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Molecular dynamics of protein complexes from four-dimensional cryo-electron microscopy
Journal of
Structural Biology Journal of Structural Biology 147 (2004) 291–301 www.elsevier.com/locate/yjsbi
Molecular dynamics of protein complexes from four-dimensional cryo-electron microscopy J. Bernard Heymann,a,1 James F. Conway,b and Alasdair C. Stevena,* a
Laboratory of Structural Biology, National Institute of Arthritis, Musculoskeletal and Skin Diseases, National Institutes of Health, Bethesda, MD 20892, USA b Institut de Biologie Structurale J.-P. Ebel, 38027 Grenoble, France Received 22 December 2003, and in revised form 4 February 2004 Available online 14 March 2004
Abstract Cryo-electron microscopy of single particles offers a unique opportunity to detect and quantify conformational variation of protein complexes. Different conformers may, in principle, be distinguished by classification of individual projections in which image differences arising from viewing geometry are disentangled from variability in the underlying structures by ‘‘multiple particle analysis’’—MPA. If the various conformers represent dynamically related states of the same complex, MPA has the potential to visualize transition states, and eventually to yield movies of the dynamic process. Ordering the various conformers into a time series is facilitated if cryo-EM data are taken at successive times from a system that is known to be developing in time. Virus maturation represents a relatively tractable dynamic process because the changes are large and irreversible and the rate of the natural process may be conveniently slowed in vitro by adjusting the environmental conditions. We describe the strategy employed in a recent analysis of herpes simplex virus procapsid maturation (Nat. Struct. Biol. 10 (2003) 334–341), compare it with previous work on the maturation of bacteriophage HK97 procapsid, and discuss various factors that impinge on the feasibility of performing similar experimental analyses of molecular dynamics in the general case. Published by Elsevier Inc. Keywords: Conformational change; Molecular movie; Molecular dynamics; Image classification; Single particle analysis; Multiple particle analysis
1. Introduction It is now increasingly appreciated that most fundamental biological processes are carried out by large macromolecular assemblies (or ÔmachinesÕ) (Alberts, 1998; Sali et al., 2003), and that these assemblies are often dynamic systems that follow elaborate duty cycles while undergoing large structural changes. Cryo-electron microscopy in combination with single particle analysis (SPA) has emerged as a powerful approach for visualizing assemblies in three dimensions (Baumeister and Steven, 2000; Frank, 2002; Frank et al., 2002; Ruprecht and Nield, 2001). This approach has pro* Corresponding author: Fax: 1-301-480-7629. E-mail address: [email protected] (A.C. Steven). 1 Present address: Division of Biology, California Institute of Technology, 1200 East California Blvd., Pasadena, CA 91125, USA.
1047-8477/$ - see front matter. Published by Elsevier Inc. doi:10.1016/j.jsb.2004.02.006
gressively improved in resolution—now better than 10 A in a growing number of cases; is relatively parsimonious in terms of the amounts of material required; and has the advantage of depicting the solution structure of the specimen, unconstrained by crystal contacts. The basic principle underlying SPA is that each member of a large set of two-dimensional cryo-EM images represents a projection of the same three-dimensional object, and after identifying as precisely as possible the viewing geometry of each projection, these data are used to reconstruct its three-dimensional structure. Although cryo-EM has been used to characterize a substantial number of conformational changes in the sense of comparing ÔbeforeÕ and ÔafterÕ states (e.g. Jontes et al., 1995), it has for the most part remained a static visualization technique. It does, however, have the potential to capture functional intermediates or transition states according to the following scenario. If in vitro
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conditions are established so that multiple conformational states are present at the same time, the various conformers may be distinguished by diversifying the projection-matching scheme used for classification to include multiple three-dimensional models, and calculating a density map for each conformer. If data are collected at successive time-points for an evolving reaction, the waxing and waning of each conformer in the sampled populations may be used to order the conformers into a time series and to perform a kinetic analysis of the reaction pathway. Such data resulting from ‘‘multiple particle analysis’’ (MPA) may also be synthesized into three-dimensional movies of the dynamic process. In this paper, we first consider several general aspects of this approach; then review the classification procedures that have been used in two dynamic studies of virus capsid maturation (Heymann et al., 2003; Lata et al., 2000); and finish by discussing certain practical aspects of the analysis and its prospects for wider applicability.
