescence measurements and sedimentation analysis (Dombroski et aZ., 1983). It has been shown that conformation of the DNA in the complexes with RecA is significantly changed from its native state. For the duplex DNA,

1. Introduction The RecA protein of Escherichia coli, in the absence of other proteins, is able to mediate several steps in general genetic recombination, including t,he search for homology, homologous pairing and strand transfer (for reviews, see Radding, 1981; Dressler & Pott,er, 1982; Howard-Flanders et al., 1984a,b). These unique activities are associated with the formation of helical RecA-DNA complexes (Stasiak et al., 1984; Flory et al., 1984). Recombination systems have been established in vitro in which RecA protein promotes the complete strand exchange reaction between a doublestranded, linear DNA molecular and a homologous, single-stranded, circular DNA molecule (DasGupta et al., 1980; Cox & Lehman, 1981, 1982; Wu et al., 1983; Stasiak et al., 1984). RecA protein also promotes the reciprocal exchange between two double-stranded DNA molecules if one contains a single-stranded region (West et al., 1981a; DasGupta et al., 1981). A key question in understanding both recombination and protein-nucleic acid interactions in C~,22-2836/86/2006~7-‘L1

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Press Inc.

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Ltd.

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Figure 1. Three different, RecA-covered circular DKA molecules are shown at the same magnification. In (a) and (1)). circaular single-stranded DNA molecules (5386 bases) are shown covered with RecA protein. In (b) ATP is present, while (a) is in the absence of any nueleotide cofactors. In (c) a double-stranded DNA molecule (4961 base-pairs) is shown fully covered with RecA protein in the presence of ATP-gamma-S. From dividing the measured contour length by the number of bases, the average rise per base-pair is 5.1 x in (c). The average rise per base is 2.1 x in (a) and 4.6 A in (b) (Keller et al., 1983). &’ A

the axial rise per base-pair increases from about 3.4 A to about 5.1 il (Stasiak et aE., 1981; Dunn et al., 1982), while the twist changes from about 35” per base-pair to about 20” per base-pair (Stasiak & DiCapua, 1982; Stasiak et al., 1983; Dombroski et al.. 1983). Complexes with the same apparent morphology are formed on double- and singlestranded DNA (Koller et al., 1983) or as selfcomplexes in the absence of DNA (McEntee et al., 1981). In the presence of ATP, RecA protein will form filaments on single-stranded DNA (Fig. l(b)) that appear to be very similar to the complexes formed in the presence of ATP-gamma-S (Flory et al., 1984; St,asiak & Egelman, 1986). These filaments exhibit a strong striation arising from a helical pitch of about 90 8, and the single-stranded DNA can be extended to about 150% of the length of the corresponding co-prepared protein-free duplex DNA. Less information exists about a second state of the RecA filament, formed on single-stranded DNA in the absence of nucleotide co-factors (Fig. l(a)). which has been described as “smooth”, with little or no visible substructure (Koller et al., 1983; Flory & Radding, 1982; Dunn et al., 1982). While no data have been directly available on the conformation of the DNA in this complex, contour-length measurements of circular single-stranded DNA molecules that

are covered

with

RecA

protein

have

shown

that the single-stranded DNA is extended from a collapsed configuration to approximately 60% of the length of the duplex form of the same DNA (Koller et al., 1983). Structural analysis of RecA filaments and DNA molecules as they participate in the events of recombination will complement the extensive biochemical studies that have been made of this system. These interactions may be visualized at low resolution in the electron microscope, and offer

information about the sequential stages of the recombination process that is not obtainable by other means (Stasiak el al., 1984). Helical filaments are ideal specimens for image analysis, since a subunit is projected at many a single image of a different angles within negatively stained filament (DeRosier & Klug, 1968). Thus, the image of a single filament can contain all the information needed for a threedimensional reconstruction. We have been able to detect. dynamical properties of the filament from static images. The variations in structure that. are observed, both between and within filaments, can be related to the mechanical properties of the R#ecA filament, and it is likely that these properties are important to the function of RecA filaments in recombination. This paper considers the structure formed in the presence of ATP-gamma-S and ATP. A second paper dealing with the state formed in the absence of nucleotide cofactors is in preparation.

2. Materials and Methods (a) Proteins and nucleic acids Purified RecA protein from E. coli and nicked circular DNA of a plasmid (pBR322 derivative, pBRPG; Stasiak et al.. 1981) containing 4961 base-pairs were kindly provided by E. DiCapua. Single-stranded circular DNA of bacteriophage 4X174 (5386 bases) was purchased from Bethesda Research Laboratories. Complexes between RecA and double-stranded DNA were formed at a protein to DNA ratio of 4O:l (w/w) (5/*g DPu’A/ml: 2OOpg RecA/ml) by incubation at 37°C for 60 min in 25 mM-triethanolamine HCl (pH 7.2), 0.5 mM-ATP-gamma-S acetate, 1 mM-magnesium (Boehringer). Two types of complex between RecA and single-st.randed DNA were formed. ATP-gamma-S and ATP complexes were formed at a protein: DNA ratio of 160 : 1 by incubation for 10 to 30 min at 37°C in 25 mM-

Structure of Helical RecA-DNA triet,hanolamine. HCl (pH 7.2). If not stated otherwise, the concent.rat.ion of magnesium acetate and ATPgamma-S was 1 mM. Reaction mixtures to generate complexes formed in the presence of ATP contained, in addition to 4 mM-ATP. a regeneration system consisting of 10 m&I-phosphocreatine and 10 units of phosphocreat’ine kinase/ml. (b) Electron

,microscopy

A sample (1 ,ul) from the relevant reaction was diluted in a 5 ~1 drop of reaction buffer (37°C) and immediately placed on an electron microscope grid made hydrophilic by glow discharge (Harrick Plasma Cleaner). After 30 s. excess solution was removed by blotting with filter paper. A droplet of uranvl acetate (27; (w/v) in water) was then applied to the grid and was subsequently removed by blotting. Care was taken t,o minimize electron dose, and most filaments used in the analysis had no electron dose prior to photographic exposure. The magnification was calibrabed with latex spheres and with tobacco mosaic virus particles. using the helical pitch. (c) Helical annlysis

and reconstructions

Electron micrographs were digitized on an Optronics PI000 densitometer, using a step size of 25pm, which corresponded to a spacing in the images of about’ 5 to 7 a. When needed, filament images were corrected for slight c*urvature using an assumption of a normal mode of bending (Egelman. 1986). masked from their surroundings and Fourier transformed. Layer-lines were extracted from the transforms based upon an interactive on an AED 767 raster graphics display of the transforms device. The helical projection of a Y-dimensional st,ructure p(r. cp. s) down a hrliv of pitch 1) is given by: p’(r, q’) =

p(r. q--&z/r),

z) d;

s The G,,,(R) from a single layer-line may be used to generate 1 component of this projection for a particular Bessel order n and layer-line 1: where t.he pit,ch of the helix being projected is equal to nc/l. c being the helical repeat’. According to Klug ut al. (1958):

q”,,(r) =

G,,,(R).Jn(2nRr)2zRdR. s

Since g,,,(r)

is. in general.

complex:

p’(r, cp’)= Re[g,.,(r) exp (--in $)I. For n # 0, this projection will have an integrated of zero. The mean-mass-weighted radius distribution:

(r)= JJ ss

density of this

p’(r. q’)r dr dp

would therefore be O/O. An alternative approach is to take the absolute value of the helical projection, which will be equal to:

(r)

Complexes

This function was used for the determination of the centroid of mass using the 95 ip layer-line. The coefficient of correlation. used in relating t,he centroid of mass t’o the pitch. is:

