determining the structure of biological macro molecules by

Progress in Biophysics & Molecular Biology 75 (2001) 121–164

Review

Determining the structure of biological macromolecules bytransmission electron microscopy, single particle analysis and

3D reconstruction

Jonathan Ruprechta,*, Jon Nieldb

aUniversity of Cambridge, Department of Biochemistry, Hopkins Building, Cambridge CB2 1QW, UKbWolfson Laboratories, Department of Biochemistry, Imperial College of Science, Technology and Medicine,

London SW7 2AY, UK

Abstract

Single particle analysis and 3D reconstruction of molecules imaged by transmission electron microscopyhave provided a wealth of medium to low resolution structures of biological molecules and macromolecularcomplexes, such as the ribosome, viruses, molecular chaperones and photosystem II. In this review, theprinciples of these techniques are introduced in a non-mathematical way, and single particle analysis iscompared to other methods used for structural studies. In particular, the recent X-ray structures of theribosome and of ribosomal subunits allow a critical comparison of single particle analysis and X-raycrystallography. This has emphasised the rapidity with which single particle analysis can produce mediumresolution structures of complexes that are difficult to crystallise. Once crystals are available, X-raycrystallography can produce structures at a much higher resolution. The great similarities now seen betweenthe structures obtained by the two techniques reinforce confidence in the use of single particle analysis and3D reconstruction, and show that for electron cryo-microscopy structure distortion during samplepreparation and imaging has not been a significant problem. The ability to analyse conformationalflexibility and the ease with which time-resolved studies can be performed are significant advantages forsingle particle analysis. Future improvements in single particle analysis and electron microscopy should

Abbreviations: 1D, one-dimensional; 2D, two-dimensional; 3D, three-dimensional; CCD, charge-coupled device;CCF, cross-correlation function; CTF, contrast transfer function; DPR, differential phase residual; EM, electronmicroscopy/electron microscope; FEG, field-emission gun; FSC, Fourier shell correlation; LDL, low-density

lipoprotein; LHCII, light-harvesting complex II; MAD, multiwavelength anomalous diffraction; MCF, mutualcorrelation function; MIRAS, multiple isomorphous replacement and anomalous scattering; MSA, multivariatestatistical analysis; NMR, nuclear magnetic resonance; OEC, oxygen-evolving complex; PCTF, phase contrast transfer

function; PSII, photosystem II; SCF, sinogram correlation function; SNR, signal-to-noise ratio; TEM, transmissionelectron microscopy.*Corresponding author. Fax: +44-1223-333345.

E-mail address: [email protected] (J. Ruprecht).

0079-6107/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 7 9 - 6 1 0 7 ( 0 1 ) 0 0 0 0 4 - 9

increase the attainable resolution. Combining single particle analysis of macromolecular complexes andelectron tomography of subcellular structures with high-resolution X-ray structures may enable us to realisethe ultimate dream of structural biology a complete description of the macromolecular complexes of the cellin their different functional states. # 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Transmission electron microscopy; Single particle analysis; Image processing; 3D reconstruction;Crystallography

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

2. Specimen preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

3. Electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4. Optical diffraction and densitometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5. Principles and methodology of single particle analysis and 3Dreconstruction by angular reconstitution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1275.1. Correcting for the contrast transfer function (CTF) . . . . . . . . . . . . . . . . . . 1275.2. Particle picking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.3. Band-pass filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1305.4. Reference-free alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315.5. Multivariate statistical analysis (MSA) . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.6. Automatic classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1325.7. Multi-reference alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1325.8. Angular reconstitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.9. 3D reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.10. Iterative refinements to the model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1355.11. Evaluating the quality of the 3D reconstruction . . . . . . . . . . . . . . . . . . . . 135

5.12. Presenting the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

6. Critical review of single particle analysis and 3D reconstruction byangular reconstitution: a comparison with other methods forstructural studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7. The ribosome: comparing single particle analysis with X-ray

crystallography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

8. Photosystem II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

9. Electron tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

10. Future prospects and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

J. Ruprecht, J. Nield / Progress in Biophysics & Molecular Biology 75 (2001) 121–164122

1. Introduction

3D structures of molecules can be obtained through the image processing of electronmicroscope (EM) images, using the techniques of single particle analysis, angular reconstitutionand 3D reconstruction. First, transmission electron microscope (TEM) images of the molecule(s)of interest randomly oriented on an EM grid are obtained. These images are 2D projections of the3D structure, because the depth of focus is much greater than the specimen thickness (DeRosierand Klug, 1968). Theoretically, if the projection angle of each image could be determined, a 3Dstructure of the molecule could be obtained by projecting the 2D images back along theirprojection angles (back-projection). However, electron micrographs of biological molecules arevery noisy and show low intrinsic contrast. Single particle analysis was developed to deal with theproblems of noise and low intrinsic contrast by increasing the signal-to-noise ratio (SNR) of themicrographs, pushing back the limits of resolution and interpretability.Even in the last three months, as this review was in preparation, the amount of information

about single particle analysis, and the number of examples of its use, have exploded. There havebeen several excellent, but concise, reviews of single particle analysis and electron cryo-microscopy (e.g. Saibil, 2000a, b; Orlova, 2000). This review will focus in depth on single particleanalysis, informing the reader of some of the principles of this technique. Whilst this has beendone in a non-mathematical way, references are provided to more detailed treatments of some ofthe topics. By critically reviewing single particle analysis, it is hoped that the reader will becomeaware of some of the advantages and also of the problems of the technique, so that they can assessthe quality of the structures they will see. The review first introduces the steps neededto produce a 3D structure by single particle analysis, from sample preparation to electronmicroscopy and then to image processing, using work that has been carried out on photosystemII as an example. Single particle analysis is then critically compared to X-ray crystallo-graphy, electron crystallography and NMR spectroscopy. This is further discussed by consideringstructural studies of the ribosome, which have been instrumental in driving many of thetechnical advances in single particle analysis, and of photosystem II. Finally, relateddevelopments such as electron tomography are considered, and the future of single particleanalysis is discussed.

2. Specimen preparation

Any specimen preparation technique must avoid the collapse of structures during pre-paration and observation, since the specimens are viewed in a vacuum in the EM (Slayter andSlayter, 1992). Also, biological specimens are extremely sensitive to bombardment by electrons,and this is a significant factor in the high noise levels of electron micrographs (discussed in Amoset al., 1982; Dubochet et al., 1988). The incident electrons lose large amounts of energy byinelastic collisions, forming highly reactive ions and free radicals, which disrupt bonds andfragment molecules. Incident electrons can also directly transfer their momentum to atomic nucleiin the structure, resulting in atom displacement. Furthermore, the atoms typically presentin biological molecules (C, H, O, N, etc.) scatter electrons weakly, producing images withlow intrinsic contrast. Therefore, to increase the attainable resolution, electron-beam damage

J. Ruprecht, J. Nield / Progress in Biophysics & Molecular Biology 75 (2001) 121–164 123

to the specimen should be minimised, and image contrast should be maximised (Chen et al.,1998).Negative staining (Amos et al., 1982; Chen et al., 1998; Slayter and Slayter, 1992) is technically

simple to perform, and provides high contrast and a low sensitivity to the electron beam.However, negative staining has several disadvantages (Kiselev et al., 1990). It only shows surfacedetail, with the distribution of the heavy metal atoms rather than the density of the specimenbeing revealed. Furthermore, negative staining imposes a limit on the resolution of 10–20 (A(Amos et al., 1982; Chen et al., 1998; Hoenger and Aebi, 1996). This is because of stain movementduring imaging, variable flattening of the 3D structure by dehydration, and stain granularity (thesize of the stain molecules prevents their penetrating the protein surface, so that details such asbundles of helices will not be revealed).Electron cryo-microscopy (also called cryo-electron microscopy, cryo-EM; Dubochet et al.,

1982, 1988; Slayter and Slayter, 1992; Baker and Johnson, 1997; Chen et al., 1998) hasrevolutionised the analysis of macromolecular structure by electron microscopy, and iscomplementing negative staining for 3D reconstruction studies. Often, single particle analysisand 3D reconstruction of negatively stained specimens will be attempted to gain a first glimpse ofthe structure. Then, images will be taken under cryo-conditions, which in principle containinformation to atomic resolution (Chen et al., 1998), and processed to produce a 3D model athigher resolution. For a detailed comparison of the relative advantages of negative stain and cryo-EM techniques, see Hoenger and Aebi (1996). In cryo-EM, samples are embedded in vitreous iceon a ‘‘holey’’ carbon grid and maintained at low temperatures (100–113K) whilst under theelectron beam. Vitreous ice is essentially a supercooled liquid, produced when water is veryrapidly cooled below 273K (at about 105K s�1) (Slayter and Slayter, 1992). This avoids damageto the specimen by ice crystal formation. Vitreous ice forms a structureless medium in which themolecules are hydrated, despite the requirement for vacuum conditions (the low temperatures leadto a very slow rate of sublimation of the ice). The specimen is therefore imaged under conditionsmore like those in its native environment. The low temperature, and the use of low doses ofelectrons (10–20 electrons/ (A2), as described in the next section, minimise beam damage (Starket al., 1996).The procedure for cryo-EM specimen preparation is as follows. The specimen is applied to a

‘‘holey’’ carbon grid, which may have been glow-discharged to improve the hydrophilicity of thecarbon film and therefore increase the amount of specimen adhering to the grid. The grid is thenblotted with filter paper, and plunged into a bath of liquid ethane held at liquid nitrogentemperature. Liquid ethane rather than liquid nitrogen is used as the cryogen because liquidethane has a higher heat capacity. Furthermore, liquid nitrogen will form a gas layer on contactwith the EM grid, which will insulate the sample and slow cooling. The blotting time is animportant factor in controlling the thickness of the ice. If the ice layer is too thick, the electronbeam may not be able to penetrate it.The frozen-hydrated specimens have to be transferred to the microscope using special

equipment designed to keep them at low temperature under liquid nitrogen (cryo-transfer). This isessential to avoid specimen warming (even at quite low temperatures, sublimation of ice may beappreciable, causing variable dehydration of the specimen) and to prevent contamination bywater vapour condensing onto the specimen.


3. Electron microscopy

There are several requirements to produce the high-quality images necessary for high-resolutionwork (Slayter and Slayter, 1992). The specimen stage must have a high degree of mechanicalstability in order to reduce specimen drift whilst an image is recorded. Vibrations and straymagnetic fields can cause a strongly directional loss of resolution. The stage design must alsominimise heating and the accumulation of electric charge. For cryo-EM work a cold stage (cooledby liquid nitrogen or liquid helium) is necessary (Dubochet et al., 1988; Fujiyoshi et al., 1991;Fujiyoshi, 1998). This should provide evenness of cooling and mechanical stability. Anti-contamination devices are required to prevent deposition of materials on the specimen. These areusually metal surfaces, such as a pair of copper blades, situated near the position of the EM grid inthe microscope, and cooled to liquid nitrogen temperature so that they trap residual gases(Dubochet et al., 1988; Baker and Johnson, 1997).Samples may be imaged under conditions in which the electron dose is minimised, thus reducing

beam damage. In this ‘‘low-dose’’ technique, three different ‘‘modes’’ are used: search, focus andexposure. First, the pin in the microscope is used to correlate the areas imaged in the exposure andsearch modes. Search mode is set at a low magnification (e.g. 2650� ), and is used to position thepin such that a good area of the grid will be imaged in exposure mode. For cryo-EM, a good areaof the grid would be one containing a hole in the carbon film}the sample will hopefully beembedded in the meniscus of ice spanning the hole. Using low magnification at this stage reducesbeam damage since the irradiation level is kept very low (less than 0.05 electrons/ (A2/s (Baker andJohnson, 1997)). Focus mode is then used to focus, at high magnification (e.g. 175 000� ), on anarea of the carbon film near the ice hole. The position of the beam in focus mode is set at anadjustable distance and angle from its position in exposure mode, such that in focus mode beamdamage is again minimised. Phase contrast is now introduced by defocusing the microscope (e.g.1–2 mm underfocus, see Section 5.1 for a discussion of phase and amplitude contrast). Finally, inexposure mode (e.g. at 40 000� ), the image is recorded of the desired area. The magnification atwhich the images are taken, the accelerating voltage, the total electron dose, and the defocus canall be varied depending on the desired resolution of the image (Baker and Johnson, 1997). It canbe seen that in low-dose regimes, the final image is taken ‘‘blind’’, and the quality can onlybe assessed after the image has been taken and analysed by optical diffraction (Section 4) or byon-line image processing which is available with the latest electron microscopes.Even the most advanced electron lenses are of poor quality in terms of spherical aberration,