2. General considerations 2.1. Accessible timescales The rapidity of cryo-fixation when a particulate suspension is quenched places a limit on those processes whose dynamics are amenable to this approach. The time required for cryo-fixation is of the order of a millisecond and since it is limited by the rate of heat transfer through a thin film or droplet of buffer, the prospects of shortening it appreciably are scant. Several ingenious experimental set-ups have been devised for initiating a reaction and then obtaining a cryo-fixed EM sample a few milliseconds later (e.g. Berriman and Unwin, 1994; Subramaniam and Henderson, 1999; White et al., 2003). However, these designs have tended to focus on capturing short-lived states, and problems potentially arise in the context of synchronization, i.e., (i) particles near the leading edge of a plunge-frozen grid will be immobilized by cryo-fixation slightly earlier than those at the trailing edge (Kasas et al., 2003), and a similar inequity applies to particles that are, respectively, near the surface or in the middle of the thin film of buffer, and (ii) even if a dynamic process is initiated at a given instant, the particles may not remain in synchrony but may diverge stochastically. Thus, processes that occur in one to a few milliseconds appear to be the fastest that can be directly tackled by time-resolved cryo-EM. An alternative approach is to slow the reaction down so that it unfolds over a much longer timescale. This is the only approach feasible for processes whose natural timescale is faster than a millisecond or so, and is also advantageous for processes in the millisecond range
because the prospects of capturing reaction intermediates are enhanced. Moreover, there is the practical advantage that if the reaction can be slowed down to occur over minutes to hours, it may be conveniently sampled by conventional cryo-EM grid preparation procedures. Slowing the reaction kinetics may be attempted either (as below) by adjusting the environmental parameters— ionic strength, temperature, etc.,—or by identifying and exploiting appropriate mutants, or by partially poisoning the reaction with chemical inhibitors. 2.2. Size of movements The main idea underlying this approach is that image classification procedures may be used to distinguish differences among a set of projections that arise from temporal changes in a given structure from those that reflect variations in viewing geometry. In this context, it is essential that the transitions of interest should involve changes that are large enough for such a separation to be feasible for images with the high noise levels typical of cryo-electron micrographs. Thus, the first step is to determine how many distinct structures are present in the complete data set and to calculate density maps for them. The second step is to order these maps into a temporal sequence. Here a further complication arises from the possibility of static structural heterogeneity. Such heterogeneity may arise from the presence of contaminants of roughly the same size; or damaged particles (e.g., complexes that have suffered proteolytic degradation or which have lost subunits); or intrinsic polymorphism. Heterogeneity from these sources may undermine achieving a coherent classification, i.e., the assumption that all the conformers visualized represent different dynamic states of the same complex. 2.3. Number of states and resolution For practical purposes, a further requirement is that the number of distinct states should be relatively small. The resolution to be achieved in a three-dimensional density map depends, among other factors, on the number of particles included. If N states are present and all are equally populated, for a given resolution to be achieved, the data set has to be at least N-fold larger than is needed for the same resolution with a single conformer. The expectation that all states be equally populated is an optimistic one and it seems more likely that states will, in general, be of different durations and thus have different occupancies in the population at large. For instance, a system undergoing simple harmonic motion in one dimension spends more time near the end-points of its cycle than near the mid-point. In consequence, the two end-points would be well (and equally) represented in a random sampling whereas positions at or near the mid-point would be relatively
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rare. In practice, the number of states is not known in advance but must be ascertained from the classification analysis. 2.4. Classification strategy An evolving system displays heterogeneity depending on the degree of synchronization and the nature of the transitions. With adequate synchronization and a relatively simple sequence of events, the data at each timepoint may be taken as approximately homogeneous, making it possible to reconstruct distinct states. Conversely, if synchronization is not well observed or the system is inherently complex, many states may coexist at any given time-point. A prudent approach is then to disregard the fact that the particle images come from different time-points, and to derive as many states as the data support. The resulting time distribution of particle images in each class—associated with a state— represents the temporal manifestation of that state in the sample. To estimate the mean lifetime of individual particles in that state, these data must be subjected to kinetic analysis.
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If the protease is absent or inactivated by mutation, procapsids accumulate and may be isolated from infected cells, although these particles are exceedingly labile (Newcomb et al., 1996). Alternatively, in vitro assembly of precursor proteins yields procapsids (Newcomb et al., 1999). In either event, with isolated procapsids maintained at moderate ionic strength and room temperature, spontaneous maturation takes place over a period of several days. This property allows convenient sampling of the preparation by conventional cryo-EM procedures. 3.2. Time-sampled cryo-EM data In one such experiment, cryo-micrographs were recorded at four time-points corresponding to 0, 24, 48, and 96 h, respectively (Heymann et al., 2003). The 0-h time-point represented the earliest time at which procapsid isolation could be completed. This was 12 h after HeLa cells were infected with the tsProt.A mutant which carries a temperature-sensitive mutation in the protease and 4 h after the infected cells were harvested. After digitization and particle picking, the data set consisted of 5000 particles from focal pair micrographs with similar numbers from each time-point.
3. Herpes simplex virus 1 procapsid maturation 3.3. MPA classification 3.1. Background The earliest HSV-1 precursor is a procapsid consisting of a spherical surface shell overlaid on a core or inner shell of scaffolding proteins, about 10% of which contain the maturational protease (VP4, 24 kDa) as a Nterminal extension (Homa and Brown, 1997; Steven and Spear, 1997). The surface shell is composed of 960 copies of the major capsid protein (VP5, 150 kDa) arranged as 150 hexamers and 12 pentamers, coordinated by 320 heterotrimers called triplexes. Each triplex has one copy of the triplex-a protein (VP19c, 50 kDa) and two copies of the triplex-b protein (VP23, 35 kDa). If the portal protein UL6 (75 kDa) is present, a single ring of UL6 subunits replaces one of the VP5 pentamers (Newcomb et al., 2001). The trigger for maturation is activation of the protease, which then cleaves the scaffolding protein near the site where it interacts with the surface shell. This event appears to prime the surface shell to undergo a spontaneous cooperative conformational change (maturation). The exact timescale on which maturation takes place in vivo is not known but it appears to be fairly rapid since procapsids are not seen in thin sections of infected cells unless the protease is inactivated (Preston et al., 1983): moreover, maturation is probably accelerated by DNA packaging, as in bacteriophages. Concomitant with surface lattice maturation, the cleaved scaffolding proteins are expelled but the protease is retained inside the capsid.