Three-dimensional reconstructions were computed by Fourier-Bessel synthesis (DeRosirr & Xoorr. 1!%70). A surface was chosen in the continuous :&dimensional density distribution by choosing a level that gave the correct volume, assuming a partial specific volume for protein of 0.75 cm3/g. Two different methods were used to display this surface. In Figs 17 and 18, sections perpendicular to the filament axis were tilted h?; 15” and superimposed along the axis t.o generate a Sdimensional representation. The tilting of the sections enables the viewer to see the shape of individual sections. whereas without tilt the viewer would see only the edge of each section. If the filament itself were t,ilted. perspective would have to be introduced to give proper dept,h-cueing. The surface that is generat.ed corresponds to a balsa wood model that has been slightly sheared. In Fig. 8. a linear interpola,tion has been used in the original %tlimensional map to generate a finely sampled surface. The shading at each pixel in this surface is a fun&on of both the 4th power of the cosine of the angle between the viewer and the normal t’o the surface and the rec*iprocal of t,he distance between the surface and the viewer. :iII surface views were displayed on. and photographed from, an Advanced Electronic Design 767 rast)er graphics syst,em. *UI computations were performed on a V.1.Y I1 ;750. and the computer programs that were used were either written by E. Egelman or from the MRC Laboratory of Molecular Biology, Cambridge. ITK. (d) Measurement

s

h,dr)lrdr

of corrrlation

length

Prints of electron micrographs of linear RecApdoublestranded DXA filaments were placed on a digitizing pad and the contours of approximat’ely 50 filaments were recorded. Filaments were carefully selected to avoid any “kinks” that are probably due t.o deformations beyond the elastic limit during the process of dehydration on the electron microscope grid. The sampling rate for the digitization of filament contours was chosen to be adequate for the degree of bending. This was det’ermined graphically by plotting the measured c.ontour length zqers?Ls the sampling rate. tTndersamp1in.g leads to an underestimate of the contour Ien@. The cbontour length converges to an asymptotic value due to the finite curvature of the filaments and, because the contour length is measured along an ideal filament axis. it is unlike the coast-line of (ireat Britain and does not displa) fractal characteristics, A sampling rat,e was chosen that yielded the asymptotic value for the cont.our lengt,h. The relationship bet,ween the mean squared end-to-end distance (R’) of a contour of length I, and the (norrelation length b is (Landau & Lifshitz, 195X): (R2)

= 2621L/b-1+exI,(-Llb)].

This definition relates the S-dimensional correlation length to the end-to-end distance for a molecule adsorbed to a d-dimensional surface. Tn 3 dimensions. the eyuation is: (12’)

= J

679

= (b2/2)[2L/b-

1 +exp(

-2L/h)].

For any given L, a mean squared end-to-end distance (K2) is measured. and 0. the correlation length, is

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determined using an iterative Newton’s method of approximation. A single filament could provide a number of independent measures of R and L by using different stretches of the filament, since R does not have to be measured from one end of the molecule to the other, but can be determined along any contour within a molecule. Typical filaments were of the order of 2.5 pm long.

(e) X-ray diffraction Samples for X-ray diffraction analysis were prepared and donated by Dr S. West. A concentrated gel (approx. 45 mg protein/ml) of RecA on linear double-stranded DNA in the presence of ATP-gamma-S was formed by cent,rifugation and placed in a glass capillary and sealed with wax. The capillary was placed in a Franks geometry camera (specimen to film distance 105 mm) on an Elliott GX-21 rotating anode X-ray generator and exposed for 4 days. The processed film was scanned on an Optronics PlOOO photodensitometer, using a 50 pm raster. The center of the pattern was found by computing the centroid of the first ring (corresponding to the 95 b layerline), and this centroid was used for circularly averaging the pattern and extracting the radial scattering function. -4 linearly increasing background due to integrated film fog was subtracted from the radial function.

3. Results (a) Single jilaments of RecA on double-stranded DNA with ATP-gamma-S (i) Measurement of correlation length Contours of filaments of RecA on linear doublestranded DNA were traced and digitized as described. The resulting data base was then used to determine b, the correlation length, for different values of L, the contour length. In principle, the correlation length determined should be independent of the contour length used. However, there are several potential sources of systematic error that could introduce a dependence. Because filament sections with sharp kinks were excluded from the analysis, it is possible that the longest filament contours used were straighter than the population in general, and one would therefore calculate a greater correlat,ion length for these filament sections than for shorter filament sections. Very short filament sections would contain the largest relative error in measurements of both R, the end-to-end distance, and L, the contour length. This might bias the result, if the error is not randomly distributed. The results, shown in Figure 2, suggest. that no systematic error occurs for long contour lengths, and that short contour lengths (less than 3000 8) lead to a slight underestimate of the correlation length. The best estimate of the correlation length from these data appears to be about 6300 A. Systematic effects of preparation for microscopy, drying onto a two-dimensional surface etc.: would appear to preclude a higher-precision determination of this number using this method. Since the RecA is polymerized onto continuous linear DNA molecules. it is possible in principle for

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5000

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Figure 2. The correlation length b determined from different contour “intervals”. The contours of approximately 50 filaments were digitized, and these contours were subdivided into contour intervals from 1000 A to 10,000 A long. For each contour interval used. the end-toend distance R for that contour was measured. This was repeated along the filament contours, starting at the end of the previous measurement, until one reached the end of a filament. Each contour interval yielded a value for (R*). the mean squared end-to-end distance. This was then used t,o determine b.

there to be gaps in the RecA polymer that would not be detectable by eye. The rigidity at these gaps would therefore be determined by the much smaller rigidity of double-stranded DNA. Thus, one must exclude the possibility that a significant fraction of the observed RecA flexibility is due to these gaps. A simple inspection of RecA self-polymers, formed in the absence of DNA, shows that this is extremely unlikely, as these self-polymers appear to be as flexible as the RecA-DNA complexes. (ii)

Variable pitch

Electron micrographs of approximately 100 negatively stained RecA filaments on both nicked circular plasmid DNA (4961 base-pairs) and linear double-stranded DNA were scanned on a digital densitometer and analyzed. Filament sections that were as straight as possible were sought, but small residual curvature was corrected for in about 70% of the filaments. No systematic differences could be found between those filaments that were found to be straight on the grid and those that were processed to correct for curvature. The computed to optical diffraction transforms (equivalent patterns) showed a strong layer-line arising from a helix of about 95 A pitch, but the actual spacing of this layer-line varied from specimen to specimen. with a range of about 90 to 100 A. This variation could be seen within the same circular filament, when one examined small sections from different (Fig. 3). A side-by-side comparison of regions regions with a long pitch with those with a short, pitch suggested that the pitch was coupled with the diameter (the longer the pitch, the narrower the diameter) and we have quantified this effect. To surmount the problem of variations in abso1ut.e magnification of t,he electron microscope, a sample of nine filament sections was selected from eight different filaments on sequential micrographs. These sections were chosen because their transforms

Structure of He&al RecA-DNA

Cmplexes

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Figure 3. The pitch of the helix that links adjacent RecA monomers in the ATP-gamma-S-double-stranded DNA complex can be quite variable, with the variation appearing to be random and occurring continuously within the same filament. A section of a RecA-covered plasmid that has been divided into 2 halves is shown in (a). The top and bottom halves have been transformed separately. The computed transforms of these sections have been sandwiched together in (b). The transform on the left, corresponding to the bottom half of the filament section, shows a 90 A pitch helix. while the transform on the right. corresponding to the top half of the filament, shows a 100 A pitch helix. This phenomenon of variable pitch has been interpreted in terms of the spring-like structure of the RecA filament in the ATP-gamma-S state that can be readily extended and compressed.

all showed a very clear and symmetrical layer-line arising from the nominally 95 A pitch helix. No other selection was imposed upon these filaments. The pitch of these filaments was measured directly from the altitude of the peak of this layer-line, using a common magnification for all the filaments. We used two methods to determine a “width” parameter for each of these sections. The first was to Fourier transform the equator, after imposing a resolution cutoff at l/25 A. This yields a smoothed projected mass distribution. and the full width of this distribution at half the maximal density was determined. The scatter plot of these values against pitch is shown in Figure 4(a). The second method attempted to avoid the problems associated with which manifest themselves the stain envelope, mainly on the equator of the transform, by using the strong layer-line arising from the nominally 95 A pitch helix. The two independent halves of this layer-line (associated with the near and far sides of t,he filament) were averaged together and used to compute a centroid of mass from this helix (see Materials and Methods). The comparison between the pitch and the radius of the centroid is shown in

Figure 4(b). The negative correlation and (b) shows that the diameter decreases as the pitch increases. (iii)

Indexing

in Figure 4(a) of a filament

other layer-lines

Additional layer-lines, usually less than 6% of the peak intensity of the l/95 A layer-line, were also observed in many specimens, and these included the second order of the l/95 A layer-line as well as those arising from other helical families. Indexing the other layer-lines for five filaments where the indexing appeared unambiguous showed that individual sections of the RecA-double-stranded DNA helix with ATP-gamma-S had from 5.1 to 6.8 subunits per turn of the nominally 95 A pitch helix. The variation in this value, like the variation in pitch, appeared both within and between different filaments. Due to the poor sample size, it has not as yet been possible to correlate the variation in pitch with the variations in the number of subunits per turn. The most ordered filament (Fig. 5) was used for a three-dimensional reconstruction. The pitch of this filament section was about 100 A, placing it at one extremum of the observed ra,npe of pit’c*h.