astigmatism, lens-current fluctuations and chromatic aberration. Spherical aberration is ageometrical property of lenses, resulting in rays that travel to the lens margins being brought to aslightly different focus point compared to those travelling very close to the lens axis, resulting in a‘‘zone of confusion’’ (Slayter and Slayter, 1992; Reimer, 1997). Astigmatism occurs when theobjective lens field is not perfectly symmetrical, resulting in the formation of line images of pointobjects, oriented uniformly across the image (Amos et al., 1982; Slayter and Slayter, 1992; Reimer,1997). Astigmatism can vary while a sample is being imaged, due to the deposition ofcontaminants onto the lens elements. Astigmatism can be corrected by looking at the granularityof the carbon film at high magnification (e.g. 175 000� ), which should remain rotationallysymmetrical while going in and out of focus (Amos et al., 1982). This can be achieved by adjustingthe field applied by electromagnetic lenses called stigmators. It is essential to compensate for


astigmatism before taking high-resolution TEM images. Chromatic aberration (Amos et al., 1982;Slayter and Slayter, 1992; Reimer, 1997) is a consequence of the dependence of the focal length oflenses on the wavelength of incident radiation. In electron microscopy, it results from variations inelectron velocity. Electron velocity is inversely proportional to electron wavelength, as describedby the de Broglie equation. Variations in electron velocity may result from fluctuations in the hightension supply, differences in the energy of electrons emitted from conventional thermionicemission guns, and energy losses as a result of inelastic scattering events. The electromagneticlenses can no longer bring the electrons of ‘‘incorrect’’ velocity to the correct focus, and thisresults in a smearing out of the contrast transfer function (CTF}see Section 5.1) at highresolutions.The development of the field-emission gun (FEG) has revolutionised cryo-EM work, and its use

should soon become standard for higher resolution work (Stowell et al., 1998). In FEGmicroscopes, very high electric fields are used to release electrons from a very fine tungsten tip(Kasper, 1982; Reimer, 1997). The increased spatial coherence (due to the higher brightness andsmaller effective size of the electron source) and increased temporal coherence (due to the smallerenergy spread) of this electron source gives great improvements in contrast transfer (see Section5.1) at high resolution compared to a conventional thermionic emission gun, especially when theimage is strongly defocused to introduce phase contrast during cryo-EM work (Walz andGrigorieff, 1998). Unfortunately, correcting for astigmatism is difficult with a FEG (Williams andBarry Carter, 1996). However, developments such as on-line image processing, allowingobservation of the power spectrum (the squared amplitude of the Fourier transform) at theelectron microscope during imaging, are simplifying this (Zemlin et al., 1996).

4. Optical diffraction and densitometry

Optical diffraction is often used to select the images with minimal astigmatism and drift forsubsequent densitometry and image processing (Reimer, 1997). The amorphous carbon film of theEM grid produces a nearly white spatial frequency spectrum (Reimer, 1997). However, electronmicroscopes do not transmit all spatial frequencies equally well, an effect described by the contrasttransfer function (CTF}Section 5.1). The missing frequencies appear as a series of rings in theFourier transform or the optical diffraction pattern. These rings are called Thon rings (Thon,1966). In an image with low astigmatism, the Thon rings show rotational symmetry. In anastigmatic image, the Thon rings appear stretched in one direction. Blurring of the Thon ringsindicates beam drift during exposure. The spacing of the Thon rings supplies information aboutthe defocus value when the micrograph was taken, and provides valuable information about thecontrast transfer function (Section 5.1).Densitometry converts the information in the TEM images into a form that is suitable for

computer analysis. Densitometry is a compromise between quality and time. Whilst it is essentialthat the images are digitised accurately, without degrading the image resolution or adding noise, itis also important that a micrograph can be scanned in a reasonable time (Mitsuoka et al., 1997).Flat-bed point-illuminating densitometers, such as the Joyce Loebl Mark 4 and the Perkin-ElmerDS, literally digitise an image point-by-point, which can take hours for a single micrograph. Line-illuminating densitometers, such as the LeafScan 45 and the Zeiss-SCAI, can scan a line at a time,


and are therefore considerably faster (Mitsuoka et al., 1997). The images are digitised usually with16-bit grey scale resolution (65,536 possible greys). Shannon’s Theorem specifies the conditionsrequired for the faithful digital representation of an image (Shannon, 1949; discussed in: Chenet al., 1998; van Lint, 1982; Mellema, 1980; Radermacher, 1988). In this context, the theoremshows that you must scan at least at half the desired molecular resolution at the specimen level. Asan example, we might hope to obtain a resolution of 5 (A in the scanned image. By Shannon’sTheorem, the minimum resolvable distance (5 (A}the Nyquist frequency) will be twice the pixelresolution. Hence, we need to achieve a resolution of 2.5 (A per pixel on the specimen level. If theimages are taken at a magnification of 40 000� , the densitometer step size would have to be10mm. However, images are often digitised to a spatial resolution corresponding to about one-quarter of the desired molecular resolution at the specimen level, this oversampling being essentialto reduce interpolation errors (Chen et al., 1998).

5. Principles and methodology of single particle analysis and 3D reconstruction by angular

reconstitution

Despite attempts made to boost contrast and reduce beam damage during specimenpreparation and imaging, further image processing is essential to obtain meaningful informationfrom the images, particularly when low-dose techniques are used which result in a low SNR in theimages. A wide range of image processing software is now available (reviewed by Carragher andSmith, 1996). In this section, the principles of image processing, single particle analysis and 3Dreconstruction will be discussed as implemented in the IMAGIC-5 image processing program (vanHeel et al., 1992b, 1996; Schatz et al., 1995; Orlova, 2000). Fig. 1 summarises the stages of theprocedure. Figs. 3, 6 and 7 illustrate key aspects of image processing and are reproduced from aninvestigation into the photosystem II (PSII) supercomplex from higher plants (Nield et al., 2000c).

5.1. Correcting for the contrast transfer function (CTF)

There are two components to contrast in an image: amplitude and phase (discussed in Amoset al., 1982; Erickson and Klug, 1971; Slayter and Slayter, 1992). Phase contrast is produced byinterference between the elastically scattered waves that pass though the objective aperture of themicroscope and the unscattered, transmitted wave. Amplitude contrast is produced whenelectrons are lost by inelastic scattering, or by high angle elastic scattering, which falls outside theobjective aperture. The contrast transfer function (CTF) describes the fidelity with which differentspatial frequencies are transmitted by the electron lenses (Erickson and Klug, 1971; Wade, 1992;Williams and Barry Carter, 1996; Reimer, 1997). High spatial frequencies represent fine detail(high-resolution information), and low spatial frequencies represent coarse detail. The CTFaccounts for the effects of spherical aberration and defocusing. The CTF has amplitude and phasecontrast components, which are additive (Amos et al., 1982; Erickson and Klug, 1971).In cryo-EM work, the phase component of the CTF (the PCTF) predominates because the

objective lens is defocused to introduce phase contrast, and amplitude contrast is low since thesamples are thin and biological specimens contain lighter atoms, which scatter electrons weakly.The PCTF limits the resolution of the images in the micrographs. Beyond the first zero crossing of


Fig. 1. Single particle analysis, image processing and 3D reconstruction}a flow chart summarising the key steps.


the PCTF and until the second zero crossing, contrast is reversed (see Fig. 2); adding theseintensities to those that lie before the first zero crossing produces artefacts. Spatial frequenciescorresponding to a PCTF of zero do not appear in the final image. For these reasons, the limit ofresolution of an image (without PCTF correction) is obtained when the first zero crossing of thePCTF is reached. By correcting for the PCTF, compensating for the contrast reversals, it ispossible to increase the resolution of the images and thus to increase the resolution of the final 3Dmodel. Correction for the PCTF is achieved as follows. Optical diffraction or the fast fouriertransform (FFT) or the power spectrum of an EM image reveals the Thon rings, which determinewhere the maxima and minima of the CTF lie (Amos et al., 1982). Areas where the CTF is positiveor negative appear as bright bands, with the zero crossings appearing as black rings. The PCTF isgiven by a simple mathematical equation (given in the legend to Fig. 2) that can be fitted to theThon rings. Correction for the PCTF can be carried out in Fourier space by multiplying the datawith the inverse of the PCTF (Erickson and Klug, 1971). The inverse function may be modified toprevent amplifying noise in the area of the zero crossings (Orlova et al., 1997). PCTF correctioncan either be applied to the 2D images, or to the 3D model in 3D Fourier space (e.g. Orlova et al.,1997; Stark et al., 1997a) provided the micrographs selected for processing are taken at the same,or similar, defocus and are therefore affected by the same PCTF}the uncorrected 3D model willthen have been modified by a 3D PCTF. Despite PCTF correction, it is impossible to extend the

Fig. 2. The phase contrast transfer function (PCTF), and the limits of resolution. The continuous line shows thevariation of the PCTF as a function of a=l (the spatial frequency), where l is the electron wavelength and a is the angleof scattering in the microscope. The PCTF is given by �sinwðaÞ where wðaÞ ¼ ð2p=lÞð�14Csa

4 þ 12D f 2Þ. Cs is the

coefficient of spherical aberration and Df is the defocusing. In this example, l ¼ 0:0042 nm, Cs ¼ 1:3mm andDf ¼ 300 nm. The dashed line shows the effect of an envelope function.


resolution beyond a point known as the information limit (Slayter and Slayter, 1992). This isbecause the PCTF is damped by an envelope function that represents limiting factors such aschromatic aberration and poor coherence of the electron beam. In the final 3D model, loss ofinformation at spatial frequencies coinciding with the zeros of the PCTF can be avoided bycombining images taken at different levels of defocus (Slayter and Slayter, 1992; Saibil, 2000b).Like the phases, image amplitudes also show CTF modulations. It is possible to correct for the

amplitude as well as the phase component of the CTF, and this may be especially important forlow spatial frequencies (Toyoshima and Unwin, 1988; Toyoshima et al., 1993). Details of oneapproach for correcting both amplitude and phase components of the CTF may be found in apaper by Mancini and Fuller (2000).If the desired resolution of the final model lies within the first zero crossing of the CTF it may

be that no explicit CTF correction need be applied. A low-pass filter can be used to excludeinformation beyond the first zero crossing, preventing the creation of artefacts. In areconstruction of the 70S ribosome at a resolution within the first zero crossing of the CTF,CTF correction was thought to enhance the low spatial frequencies while making smaller detailsless clear, and figures in the paper are shown without CTF correction (Stark et al., 1997a).However, Zhu and colleagues have criticised this approach. They believe that CTF correction ofthe amplitudes of low-frequency components is important, and they have developed the necessarycomputer programs to do this (Zhu et al., 1997).An additional consideration is that the envelope function decreases the amplitudes of high

spatial frequencies. Efforts are now being made to correct for this, for example by using low-resolution X-ray data to calculate an inverse temperature factor to boost the high spatialfrequencies (Mancini and Fuller, 2000; also see Section 7). Similar techniques are used in electroncrystallography (e.g. Unger and Schertler, 1995).

5.2. Particle picking

A data set of at least several thousand particle images should be obtained from the micrographsby picking all discernible particles that are not overlapping or in close contact with other particles(Harauz et al., 1988). The single particle images are cut into x� x pixel boxes. The size of the pixelboxes is selected to just enclose the single particle images, removing as much background aspossible. Particle picking can be done directly in IMAGIC (van Heel et al., 1996), or by using theprogram XIMDISP (Crowther et al., 1996; Smith, 1999) and then importing the stack of singleparticle images into IMAGIC.