At the outset, representations of the initial and final states were available. Our strategy was to use linear combinations of these density maps2 to define a first set of references that were then used to sift out images of potential intermediates according to the scheme given in Fig. 1A. The data were sorted by correlation-based projection-matching with multiple references. After a first round of classification, a second set of references was calculated, and this process was iterated to convergence. At each iteration, classes with too few particles to produce an adequately defined density map were eliminated and their particles reassigned. Outliers—i.e., particles whose correlation coefficients with any model did not exceed a given threshold—were eliminated: this corresponded to about 35% of the total data. Finally, a set of 17 density maps were obtained (Fig. 2; Table 1). This strategy involves certain assumptions that were adopted for pragmatic reasons. In the first place, it assumes that the end-states represent the extreme structural differences exhibited by the maturing capsid and that intermediates are intermediate not only on the temporal pathway but also in terms of physical resemblance (expressed in terms of correlation coefficients). In fact, it is not ruled out a priori that there may be intermediates that are distinctly different from either 2 The term ‘‘density map’’ refers to the three-dimensional matrix of density values produced in a reconstruction.
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Second, it was assumed that maturing particles continue to observe icosahedral symmetry for most of the time, i.e., the maturation pathway consists of a succession of rapid transitions between relatively long-lived intermediates that are themselves icosahedrally symmetric. That this assumption is not necessarily valid is suggested by observations on maturing bacteriophage T4 giant capsids of a wave-like propagation of the transition front over their surface lattice (Steven and Carrascosa, 1979). If the assumption of icosahedral symmetry were to be significantly in error, correlation coefficients would be lower than expected, as would the resolution of reconstructions. Table 1 illustrates that the long-lived states at the extremes (maps 1–4 and 14–17) show higher resolutions than the shorter-lived intermediates. The lower numbers of numbers of particles obtained for the short-lived states contribute to the lower resolutions of these maps. The rejected low-scoring images may be in non-icosahedral transition states, or permanently damaged or distorted. However, the fact that the resolutions achieved were similar to those obtained with comparable numbers of homogeneous particles (data not shown) suggests that the transitions are strongly cooperative, i.e., maturation consists of a succession of rapid subtransitions through relatively longlived intermediate states. In such a state, the particle observes icosahedral symmetry to a good approximation, while in a subtransition it may depart from this symmetry (Heymann et al., 2003). For capsid maturation studies, the assumption of icosahedral symmetry may be more appropriate for portal-lacking mutants, as observations in the T4 (Steven and Carrascosa, 1979) and T7 (Cerritelli et al., 2003) systems suggest that the structural transformation may initiate in the portal vertex. 3.4. Comparing density maps
Fig. 1. Classification strategies for (A) maturing HSV-1 capsids and (B) maturing HK97 capsids.
end-state, and such intermediates may not be captured in such an analysis. Nevertheless, the nature of the competitive classification used here emphasizes differences between particles and should provide a reasonable representation of specimen heterogeneity. The main requirement is that the particles must resemble the reference maps to some extent. In support of this notion, acceptable orientations for procapsid particles were found using the mature capsid as reference (data not shown). If there were grossly different major states, they would probably be detected early in the analysis, e.g., during particle-picking.
An important requirement in MPA is for distance measures between density maps. These measures are needed for several purposes: to assess whether two maps are sufficiently similar to represent the same structure; conversely whether they represent significantly different states; and to assess relative proximity among multiple states. While recognizing that there is scope for further work to define more discriminating distance measures and to take into account the effects of noise, we have used a Euclidean distance-like measure, based on crystallographic R-factors, but defined in real-space as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P u 2 ðpi pj Þ u Ri;j ¼ tqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2; P 2P ðpi hpi iÞ ðpj pj Þ where the sums are over all voxels in a pair of maps (pi , pj ).
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Fig. 2. Procapsid and mature HSV-1 capsid maps (from Heymann et al., 2003). The main differences are angularization of the capsid and formation outward shift of the pentons (darker blue), and molecular rotations affecting hexon subunits. Blue: of the continuous floor, resulting from a 20 A VP5; Green: Triplex.
A small distance between two maps denotes close resemblance between them. If, in the present context, we equate closeness with temporal proximity, such measures may be used to order a set of maps (in our case, 17) sequentially. For this purpose, we converted the R-factor-based measure as follows: Di;j ¼ lnð1 Ri;j Þ:
The latter measure, Di;j , was found to be almost additive such that the distance between two maps was approximately equal to the sum of the distances between all intervening maps. An exhaustive permutation algorithm was implemented to find the order of maps that minimized the difference between the measure distances and the sums of distances of intervening adjacent maps:
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Table 1 Final set of HSV-1 capsid density maps Map (n)
Particles
Average CCa
b Resolution (A)
Time constant (h)c (transition n
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
521 252 183 153 81 81 83 79 76 71 68 62 57 152 194 283 636
0.275 0.273 0.275 0.263 0.259 0.258 0.258 0.255 0.259 0.263 0.268 0.272 0.276 0.280 0.314 0.318 0.323
23 24 24 25 25 25 26 27 26 26 25 25 24 24 23 22 21
16.9 7.8 6.7 6.0 3.0 2.9 2.8 2.6 2.4 2.3 2.3 2.1 2.0 6.2 9.4 17.9
n þ 1)
The resolution achieved reflects both the number of particles and quality as given by the average correlation coefficient. The first order time constants derived from the particle distributions at each time-point are inversely related to the numbers of particles in each map. a Average correlation coefficient for particles used in the reconstruction. b Fourier shell correlation, 0.5 cutoff. c First order time constant.