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Figure 4. (a) A scatter plot of helical pitch versus full widt.h half maximum (FWHM) of the low-pass filt,ered projected filament density for 9 uniform sections of filaments. The continuous line is the linear regression fit to these points. The simple correlation coefficient of pitch ~:crsus FWHM is -0.6574, with a standard error of 0.2848. showing a negative correlation. Although there is no reason to believe that the functional relationship between these 2 parameters is a linear one, there does not appear to be any systematic deviation from the linear regression. (b) A scatter plot of helical pitch versus the centroid of the radial modulation along the one-start helix for the same 9 filaments shown in (a). The continuous line is the linear regression, and again there does not appear to be any systematic deviation. The simple correlation coefficient of pitch verau~ radius is -0.6737, with a standard error of 0.2793, showing a negative correlation. Student’s t test was used to examine the possibility that the population from which this sample was drawn had a correlation coefficient of 0.0. but finite sample fluctuations accounted for the non-zero correlation coefficients measured. The probability associated with this occurring is about 0.05 for each of the 2 plots ((a) and (b)). Since these plots employ independent determinations of width, the probability of both events occurring is about 06025, and therefore the null hypothesis is rejected and the correlation is seen to be significant. (c) A scatter plot of the centroid of the

(bl

Figure 5. The RecA-covered double-stranded DNA in (a) was prepared with ATP-gamma-S. The filament section shown within the box (b) is an enlargement of the area indicated by the arrow in (a) after correction for bending. The image in (b) is 120 A wide. This section gave rise to the best data of all filaments examined in the ATP-gamma-S state on double-stranded DNA; and these data were used for the 3-dimensional reconstruction shown in Figs 8 and 9.

radial modulation versus the full width half maximum of the projected density, using the data from (a) and (b). This plot gives a graphical estimate of the amount of error associated with a determination of the filament diameter from these 2 methods. The linear regression line that is shown has a slope of 1.86 and a y-intercept of 4.3 (the standard error of the regression coefficient or slope is O-77). The deviations from the linear regression line shown do not suggest any systematic effects.

Structure of Helical RecA-DNA

Complexes

6t33

F‘igure 6. The computed transform of the filament section in Fig. 5(b). The strongest layer-line (11) is at l/l00 A, and the peak intensity on that layer-line is about 16 times greater than for any other layer-line. The layer-lines are indexed (SW Fig. 7(a)) as arising from a helix with 56 subunits in 11 turns of a 100 A pitch right-handed helix. Similarly. the symmetry of this section (determined from the indexing), 5.1 subunits per turn, placed it at an extremum of the observed range of “twist”. Five layer-lines (Fig. 7) were extracted from the Fourier transform (Fig. 6). The indexing, or assignment of Bessel orders, to these layer-lines was unambiguous. The lst, 11th and 23rd layer-lines were clearly seen to contain odd Bessel orders from the 180” phase differences across the meridian. The radial position of the maximum of the 23rd layerline indicated that it was most certainly of order 3. Since the vector in the n, 1 plot from the origin to the 1st layer-line is the same as the vector from the 22nd to the 23rd, it is clear that the sign of n on the 23rd layer-line is opposite to that of the n = 2 on the 22nd layer-line. It has been determined from shadowing (DiCapua et al., 1982) that the 95 w pitch helix is right-handed, and this was all that was needed to determine the n, 1 plot shown in Figure 7. The layer-lines contain two independent sets of information, arising from the near and far sides of the helix. For an ideal filament, these two data sets would be related strictly by helical and the observed correspondence symmet)ry, between t.he two sides is a measure of the degree of helical preservation in the filament. The amplitudeweighted mean phase residual between the near-far layer-line peaks was 7”, which showed that the internal symmetry was well maintained (the residual would be zero for perfect symmetry and 90” for the complete absence of correlation). (iv) ATP-gamma-S reconstruction The layer-lines from Figure 7 were used in a Fourier-Bessel synthesis (DeRosier & Moore, 1970)

and the resulting three-dimensional reconstruction is shown in Figures 8 and 9. The reconstructed density is actually the stain exclusion volume wit.hin the uranyl acetate stain. and an interpretation must be provided as t)o how or if the DNA is visualized within this volume. Firstly, simple geometric arguments dictate that the DiVA must be confined to a region near the RecA filament. axis. For a helical path through the region of hydrogenbonding between base-pairs: r = J(l’-a’)

x N 27T

’

where r is the radius of the path, 1 is the local separation per base-pair along the helical path, a is the axial rise per base-pair, and N is the number of base-pairs per turn. The maximum observed axial rise per base-pair in double-stranded DNA is 7.6 A (Arnott & Chandrasekaran, 1981), and one may use this value for the maximum local separation as well, consistent with stereochemical constraints. Using the measured axial rise of 5-l a and 18.6 base-pairs per turn (Stasiak et al., 1983) for the average RecAATP-gamma-S state, one finds for this path a maximum radius of about 17 A. Since the RecA complex is at least 50 & in radius, this demands that the DNA be located within a relatively small volume around the filament axis. In the reconstruction of Figures 8 and 9, the relatively extended state of this complex means that an even tighter constraint exists on the DNA path. Using 56jll units per turn of RecA, a constant stoichiometry of monomer (see three base-pairs per RecA Discussion), and a pitch of 100 A, one finds a projected rise per base-pair of 6.55 A. Imposing the

684

E. H. Egelman

local path length constraint of 7.6 A, one finds a maximum allowable radius for the DNA base-pair path of 9.4 A. This radius is illustrated in Figure 9. Tf the DNA were binding stain (staining positively) it would appear as a hole near the filament axis in the density distribution. If the Dp\‘A were excluding stain (staining negatively) then it would be present within the reconstructed density. Ionic considerations led us to expect the DNA to bind uranyl acetate positively, but naked double-stranded DNA prepared under the same conditions used for the complexes revealed a negative staining of the DNA (data not shown). However, the staining properties of naked doublestranded DNA are ambiguous in answering how the DNA is staining within the complex, since the chemical properties of the DNA could well be modified in the complex with protein. In either case the ability to resolve the DNA would be limited by two factors. Firstly, the double-stranded DNA accounts for only about 4.69/h of the mass of the total complex (DiCapua et al., 1982). Secondly, the resolution of detail falls off as one approaches the filament axis. Therefore, we can only place the DNA within a rather localized volume near the filament axis in this state without direct evidence for its exact position. As it turns out

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(see Discussion), our interpretation at this resolution of the relationship between the DNA strand, the RecA subunits bound to it, and external DNA molecules does not depend upon an exact determination of where the DNA is within the relatively small volume we have defined near the filament axis. Since the DNA accounts for less than .50/bof the mass of the complex, the general features of the reconstructed density can be treated as arising

23

4.

(I

and A. Stasiak

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III

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;I2345670 (a)

Figure 7. (a) The n, 1 plot for the filament in Fig. 5 is shown. This plot. shows which order, n. of a Bessel function may occur on which layer-line, 1. This plot shows only the layer-lines and their respective Bessel orders that are allowed to exist. The actual layer-lines that will be observed will have relative strengths determined by the shape and orientation of the subunit, and some layerlines t,hat are permitted may have vanishingly small st.rength and thus never be observed. (b) Five layer-lines have been extracted from the transform of the filament. The independent data arising from the near and far sides have been averaged (the amplitude-weighted phase residual between the near and far maxima was 7’). The lst, maximum on the 1st layer-line is most likely noise, and will only contribute to the reconstruction at a radius beyond the bounds of the filament (amplitudes shown).

0 005

0 015 0 010

0 025 0 020 (s-‘) (b)

0 035 0 030

Structure of Helical RecA-DNA

Complexes

685

a uniform polarity as a consequence of nucleation being rate limiting, with rapid polymerization occurring after a nucleation point forms. If nucleation were not rate-limiting, it would be possible to have short regions of random relative polarity over the molecule.