5.3. Band-pass filtering

Band-pass filters are applied to suppress the highest and lowest spatial frequencies of theimages. Very low spatial frequencies can represent gradual fluctuations in the average densitiesarising from the amount and uniformity of staining; very high spatial frequencies include noise(Harauz et al., 1988). Band-pass filtering influences the success of the subsequent alignment steps,which involve the use of correlation functions that can overweigh certain spatial frequencies (vanHeel et al., 1992a). By using Gaussian-based filters, the creation of artefacts at the high and lowcut-off points can be avoided. The spatial frequencies can be restored after an initial 3D model has


been reconstructed. This is especially important for the high spatial frequencies, which include thedesired high-resolution information.The particles are now surrounded by a circular mask, removing unnecessary background. The

images are normalised to zero average density and an arbitrary standard deviation (van Heel et al.,1992b).

5.4. Reference-free alignment

Reference-free alignment (Dube et al., 1993) is the first alignment step in the image processing,and is used to centre the particles. The single particle data set is compared to a rotationallyaveraged total sum of the band-pass filtered particles, resulting in a translational alignment thatcentres the images in their x � x pixel boxes. Alignment is achieved by using cross-correlationfunctions (CCFs) (Frank, 1980; Reimer, 1997). The basis of this approach is that the two imagesto be aligned are translationally shifted relative to each other by known vectors, and in eachposition, the product of equivalent pixels in the overlapping area are averaged over the area ofoverlap. This product is the CCF at the position of the shift vector (Frank, 1980; Frank et al.,1988). The CCF shows a peak at the place where a motif present in both images overlaps. Goodalignment is therefore achieved when the CCF reaches a maximum. By searching for peaks in theCCF and shifting molecules by the appropriate vector, translational alignment of the two imagescan be achieved. The CCF is actually evaluated in Fourier space, taking advantage of theconvolution theorem (which states that the Fourier transform of the product of two functions isthe product of their individual transforms, this latter being easier to calculate). The rotationallyaveraged total sum and the image to be aligned are Fourier transformed, then these transformsare complex conjugate multiplied together, and the desired CCF is produced by inverse Fouriertransformation (van Heel, 1992b).The reference-free alignment step is iterated several times until a good alignment is achieved

(the distance, in pixels, in which each image is shifted becomes very small). Initially performing areference-free alignment prevents the data set being biased towards a particular reference at anearly stage in the analysis, and uses an averaged image with a higher SNR than a raw image (Dubeet al., 1993).

5.5. Multivariate statistical analysis (MSA)

The multivariate statistical analysis (MSA) technique of correspondence analysis is next used toidentify the principal components of variation in the set of images, as a preliminary to placing theimages into groups of similar molecular images in similar rotational orientations (Frank and vanHeel, 1982; Frank, 1984, 1990; Lebart et al., 1984; van Heel and Frank, 1981).Each image of x � x pixels can be considered as a point in (x� x)-dimensional space, where

each axis represents the density value at a single pixel. The entire set of images forms a cloudwithin this space. The distances between points in this space may be interpreted in terms of thesimilarity of the corresponding images. The cloud may be structured into subclouds,corresponding to different subsets of images (classes). The set of points in (x� x)-dimensionalspace are arranged into a large input matrix. Distances between points in the (x� x)-dimensionalspace are measured using metrics such as the w2 metric. The w2 distances between any two rows or


columns of the input matrix are calculated, producing a symmetric matrix (van Heel and Frank,1981). Next, the eigenvalues and eigenvectors (also called eigenimages or factors) of thissymmetric matrix are determined (van Heel and Frank, 1981). The w2 metric cannot deal withimages that have a zero average density, as may be the case with phase contrast EM images whichcan be treated as a modulation relative to a constant background (Borland and van Heel, 1990).For this reason, the modulation metric was developed (Borland and van Heel, 1990). IMAGICallows the user to define which metric is used (van Heel et al., 1996). To determine the majorcomponents of variation, a new rotated co-ordinate system is described in which the first axis isthe eigenvector representing the greatest interimage variance (associated with the largesteigenvalue), the second axis is the eigenvector representing the largest remaining interimagevariance, and so on (van Heel et al., 1992b). By only considering the significant eigenvectors(typically the first 5–50 (Sherman et al., 1998)), the images can be considered as points in a muchsmaller than (x�x)-dimensional space. This reduces the total amount of data, vastly speeding upthe image processing, whilst also reducing the effects of noise. Since the eigenvectors show thevariation in the dataset, they can provide useful information about conformational flexibility orsubstrate binding, as will be discussed later in the context of the ribosome.A map plotting different combinations of the significant eigenvectors against each other can

reveal classes of images that have certain features in common. The program WEB can be used toproduce these maps, and it is possible to create an average of images that fall within a selectedarea (Frank et al., 1996).

5.6. Automatic classification

The hierarchical ascendant classification algorithm is used to generate a specified number ofclasses (van Heel and St .offler-Meilicke, 1985). This algorithm begins with as many classes as thereare images. It then merges the classes that are closest together. At each step, two classes aremerged if the resulting increase in total intra-class variance is minimal. The images in each of theseclasses are then averaged to produce ‘‘characteristic views’’ (known as class averages or classums).In a set of similar aligned images, the noise at any position varies from image to image, but theinformation from the molecules is the same. The averaging procedure boosts the common signalby a factor of n1=2, where n is the number of images, whilst repressing random noise (Chen et al.,1998). The class averages therefore have a higher SNR than the raw images, and are much moreeasily interpreted.

5.7. Multi-reference alignment

Having produced the first class averages, some are selected and used as references to searchthrough and align the entire data set, generating improved class averages. In this multi-referencealignment (Schatz et al., 1995), each image is translationally and now also rotationally aligned, inturn, to selected class averages, using cross-correlation functions. MSA and automaticclassification are then used to generate new class averages. After a few iterations, good classaverages with greatly improved SNRs can be achieved (see Fig. 3a). The progress of the iterationscan be followed visually by inspecting the class averages, and to a certain extent by looking at


changes in the total sum of the aligned images after each iteration. After the first multi-referencealignment, the total sum of the images should appear less rotationally symmetric.

5.8. Angular reconstitution

Having generated a set of good class averages, it is desirable to construct a 3D model fromthem. The first step towards this is to determine projection directions (Euler angles) for the classaverages. This is done using the angular reconstitution technique (van Heel, 1987a; Seryshevaet al., 1995), which is based on the common line projection theorem (van Heel, 1987a). This statesthat two 2D projections of the same 3D object have at least one 1D line projection in common.The common line projection is equivalent to the common tilt axis of the two projections, which isperpendicular to the projection directions of both input class averages.To find the common line projection(s) between two 2D class averages, the sinogram of each

class average is calculated. A sinogram is a collection of the 1D line projections of a 2D classaverage. The first line projection is obtained by summing all the horizontal lines in the 2D classaverage (Serysheva et al., 1995). The second line projection is usually in a direction 18 away fromthe first. The sinograms are compared pairwise using sinogram correlation functions (SCFs),which have maxima at the position corresponding to a pair of shared line projections (Fig. 4). Aleast-squares fitting procedure is used to identify the position of the peaks in the SCF, giving theorientation of the common tilt axis between the two class averages. From the common tilt axis,the Euler angles of the class averages can be determined (for a mathematical description, see van

Fig. 3. Single particle analysis of the plant photosystem II supercomplex. (a) A selection of typical class averages usedfor the 3D reconstruction. (b) Reprojections of the 3D map in identical orientations with the corresponding class

averages. (c) Surface rendered views of the final 3D map in the same orientation as the class averages. Reprinted withpermission from Nature Structural Biology (Nield et al., 2000c, # 2000, Macmillan Magazines Limited).


Heel, 1987a). When the best Euler angles have been assigned to an input class average, the peaksin the SCF have their highest value, which should be the same for each peak (Serysheva et al.,1995). The standard deviation of the peak heights can thus be used to exclude poor class averages,and can provide useful information about the progress of the reconstitution (see Section 6).

5.9. 3D reconstruction

An initial 3D reconstruction is gained by back-projecting the class averages along their assignedEuler angles, using the exact-filter back-projection algorithm (Harauz and van Heel, 1986;Radermacher, 1988; Schatz et al., 1995). This algorithm takes into account the heterogeneousdistribution of projection directions that are typically encountered in the class averages, bydownweighting over-populated class averages (Orlova, 2000).The 3D reconstruction is then reprojected along the Euler angle directions assigned to the class

averages. These resulting reprojections illustrate how well the class averages fit to the 3D model(compare the reprojections shown in Fig. 3b with the class averages in Fig. 3a). Poor classaverages can be identified, and then removed from the dataset. This identification can either bedone visually or by using a list of the errors between the class averages and their correspondingreprojections that is generated by IMAGIC. Many class averages will have been discarded by the

Fig. 4. Determining Euler angles using sinograms and sinogram correlation functions (SCF). Left, a self-sinogramcorrelation function. The class average is shown in a and again in b. The sinograms of the class average are shown in cand d. Finally, e shows the sinogram correlation function, with symmetry-related peaks being colour-coded. Right, a

cross sinogram correlation function between two different class averages shown in a and b. The sinograms are in c andd, and the cross sinogram correlation function in e. The four colour-coded dots indicate the optimal Euler angleorientations of these two class averages. Reprinted with permission from Nature Structural Biology (Serysheva et al.,

1995, # 1995, Macmillan Magazines Limited).


end of this procedure. For example, from a pool of 400 initial class averages maybe 200 will bekept. This is only an approximate figure, and it will depend on the size and quality of the originaldata set. The remaining class averages can be back-projected to produce a more reliable 3Dmodel.

5.10. Iterative refinements to the model

The 3D model is refined as follows (Schatz et al., 1995; Serysheva et al., 1995). The reprojectedimages from the latest model are used as references for a multi-reference alignment of the entiredata set of raw, band-pass filtered images. Following MSA and automatic classification, raremolecular orientations that were missed can now be recognised and grouped into statisticallysignificant classes.In the subsequent angular reconstitution, instead of comparing each new input class average

with every other one, they are now compared to the reprojections from the previous model. Thesereprojections are known as the ‘‘anchor set’’, and each has assigned Euler angles. This is animprovement because the reprojections contain less noise than the original input class averagesdue to the averaging that occurs when the 2D class averages are merged to produce the 3Dreconstruction (compare Figs. 3b and a). Unlike the input class averages, they also share acommon 3D origin and a common rotational orientation in the plane of the EM grid (Schatz et al.,1995; Serysheva et al., 1995).The procedure of alignment, MSA, classification and angular reconstitution is iteratively

applied to refine the 3D results. Poor class averages are discarded before the next round ofiteration. In the later stages of image processing, the CCF may be replaced by the mutualcorrelation function (MCF) (van Heel et al., 1992a). The multiplication in Fourier space duringthe calculation of the CCF makes strong spatial frequencies (usually low-resolution information)overwhelmingly stronger than the weak spatial frequencies. The MCF has been developed tobetter weigh fine, high-resolution, details in the images (van Heel et al., 1992a). In the MCF, theFourier components are divided by the square roots of their amplitudes.After 3D reconstruction and further iterative refinements, the 3D model shows no further

improvement (no further reduction in the error measures is seen).

5.11. Evaluating the quality of the 3D reconstruction

The resolution can be determined by measuring the Fourier shell correlation (FSC) betweentwo independent 3D reconstructions (van Heel and Harauz, 1986; Orlova et al., 1997), each basedon half of the available class averages (Fig. 5). FSC measures the normalised cross-correlationcoefficient between two 3D volumes as a function of spatial frequency. The resolution can bedetermined as the reciprocal of the spatial frequency at the intersection of the FSC function with afunction that represents three times the standard deviation of random noise (3s) (the 3s thresholdcriterion) corrected for the molecular point-group symmetry. Alternatively, resolution can bedetermined as the reciprocal of the spatial frequency when the correlation coefficient equals 0.5(the FSC=0.5 criterion).


5.12. Presenting the model

Initial 3D surface-rendering can be performed in IMAGIC, with thresholds selected to produceexpected molecular weights (Fig. 3c). The model can be presented as a series of cross-sections,revealing internal detail, as in Fig. 6. These cross-sections can be printed out, glued ontoStyrofoam sheets and cut at a particular contour level to produce a physical model. The AVS/Express software package (Sheehan et al., 1996) can be used to produce surface-rendered images,as shown in Fig. 7. AVS/Express allows easier manipulation of the model than IMAGIC, such asrotations and magnifications, and the use of colour.