" min
X i;j
Di;j
j1 X
!# Dk;kþ1
:
k¼i
Once this order was determined, we found it useful to reduce the noise level in each map (thus rendering them more uniform in quality) for the next cycle of classification by adding fractions of the preceding and succeeding maps to each with weights (0.5, 1.0, and 0.5). No such averaging was performed after the last round of classification.
same views) of the procapsid and the mature capsid by the same measure and obtained an average value of 0.599 0.037. These data imply that the differences between maps, although less pronounced than differences in viewing geometry, are quite strongly expressed. Because the orientation selection is stronger than the conformational discrimination, it is unlikely that a wrong view assignment would be confused with a different conformation of the HSV-1 capsid. 3.6. Classification
3.5. Differences among projections: viewing geometry versus intrinsic conformational variability Time-resolved processing of 2D images requires a distinction between assigning particle images to particular orientations (i.e., viewing geometry), and classifying them with respect to different reference maps (i.e., intrinsic variability). In order to make an overall assessment of this distinction, we performed the following experiment. For a given density map, a set of projections covering the asymmetric unit was generated and pairwise correlation coefficients calculated between them, excluding self-comparisons which have a correlation coefficient of unity. The coefficient used was an average of the three calculated in the PFT program (Baker and Cheng, 1996). For the procapsid (map 1), we obtained a value of 0.413 0.056 (SD) and for the mature capsid (map 17), 0.399 0.060. These figures, typical of the correlation coefficients between projections from different views, afford a baseline for incorrect comparisons. Next we compared corresponding projections (i.e., the
At the outset, we assumed that the number of distinct states would be manageably small. Otherwise, there would be insufficient particles in each class to produce resolution range, well-defined density maps in the 20 A for which we estimate that 100–200 particles are needed for a capsid of this size. Based on these considerations, we chose to start with 21 models. The number of particles eventually assigned to a given structural state would reflect its longevity. To maximize the discriminatory power of the projection-matching protocol, we considered which spatial frequencies should be emphasized. For instance, the strong low-frequency components of the images would be essentially the same for each image; on the other hand, the highest frequencies are very noisy and therefore error-prone for classification purposes. To determine an appropriate frequency band, we calculated a Fourier shell correlation between the procapsid and mature capsid maps (Fig. 3). It shows low correlations (and hence marked differences) in the frequency range of
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yielding time constants indicative of the life-times of transition states (Table 1). It is noteworthy that that starting procapsid preparation was not homogeneous (t ¼ 0; Fig. 5), suggesting that conformational heterogeneity has been a limiting factor on the resolution of procapsid reconstructions to date (Newcomb et al., 1999; Trus et al., 1996). The numbers of particles in states 8–10, when the major transition is taking place, are never high, indicating that this switch is relatively fast and consequently is relatively poorly perceived.
Fig. 3. Resolution dependence of the consistency between density maps of the HSV-1 procapsid and the mature capsid. Consistency was assessed by the FSC (solid line) and DPR (dotted line) measures. The range in which there is relatively strong signal and in which the two was used for classification. states differ most (25–60 A)
1 to (60 A) 1 . Accordingly, this range was used (25 A) throughout the classification process. To illustrate the discrimination occurring in classification of the original data, we compare in Fig. 4A two particles with the corresponding reprojections of 7 of the 17 density maps. The particle in the top row is viewed close to a twofold axis, and its Euler angles were consistently determined by all 7 models (see Fig. 4 legend): however, the correlation coefficients reveal the marked distinction between procapsid-like states (maps 1 and 7) and mature capsid-like states (maps 9, 10, 11, and 17), with the major switch occurring between maps 7 and 8 (Heymann et al., 2003). The capsid in the second row is a relatively mature particle viewed close to a fivefold axis. Accordingly it appears round in projection even though the particle is quite polyhedral. In this case, the procapsidlike maps (1, 7, and 8) with correlation coefficients of 0.2 consistently misidentify the projection whereas the mature capsid-like maps (9, 10, 11, and 17) with correlation coefficients of 0.35 assign the same (correct) Euler angles. According to relatively small margins in the correlation coefficient, this particle was assigned to class 11. 3.7. Ordering into a time series Although the starting references followed a logical order in relation to the initial and final states, there was no guarantee that the 17 distinct maps finally realized would be time-ordered. We explored this aspect in two ways. First we ordered them according to a ‘‘minimum difference between successive states’’ criterion (see Section 3.5). However, a more conclusive ordering was obtained by studying the kinetics of the time series, i.e., the percentage of particles assigned to each class at each time-point were tabulated, and their kinetics (Fig. 5) confirmed the inferred ordering. This process was then modeled as a succession of first order kinetic transitions,
4. Bacteriophage HK97 capsid maturation 4.1. Background Prohead I, the HK97 procapsid, has a T ¼ 7 icosahedral shell of 60 hexamers and 11 pentamers of a single 42 kDa protein with the portal protein, ring at the twelfth vertex. It also contains 50 copies of the maturational protease (Hendrix and Duda, 1998). Neither the protease nor the portal is required to produce correctly formed particles, but these proteins are needed for maturation and DNA packaging to ensue. Prohead I is converted to Prohead II by excision of the amino-terminal 11 kDa of the capsid protein. Prohead II is metastable and may be transformed to the larger, thin-walled, flat-faceted Head. In vivo, this transition is promoted by DNA packaging: in vitro it may be triggered by any of several chemical stimuli (Conway et al., 1995; Duda et al., 1995). In Head II, stabilizing covalent cross-links are formed between neighboring subunits (Wikoff et al., 2000). 4.2. Time-sampled cryo-EM data Acidic conditions promote maturation of Prohead II and slight variations in pH around the value of 4 strongly influence the rate at which this reaction proceeds (Lata et al., 2000). A preparation of purified portal-less Prohead II was set to pH 4.18 and sampled for cryo-EM thirteen times at unequal intervals over the following 20 h. From visual inspection of the micrographs, it was apparent that Prohead II rapidly increased in size by about 50% of its final expansion and then converted more slowly to a spherical thin-walled state. Upon reversion to neutral pH, the latter particle rapidly converted to the polyhedral Head II morphology. 4.3. MPA classification Since the primary feature of HK97 maturation is the large size change (ÔexpansionÕ) and it was apparent that early intermediates were 10% bigger than Prohead II, size was used as the initial arbiter and a set of reference models was generated as versions of Prohead II enlarged