Figure 8. A surface view of the S-dimensional density distribution reconstructed from the data shown in Fig. 7. The surface has been chosen so that the full molecular

volume of the complex is seen, assuming a partial specific volume of 0.75 cm3/g. This surface produces an outer diameter of about 100 A for the reconstruction shown. The width of the box, shown in Fig. 3, that contained the

filament was 120 A, so there are about 10 d on either side of the filament within the box. This filament is somewhat narrower t.han most others that have been examined, and this appears to be coupled with the fact that the pitch of this particular filament section was the most extended.

entirely from the RecA protein. One sees axially elongated subunits that are arranged along a helical “yoke” at a radius of about 20 to 25 A. The subunits appear to extend about 50 A axially, and to be about 40 A in diameter in the plane perpendicular to the filament axis (Figs 9 and 10). The subunits are arranged in a spring-like manner, with contacts between subunits appearing to be limited to this helical yoke. The coil-like structure with the resulting deep helical groove along the 90 to 100 A4 pitch helix is not surprising, since the of most of the power in the concentration diffraction pattern into the l/95 A layer-line shows that the mass in the structure must be arranged predominantly along this helix. The reconstruction displays a clear polarity. Since the double-stranded DNA has no net polarity, the polari@ of the RecA filament must be a random (‘onsequence of nucleation. A single region displays

(v) X-ray powder pattern It is clearly important to determine if the struct.ure of the RecA filaments as seen in t,he electron microscope is representative of filaments in solution or merely an artefact of specimen preparation for electron microscopy. The layer-lines (Fig. 7) from the most ordered filament found show that all layer-lines other than the l/95 ,& one have an intensity less than l/16 that of the l/95 A layerline. A typical filament, however, often only has one layer-line (the l/95 A one) seen in the transform of the electron microscopic image. This is due to both helical disorder and the presence of noise in images which will effectively mask the weaker layer-lines. A direct comparison between the diffraction of filaments in solution and the transforms of the electron microscopic images would be useful in determining whether the patterns which are seen from the electron microscopic images are artefactual. Towards this end, an X-ray “powder pattern” from an unoriented hydrated gel of RecA protein on DNA was recorded. A comparison is made in Figure 10 between the circularly averaged scattering generated by the layer-lines in Figure 7 and the actual radial scattering recorded from the powder pattern. The agreement’ is quite good, and one sees that no strong peaks other than that corresponding to the l/95 A layer-line are recorded in the X-ray pattern. Thus, even in the best case, using a carefully selected image giving rise to the strongest set of layer-lines, one would expect that only one observed peak would be seen within 30 A resolution in the X-ray powder pattern. The worst case, or more typical filament, yields a circularly averaged scattering virtually identical with that in Figure 10(b), and the powder pattern demonstrates that filaments in solution must have a structure that is at least consistent at, low resolution with that observed in the electron micrographs. An interesting consequence of t,he coupling between the pitch and the diameter of filaments (Fig. 4) is that the peak of the l/95 A layer-line moves in to t’he meridian as the altitude of the layer-line

increases.

This

is a consequence

of t,he

fact that the diameter increases as the pitch decreases. Thus, the variable pitch of the filaments does not significantly broaden the circularly averaged peak of the l/95 a layer-line. That is why the observed X-ray pattern appears to have a width for this first ring that is comparable to t.hat obtained from a single filament. Tn the absence of the pitch-diameter coupling, one would expect that t’he solution scattering, which averages over filament sections with different pitch, would generate

a first

ring

that

is broader

than

that

generated by a single filament, section of fixed pitch.

686

E. H. Egelman and A. Stasiak

O. Q @iI

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0

* 0

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y)Q % l

0

0

IO

Figure 9. The 3-dimensional reconstruction contains more information than that shown by the surface in Fig. 8, and the variation of the reconstructed density within that surface may be displayed. The electron density contours from sequential sections cut perpendicular to the filament axis are plotted. The filament axis is indicated in each section by a dot, and the scale bar in section 0 represents 50 A. The sections are spaced 4.9 A apart, which c*orresponds to l/4 of the axial rise per subunit (100 Aj5.09). Section 0 is at the top, and section 11 is 53.9 A below it,. Helical symmet,ry dictates that every se&on is related to another section 4 above it by a counter-clockwise rotation of 360”/5-09, or 70.7”. The top of what appears to be one subunit is marked by an arrow in section 1, and the bottom of the same subunit is marked by another arrow in section 11. Thus, what appears to be a single subunit extends axially for about 50 A. A circule of radius 9.4 A is drawn about the filament axis in section 0, and this indicates the maximum radius for the DNA path in this extended filament (see the text).

Structure of Helical RecA-DNA

s(a-9 Figure 10. A comparison is made between a radial plot (b) of the X-ray “powder pattern” obtained from a gel of RecA on double-stranded DKA with ATP-gamma-S, and a simulated pattern (a) obtained from circularly averaging the layer-lines of Fig. 7. Since the layer-lines of Fig. 7 are those obtained from the most ordered filament found. they represent an upper limit in predicting the amount, of information (or number of peaks) that would be found in a real powder pattern. It is clear that the prediction of only one peak to be found within 30 A resolution is upheld. This peak would only be centered at l/95 A (or 0,0105 A-‘) if the maximum of this layer-line occurred on the meridian. Since it does not, the actual spacing that is observed is greater than l/95 A.

(0)

Complexes

687

(vi) Filament-filament interactions RecA-DNA filaments can be seen frequently to aggregate together in side-by-side interactions, particularly when linear double-stranded DNA is closed circular plasmids used. Occasionally, decorated with RecA will collapse upon themselves and regions will be seen with a side-by-side alignment and slight interdigitation of filaments (Fig. 11). Analysis of such regions frequently shows the presence of “forbidden” meridional reflections. These reflections are forbidden by strict helical symmetry, and indicate that the component filaments are deformed from helical symmetry by axial perturbations of mass within the filaments. In a regular helix, every subunit is related to its neighbor by a fixed rotation and axial translation, The existence of a forbidden meridional reflection shows that the axially projected density of every subunit is not related to its neighbor by a constant translation, arising from either unequal axial translations between subunits or non-equivalent tilts of subunits. The gradual coiling of filaments about each other (DiCapua et al., 1982) cannot by itself give rise to the observed forbidden meridional reflection. Rather, a periodic variation must have been introduced by the interdigitation of the two filaments. The magnitude of the perturbation cannot be calculated without a knowledge of the projected mass density of the subunits, which is at low resolution. Nevertheless, the lacking existence of the perturbations shows that the axially projected mass of subunits may be displaced

(b)

Figure 11. Two strands from within the same RecA-decorated plasmid can be seen to aggregate in a side-by-side manner in (a). The computed transform of the region indicated by the arrow in (a) is shown in (b). A “forbidden” meridional reflection (arrows) is apparent in the transform, which would not be present if the 2 component filaments were interdigititated without deforming each other. The existence of this reflection shows that mass within the filaments can be shifted axially away from positions dictated by helical symmetry, and this provides independent evidence that the variable pitch observed within single filaments reflects the intrinsic compressibility and extensibility of RecA filament,s in solution.

E. H. Egelnmn and A. Stasiak

688

(a )

(b)

Cc)

(d)

Figure 12. (a), (b), (e) and (d) Negatively stained images of bundles of RecA-double-stranded filaments. The axial periodicity of about 570 A is indicated by the arrows.