6. Critical review of single particle analysis and 3D reconstruction by angular reconstitution:

a comparison with other methods for structural studies

In this section, single particle analysis will be compared to X-ray crystallography, electroncrystallography and NMR spectroscopy (for reviews of the principles behind electron crystal-lography see Amos et al., 1982; Slayter and Slayter, 1992; Walz and Grigorieff, 1998; Glaeser,1999). 3D reconstruction using the angular reconstitution technique that is implemented inIMAGIC will be compared to the related random-conical tilt method.

Fig. 5. Determining the resolution using the Fourier shell correlation (FSC) technique.


Fig. 6. 10 A thick sections through the 3D map of the plant photosystem II supercomplex at 24 A. (a) Surface

representation of the 3D map indicating the 10 A thick sections taken. (b) Projection map of the transmembrane regiontowards the stromal surface of the chloroplast thylakoid membrane. (c) Projection map of the region close to thelumenal surface. (d) Projection map of the region occupied by the extrinsic proteins of the photosystem II oxygen-

evolving complex. Reprinted with permission from Nature Structural Biology (Nield et al., 2000c, # 2000, MacmillanMagazines Limited).


A significant advantage of structural studies by single particle analysis is that there is no need togrow crystals. Crystallisation has traditionally limited the speed with which a structure can bedetermined by X-ray or electron crystallography. The 2D or 3D crystallisation of proteins can beproblematical, given the many variables that can influence crystal formation, and the requirementfor good-quality crystals that diffract to a high resolution (Rhodes, 2000). For electroncrystallography, it is also necessary to achieve uniform flatness across the 2D crystal, otherwisethere is a loss of resolution perpendicular to the crystal plane (Stowell et al., 1998). Despite thesedifficulties, X-ray crystallographers are seeking new methods to crystallise increasingly complexproteins (reviewed in Ostermeier and Michel, 1997), including the use of lipidic cubic phases toproduce 3D crystals of membrane proteins (Rummel et al., 1998). Several new methods have beendeveloped to grow 2D crystals of soluble and membrane proteins for electron crystallography,exploiting affinity tags on overexpressed molecules (reviewed in K .uhlbrandt and Williams, 1999)and using streptavidin as an adaptor molecule for crystallisation on a biotinylated lipid monolayer(see, for example, Darst et al., 1991; Avila-Sakar and Chiu, 1996; Levy et al., 1999; reviewed inKornberg and Darst, 1991). Furthermore, image processing programs used in single particleanalysis, such as IMAGIC-5, can now be used to correct for imperfections and short-rangedisorder in 2D crystals (Sherman et al., 1998; Walz and Grigorieff, 1998).Sample preparation for single particle analysis is usually easier and quicker than crystallisation.

The ease of sample preparation, and the fact that for cryo-EM the vitrification process is not verysensitive to the buffer components, makes it possible to make rapid progress in studying differentfunctional states of molecules (e.g. bound to different substrates or cofactors). Cryo-EM andsingle particle analysis has revealed conformational changes in the GroEL-GroES ATPase cycle(Chen et al., 1994; Roseman et al., 1996). However, the angular reconstitution technique requiresa random orientation of particles on the EM grid in order to uniformly cover the asymmetric

Fig. 7. Surface-rendered view of the 3D map of the plant photosystem II supercomplex at 24 A, visualised using AVS

Express. The extrinsic oxygen-evolving complex proteins are labelled, A/A0 (the 33 kDa protein) and B/B0 (23 and17 kDa proteins). The putative membrane-spanning region is shown. Overall dimensions are also indicated. Reprintedwith permission from Nature Structural Biology (Nield et al., 2000c, # 2000, Macmillan Magazines Limited).


triangle of the molecular point group symmetry (Orlova et al., 1997), producing a 3D structurewith an isotropic resolution (Fig. 8). An overabundance of one type of view can lead to a 3Dreconstruction artefact, as shown by Boisset in reconstructions using a ‘‘human head phantom’’ asa test volume (Boisset et al., 1998). The orientations taken up by proteins on an EM grid can beaffected by molecular properties such as shape and hydrophobicity, and grid preparation such asglow discharging. As yet, there is no reliable way to ensure a random orientation of particles(Chen et al., 1998). If preferred orientations are observed, a broader range of orientations may beobserved by tilting the specimen by a small amount (10–308) in the EM (van Heel, 1992b; Bakerand Johnson, 1997) or alternatively the random-conical tilt method may be used (describedbelow).Another advantage of single particle analysis is the ability to deal with heterogeneous

populations of molecules. MSA and automatic classification allow a heterogeneous population tobe sorted into classes of similar molecules, generating more homogeneous sub-populations thatcan be analysed individually. This approach, which has been called ‘‘computational purification’’,has been exemplified in a recent study of low-density lipoproteins (Orlova et al., 1999). Singleparticle images of low-density lipoproteins (LDL) were grouped into 60 classes using MSA andautomatic classification. The class averages showed striking variations in the number of striationsamong similarly oriented particles (Fig. 9a). The classes with three striations were prominent, and

Fig. 8. The Euler angle distribution for the class averages used in a reconstruction of the Haliotis tuberculatahemocyanin type 1 didecamer. This molecule has D5 point group symmetry, and the asymmetric triangle is indicated inthe figure. The red dots show the projection directions. The uniform coverage of the asymmetric triangle is important to

reduce artefacts. Reprinted with permission from the Journal of Molecular Biology (Meissner et al., 2000, # 2000,Academic Press Limited).


were used to reconstruct a 3D model (Fig. 9b and c). This indicated that the striations resultedfrom internal structure in the inner core of the LDL particle. The authors hope to produce 3Dmodels of the other classes once more data has been obtained. It is, however, essential to ensurethat particles with the same structure are used in the generation of the 3D model, so that themodel is accurate and meaningful. In the study by Orlova and colleagues, the angularreconstitution technique helped verify that particles with the same structure were used in theimage processing. If this had not been the case, the standard deviation of peaks found in thesearch of the Euler angles would have increased as the class averages were added stepwise intothe angular reconstitution. Furthermore, the 3D map would have become blurred, and thereprojections would have become different to the input class averages and raw images (Orlovaet al., 1999). Computational purification has also been used to reveal different conformations ofan archael chaperonin (Schoehn et al., 2000) and in studies of photosystem II (Section 8). It can beanticipated that its use will increase in the future. Heterogeneous populations of molecules arevery difficult to study by X-ray or electron crystallography for two main reasons: it is likely to beextremely difficult to crystallise them, and even if crystals can be produced, the different moleculeswill diffract differently, making analysis complicated. Single particle analysis, MSA and automaticclassification are thus at an advantage when studying protein complexes that are unstable andproduce a heterogeneous population of molecules differing in subunit composition, e.g. PSII(Section 8), or in studying conformational flexibility in proteins (reviewed by Saibil, 2000a; andsee Section 7).The techniques of cryo-EM have encouraged the use of time-resolved EM studies. Transient

states can be observed by initiating a reaction on the EM grid by flash photolysis of cagedreactants followed by vitrification after a fixed time interval (Chen et al., 1998). Alternatively, thecryo-EM plunger (Berriman and Unwin, 1994; Chen et al., 1998) can be used. This device can

Fig. 9. Computational purification used in single particle analysis of low-density lipoproteins (LDL). (a) Some classaverages after the first round of alignment and classification. The heterogeneity is striking. (b) 3D model reconstructedfrom class averages showing three striations. (c) A cutaway view of the 3D model showing the outer shell and the inner

core structure. Reprinted with permission from Proceedings of the National Academy of Sciences (Orlova et al., 1999,# 1999, National Academy of Sciences, U.S.A).


rapidly mix a solution of ligand sprayed onto a protein complex supported on an aqueous film onan EM grid. Rapid freezing in liquid ethane can trap the complex. By altering the time intervalbetween spraying and freezing, it has been possible to observe conformations associated withreaction times of 1–100ms. This technique has been used to study the structure of the open-channel form of the acetylcholine receptor by electron crystallography (Unwin, 1995), and canalso be applied to single particle work. Computer-controlled cryo-EM plungers have now beendeveloped, allowing the interactions of three different molecules to be studied (White et al., 1998).Two solutions can be mixed and held in a delay line, before spraying onto a grid containing thethird molecule. Computer-control allows the precise, reproducible, adjustment of individualparameters. The ability to sort and classify particles that may be in different conformational statesor bound to different substrates or cofactors using MSA may be a significant advantage for time-resolved studies using single particle analysis. Time-resolved X-ray crystallography has thedisadvantage that the vast majority of the molecules in a crystal must be in the same conformationat the same time, in order to produce strong diffracted beams. At the moment, time-resolved X-ray crystallographic studies are technically considerably more difficult to perform than time-resolved cryo-EM studies. Furthermore, it is possible that large conformational changes will berestricted in the context of a 3D crystal, or will result in the crystal fracturing. This is less of aproblem with 2D crystals or single particles, because the molecules are less constrained. This is apossible reason for differences in the M state of bacteriorhodopsin revealed by X-ray and electroncrystallography (K .uhlbrandt, 2000). Despite this, time-resolved X-ray crystallography isproducing impressive results (reviewed in Stoddard, 1998), including structures of intermediatesin the bacteriorhodopsin photocycle (Edman et al., 1999; Royant et al., 2000; Sass et al., 2000).Recent results from X-ray and electron crystallographic studies of bacteriorhodopsin have led toan atomic model for proton pumping (Royant et al., 2000; Sass et al., 2000; Subramanian andHenderson, 2000; reviewed in K .uhlbrandt, 2000).A significant advantage for electron microscopy compared to X-ray crystallography is that we

can directly obtain information about phases from EM. This is because in the electronmicroscope, electromagnetic lenses can focus diffracted electrons to form images that containinformation about phase as well as amplitude. The significance of this has been dramaticallydemonstrated in the atomic model of the ab tubulin dimer, obtained by electron crystallography(Nogales et al., 1998). The final resolution of the electron density map is at 3.7 (A, but shows awell-defined connectivity that is readily interpretable in terms of secondary structure elementsbecause of the high-quality phase information obtained directly from the EM images. Thisallowed an atomic model to be built, despite the fact that the resolution of the density map islower than would be used to produce an atomic model from data derived by X-raycrystallography (Chiu et al., 1999). This shows the potential advantage of electron microscopystudies in general over X-ray crystallography. However, multiple wavelength anomalousdiffraction (MAD) phasing is now being increasingly used in X-ray crystallography, producinghigh-quality phase information very quickly (Hendrickson, 1991; reviewed in Smith, 1991; Ealick,2000). The future significance of the ability to directly determine the phases by EM may thereforebe that high-resolution X-ray structures could be successfully modelled into larger structuresproduced by single particle analysis that are at much lower resolutions.Single particle analysis and its derived 3D reconstructions cannot yet compete with electron or

X-ray crystallography in terms of resolution. The best resolutions quoted for single particle


analysis are 7.4 (A for the hepatitis B core protein (B .ottcher et al., 1997; Fig. 10) and 7.5 (A for the70S ribosome (Matadeen et al., 1999), although 15–30 (A is more usual. This compares for instanceto 0.83 (A for the 46 amino acid residue protein crambin by X-ray crystallography (Stec et al.,1995). Significant achievements for electron crystallography include the structures of light-harvesting complex II at 3.4 (A (K .uhlbrandt et al., 1994), bacteriorhodopsin at 3.5 (A (Hendersonet al., 1990; Grigorieff et al., 1996), the ab tubulin dimer at 3.7 (A (Nogales et al., 1998), andaquaporin-1 at 3.8 (A (Murata et al., 2000). Although these are different molecules posing differentchallenges for structural studies, similar trends have been revealed in molecules that have beenstudied by more than one of these techniques, such as the ribosome (see Section 7). Resolution inthe EM is limited to about 50 times the wavelength of the incident electrons (Amos et al., 1982),due to the small apertures that are used in electron microscopes to reduce aberrations in theelectromagnetic lenses (Saibil, 2000b). Given that the high-energy electrons produced in currentmicroscopes have a wavelength between 0.015 and 0.040 (A (Chiu et al., 1999), there is notheoretical limit to obtaining atomic resolution by single particle analysis. The limit is imposed byseveral factors, such as beam-damage. Electrons cause less damage than X-rays (Henderson,1995) and have a greater scattering power (Chiu et al., 1999), but because of the small sample size(single particles or 2D crystals versus 3D crystals), beam damage is a more significant problem forsingle particle analysis and electron crystallography than for X-ray crystallography. Specimenmovement, beam-induced specimen charging, astigmatism, aberrations, beam drift, and theinability to correct for the CTF perfectly, further limit the resolution for single particle analysisand electron crystallography. Specimen charging is thought to lead to several problems, includingspecimen movement, film breakage upon irradiation, and blurring of electron diffraction patterns.