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Fig. 4. Projection matching of two images of (A) maturing HSV-1 capsids with 7 of the 17 models, and (B and C) maturing HK97 capsids with the 5 models. The top particle is viewed near a 2-fold axis and the bottom particle near a 5-fold axis, in each case. The corresponding correlation coefficients are given. For the HSV-1 capsid, the orientations for the 2-fold view particle were consistent for all maps (h : 89:0 89:5, / : 3:0 0:0, x : 158:6 158:9). The orientations for the 5-fold view particle showed a distinction between procapsid-like maps (maps 1–8: h, 81.0; /, 9.6; and x; 253:5 253:8) and mature capsid-like maps (maps 9–17: h, 89.0; /, 25.5; and x, 139.6).
by increments of 2% (Fig. 1B). Additional reference maps were taken as similar variants of a reconstruction calculated from all data at the 37 min time-point. Then each particle image was matched with reprojections from all maps to assign its orientation and size class. Reconstructions were calculated from each size class at each time. Similar maps from different time-points were combined to produce a new set of references and this process was iterated several times. Finally a conservative decision was made as to the number of distinct intermediates. Two, of the same size and with relatively subtle differences between them, were called Expansion Intermediates I and II. A third transition state, EI-III, was the end product at low pH. This particle is fully
expanded but spherical rather than polyhedral in shape. Finally, the five density maps—Prohead II, Head II, and the three Expansion Intermediates were used to produce movies by morphing (Lata et al., 2000). In retrospect, classification was facilitated by the apparent maintenance of icosahedral symmetry by the maturing capsids and the relatively large differences between all states except EI-I and EI-II (Fig. 4B). There may in fact be other similar states that a more exhaustive classification with higher resolution reference maps would distinguish. Of note and (these were at 25 A) some surprise in view of the convoluted surfaces of the starting models was the successful determination of a structure for the thin-walled, smooth-surfaced, and
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classes corresponding to relative scale factors of 0.90, 0.95, 1.0, 1.05, and 1.10. The variations were attributed to expansion and contraction of a flexible, Ôspring-likeÕ peptide that connects adjacent trimers in this particle. The size distribution was Gaussian-like indicating that, whatever the dynamics of this particle are, they do not represent simple harmonic pulsation in which case the largest and smallest particles would predominate. The comparable quality of the differently sized reconstructions was inferred to indicate cooperative dodecahedral motions. 5.2. Numbers of states and numbers of particles
Fig. 5. HSV-1 particle distributions as determined (A) in the initial classification, (B) after several iterations of classification and for the final 17 maps. The distributions show a preponderance of initial procapsid-like forms and forms close to the mature capsid, while the intermediate, short-lived forms are poorly represented.
spherical EI-III. The skew T ¼ 7 lattice of the HK97 capsid was probably a major factor for this result.
5. Discussion
Resolution in time (the number of states) and spatial resolution are inter-dependent and both parameters are limited by the amount of data available. Given higher spatial resolution in the reference maps, more subtle differences may be detected between states and consequently, better time resolution obtained. Given better time resolution, the models should identify classes of particles that are more internally consistent and hence yield higher resolution density maps. However, in practice, given a fixed amount of data, the question arises of how to choose an optimal number of states as a starting point for MPA. In the HSV-1 case, the initial choice of 21 reference maps was based on the maximum number of recon range at, structions that could be expected in the 20 A say, 150–200 particles per reconstruction, allowing for a certain fraction of non-classifiable rejects. For particles of lower symmetry, the number per particle would be correspondingly higher by a factor of approximately (60.Dp )/(Np .DHSV ), where Np is the order of symmetry
5.1. Equilibrium and non-equilibrium systems In a non-equilibrium situation, as in time-course experiments with an evolving system, each time-point samples a different distribution of states. For a dynamic system in equilibrium, on the other hand, the distribution of states remains constant over time. Dynamics of the latter kind were observed for the pyruvate dehydrogenase complex (PDC) of Saccharomyces cerevisiae on the basis of large size variations, ranging between +/ ) 10%, detected by cryo-EM (Zhou et al., 2001). PDC has an dodecahedral core of 60 E2 (dihydrolipoamide acetyltransferase) subunits. The observed size variations were well beyond the 1–2% range of magnification variations across or between micrographs (Aldroubi et al., 1992), and were interpreted as exhibiting dynamic properties of PDC related to its function. A first reconstruction was calculated from a small set via the common of particles to a resolution of 25 A lines approach. The particles were then classified by size and finally reconstructions were calculated for five size
Fig. 6. Relatedness between the 17 different maturation states determined for the HSV-1 capsid. Relatedness is expressed in terms of the resolution of pairwise comparisons according to the differential phase residual (DPR) criterion. This measure reveals a sharp distinction between procapsid-like and mature capsid-like maps. Scale: Resolution based on the 45° cutoff of the DPR curve.