DT;A-ATP-gamma.3

in individual RecA filaments when interdigitation occurs between filaments. One often observes “bundles” of more than two RecA filaments, where the filaments coil about each other. It has been noted from shadowed images that these bundles are supercoiled in a left-handed sense stained (DiCapua et al., 1982). Four negatively bundles were chosen for further analysis. All appeared in preparations of RecA-linear doublestranded DNA-ATP-gamma-S, and it is unknown whether DNA is contained within each of the RecA filaments in these bundles, since linear self-filaments can also form in such conditions. However, shadowed micrographs of bundles (Fig. 3(c) of DiCapua et al., 1982) have actually shown DNA extending from the end of individual RecA filaments that enter these bundles. Moreover, similar bundles can be formed in preparations of RecA on circular DNA molecules, and one can see circular molecules entering these bundles. The images of the bundles in negative stain (Fig. 12) are quite different from the shadowed obvious that image and it is not immediately filaments are coiling about each other when this structure is seen in proje&ion, as in negative stain. Neither is it obvious how many filaments are contained in these bundles. The bundle in projection is seen as two light stripes (denoting protein) separated by a dark stripe running along the axis of the bundle (denoting a stain-filled

the bundle cannot be generated by two filaments lying side-by-side. There is an axial periodicity within each bundle of about 550 to 600 A, suggesting that the bundle is rotating about the central axis. A simulation of the coiling of filaments as seen in projection (Fig. 13) shows how the rotation of the bundle will appear in negative stain. The transforms of these bundles (Fig. 14) show a pattern of layer-lines consistent with a helical structure. Analysis of the four best transforms yielded a single indexing scheme for the layer-lines, which is shown in Figure 15. Although the actual spacing of varied somewhat between the the layer-lines different bundles, the indexing is expressed in terms of the smallest integer values which are reasonably accurate. The near 0” phase difference across the meridian on the first (l/570 A) layer-line shows that the order of this layer-line is even, and its radial position indicates that it must be Bessel order either 4 or 6. This layer-line corresponds to the long-pitch coiling of the entire bundle. Both Bessel orders 4 and 6 give rise to helical modulations that are consistent with the size and radial density distribution of the bundle. The layer-line at about

region). Comparisons between the bundles and single RecA-DNA filaments in the same micrographs show that. the much higher contrast within

this layer-line

l/95 A can be indexed as a Bessel function of order 0. with the structure factor close to zero at, the meridian. The order of all other reflections is immediately given once the order of the first layerline is determined to be either 4 or 6. The order of

has been taken

reasons. (1) Shadowed shown bundles of six

to be 6 for four

micrographs have clearly filaments. and not four.

Structure of Helical RecA-DNA

(a)

(b)

Cvmplexes

(c)

689

(d)

Figure 13. The coiling of 6 solid cylinders is shown in a surface view in (a) and in projection in (b). The cylinders are taken to be at a radius of 107 a with respect to the bundle axis, and to be 106 A in diameter. The pitch of the coiling is 3500 A. The axial periodicity in (b) is the only indication in projection of the coiling, demonstrating the different appearances of coiling in shadowing (surface view) (a) and negative stain (projection) (b). In (c) the solid cylinders have been replaced by t,he reconstruction of the RecA-double-stranded DNA-ATP-gamma-S filament of Figs 8 and 9. and the coiled bundle is seen in projection. The axial periodicity that is present. in (b) is preserved in (c). but the image looks vastly different when we replace solid cylinders with a realistic model for the component filaments. Tn (d) we see a tnicrograph of a real coiled bundle

(2) Using the order 6 assignment in a reconstruction generates a picture of component filaments t)hat are very similar to the reconstructed ATPgamma-8 single filament (Figs 8 and 9), while the use of Bessel order 1 generates an unrecognizable substructure for the bundle. (3) One of the bundles yielded a second layer-line, which would have to be Bessel order either 8 or 12 in this indexing scheme. The mean radial density distribution is that of an annulus of density centered at about 100 A in radius. with a pronounced stain-filled center. An assignment of Bessel order 12 to this layer-line generates a helical modulation within this annulus, while that of Bessel order 8 generates modulation within the stain-filled hole. (4) A simulation of the bundle using six copies of the reconstructed filament, of Figures 8 and 9 generates layer-lines virtually identical with those observed (Fig. 14).

The indexing that has been used corresponds to that of a six-start helix that has a repeating subunit whose rise is 95 A. This subunit, is in axial register in each of the six strands. This indexing scheme makes no assumption about either the bundle being composed of continuous filaments or the component filaments having a helical st’ructure. Rather, the bundle itself is treated as a six-start, helix with an asymmetric unit placed every 95 w along each of the strands. Since there are six identical filaments in the bundle, the 570 a periodicity that is seen in projection corresponds to 60” rotations of the bundle, and the pitch of the slow coiling is approximately 3420 A ( x 6 x 570 d). Finally: the hand of the supereoiling must be assigned to complete the indexing. It was initially assumed that the supercoiling must be left-handed, as was observed in a shadowed micrograph of a six-

E. H. Egelman

and A. Stasiak

Figure 14. The computed transform of a real bundle (right) is compared with that, of a simulated bundle (left). The indexing scheme used (Fig. 15) calls the layer line at l/570 A layer-line 1, and the layer-line at l/95 A is labeled layer-line 6. A very weak 13th layer-line can be seen in the real bundle. The layer-lines of the model are broader than that of the real bundle due to the shorter length of structure transformed. layer-line

filament bundle (DiCapua et al., 1982). However, this assumption generated component filaments in the bundle that were a mirror-image of the RecA helix reconstructed from isolated single filaments; that is, the component filaments were left-handed. If one assumes that the supercoiling is righthanded, then right-handed component filaments are reconstructed in the bundle. It seems more plausible, therefore, that the supercoiling is righthanded than that the component filaments have become left-handed. Similarly, a simulation of the bundle using left-handed supercoiling generates different layer-line intensities from those of the observed bundles (data not shown). Two sets of layer-lines (corresponding to the near and far sides of the bundle) were extracted from the transforms of each of the four bundles and were averaged together (near plus far). What appeared to be the best set was then used as a reference, and the rotation and axial shift were found for each of the other three sets that brought the layer-lines into best agreement. The criterion for best agreement was the average of the shifts that generated the minimum amplitude-weighted phase residual and vector residual (for an ideal filament in the absence of noise these would, of course, both be the same). The relative polarity of each of these three bundles with respect to the reference bundle was found by comparing the residual for both possible polarities. The mean amplitude-weighted phase residual for

the “best” polarity was 44”, and 66” for the “worst” polarity. One must consider the possibility that filaments in the bundle are actually antiparallel, but at low resolution the polarity is not great and one therefore fails to see the Bessel order 3 layer-lines that would be present in this scheme. If this were the case, the bundle should have no real polarity at this resolution, and the observed differential in phase residuals for opposing polarities is due to random noise. To answer this question the four data sets were averaged together (Fig. 15) and the averaged data set was then used as a new reference data set. The same search for rotation, axial shift, and polarity with respect to the reference data set was conducted for each of the eight individual data sets (near and far) from the four filaments (Fig. 16). The purpose of this second search was to assess both the quality of the individual data sets and the reliability of the determination of polarity. If we discount the possibility that both the near and far data sets will individually display the polarity opposite to that determined for the near-plus-far averaged set, there are only two possibilities for the individual sets: they will each display the same polarity as the averaged set or they will each display opposing polarities. For a non-polar structure in the presence of random noise, one would expect both possibilities to be of equal likelihood. In this case, the resulting polarity of the

Structure of Helical RecA-DNA near-plus-far averaged set stems from the fact that a component of the random noise still exists after averaging. Figure 16 shows that each of the eight dat.a sets displayed the same polarity as t,hat determined from the near-plus-far averaged sets. For a non-polar structure with random noise, the probability that, all eight data sets would display the same polarity as that determined by the four averaged sets is of the order of l/16, and the initial assignment, of polarity appears to be significant. The reconstruction (Fig. 17) shows six equivalent filaments coiling about a central axis, with a radial distance of about 107 A between the center of each filament and the central axis. Because of the 6-fold symmetry. the center-to-center separation of each filament is also about 107 A, and filaments are making one extensive contact every 95 A repeat. This contact’ appears as a “bridge” of density between the filaments. The individual filaments are clearly resolved as tjhemselves being right-handed helices wit)h a pitch of 95 A. The individual filaments display a deep groove and a “spring-like” construction and appear to be quite similar to the reconstruction of an isolated RecA-double-stranded DNA filament. The reconstruction, which generates helical comfronent filaments in the bundle, demonstrates the correctness of the indexing scheme used, since no

assumption

about the helicity

of the asymmetric

unit, is involved in indexing the layer-lines. Further, of the phases of the layer-lines, using randomization the observed intensities and indexing scheme.

produced asymmetric units character (data not shown).

that

Complexes

691

Although the indexing scheme that is shown in Figure 15 corresponds to one right-handed supercoil for every 36 turns of the 95 A pitch helix, the actual ratio measured from each of t.he bundles was 33.4, 36.0? 36.6 and 39.6, for an average value of 36.4. The supercoiling is induced by the establishment of equivalent contacts between filaments at, every turn of the 95 A helix. If filaments had exactly six units per turn, there would be no supercoiling and the six filaments would all follow a path parallel to the

r

Layer IIlK! 7 - 200-00

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Layer line I

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(a)

Figure 15. (a) The n, 1 plot for the transforms of Fig. 14. The bundles index as a 6-start helix with a repeating subunit whose rise is 95A. (b) The layer-lines extracked from the transforms of 4 bundles, after averaging of near and far sides (thus, 8 data sets have been averaged together). The indexing of these layer-lines is as shown in (a). Ampkudes are shown.