Fig. 10. 3D map of the hepatitis B virus core protein shell at 7.4 A resolution, currently the highest obtained by single

particle analysis. This map revealed a novel fold for viral capsid proteins. Reprinted with permission from Nature(Bottcher et al., 1997, # 1997, Macmillan Magazines Limited).


A model has been proposed for the effects of specimen charging (Brink et al., 1998). Duringimaging, a fraction of the incident electrons are inelastically scattered, and the resulting energytransfer is proposed to lead to the emission of secondary and Auger electrons from the specimen.This creates a positive charge on the specimen, which could act as an electromagnetic lens, causingfocus changes and blurring or movement of the specimen. The number of single particle imagesthat can be handled by the image processing programs is a further factor that can limit theattainable resolution for single particle analysis. The more single particle images that are used inthe reconstruction, the higher the resolution of the final model. Orlova has described a simpleformula for the number of images needed to obtain a 3D model at a given resolution usingangular reconstitution (Orlova, 2000). Molecular symmetry can decrease the number of imagesneeded for a given resolution by providing redundant motifs in the specimen and geometricconstraints for the alignment steps (Chiu et al., 1999; DeRosier and Klug, 1968).There is no upper limit to the size of molecule that can be studied by single particle analysis.

This is a significant advantage compared to NMR spectroscopy, where a maximum size of about100 kDa is imposed with the latest multi-dimensional techniques (Wider and W .uthrich, 1999). X-ray crystallographic studies of 3D crystals with very large unit cells can be difficult (reviewed inMurali and Burnett, 1991). These crystals may fail to diffract to high resolution, are often sensitiveto radiation damage (possibly because of a high solvent content), and it may not be possible toresolve individual reflections in the diffraction pattern. The largest asymmetric structure solved todate by X-ray crystallography is the 70S ribosome (Cate et al., 1999). A minimum size of 100 kDais thought to be imposed on single-particle analysis by the requirements of molecular alignment(Henderson, 1995). Larger macromolecules are easier to align because, at any given resolution,there is more scattering of the electrons, and thus the image contains more of the information usedto determine the rotational and translational orientations. The a-latrotoxin dimer (260 kDa)(Orlova et al., 2000; reviewed by Saibil, 2000c) and the haemagglutinin trimer (252 kDa) (B .ottcheret al., 1999) are so far the smallest structures solved by single particle analysis.X-ray or electron crystallography and NMR spectroscopy are therefore the methods of choice

for studying individual molecules or small macromolecular complexes. Single particle analysis isvery useful for studying large complexes that are difficult to analyse by these higher resolutiontechniques. It is also of great value in time-resolved studies, in analysis of different functionalstates of macromolecules, and in studying conformational flexibility in large complexes.The random-conical tilt method is an alternative 3D reconstruction technique that can be used

in single-particle analysis (Frank et al., 1988; Radermacher, 1988; Frank and Radermacher, 1992;Frank, 1996; Chen et al., 1998) and has been implemented in the programs SPIDER and WEB(Frank et al., 1996). In contrast to angular reconstitution, it makes use of molecules aligned inpreferred orientations on an EM grid. A high-tilt (45–608) image is recorded under low-doseconditions, followed by a second untilted image of the same area. The particles from the untiltedimages are aligned using rotational CCFs, supplying information about their in-planeorientations. The particles from the tilted images are translationally aligned, and then a 3Dreconstruction of the tilted images is performed, using the in-plane orientations determined fromthe untilted images and the common tilt angle. MSA and classification procedures can be used togroup the untilted images into classes. Class averages can be produced of the corresponding tiltedimages, and these class averages can then be used for 3D reconstruction. This technique hasseveral disadvantages compared to angular reconstitution. First, the untilted image is taken of an


area that has already been exposed to electron damage (van Heel et al., 1992b). Although thisimage is not directly used in the 3D reconstruction, it is used to orient the tilted images. Secondly,specimens cannot be viewed at tilt angles greater than 60–708 because of the fragile nature of EMspecimens (Chen et al., 1998). This results in a missing cone in Fourier space that cannot besampled (the ‘‘missing cone problem’’). This produces a non-isotropic resolution in real space,with the resolution being lower in a direction perpendicular to the specimen plane (Chen et al.,1998; Radermacher, 1988; Schatz et al., 1995). Furthermore, highly tilted images are difficult torecord and are of poorer quality than untilted images (Chen et al., 1998). Since the defocus levelwill change across a tilted image, it may be necessary to correct for the CTF separately fordifferent areas of the EM image (Schatz et al., 1995). For these reasons, angular reconstitutionmay be preferred to the random-conical tilt method. For particles with icosahedral symmetry,such as some viruses, particle orientations can be determined using a further technique developedby Crowther (1971). In this technique, particle orientations are determined in reciprocal space bysearching for symmetry-related peaks in the Fourier transforms of individual particles (Crowther,1971; Fuller et al., 1996; Saibil, 2000b), but this technique will not be discussed in detail here.Single particle analysis and 3D reconstruction techniques are continually developing to resolve

problems. A key difference between single particle work and crystallographic approaches is that insingle particle analysis there are currently no universally accepted resolution criteria like R-factors(Rhodes, 2000). Instead, criteria such as the Fourier shell correlation (FSC) are used to obtain anestimate of the reproducible resolution, and there is currently no consensus about the thresholdthat should be used (Stewart et al., 1999). Penczek has criticised the determination of resolutionfrom the intersection point of the FSC function with the 3s curve (Malhotra et al., 1998). Heasserts that the approach gives higher resolutions than if the resolution limit is set at the pointwhere the correlation coefficient drops below 0.5. He proposes a method for transferring FSCresults into more objective SNR values. Setting the limit at the point where the correlationcoefficient reaches 0.5 corresponds to an SNR of 1.0. Use of the FSC=0.5 threshold has beensupported by comparisons of cryo-EM and X-ray structures of adenovirus type 2 (Stewart et al.,1999). On the other hand, van Heel has compared the X-ray crystal structure of the Thermusthermophilus 70S ribosome at 7.8 (A (Cate et al., 1999) with his cryo-EM structure of the E. coli50S subunit at 7.5 (A (Matadeen et al., 1999). He states that the cryo-EM structure does have theslightly higher resolution, and that the 3s criterion gives a conservative estimate of the resolutioncompared to accepted criteria used in X-ray crystallography (van Heel, 2000). Despite this,comparison of A-form rRNA helices in the two papers shows that, for the X-ray structure, thedeep major grooves, wide minor grooves and the ridges for the phosphates are as expected forthe resolution, and agree well with the atomic models of the ribosome. This is not apparent in thecryo-EM structure. It is to be hoped that as more structures are solved at comparable resolutionsby X-ray crystallography and single particle analysis, a resolution criterion for single particleanalysis that is equivalent to those used in crystallographic studies may be developed. A furtherproblem with the Fourier shell correlation technique is that the two 3D reconstructions are notstatistically independent, each having been derived from an earlier 3D model. For low SNRimages, this may lead to an overestimation of the resolution, because of correlation between noisein the images (Grigorieff, 2000). This correlation of noise is introduced by alignment of the dataset to common references before it is split in half. Alternative methods of determining theresolution have been described, such as the differential phase residual (DPR). This uses a sum of


Fourier space amplitudes, rather than a multiplication, to weight the phase differences betweentwo signals in Fourier space (Frank et al., 1981; Penczek et al., 1994). It has been pointed out thatthis is flawed, since the differential phase residual changes when one image is multiplied by aconstant, despite this not changing the information content in the images (van Heel, 1987b;Orlova et al., 1997). A complete description of the resolution should thus include the criterionused, and the stated resolution of a model should probably not be implicitly trusted. Currently,resolution may best be assessed by determining the closest features that can be interpreted in the3D map, given data from other techniques. The selection of references for multi-referencealignment still has an unfortunate degree of subjectivity, which will have to be addressed in thefuture. These points highlight the fact that at the moment the theory and practice of single particleanalysis and 3D reconstruction are less well developed than those behind the crystallographicapproaches and NMR spectroscopy.

7. The ribosome: comparing single particle analysis with X-ray crystallography

The ribosome is a very attractive target for atomic resolution structural studies because theywill lead to a dramatic increase in our understanding of the mechanism of protein synthesis,RNA–RNA and protein–RNA interactions. Over the past couple of years, tremendous advanceshave been made. The 50S subunit of Haloarcula marismortui (H. marismortui) has recently beendetermined at 2.4 (A resolution by X-ray crystallography, allowing almost the entire length of 23SrRNA, 5S rRNA and 27 of its 31 proteins to be fitted into the electron density map (Ban et al.,2000; reviewed by Cech, 2000). This has been followed by the X-ray structure of the 30S subunitof Thermus thermophilus (T. thermophilus) at 3 (A resolution, allowing all of the ordered regions of16S rRNA and 20 associated proteins to be fitted into the electron density (Wimberly et al., 2000;Carter et al., 2000; reviewed by Williamson, 2000).For many years, it proved difficult to grow 3D crystals of sufficient order and size for X-ray

crystallography. Yonath and co-workers obtained crystals of the 50S subunit fromH. marismortuiin the 1980s (e.g. Shevack et al., 1985). However, because of the large asymmetric unit, accuratephase determination required the use of very large numbers of heavy atom derivatives to producemeasurable differences in the diffraction patterns, with each heavy atom having to be located veryaccurately. The ribosomal crystals grown by Yonath’s group have shown extreme radiationsensitivity (including deformed diffraction spots and unit cell dimensions that increase duringexposure to the X-ray beam), poor isomorphism and non-isotropic mosaicity (Harms et al., 1999).These problems dramatically stalled progress, leading to single particle analysis and 3Dreconstruction being seen as an attractive alternative.Recently, the problems with the X-ray crystallographic approach have been resolved. Heavy

metal clusters of tungsten and tantalum atoms and synchrotron radiation sources have been usedto produce measurable differences in the diffraction patterns, greatly reducing the number ofheavy atom derivatives that have to be made. This has provided low-resolution phase information(Ban et al., 1998, 1999; Cate et al., 1999; Clemons et al., 1999). Subsequently, most phasinginformation has come from anomalous scattering from osmium and iridium compounds (Banet al., 1999, 2000; Clemons et al., 1999; Wimberly et al., 2000). The Yale group, working on the50S subunit, did not encounter the problems of extreme radiation sensitivity and cell dimension


change in their crystals, despite the fact that they were working on the same crystal form, andcollected the entire 2.4 (A data set using only two crystals. X-ray structures have been pro-duced which are at much higher resolutions than were obtained by cryo-EM work, and haverevealed a wealth of information about ribosome structure (Ban et al., 1998, 1999, 2000; Cateet al., 1999; Clemons et al., 1999; Nissen et al., 2000). Rather than being an exhaustive review ofstructural work on the ribosome (good reviews can be found in Green and Puglisi, 1999; Daviesand White, 2000; van Heel, 2000; Puglisi et al., 2000; Brimacombe, 2000), this section willcompare the use of single particle analysis and X-ray crystallography as revealed by work on theribosome, and will describe some of the resulting technical developments in single particleanalysis.In 1976, Lake published the first attempt to model the 30S and 50S subunits, and the 70S