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of the particle, Dp is its diameter, and DHSV is that of the However, this number (21) was HSV-1 capsid (1250 A). never deemed fixed. Relationships between classes were assessed by pairwise comparisons, allowing for combining two classes when their maps were clearly much more closely related than other pairs. In the end, 17 maps were obtained. We have compared them pairwise in Fig. 6 according to the differential phase residual criterion which illustrates the property that the first 7–8 are essentially procapsid-like and the final 7–8 are mature capsid-like. In the absence of a more rigorous criterion that they are all independent, the strongest argument in favor of this conclusion is that they could be interpreted in a self-consistent manner as sequential movements of the capsid building blocks (Heymann et al., 2003). 5.3. Starting models for multiple particle analysis A general problem to be confronted in analyses of this kind is how to define the reference maps to be used in the initial stages of MPA by projection-matching. Subsequently, it is expected that the data will take over and home in on a final set of models that is maximally consistent—by some quantitative criterion—with the full data set. In the two procapsid maturation studies, rather different strategies were followed, both of which have advantages. The HK97 analysis (Lata et al., 2000) made the initial assumption that at each time-point the population was homogeneous, apart from the visually evident distinction between spherical thin-walled EI-III and the 10% smaller thicker-walled EI-I- and EI-II-like particles. This assumption was then relaxed by allowing each particle to move up or down by one time-point/ class at each iteration. Eventually, a conservative decision was made—largely by visual criteria—as to the number of distinct classes—taken to be two, EI-I and EIII. If, in another system, fewer time-points were taken and more models needed, they could be generated by say, averaging maps N and N þ 1 to obtain another proto-intermediate. In the HSV-1 system, end-point maps were again available and were used in linear combinations to generate a set of proto-intermediates. Alternatively and perhaps better, stepwise morphing could have been used for this purpose. The number of classes detected at the end of this analysis was considerably larger—17 as compared with 5 for HK97; but conversely, the number of major transitions is larger for HK97 than HSV-1— three (Prohead II to EI-I; EI-II to EI-III; and EI-III to Head II) as compared to one (the big switch between states 8 and 9). However, there is an explanation for the proliferation of microstates in the HSV-1 system. This capsid has a larger triangulation number and hence a larger number of quasi-equivalent variants of each interaction. Thus, the incremental changes among the
procapsid-like states and the mature capsid-like states represent, to a large extent, the staggering of the same local switching events between different quasi-equivalent sites (Heymann et al., 2003). In the absence of end-states, how does one define appropriately diverse starting models? One plan would be first to define a single majority-species model by SPA that accounts for a certain percentage of the data according to some threshold on correlation coefficients. The data rejected by this criterion may then be analyzed for a second majority-species model, and so on. An alternative approach would be to perform classification and class-averaging of cryo-tomograms (Nitsch et al., 1998). With tomograms, the problem of orientation-dependent variations in projections does not arise. However, because each tomogram stems from only one particle, the noise-levels are relatively high and averaging is desirable. Despite the risks that the classification may be biased by clustering particles whose resolution anisotropy is in the same orientation relative to the particle; and individual tomograms may not convey enough detail to be effective in discriminating subtle differences when applied to high resolution zero-tilt projection data, this appears to be a very promising approach. 5.4. Prospects: the art of the possible From the foregoing appraisal, it emerges that the application of cryo-EM for time-resolved studies by MPA is limited to transitions that are naturally slow (s 1 ms) or may be slowed down, are large in scale, and take place in large complexes (>250 kDa and preferably >1 MDa). Although conformational changes appear widespread in many contexts such as mechanoenzymes; macromolecular assembly and activation; virus maturation, etc., it remains to be seen how many are amenable to this approach. On the other hand, there has not previously been an experimental approach that is applicable to slow transitions of large complexes and they may be quite common. Despite the intimidatingly large data sets that such studies will require, particularly for particles of lower symmetry, the ongoing progress in cryo-EM data acquisition and image processing resources offers a strong incentive to explore this approach further.
Acknowledgments We thank Benes Trus, Ramani Lata, and Jack Johnson for insightful discussions of time-resolved imaging; Naiqian Cheng for superb cryo-microscopy; and William Newcomb and Jay Brown (HSV) and Robert Duda and Roger Hendrix (HK97) for providing excellent preparations of purified capsids.