(EL-‘, (bl

00

E. H. Egelmun and A. Stasiak

692

by re-indexing the layer-lines from a 56/11 helix to a 35/6 helix. In this new scheme, the previous 1st layer-line (lying near the equator) now became the 5th layer-line, and the very strong 11th layer-line was re-indexed as the 6th layer-line. The resulting filament generated by Fourier-Bessel inversion was then supercoiled at a radius of 107 A about a central axis, with a supercoil pitch 32.4 times 95 A, such that:

75.o70.0 65.06O.P t 55.0f g 50.0-

6 x 32.4 ~ = 5.833. 32.4 + 1

45.o 40.0 ,,.,,,: 30.0

, , ( , , , , , 35.0 40-O 45.0 50-O55-O60-O 65.0 70.0 75.0 Best-fit

reslduol (degrees)

Figure 16. The 8 individual data sets from the 4 bundles (corresponding to near and far sides) were used to find individual amplitude-weighted phase residuals using the polarity found for the averaged data set (best) and the opposite polarity (worst). A complete search was made for each set over rotation, axial translation, and radial scale. It can be seen that all data points lie above the diagonal line, where the diagonal line indicates equal residual for the 2 polarities. The area above the diagonal corresponds to lower residuals for the averaged polarity than from the opposing polarity. Only 1 point falls very near the line. indicating no clear polarity, but this data set was still used in the average.

central axis of the bundle. Because there are not exactly six subunits per turn, the twisting of the filaments that takes place in component establishing equivalent contacts is relaxed by the long-pitch supercoiling. In the supercoiled bundle, t,here must be six subunits for every 95 A repeating unit. (one turn of the 95 A pitch right-handed helix) for equivalent contacts to be made (alternatively, t,here could be an integer multiple of 6, e.g. 12. 18 etc.. but this need not be considered). Since there is one right-handed supercoil turn for every 36.4 right-handed turns, or 37.4 net right-handed turns, t.he t’rue filament symmetry is (6 x 36.4)/37.4, or 5.840 units per turn. The supercoiling thus serves as a sensitive vernier with which to measure the average number of units per turn. The error associated with this value is determined by the with which the mean spacing of the accuracy crossover subunit repeat (95 A) and the supercoil (570 x) can be measured. Taking 0.5 pixels in t,he Fourier transform as the standard error of each. that the error in each of the an d assuming measurements is uncorrelated, the standard error of the mean would be about 0.007. To illuminate the reconstruction further, a synthesized bundle was created using the reconstructed single filament of Figures 8 and 9. First, the twist of that filament, 5.09 units per turn, was art,ificially changed to be 5.83 units per turn (close to that of the twist of the filaments in the bundles)

The transform of this bundle was computed, and a reconstruction (Fig. 17) comparable to that of the real bundle was generated by using only those five layer-lines contained in the averaged data set. The reconstruction appears to be quite similar to that of the real bundle, with the main difference being that the bridges of density connecting filaments in the real bundle are absent in the synthesized bundle. This shows clearly the extent to which the component filaments in the real bundle are deformed from true helical symmetry to establish these contacts. (b) RecA on single-stranded DNA with ATP

or with ATP-gamma-S We have found the RecA-single-stranded DNAATP state more disordered than the RecA-doublestranded DNA-ATP-gamma-S state and the filaments are therefore not as well-suited to threedimensional reconstruction. The increased disorder can be explained by the constant ATP hydrolytic activity of the RecA protein in such complexes. It has been shown that hydrolysis of ATP stimulates displacement of RecA monomers from t’he complex (Menetski & Kowalczykowski: 1985), thus inducing local lesions and irregularities. The average contour lengths of such filaments are almost 10% short,er t’han the contour lengths of the same number of bases in the ATP-gamma-S state, yet selected regions can be found where the average pitch is comparable to that found in t,he ATP-gamma-S state. Filaments in this st,ate that are fixed with glutaraldehyde show a significant compression. with the contour length decreasing by about 30°jC,. so that the average measured spacing between bases is approximately 3.4 A4 (Koller et al., 1983: Flory et rrl., 1984). No condit,ions were found where filaments in this state exhibit.ed the amount of helical symmetry found in the RecA-double-stranded DNA-ATPgamma-S stat’e. The best’ filaments yielded two layer-lines. l/95 A, Bessel order 1, and 1147.5 14, Bessel order 2, but even these two layer-lines could not average together as well as had been done for the ATP-gamma-S state (Stasiak & Egelman, 1986). The polarity of different filaments appeared to be ambiguous, and one could find the near and far sides giving opposite polarities. Despite all these problems, there has been no systematic indication that. the density distribution along the 95 A pit,ch helix of t,he RecA-single-stranded DNA-ATP state

Structure

of Helical

RecA-DNA

(b)

(0)

Complexes

693

Cc)

Figure 17. (a), (b) Surface views of reconstructions from real bundles; and (c) a surface view of a model constructed from a single RecA filament. The surface level has been chosen to yield the correct molecular volume for the 6 component, filaments. (a) This was made from the layer-lines of Fig. 15, and is the average of 8 sides (4 bundles), while (b) is a near-plus-far average from the best single bundle. The model in (c) was reconstructed using the same layer-lines used in (a) and (b). The filaments in (a) and (b) are seen to be bridged by a large density. which is absent in (c). The filaments arr right-handed helices, and they are coiling in a right-handed manner.

is different from that of the RecA-double-stranded DNA-ATP-gamma-S state. Filaments of RecA on single-stranded DNA with ATP-gamma-S have been prepared only under conditions where aggregation occurs into bundles. These bundles have been less ordered than those formed with double-stranded DNA, and they do not exhibit t.he supercoiling that, is clearly seen in the double-stranded DXA bundles (Fig. 12). The strong helical pitch of about 95 a is clearly seen in these bundles, but it is possible that the arrangement of filaments is different in t’hese aggregates from those formed with double-stranded DNA.

4. Discussion (a) Helical

disorder

and jexibility

The RecA filament’s that have been examined, both with ATP and ATP-gamma-S, are characterized by large amounts of helical disorder. That is, the observed relationship between monomers in the filaments are not given by a strict helical symmetry, but rather, there are large fluctuations from the ideal geometry. The most striking observable with the naked eve, is deviation, bending. The correlation length of 6000 A, wh\ch we

have measured, is extremely small for a structure with the mass per unit length of RecA filaments. For purposes of comparison, the correlation length of double-stranded DNA is about 500 A (Hagerman & Zimm, 1981). However, the flexural rigidity of a filamentous polymer should scale as the square of the mass per unit length (assuming, of course, no change in geometry or composition). Since the RecA filament has about 20 times the mass per unit length of double-stranded DNA, we would expect an increase in correlation length by a factor of about 400 from DNA to RecA. Inst’ead, we observe only an increase by a factor of about) 12. Similarly. F-actin has only about 600/; of the mass per umt length as RecA, but is about ten times as rigid (Oosawa, 1980). The observed variation in pitch within filaments is about lOo/o. and the observed variation in twist (t’he angle of rotation between subunits) is about’ 15% in the ATP-gamma-S state in the instances where we have been able to determine the number of units per turn. Selected regions have been found where helical symmetry appears to be obeyed locally. The most obvious question is whether the disorder that is seen (i.e. variations in pitch. variations in the number of units per turn, and