ribosome, from E. coli (Lake, 1976), based on the visual interpretation of raw, noisy micrographsof particles imaged in negative stain. The subjective nature of such interpretations led to thedevelopment of MSA, automatic classification and averaging techniques which could be used toproduce characteristic class averages of ribosomes (e.g. Frank et al., 1982; van Heel and St .offler-Meilicke, 1985; Verschoor et al., 1984). The more sophisticated image processing techniquesallowed much more detailed analysis of structure. The importance of the MSA technique wasillustrated by eigenvector analysis of the 50S subunit indicating conformational flexibility in theL7/L12 stalk (Harauz et al., 1988). This has subsequently been confirmed by the fact that the L7/L12 stalk region consistently appears less elongated in the X-ray structures (Ban et al., 1998, 1999,2000; Cate et al., 1999) than in cryo-EM work (Stark et al., 1995, 1997b). However, it is interestingto note that the L7/L12 stalk appears to be bent inwards in some cryo-EM specimens (Frank et al.,1995; Stark et al., 1995,1997a; Matadeen et al., 1999) compared to negative stained specimens (e.g.Harauz et al., 1988). It was thought that the extended stalk might be an artefact produced bynegative staining. Nevertheless, extended stalks can be produced in cryo-EM samples undercertain conditions (Agrawal et al., 1996; Malhotra et al., 1998). The presence of the extended stalkseems to depend on glow-discharging of the EM grids (Matadeen et al., 1999) and the displaythreshold (Malhotra et al., 1998). This further supports conformational flexibility, and illustratesthe importance of using a range of sample preparation conditions (stains, cryo-EM, glow-discharging of grids) before reaching firm conclusions about a structure.In the 1990s, cryo-EM revolutionised studies of ribosome structure in terms of the attainable

resolution. In 1995, Frank produced a 25 (A structure of the 70S E. coli ribosome based on imageprocessing of micrographs from untilted specimen grids (Frank et al., 1995). This revealed achannel in the 30S subunit, predicted to be a pathway for incoming mRNA, and a bifurcatingtunnel in the 50S subunit, possibly constituting a pathway for the nascent polypeptide chain,preventing its hydrolysis (Green and Puglisi, 1999). CTF correction was applied to this structure,and the CTF-corrected model showed fewer tunnels than the uncorrected model. This illustratesthe importance of using CTF correction to restore the correct weight of low spatial frequencies(Frank et al., 1995). This was followed later in the same month by the structure of the E. coli 70Sribosome at 23 (A (Stark et al., 1995). The authors attributed the higher resolution, compared toearlier work in the 30–55 (A range, to the use of the angular reconstitution rather than the randomconical tilt method. This study showed an extensive system of channels in the 50S subunit (calledthe exit channel complex}ECC). The diameter of the channels was about 20 (A. Higher resolutionrRNA structures, in particular double-helical regions of 16S rRNA, could be fitted into this


model. With the benefit of the atomic structures of the ribosome, it is now apparent that some ofthe extensive channels revealed by these cryo-EM studies are only seen at low resolution. All atomCPK representations of the ribosome show few gaps inside the molecule, with the exception of thecleft and channel for mRNA in the 30S subunit, and the exit channel for the nascent polypeptidein the 50S subunit.The structure of the 50S subunit from E. coli has recently been published at 7.5 (A resolution

(Matadeen et al., 1999). This represents a dramatic increase in the resolution obtainable by singleparticle analysis, and is significant since it reaches a nominal resolution comparable to thatobtained for the hepatitis B virus core protein shell (B .ottcher et al., 1997). This resolution wasachieved by processing about 16,000 particles, compared to about 6000 for the hepatitis Bstructure in which the icosahedral symmetry of the particle could be exploited. However, it isimportant to note that the resolution of the 50S subunit is based on FSC with the 3s thresholdcriterion, whereas that for the hepatitis B virus is based on the FSC=0.5 criterion. Indeed, the 50Sstructure is not comparable to the hepatitis B structure, where the fold of the coat protein could bededuced from the structure, or to the 7.8 (A crystal structure of the 70S ribosome (Cate et al.,1999). The increase in resolution obtained in this study is attributed to the development of a novelprogram for correcting the CTF, implemented in IMAGIC (Matadeen et al., 1999). This programallows the detection of local defocus and astigmatism variations within a single micrograph. CTFcorrection was then applied by reversing the phases beyond each CTF zero crossing, using thelocal parameters. The CTF correction was not used to alter the amplitudes. The image processingwas begun by extracting the 50S subunit from an earlier cryo-EM reconstruction of the 70Sribosome. Reprojections from this earlier model were then used as references for a multi-referencealignment of the dataset. This approach can vastly speed up the time taken for image processing.A further interesting point revealed in this study is the use of the eigenvectors produced by MSAto look for magnification differences within the dataset. The final model shows the classicalfeatures expected of the 50S subunit, such as the central protuberance, the A-site finger, the L7/L12 stalk and the L1 protuberance. It has also revealed new details, including a collar around theL1 stalk into which the L9 ribosomal protein could be modelled. Regions of 23S rRNA could alsobe modelled into the structure, and a second stalk-like structure has become visible below the L7/L12 stalk. By comparing this structure with a 13 (A map of kirromycin stalled 70S particles, theauthors have revealed conformational changes in the 50S subunit between the free and bound (inthe 70S complex) forms.Shortly after this, the structure of the E. coli 70S ribosome at 11.5 (A resolution (on the basis of

the FSC=0.5 criterion) was published (Gabashvili et al., 2000). This was based on the processingof 73,523 particles of the ribosome bound to fMet-tRNAf

Met, i.e. in its initiation-like complex. Inthis study, the authors used a novel technique for correcting the under-representation of theFourier amplitudes at higher spatial frequencies. This under-representation is due to specimencharging, specimen drift, instrumental instabilities and partial coherence (Gabashvili et al., 2000).X-ray solution scattering measurements were used to correct the Fourier amplitudes up to the1/11.5 (A�1 cut-off. The quality of the reconstruction was assessed by comparing the tRNA partwith low-resolution (about 10 (A) maps calculated from the atomic co-ordinates of yeast initiatortRNA and E. coli fMet-tRNAf

Met. The shape and the geometry of the tRNA in the cryo-EM mapagrees well with that of E. coli fMet-tRNAf

Met, supporting the reliability of other fine details in thereconstruction. The final reconstruction shows great detail}RNA helices (showing the right-


handed twists and deep grooves characteristic of A-form rRNA), peripheral proteins andintersubunit bridges can be identified. The resolution actually appears comparable to the 7.5 (Astructure of the 50S subunit (Matadeen et al., 1999). The L1, L6, L14, L11 ribosomal proteins, afragment of 23S rRNA, and the a-sarcin-ricin loop can be modelled in, and EF-G can bepositioned to contact the a-sarcin-ricin loop.Single particle analysis of the unbound 30S subunit (i.e. not attached to 50S) has proved

problematical, and only low resolutions have been achieved. Marin van Heel’s group havedetermined the structure of the 30S subunit from T. thermophilus at 25 (A (based on the 3scriterion) (Harms et al., 1999). The authors attribute the low resolution to the flexibility andinstability of 30S particles, resulting in the structures produced by single particle analysisrepresenting a range of conformations, decreasing the resolution (Harms et al., 1999). JoachimFrank’s group have published the structure of the 30S subunit from E. coli at 23 (A (based on theFSC=0.5 criterion) (Gabashvili et al., 1999). The authors noticed that the final 3D model wasblurred compared to the structure of the 30S subunit in a model of the 70S ribosome. They alsoattributed the low resolution to conformational flexibility in the 30S subunit, so that the 23 (Amodel represents an average of different conformations. Computer simulations of conformationalflexibility in 50S-bound 30S confirmed this. Averaging of the resulting models led to the dis-appearance of fine structural details, and the average looked more like the 23 (A model. The highhomogeneity of the 30S sample after sucrose density gradient centrifugation showed that thestructural heterogeneity was not an artefact produced by the isolation or purification steps, butrather represented real conformational flexibility in the 30S subunit. The authors then decided tocomputationally purify the data set, aiming to produce sub-populations of particles, which couldbe separately reconstructed to give 3D models of the different conformers. They proceeded byinitially hypothesising that the conformations favoured by the 50S-bound 30S subunit would berepresented in the conformations assumed by unbound 30S. Two previously publishedreconstructions showed 30S in different conformations}these earlier models were the 70Sribosome binding fMet-tRNAf

Met (Malhotra et al., 1998) and the 70S ribosome binding EF-G(Agrawal et al., 1998). The 30S subunit was extracted from each of these models and used asreferences for the computational purification. Particles were compared in turn to both models,and assigned to one or the other on the basis of cross-correlation coefficients. 3D models werecalculated for each sub-population, and then the particles were reassigned to these new models.This procedure was iterated until stable results were obtained. The resolution of the 3D models ofthe conformers was 32 (A (FSC=0.5 criterion). This is lower than the model representing the‘‘average’’ structure, due to the smaller number of particles used to produce the models for eachconformer compared to the average (Gabashvili et al., 1999). However, the conformers showedbetter structural details than the ‘‘average’’ structure at 23 (A. By comparing the conformers withmodels of the 50S-bound 30S subunit, conformational flexibility in the 30S subunit uponassociating with the 50S subunit has been revealed, in particular, the relative movements of threemain structural domains (the head, platform and main body). As a consequence of this study, theauthors make two important points about the technique of computational purification. First,there is a compromise between achieving a high degree of homogeneity and a high enoughresolution to allow the reconstructions of the different conformers to be compared. This is becausea high degree of homogeneity requires a large number of sub-populations, thus fewer particles ineach sub-population, resulting in a lower resolution. The authors suggest that particles should be


drawn from two distant regions of the conformational space, and then the sub-populations shouldbe made large enough to produce reconstructions at a moderate resolution. Secondly, smallconformational changes may not be detected by the procedures used for conformationalpurification, and may thus be averaged out in the final maps of the conformers. Conformationalpurification therefore requires the processing of many thousands of particles to produce large sub-populations, and may not reveal fine conformational changes.The cryo-EM structures have been validated by the recent X-ray structures, indicating that

neither specimen preparation nor single particle analysis and 3D reconstruction are producingdistorted structures. The 5.5 (A (Clemons et al., 1999) and 3 (A (Wimberly et al., 2000) structures ofthe 30S subunit from T. thermophilus confirms the overall shape and dimensions revealed by cryo-EM structures. The 5 (A (Ban et al., 1999) and 2.4 (A (Ban et al., 2000) maps of the 50S subunitfrom H. marismortui have the same overall shape as that determined from cryo-EM work. In the5 (A structure, four tungsten clusters line the polypeptide exit channel, suggesting that the diameterof the channel is about 20 (A. This has been confirmed by higher resolution X-ray studies, showingthat the diameter of the tunnel varies from 10 to 20 (A, and is on average 15 (A (Nissen et al., 2000).Comparing this to the value of 20 (A obtained by Stark and colleagues (1995) indicates thatstructure flattening due to variable dehydration under the vacuum conditions of the EM has notbeen a significant problem in the cryo-EM work. Interestingly, electron density for the L1 proteinis visible in the 7.5 (A cryo-EM structure (Matadeen et al., 1999) and at a similar position in the9 (A X-ray structure (Ban et al., 1998), but is missing in the higher resolution X-ray maps (Banet al., 1999, 2000). It has been pointed out that in the 5 (A map the authors have positioned theL11-rRNA complex in densities assigned to the L7/L12 stalk in the cryo-EM models (Matadeenet al., 1999). It may be significant that there is no electron density for the N-terminal domain ofL11 in the 5 (Amap (Ban et al., 1999). Furthermore, in the 7.5 (A cryo-EMmap, there is insufficientdensity in this region to accommodate the L11-rRNA complex (van Heel, 2000). All of L11 ispresent in the 11.5 (A cryo-EM structure (Gabashvili et al., 2000) but this disagrees with theposition in the 7.5 (A cryo-EM map (Matadeen et al., 1999). Unfortunately, there is no clearelectron density for L11 in the 2.4 (A map, so this problem remains unresolved. The 7.8 (A map ofthe 70S subunit from T. thermophilus (Cate et al., 1999) confirms the general shape of theribosome revealed by single particle analysis, such as the 3-pointed crown appearance of the 50Ssubunit. Comparison of the 11.5 (A cryo-EM structure of 70S with X-ray crystal structures showsthe high degree of similarity between them (Gabashvili et al., 2000). A few differences have beennoticed, for example in the intersubunit region, and this has been attributed to the constraints ofcrystal packing (Gabashvili et al., 2000). Some other small differences between cryo-EM and X-ray structures have been attributed to the evolutionary separation of the organisms, for example,H. marismortui does not have the L9 ribosomal protein (discussed in van Heel, 2000).Compelling evidence for the fact that experimental conditions, single particle analysis and 3D

reconstruction are not producing incorrect or misleading structures comes from the use of cryo-EM structures to solve the phases for the 9 (A map of the 50S subunit (Ban et al., 1998) and the7.8 (A map of the 70S ribosome (Cate et al., 1999). In both cases, cryo-EM images were positionedin the crystal lattice and used to provide initial phases for low-resolution reflections. These wereaccurate enough to locate the bound heavy metal clusters using difference Fourier maps. For the50S map, phases were subsequently determined by multiple isomorphous replacement andanomalous scattering (MIRAS) from the bound heavy metal clusters (Ban et al., 1998). For the