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References Alberts, B., 1998. The cell as a collection of protein machines: preparing the next generation of molecular biologists. Cell 92, 291–294. Aldroubi, A., Trus, B.L., Unser, M., Booy, F.P., Steven, A.C., 1992. Magnification mismatches between micrographs: corrective procedures and implications for structural analysis. Ultramicroscopy 46, 175–188. Baker, T.S., Cheng, R.H., 1996. A model-based approach for determining orientations of biological macromolecules imaged by cryoelectron microscopy. J. Struct. Biol. 116, 120–130. Baumeister, W., Steven, A.C., 2000. Macromolecular electron microscopy in the era of structural genomics. Trends Biochem. Sci. 25, 624–631. Berriman, J., Unwin, N., 1994. Analysis of transient structures by cryo-microscopy combined with rapid mixing of spray droplets. Ultramicroscopy 56, 241–252. Cerritelli, M.E., Conway, J.F., Cheng, N., Trus, B.L., Steven, A.C., 2003. Molecular mechanisms in bacteriophage T7 procapsid assembly, maturation, and DNA containment. Adv. Protein Chem. 64, 301–323. Conway, J.F., Duda, R.L., Cheng, N., Hendrix, R.W., Steven, A.C., 1995. Proteolytic and conformational control of virus capsid maturation: the bacteriophage HK97 system. J. Mol. Biol. 253, . Duda, R.L., Hempel, J., Michel, H., Shabanowitz, J., Hunt, D., Hendrix, R.W., 1995. Structural transitions during bacteriophage HK97 head assembly. J. Mol. Biol. 247, 618–635. Frank, J., 2002. Single-particle imaging of macromolecules by cryoelectron microscopy. Annu. Rev. Biophys. Biomol. Struct. 31, 303– 319. Frank, J., Wagenknecht, T., McEwen, B.F., Marko, M., Hsieh, C.E., Mannella, C.A., 2002. Three-dimensional imaging of biological complexity. J. Struct. Biol. 138, 85–91. Hendrix, R.W., Duda, R.L., 1998. Bacteriophage HK97 head assembly: a protein ballet. Adv. Virus Res. 50, 235–288. Heymann, J.B., Cheng, N., Newcomb, W.W., Trus, B.L., Brown, J.C., Steven, A.C., 2003. Dynamics of herpes simplex virus capsid maturation visualized by time-lapse cryo-electron microscopy. Nat. Struct. Biol. 10, 334–341. Homa, F.L., Brown, J.C., 1997. Capsid assembly and DNA packaging in herpes simplex virus. Rev. Med. Virol. 7, 107–122. Jontes, J.D., Wilson-Kubalek, E.M., Milligan, R.A., 1995. A 32 degree tail swing in brush border myosin I on ADP release. Nature 378, 751– 753. Kasas, S., Dumas, G., Dietler, G., Catsicas, S., Adrian, M., 2003. Vitrification of cryoelectron microscopy specimens revealed by high-speed photographic imaging. J. Microsc. (Oxford) 211, 48–53. Lata, R., Conway, J.F., Cheng, N., Duda, R.L., Hendrix, R.W., Wikoff, W.R., Johnson, J.E., Tsuruta, H., Steven, A.C., 2000. Maturation dynamics of a viral capsid: visualization of transitional intermediate states. Cell 100, 253–263. Newcomb, W.W., Homa, F.L., Thomsen, D.R., Booy, F.P., Trus, B.L., Steven, A.C., Spencer, J.V., Brown, J.C., 1996. Assembly of the
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herpes simplex virus capsid: characterization of intermediates observed during cell-free capsid formation. J. Mol. Biol. 263, 432– 446. Newcomb, W.W., Homa, F.L., Thomsen, D.R., Trus, B.L., Cheng, N., Steven, A., Booy, F., Brown, J.C., 1999. Assembly of the herpes simplex virus procapsid from purified components and identification of small complexes containing the major capsid and scaffolding proteins. J. Virol. 73, 4239–4250. Newcomb, W.W., Juhas, R.M., Thomsen, D.R., Homa, F.L., Burch, A.D., Weller, S.K., Brown, J.C., 2001. The UL6 gene product forms the portal for entry of DNA into the herpes simplex virus capsid. J. Virol. 75, 10923–10932. Nitsch, M., Walz, J., Typke, D., Klumpp, M., Essen, L.O., Baumeister, W., 1998. Group II chaperonin in an open conformation examined by electron tomography. Nat. Struct. Biol. 5, 855–857. Preston, V.G., Coates, J.A., Rixon, F.J., 1983. Identification and characterization of a herpes simplex virus gene product required for encapsidation of virus DNA. J. Virol. 45, 1056–1064. Ruprecht, J., Nield, J., 2001. Determining the structure of biological macromolecules by transmission electron microscopy, single particle analysis and 3D reconstruction. Prog. Biophys. Mol. Biol. 75, 121–164. Sali, A., Glaeser, R., Earnest, T., Baumeister, W., 2003. From words to literature in structural proteomics. Nature 422, 216–225. Steven, A.C., Carrascosa, J.L., 1979. Proteolytic cleavage and structural transformation: their relationship in bacteriophage T4 capsid maturation. J. Supramol. Struct. 10, 1–11. Steven, A.C., Spear, P.G., 1997. Herpesvirus capsid assembly and envelopment. In: Chiu, W., Burnett, R.M., Garcea, R.L. (Eds.), Structural Biology of Viruses. Oxford University Press, New York, pp. 312–351. Subramaniam, S., Henderson, R., 1999. Electron crystallography of bacteriorhodopsin with millisecond time resolution. J. Struct. Biol. 128, 19–25. Trus, B.L., Booy, F.P., Newcomb, W.W., Brown, J.C., Homa, F.L., Thomsen, D.R., Steven, A.C., 1996. The herpes simplex virus procapsid: structure, conformational changes upon maturation, and roles of the triplex proteins VP19c and VP23 in assembly. J. Mol. Biol. 263, 447–462. White, H.D., Thirumurugan, K., Walker, M.L., Trinick, J., 2003. A second generation apparatus for time-resolved electron cryomicroscopy using stepper motors and electrospray. J. Struct. Biol. 144, 246–252. Wikoff, W.R., Liljas, L., Duda, R.L., Tsuruta, H., Hendrix, R.W., Johnson, J.E., 2000. Topologically linked protein rings in the bacteriophage HK97 capsid. Science 289, 2129–2133. Zhou, Z.H., Liao, W., Cheng, R.H., Lawson, J.E., McCarthy, D.B., Reed, L.J., Stoops, J.K., 2001. Direct evidence for the size and conformational variability of the pyruvate dehydrogenase complex revealed by three-dimensional electron microscopy. The ‘‘breathing’’ core and its functional relationship to protein dynamics. J. Biol. Chem. 276, 21704–21713.