694

E. H. Egelman

variable curvature), as well as the structures that represent the filaments in are reconstructed, solution or are due mainly to specimen preparation for electron microscopy. There are five reasons for believing that the electron micrographs give a faithful, rather than artefactual, image of the filament and its deformability. from a (1) The X-ray powder pattern RecA + double-stranded DNA + ATP-gamma-S gel is completely consistent with the observed transforms of electron microscopic images. If the filaments in solution have a helical structure different from that seen in the electron micrographs, one would expect these differences to appear between the observed powder pattern and the simulated pattern generated from the extracted layer-lines (Fig. 10). (2) Bi-polar side-by-side aggregates of RecA state show filaments in the ATP-gamma-S perturbations of the axial arrangements of subunits within the component filaments (Fig. ll), which is consistent with an intrinsic compressibility and extensibility seen within isolated filaments. It is expected that inter-filament interactions might stabilize the disordered structure of single filaments. Instead, when two disordered filaments interdigitate we see that, deviations from helical symmet,ry (axial pert,urbations of the subunit density) become readily apparent. The deformability of isolated filaments, manifested in random disorder, appears in the filament pairs as periodic deformations. Although it’ is possible that such deviations from helical symmetry could be caused by artefacts associated with the distribution of stain, it is equally consistent with the picture that we have of a very deformable structure. In the bundles of six filaments, we see deformations of the component filaments in the form of bridges between adjacent filaments. However, we do not see the deformations of the axially projected density within the bundles that we see in the side-by-side aggregates, and this is most likely a consequence of the fact that different bonding rules are involved in these different structures. (3) Electron micrographs of RecA-ATPgamma-S-double-stranded DNA filaments in the frozen hydrated state (W. Chiu & M. Schmid, personal communication) display the same amount of variation in pitch (approx. 10%) within filaments that is observed in negative stain. Since these filaments are rapidly frozen in ice, unstained, and not) subjected to dehydration, the preparation of our material for conventional negative stain electron microscopy can be discounted as a source of the observed pitch variation. (4) The flexural rigidity of actin has been wellcharacterized using solution methods (for a review, microscopic see Oosawa, 1980). An electron measurement of the flexibility of F-a&in, using a method similar to that used here (Takebayashi et al., 1977), was in excellent agreement with the solution studies, demonstrating t’hat specimen electron and dehydration for preparation

and A. Stasiak

microscopy does not significantly change the observed flexural rigidity, at least for actin. It seems reasonable to assume that other helical protein polymers, such as RecA filaments, will behave in a similar manner. (5) The three-dimensional reconstruction reveals a spring-like construction for the ATP-gamma-S state. This geometry alone could explain compressibility and extensibility, as well as flexural rigidity, without having to postulate specific hinges or joints within the filament. The flexural and torsional rigidity of such a structure, even if it were const’ructed of a homogeneous and isotropic material, is not determinable in a simple analytic manner. This is because the linear strain assumption used to calculate the stress-strain relations rapidly breaks down and the problem becomes statically indeterminate (Bisplinghoff et al., 1965). The spring-like geometry of the RecA reconstruction can also explain the observed coupling (Fig. 4) between pitch and diameter. When a simple spring is unextended (i.e. when the pitch is very small compared to the diameter) extensions and effect on the compressions have a negligible diameter. When the spring has been greatly extended (i.e. when the pit.ch is a significant fraction of t,he diameter) axial extensions and compressions lead t,o radial compressions and extensions, respectively. The reconstruction clearly shows an extended spring-like geometry. (b) Polarity

of the

reconstruction

The reconstructed single filament displays a clear polarity, consistent’ with a functional directionality of RecA in the strand exchange reaction (Cox & Lehman, 1981; West et al., 1981b; Kahn et al., 1981; Regist’er & Griffith, 1985). An important step in relating structural models of RecA filament,s to the strand exchange reaction will be to determine the polarity of the reconstructed filaments with respect to the polarity of single-stranded DNA in reactions. This work is in progress. (c) The specificity

of filament-JiEament

interactions

Since RecA polymerizes on DNA in a unidirectional manner from a nucleation point that appears to occur randomly (Register & Griffith, 1985; Cassuto & Howard-Flanders, 1986), we know that a collapsed circular molecule (Fig. 11) will bring antiparallel DNA strands into contact. An alternative that can be excluded is that two or more areas of nucleation occurred on the same molecule and polymerization proceeded in both directions. This would mean that a circular molecule would not always have a RecA covering of the same polarity. Unfortunately, most circular molecules yielded at best only one section of a quality high enough to determine relative polarity. The quality of the interdigitated molecules (Fig. 11) is also not’ high enough to determine with confidence whether the

Structure of Helical RecA-DNA interdigitated regions are polar (indicating uniform polarity) or bi-polar (indicating opposing polarity), since any noise will always turn a bi-polar structure into a polar structure. In the few instances when more than one section of high quality has been found on the same circular molecule, the polarity has always been found to be uniform (data not shown). The main argument for uniform polarity, however, resides in the observed kinetics of polymerization, where nucleation appears to be the rate-limiting step in the polymerization reaction. Thus, once a nucleus for RecA polymerization forms, it will polymerize rapidly. The consequence of this is that when a low RecA to DNA mixture is used, one finds circular DNA molecules that are either fully decorated with RecA or completely undecorated. The probability for more than one nucleation point forming on the same circular molecule before polymerization is complete is therefore small, and it can be assumed that the interdigitated strands are of opposite polarity. The arrangement of filaments in the supercoiled bundle is one of uniform polarity. Further, the filament-filament interactions in the bundles do not generate the axial perturbations of density that appear in the side-by-side aggregates. If the same bonding rule existed in the bundles as in the sideexpect these by-side aggregates, one would perturbations to be seen easily. Instead, the axially projected density of the filaments in the bundle appears at low resolution to be absolutely uniform, consistent with an equal translation along the axis of about 16 A (x95 A/6) between successive monomers. Thus, there must be at least two bonding rules governing filament-filament interactions (one parallel and the other antiparallel). It has been proposed (Tsang et al., 1985) that RecA-RecA interactions are important in forming nucleoprotein aggregates in vitro that accelerate the strand exchange reaction. (d) Symmetry and stoichiometry Our observations of from 5.1 to 6.8 monomers per turn of the 95 A pitch helix in the ATP-gamma-S state are quite consistent with the mass per unit length measurements of DiCapua et al. (1982) (who found an average value of about 6.5 RecA monomers per turn). The most ordered filament section, used for the three-dimensional reconstruction, had a symmetry of about 5.1 units per turn, placing it at one extreme. It is possible that this filament section was more ordered than all others examined precisely because it was found at one extreme of pitch (fully extended at 100 A) and twist. The measurements of monomers per turn from the three-dimensional reconstructions require an assumption that every asymmetric unit is one RecA monomer. This assumption seems plausible, given that the choice of a reasonable contouring threshold for the three-dimensional reconstruction yields a volume for each asymmetric unit of about 45,000 A3, which is consistent with the known

Complexes

molecular weight of RecA of 37,842 (Sancar et al., 1980) and a partial specific volume for protein of about 0.75 cm3/g. The supercoiling of six filament bundles of filaments (Figs 12 to 15) has shown that the symmetry of individual filaments in the bundle relaxes to a mean of 5.840 (&0907) units per turn. DiCapua et al. (1982) were able to measure the average number of DNA base-pairs per turn of the RecA helix to high accuracy, and their value was 18.58 ( kO.07). If one imposes an integral stoichiometry of three base-pairs per RecA monomer, the number of RecA monomers per turn would be 6.19. This value for the twist, slightly greater than 6, would explain the left-handed supercoiling seen in shadowed images. It is possible that conditions for negative staining change the twist to a value slightly less than 6, generating right-handed supercoiling. The change in twist per monomer would be about 3”. Given the deformability of the RecA filament, and the fact that these different observations have been made under different conditions, this amount of change does not appear to be unreasonable. Studies are in progress to see if the conditions used in uranyl acetate staining have a small but systematic effect on the twist of RecA filaments. (e) Functional

aspects of the three-dimen,sional structure

RecA filaments have been examined under several different conditions: on double-stranded DNA with ATP-gamma-S, and on single-stranded DNA with ATP or ATP-gamma-S. Although it has only been the double-stranded DNA wit’h ATPgamma-S state which has provided detailed information, several lines of evidence suggest that the structure of the RecA protein helix in these complexes is the same. Firstly, self-complexes of RecA without added DNA (McEntee et al., 1981), as well as complexes with single-stranded DNA (Keller et al., 1983) can be formed with ATP-gamma-S, and these have the same basic helical parameters as the complex formed with double-stranded DNA. Complexes of RecA and single-stranded DNA formed with ATP appear to be quite similar to the ATP-gamma-S-double-stranded DNA complex, although less well-ordered. This suggests that the ATP-gamma-S state is basically the same as the ATP state, but that it has been stabilized by the use of the non-hydrolyzable analog. Most. importantly, experiments have shown (Honigberg et al., 1985) that the ATP-gamma-S complex itself can mediate the recognition of homology. The RecA-single stranded DNA-ATP complex can be viewed as both the initiation complex (or pre-synaptic complex; Cox & Lehman, 1982; Flory et al., 1984) and the real synaptic state (Stasiak et al., 1984), in which homologous recognition and strand exchange can take place. The ATP state has been directly visualized during the strand exchange reaction (Stasiak et al., 1984) and RecA in this state