70S map the located heavy atom clusters were subsequently used in MAD phasing experiments(Cate et al., 1999). The molecular replacement search showed a very good match, implying thatthe cryo-EM structure was very superimposable on the X-ray structure. The validity of cryo-EMstructures of the T. thermophilus 70S ribosome is supported by studies in which pure molecularreplacement searches, using a cryo-EM structure, were used to reveal the packing of the moleculesin the 3D crystals (Harms et al., 1999).Single particle analysis has been especially useful in the study of ribosomes binding their

ligands. This is because cryo-EM allows molecules to be studied in a wide range of solutionconditions without the requirements of crystallisation, allowing ligands and antibiotics (whichcan stall the ribosome in particular states) to be added, while single particle analysis allowscomputational purification of the resulting sample. In 1996, a 3D cryo-EM structure of poly(U)-programmed E. coli 70S ribosomes with the A, P and E sites bound by deacylatedtRNAPhe molecules was published (Agrawal et al., 1996). The following year, 20 (A structuresof the E. coli 70S ribosomes in their pre- and post-translocational states were published(Stark et al., 1997a). Density difference maps were used to reveal the positions of the tRNAmolecules in the A, P and E sites, and atomic models of the tRNA molecules were fitted to thedensity maps. The positions of the tRNA molecules disagree with those proposed by Agarwal,and the authors attribute this to the fact that the earlier model is ‘‘non-physiological’’, withthree tRNA molecules bound per ribosome. A model of three tRNAs bound to the A, P and Esites of the ribosome is shown in the 70S X-ray structure (Cate et al., 1999). These bindingsites were located by difference mapping. It has been stated that the positions of tRNAsin the A and P sites support the work of Stark and disagree with that of Agrawal (van Heel, 2000).The positions of A, P and E site tRNAs in the 11.5 (A cryo-EM structure (Gabashvili et al., 2000)agree well with those in the 70S X-ray structure (Cate et al., 1999) (reviewed in Davies and White,2000). A 3D reconstruction of kirromycin stalled E. coli ribosomes binding the aminoacyl-tRNA �EF-Tu �GTP ternary complex at 18 (A has been published (Stark et al., 1997b). This 3Dreconstruction was performed using an earlier model of a pre-translocational ribosome as aninitial ‘‘anchor set’’. It might be thought that this could bias the model towards the earlierstructure. However, given the iterative refinements that were applied, the effect is likely to benegligible. EF-G has been visualised bound to the naked E. coli 70S ribosome (lacking mRNAand tRNA) (Agrawal et al., 1998), and now bound to the ribosome in pre- and post-translocational complexes (Agrawal et al., 1999; Stark et al., 2000). These cryo-EM studies haveproved useful in the interpretation of the X-ray crystal structures, for example the 50S structure at5 (A (Ban et al., 1999) used cryo-EM work to position EF-G and EF-Tu complexed with anaminoacyl-tRNA and GTP onto the ‘‘factor binding domain’’. Comparison of cryo-EMstructures in different functional states obtained by single particle analysis has now led to a low-resolution picture of translocation, indicating that it is a two-step process (Frank and Agrawal,2000).The eukaryotic ribosome has also been studied by single particle analysis, at 25 (A for the rat

liver ribosome (Dube et al., 1998b), and 21 (A for the rabbit reticulocyte ribosome (Dube et al.,1998a). It is much more complex than the prokaryotic ribosome. For example, the prokaryoticlarge subunit has 31 proteins and the small subunit 21, compared to the eukaryotic large subunitwith 49 proteins and the small subunit with 33 (Lewin, 2000). As yet the eukaryotic ribosome isnot accessible to X-ray analysis.


Cryo-EM work has thus been of vital importance in obtaining medium resolution structures ofribosomes, and in studying their functional interactions with ligands, providing a wealth of dataand biochemically testable hypotheses. The potential for structure distortion problems with cryo-EM, single particle analysis and 3D reconstruction does not appear to have been realised. Thisconclusion has been supported by comparisons of virus structures solved by X-ray crystal-lography and cryo-EM (reviewed by Baker and Johnson, 1996). However, only in the last coupleof years has single particle analysis provided high enough resolutions to enable X-ray crystalstructures of ribosomal components to be modelled into the electron density with real confidence(Malhotra et al., 1998; Matadeen et al., 1999; Gabashvili et al., 2000). X-ray crystallography hasnow revolutionised structural studies of the ribosome, and this work has partly been driven by theuse of cryo-EM structures as phasing models. The 2.4 (A resolution structure of the 50S subunitfrom H. marismortui (Ban et al., 2000) has already revealed that the ribosome is a ribozyme and isproviding fascinating details of RNA tertiary structure interactions (Nissen et al., 2000; reviewedin Cech, 2000). The 3 (A structure of the 30S subunit from T. thermophilus (Wimberly et al., 2000)has provided information about protein–RNA and RNA–RNA interactions, with the latterfrequently using the minor groove as an interaction surface. The same group has now revealedmolecular details of the interactions made by A-, P- and E-site codons and tRNA with the 30Ssubunit, and have studied the structural basis for the action of the antibiotics paromomycin,streptomycin and spectinomycin (Carter et al., 2000). Furthermore, the atomic resolution 30Sstructure has revealed that the initial step in decoding tRNA may involve the flipping out of basesA1492/A1493, allowing them to form a decoding surface that can monitor the width of the minorgroove of the codon–anticodon helix, allowing discrimination of cognate and near-cognatetRNAs (Carter et al., 2000). However, crystals suitable for X-ray diffraction analysis have onlybeen obtained from halophilic or thermophilic bacteria. E. coli and eukaryotic ribosomes stillremain stubbornly resistant to analysis by X-ray crystallography, and at the moment are onlyamenable to cryo-EM and single particle analysis. By using the atomic resolution crystalstructures to interpret models of the different functional states of the ribosome that are beingrevealed by cryo-EM and single particle analysis, it should become possible to obtain a completeknowledge of protein synthesis at the atomic level.

8. Photosystem II

Photosystem II (PSII) is the multisubunit membrane protein found in cyanobacteria, red andgreen algae, and higher plants that harnesses light energy in order to split water into molecularoxygen and reducing equivalents (for reviews of the structure and function of PSII, see Barberet al., 1997; Barber, 1998; Barber and K .uhlbrandt, 1999). PSII catalyses one of the most stronglyoxidising reactions known to occur in biology (Hankamer et al., 1997), ultimately reducing carbondioxide to organic molecules, thereby producing almost all global biomass (Boekema et al.,1998a). It has therefore long been the target of structural studies. These have proved to beparticularly difficult because of the labile nature of this macromolecular complex. As will bediscussed below, it is possible to isolate different complexes of PSII varying in the amount ofperipheral proteins they contain. Furthermore, some of the proteins themselves are intrinsicallyunstable, for example the D1 protein has a half-life of approximately 30 minutes in moderate light


(Barber, 1998). The relative ease with which single particle analysis can study membrane proteinsand the ability to computationally purify the data set has allowed this technique to play a crucialrole in recent structural studies of PSII. This section will show how single particle analysis hasadvanced our understanding of the structure and function of PSII. First, it is important to brieflysummarise some aspects of PSII structure.PSII essentially consists of two components: the reaction centre and an inner antenna light-

harvesting system. The reaction centre is responsible for the light-driven water-splitting reaction.It consists of the D1 and D2 proteins, the a- and b-subunits of cytochrome b559, and the PsbIprotein. The D1 and D2 proteins bind the cofactors necessary for the light-driven chargeseparations. The function of the inner antenna, which is composed of the chlorophyll a-bindingproteins CP43 and CP47, is to funnel light-energy towards the reaction centre. CP43 and CP47,together with D1 and D2, the a- and b-subunits of cytochrome b559 and some other lowmolecular weight proteins (less than 10 kDa), form a core responsible for all the electron transferreactions. This core has been observed predominantly in a dimeric form. The full PSII complexcapable of oxygen-evolution consists of the reaction centre, the inner antenna, and an extrinsicoxygen-evolving complex (OEC) which binds the Mn4 cluster. The OEC consists of the proteinsPsbO (33 kDa), PsbP (23 kDa) and PsbQ (16/17 kDa) in higher plants, and PsbO, PsbV (15 kDa)and PsbU (12 kDa) in cyanobacteria. Outside of these ‘core’ PSII components is a family ofmembrane-bound chlorophyll a=b-binding (Cab) proteins, including light-harvesting complex II(LHCII). The membrane-bound Cabs are not present in cyanobacteria, where they are replacedby soluble extrinsic phycobiliproteins. When the components of the PSII core are bound to theCab proteins CP29, CP26 and LHCII, they constitute the PSII-LHCII supercomplex (Boekemaet al., 1995; Barber and K .uhlbrandt, 1999).Single particle analysis of PSII has so far been dominated by studies of negatively stained

specimens. In 1995, work was published on PSII reaction centre cores from both spinach and thethermophilic cyanobacterium Synechococcus elongatus (S. elongatus), and also the spinach PSII-LHCII supercomplex (Boekema et al., 1995). Alignment and MSA techniques, implemented inIMAGIC, were used to produce class averages for these different PSII complexes. The resultingtop-view class averages showed two-fold symmetry, and the side-views showed protrusionsattributed to the extrinsic proteins of the OEC. Comparison of the top views of the supercomplexwith the dimeric core complexes provided, for the first time, evidence that the core complex waslocated in the centre of the supercomplex, with the peripheral regions accommodating the Cabproteins. Top-view class averages were produced of core dimers following Tris-washing at pH 8.0,a treatment that removes all of the OEC lumenally bound mass including PsbO, the major 33 kDaOEC protein. Calculating a difference map of Tris-washed and non-washed core dimers localisedthe likely position of at least this 33 kDa subunit. Combined with other biochemical data, thissingle particle work led the authors to propose a tentative structural organisation for thesupercomplex. Their conclusions still stand, although more components have been assignedplaces. Furthermore, this work provided support for earlier ideas that PSII is a dimer in vivo, dueto the two-fold symmetry and the observation that monomeric core complexes with bound LHCIIare never seen. The supercomplex analysed in this study lacked the 23 kDa extrinsic protein.Subsequently, the conditions used in the preparation of PSII from spinach were altered,successfully resulting in the purification of supercomplexes containing the 23 kDa protein, whichcould be analysed to produce top- and side-view class averages (Boekema et al., 1998a). MSA was


used to separate a group of single particle images into those containing the 23 kDa protein andthose lacking it. Difference maps were then used to indicate the position of the 23 kDa subunit.Projection maps produced by single particle analysis have been combined with higher resolutionprojection maps of the reaction centre subcore (the PSII core lacking CP43) (Rhee et al., 1998)and the structure of the LHCII trimer (K .uhlbrandt et al., 1994), both obtained by electroncrystallography, to produce improved models of the subunit positioning (Barber et al., 1999). Theresulting model was supported by other biochemical data, such as cross-linking studies.One of the first examples of the use of single-particle cryo-EM in the PSII field came with the

publication of the 3D structure of the higher plant PSII-LHCII supercomplex from higher plants,at a resolution of 24 (A (Nield et al., 2000c and see Figs. 3, 6 and 7 in this review). Computationalpurification proved to be necessary and of great help in this study. Reference-free alignment ofalmost 16,000 particles identified sub-populations differing in size and shape. These sub-populations represented complexes that had lost some peripheral proteins during samplepreparation. Each sub-population was treated separately to produce a 3D reconstruction. Thesereconstructions provided a framework in which higher resolution structures obtained by electroncrystallography (Rhee et al., 1998; Hankamer et al., 1999) could be incorporated. For the firsttime, this allowed the binding sites of the OEC proteins to be related to the underlying intrinsicmembrane proteins, information that will be essential for understanding the water-splittingreaction. This structure further emphasises the dimeric nature of the complex, and the OECproteins are revealed as having a tetrameric appearance and being bound to the lumenal surface,as had been indicated in earlier freeze-etch studies at lower resolution (Seibert et al., 1987). Thismodel has been refined, giving a better distribution of protein density in the peripheral regions,allowing the LHCII trimers to be positioned more accurately (Nield et al., 2000a), shown here inFig. 11. Recently, single particle analysis of negatively stained PSII supercomplexes, obtainedafter treatment to remove the extrinsic proteins, has revealed significant conformational changesin the peripheral light-harvesting system (Boekema et al., 2000a). This has indicated that the roleof the extrinsic subunits may be to ensure a directed transfer of excitation energy through theperipheral antenna proteins CP26 and CP29, or to maintain sequestered domains of inorganiccofactors, a requirement for the water-splitting reaction (Boekema et al., 2000a).The 3D structure of the higher plant PSII supercomplex was followed by 3D structures of the