E. H. Egehan

696

(a)

(b)

Figure 18. Two different models for the position of the double-stranded DNA in the reconstruction of Figs 8 and 9 are shown. The DXA is modeled as a solid cylinder, of radius 8 A, with the axis of the cylinder following a helical path of radius 10 A about the RecA filament axis. The DNA is indicated by an arrow. Because the DNA is being modeled as a solid cylinder. the total volume for the DPU’A is about 3 times greater than the known molecular volume, so the relative weight of the DKA to the protein in these pictures is disproportionately large. The radius of 10 A chosen for the path of the DNA in these models is slightly larger than the 9.4 a maximum radius calculated, and thus represents one extreme. The other extreme, of 0 A radius, would place the DNA along the filament axis. The phase of the DNA in the 2 models is 180” apart. In (a) the DNA occupies a stain-excluding region of the reconstruction, and would thus correspond to negative staining of the DNA. In (b) bhe DNA occupies a “whole“ or stain-filled region of the reconstruction, and this would correspond to a positively stained DX.4. As (‘an be seen in t)he Figure, the interpret’ation of an internal I)iVA molecule that is accessible to external DNA molecules does not, change wit,h different assumed posit,ions for l)I%A within the complex. was shown to keep single-stranded IINA in an extended conformation ready for contact, with naked double-st,randed DNA molecules. After the contact between RecA-complexed single-stranded DNA and homologous double-stranded DNA is established, the homologous double-stranded I)NA seems to be taken into the interior of the complex. It, is probably within this complex that the nucleotide chains are brought into axial alignment and homologous pairing is possible. Once this happens, strand exchange can occur (Stasiak et al.. 1984; Stasiak & Egelman, 1986). It is reasonable to examine the ATP-gamma-S reconstruction in the context of these known functions.

and A. Stasiak

The ambiguity about the staining of the DNA, the low resolution of the reconstruction, and the small relative mass of the DNA with respect to the protein in the complex all contribute to an uncertainty in defining the position of the doublestranded DNA in the reconstruction of Figures 8 and 9. However, path length considerations dictate that the DNA on average must be within a radius of about 17 A, and in the particular case of the extended filament used in the reconstruction, within a radius of 9.4 d. Two models of the DNA in the complex are shown in Figure 18, corresponding to the cases of negative and positive staining of the DNA. What is evident is that one surface of the DNA in both models is relatively exposed to external molecules through the deep helical groove. It has been shown (Stasiak & DiCapua, 1982) t,hat double-stranded the helical DNA adopts parameters of RecA in the ATP-gamma-S complex. The twist of DNA is changed from about 36” per base-pair in B-DNA to about 20” per base-pair in the complex. Since the stoichiometry is three basepairs per RecA molecule, every group of t,hree basepairs undergoes the same amount of twist, about) 58”, as every RecA monomer. Thus, contacts between the RecA and DNA wit’hin the complex would be equivalent for every monomer. Several studies have attempted to determine what part of DNA binds to the RecA protein. These studies have suggested that RecA binds to the minor groove of double-stranded DNA (Dombroski et al., 1983) and to the phosphate backbone of single-stranded DNA (M. C. Leahy & C. M. Radding, unpublished results). The solid-cylinder DNA models of Figure 18 can be extended to molecular models (see Howard-Flanders et al., 1984aJ) to picture DNA bases that are exposed in the deep helical groove of the RecA protein filament. Since the DNA is following t,he same helical parameters as t,he RecA filament, the bases would be continuously exposed along the helical groove. This would provide the basis fi)r enzymatically mediated homologous recognition, in which external DNA molecules can make transient contacts with an int,ernal TINA molecule until homologous contact’s are est’ablished. \Ve thsnk Theo Keller. Elisabeth DiCapua and Alicja Staxiak for their assistance; R. West, for the preparation of RecA sa,mplrs for X-ray diffract)ion: K. Y. Roe for measurements of filament curvature; and Paul HowartlFlanders for his support, suggestions and encouragement. X-ra) and computational facilities were generously provided by the Yale W.E.R.M.S. group. This research was supported in part) by BRSG grant RR0.5358. I)irisioll of Research Resources, X.1.H.. and by Schweizerischrr SaGonalfonds zur Forderung der Wissenschaftlichen Forschung grant 3.279-0.82 to Th. Koller.

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Structure

of

Helical

Bisplinghoff, R. L., Mar, J. W. & Pian, T. H. H. (1965). Statics of Deformable Solids. Addison-Wesley, Reading, MA. (lassuto, E. & Howard-Flanders, P. (1986). Nucl. Acids Res. 14, 1149-1157. (“ox. M. M. & Lehman, I. R. (1981). Proc. Nat. Acad. Sci., U.S.A. 78, 6018-6022. Cox, M. M. & Lehman, I. R. (1982). J. BioE. Chem. 257. 8523-8532. DasGupta, C.. Shibata. T., Cunningham, R. P. & Radding. C. M. (1980). CeEf, 22, 437446. I)asGupta. C.. Wu. A. M., Kahn, R., Cunningham, R. P. & Radding, C. M. (1981). Cell, 25, 507-516. I)eR,osier, I). *J. & Klug. A. (1968). Nature (London), 217, IBO--134. DeRosier. D. *J. 8: Moore, P. H. (1970). J. Mol. Biol.. 52, 355369. lli(:apua, E.. Engel, A.. Stasiak. A. & Koller. Th. (1982). J. Mol. Biol. 157, 87-103. Dombroski. 1). F., Scraba. I>. G., Bradley. R. B. & Morgan. A. R. (1983). ~V~;ltc/.Acids Res. 11. 74877504. Drrssler, I). Br Potter, H. (1982). Annu. Rev. Biochem. 51. 727 -761. I)unn. K., Chrysogelos, S. & Griffith, J. (1982). Cell, 28. 7577765. Egelman. E. H. (1986). Ultramicroscopy, in the press. Flory. ,J. & Radding, C. M. (1982). Cell, 28, 7477756. Flory. tJ.. Tsang, S. S. & Muniyapa, K. (1984). Proc. Nat. Acu.d. Sci., U.S.A. 81. 7026-7030. Hagerman. P. J. & Zimm. B. H. (1981). Riopolymers, 20, 1481-1502. Honigberg S. M., Gonda, D. K., Flory, J. & Radding, C. M. (1985). J. Biol. Chem. 269, 11845511851. Howard-Flanders, P.. West, S.C. & Stasiak, A. (1984a). Nature (London), 309, 2 15-220. Howard-Flanders. P.. West, S. C., Rusche, J. R. & Egelman, E. H. (19846). Cold Spring Harbor Symp. Quant. Biol. 49, 571-580. Kahn. R.. Cunningham. R,. P., DasGupta, C. & Radding, C. M. (1981). Proc. Nat. Acad. Sci., U.S.A. 78. 478647!JO.

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A., Crick, F. & Wyckoff, H. W. (1958). Acta Crystallogr. 11, 199-213. Koller, Th., DiCapua, E. & Stasiak, A. (1983). In Mechanisms of DNA Replication and Recombination, pp. 723-729, Alan R. Liss, Inc., Eew York. Landau, L. D. & Lifshitz. E. Mol. (1958). Statistical Physics, Pergamon. Oxford. McEntee, K.. Weinstock, G. M. & Lehman, I. R. (1981). J. Biol. Chem. 256, 8835-8844. Menetski.
Edited by A. Klug