PSII supercomplex from the green alga Chlamydomonas reinhardtii and the core complex from S.elongatus (Nield et al., 2000b). These structures were at the lower resolution of 30 (A, and are basedon image analysis of negatively stained samples. The C. reinhardtii supercomplex is very similar tothe higher plant supercomplex, whilst the S. elongatus core complex is very similar to the higherplant core complex. By building higher resolution models of the core into these structures, it hasagain been possible to relate the positions of their OEC proteins to the underlying intrinsicmembrane proteins. The S. elongatus core complex structure supports earlier work presenting top-view class averages of the complex (Kuhl et al., 1999). This earlier work also shows class averagesof ‘‘double dimers’’}two core complexes interacting via their tips, hinting at the possiblearrangement of these core complexes in vivo.Boekema and colleagues have performed several elegant studies attempting to search for

complexes larger than the supercomplex that may exist in vivo (Boekema et al., 1998b, 1999b,1999a, 2000b). They have successfully taken the approach of subjecting PSII membranes to partialdetergent treatment, analysing the solubilised particles by single particle analysis, and again using


MSA to computationally purify the dataset. This work has shown that LHCII can bind in threetypes of binding sites, called strong (S), moderate (M) and loose (L) (Boekema et al., 1998b,1999b), and has identified three different PSII megacomplexes (Boekema et al., 1999b, 1999a).Later work, using MSA to classify images of crystalline arrays of PSII from the granal membranesof spinach has indicated that crystalline regions contain predominantly supercomplexes, and thatthe megacomplexes may be relegated to non-crystalline areas (Boekema et al., 2000b). This workhas further identified that PSII-LHCII supercomplexes in one membrane are usually adjacent todomains containing only LHCII in the opposing membrane, hinting at resonance energy transferfrom LHCII domains to PSII-LHCII complexes across the membranes. The main conclusionfrom this work is the heterogeneous nature of the associations between PSII and LHCII. It hasbeen proposed that the formation of these different complexes may allow PSII to react to light and

Fig. 11. Superposition of the helical organisation of the known subunits of the PSII-LHCII supercomplex, derivedfrom electron crystallography (Kuhlbrandt et al., 1994; Rhee et al., 1998; Hankamer et al., 1999) on the latest model of

the supercomplex obtained by single particle analysis of cryo-EM images. Adapted from Fig. 7 of Nield et al., 2000a,with the permission of The Royal Society, London.


stress conditions by providing different routes of excitation energy transfer (Boekema et al.,1999b).In just five years, single particle analysis has led to rapid progress in our understanding of PSII

structure at the macromolecular level. The ability to rapidly computationally purify and studyindividual complexes has led to new insights into the arrangement of PSII, and to new proposalsfor its function. By modelling higher resolution structures into the maps provided by singleparticle analysis, we are beginning to understand the arrangement of proteins within thesupercomplex. Future work will involve obtaining higher resolution structures of supercomplexesand megacomplexes, using cryo-EM to model in structures obtained by X-ray and electroncrystallography, thus gaining a near atomic resolution picture of these complexes.

9. Electron tomography

Electron tomography of organelles and whole cells has now grown out of the 3D reconstructionmethods used in single particle analysis (reviewed in Baumeister et al., 1999). In electrontomography, specimens with a thickness of 0.25–2.0mm are imaged in TEMs operating at higheraccelerating voltages than are used in single particle analysis or electron crystallography (400–1200 kV compared to about 120 kV). The higher voltages are essential due to the increasedspecimen thickness. The specimen is imaged using tilts of 60–708 at increments of 1–28. Theimages have to be precisely aligned, and finally back-projected to produce the 3D model.Tomographic reconstruction can be implemented in SPIDER (Frank et al., 1996) using alignmentand weighted back-projection algorithms (for example McEwen et al., 1986; Deng et al., 1999) orin related image processing programs (e.g. Perkins et al., 1997b). Electron tomographicreconstruction of cilia (McEwen et al., 1986), a whole cell of the archaebacterium Pyrodictiumabyssi (Baumeister et al., 1999) and mitochondria (e.g. Mannella et al., 1997; Perkins et al., 1997a;Deng et al., 1999) have been attempted. Currently, the resolution lies in the range 50–70 (A(Baumeister et al., 1999), but improvements in the technique should decrease this towards thelimit of about 28 (A imposed by radiation damage (Glaeser, 1999). Low-dose automated methodsare now available (e.g. Rath et al., 1997), allowing specimens to be imaged whilst embedded invitreous ice (after plunging in liquid ethane). This cryo-electron tomography has recently beenapplied to Neurosporamitochondria (Nicastro et al., 2000). Tomographic studies of mitochondriahave led to improved models of cristae structure. Furthermore, studies of mitochondria frompatients suffering from mitochondrial myopathies may reveal more information aboutmitochondrial function and the effects of disease (Frey and Mannella, 2000). For examples ofelectron tomography using the programs SPIDER and Sterecon, see http://www.wadsworth.org/spider doc/spider/vrml/uncomp/index.html.

10. Future prospects and conclusion

Improvements to single particle analysis and 3D reconstruction are continually beinginvestigated. In future, it will be important to find ways to reduce specimen drift and beam-induced charging (Chiu et al., 1999). Microscopes with liquid helium cooled superconducting


objective lenses have been developed, such as SOPHIE (Superconducting Objective lens in aPHIlips Electron microscope) (Zemlin et al., 1996). These microscopes keep the specimentemperature near 4K, and their use has been shown to lead to a two-fold reduction in beam-damage compared to liquid nitrogen temperatures. This is based on a quantitative evaluation ofthe rate at which diffraction spots from 2D crystals of bacteriorhodopsin fade (Stark et al., 1996).Stages cooled by superfluid helium have been produced, reducing vibration problems that areassociated with conventional cryo-microscopes, and allowing very high instrumental resolutionsto be achieved (better than 2 (A) (Fujiyoshi et al., 1991; Fujiyoshi, 1998). The operation of thesemicroscopes requires considerably more sophisticated instrumentation and there are practicalproblems associated with the poor conductivity of carbon and ice at liquid helium temperatures(Stowell et al., 1998). Improvements in the resolution of charge-coupled device (CCD) camerasmay eventually see them replacing photographic film for high resolution TEM work, removing theneed for densitometry (for a recent review see Faruqi and Subramanian, 2000). Image processingprograms are continually being developed and updated. These should eventually provide morereliable methods of compensating for instrumental factors, such as better CTF correction (e.g.Conway and Steven, 1999; Skoglund et al., 1996). Frank and colleagues have developed a methodof 3D reconstruction that includes CTF correction, eliminating CTF correction as a separate stepin the image processing (Zhu et al., 1997). Grigorieff has developed FREALIGN (FourierREconstruction and ALIGNment) which can correct for the CTF in an image (includingastigmatism, and both amplitude and phase contrast components), calculate a 3D reconstruction,and then refine the angles and translational orientations of particles (Grigorieff, 1998). An excitingrecent software development is EMAN (Electron Micrograph ANalysis) (Ludtke et al., 1999).This program is designed specifically for high-resolution (beyond 10 (A) single particle analysis,and can employ both amplitude and phase CTF correction. As data-handling capacity increases,it should become possible to successfully align and assign the orientations to larger single particledata sets, increasing the attainable resolution. Eventually, it should become possible to automatedata collection and structure determination, as is now usual for X-ray crystallography.The use of medium resolution structures obtained from single particle analysis as phasing

models for X-ray analysis of macromolecular complexes may increase in the future, particularlywhen conventional methods of phasing cannot be applied. There is, however, an importantcaveat. Flexible particles, such as the 30S ribosomal subunit, may result in a reconstruction thatrepresents an average of a range of conformations. This is unlikely to be suitable for molecularreplacement searches, since the conformation of the molecule in the crystals is likely to be differentto that in the reconstruction (Harms et al., 1999).It is now possible to gain atomic resolution details of macromolecular complex complexes by

combining high-resolution X-ray structures of individual components with the medium resolutionstructure of the entire assembly, obtained by electron microscopy. With X-ray crystallographyand NMR spectroscopy dominating the high-resolution study of individual protein molecules, thefuture of single particle analysis probably lies in producing moderate resolution structures of largecomplexes that will serve as the scaffold for hanging the high-resolution structures of components.It has been suggested that structures determined by EM need to be at less than 7 (A in order todecrease the positional uncertainty when modelling X-ray structures within them (Chiu et al.,1999). This currently lies at the limit of the attainable resolution with single particle analysis.However, Rossman believes that combining X-ray structures with a cryo-EM model at 22 (A can


produce structural information accurate to 2.2 (A (Rossmann, 2000), and domains of GroEL froma crystal structure have been successfully docked into 12 and 15 (A cryo-EM maps (Roseman,2000). Recent examples of the success of this combined approach are the analysis of clathrin(Musacchio et al., 1999), PSII (Nield et al., 2000a-c), and Semliki Forest Virus (Mancini andFuller, 2000). Combining electron tomographic analysis of organelles with molecular structures isa very exciting prospect.It will become important to develop a single database, analogous to the Protein Data Bank

(PDB), for storing 3D models obtained by single particle analysis and electron tomography,allowing users to download and manipulate the models (e.g. to import higher resolution data).Proposals for such a database have been made (Marabini et al., 1996; Carazo and Stelzer, 1999)and some prototypes can be seen at http://www.wadsworth.org/spider 3d/home page.html andhttp://www.bioimage.org/. Structures derived from single particle analysis are now beingdeposited in the Molecular Structures Database (MSD), which is superseding the PDB (Manciniand Fuller, 2000). There may however be a reluctance to provide models for such databases, sincethey provide the ideal references for multi-reference alignment, vastly speeding up the processingof a competitor’s images!In 1982, a paper commented on the potential of single particle analysis and MSA to help us

‘‘recognise subtle differences in molecular structure’’ (Frank et al., 1982). By 2001, it can be seenthat this hope has been surpassed. Single particle analysis will help us to realise the ultimate aim ofstructural biology}the atomic resolution description of the macromolecular complexes of the cellin their different functional states.

Acknowledgements

We would like to thank Professor Sir Tom Blundell (Department of Biochemistry, University ofCambridge), Dr. Venki Ramakrishnan (MRC Laboratory of Molecular Biology, Cambridge) andDr. Gebhard Schertler (MRC Laboratory of Molecular Biology, Cambridge) for their criticalcomments on the manuscript. Any errors or misinterpretations remain the sole responsibility ofthe authors.

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