Structural Biology Journal of Structural Biology 147 (2004) 291–301 www.elsevier.com/locate/yjsbi
Molecular dynamics of protein complexes from four-dimensional cryo-electron microscopy J. Bernard Heymann,a,1 James F. Conway,b and Alasdair C. Stevena,* a
Laboratory of Structural Biology, National Institute of Arthritis, Musculoskeletal and Skin Diseases, National Institutes of Health, Bethesda, MD 20892, USA b Institut de Biologie Structurale J.-P. Ebel, 38027 Grenoble, France Received 22 December 2003, and in revised form 4 February 2004 Available online 14 March 2004
Abstract Cryo-electron microscopy of single particles offers a unique opportunity to detect and quantify conformational variation of protein complexes. Different conformers may, in principle, be distinguished by classification of individual projections in which image differences arising from viewing geometry are disentangled from variability in the underlying structures by ‘‘multiple particle analysis’’—MPA. If the various conformers represent dynamically related states of the same complex, MPA has the potential to visualize transition states, and eventually to yield movies of the dynamic process. Ordering the various conformers into a time series is facilitated if cryo-EM data are taken at successive times from a system that is known to be developing in time. Virus maturation represents a relatively tractable dynamic process because the changes are large and irreversible and the rate of the natural process may be conveniently slowed in vitro by adjusting the environmental conditions. We describe the strategy employed in a recent analysis of herpes simplex virus procapsid maturation (Nat. Struct. Biol. 10 (2003) 334–341), compare it with previous work on the maturation of bacteriophage HK97 procapsid, and discuss various factors that impinge on the feasibility of performing similar experimental analyses of molecular dynamics in the general case. Published by Elsevier Inc. Keywords: Conformational change; Molecular movie; Molecular dynamics; Image classification; Single particle analysis; Multiple particle analysis
1. Introduction It is now increasingly appreciated that most fundamental biological processes are carried out by large macromolecular assemblies (or ÔmachinesÕ) (Alberts, 1998; Sali et al., 2003), and that these assemblies are often dynamic systems that follow elaborate duty cycles while undergoing large structural changes. Cryo-electron microscopy in combination with single particle analysis (SPA) has emerged as a powerful approach for visualizing assemblies in three dimensions (Baumeister and Steven, 2000; Frank, 2002; Frank et al., 2002; Ruprecht and Nield, 2001). This approach has pro* Corresponding author: Fax: 1-301-480-7629. E-mail address: [email protected] (A.C. Steven). 1 Present address: Division of Biology, California Institute of Technology, 1200 East California Blvd., Pasadena, CA 91125, USA.
1047-8477/$ - see front matter. Published by Elsevier Inc. doi:10.1016/j.jsb.2004.02.006
gressively improved in resolution—now better than 10 A in a growing number of cases; is relatively parsimonious in terms of the amounts of material required; and has the advantage of depicting the solution structure of the specimen, unconstrained by crystal contacts. The basic principle underlying SPA is that each member of a large set of two-dimensional cryo-EM images represents a projection of the same three-dimensional object, and after identifying as precisely as possible the viewing geometry of each projection, these data are used to reconstruct its three-dimensional structure. Although cryo-EM has been used to characterize a substantial number of conformational changes in the sense of comparing ÔbeforeÕ and ÔafterÕ states (e.g. Jontes et al., 1995), it has for the most part remained a static visualization technique. It does, however, have the potential to capture functional intermediates or transition states according to the following scenario. If in vitro
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conditions are established so that multiple conformational states are present at the same time, the various conformers may be distinguished by diversifying the projection-matching scheme used for classification to include multiple three-dimensional models, and calculating a density map for each conformer. If data are collected at successive time-points for an evolving reaction, the waxing and waning of each conformer in the sampled populations may be used to order the conformers into a time series and to perform a kinetic analysis of the reaction pathway. Such data resulting from ‘‘multiple particle analysis’’ (MPA) may also be synthesized into three-dimensional movies of the dynamic process. In this paper, we first consider several general aspects of this approach; then review the classification procedures that have been used in two dynamic studies of virus capsid maturation (Heymann et al., 2003; Lata et al., 2000); and finish by discussing certain practical aspects of the analysis and its prospects for wider applicability.
2. General considerations 2.1. Accessible timescales The rapidity of cryo-fixation when a particulate suspension is quenched places a limit on those processes whose dynamics are amenable to this approach. The time required for cryo-fixation is of the order of a millisecond and since it is limited by the rate of heat transfer through a thin film or droplet of buffer, the prospects of shortening it appreciably are scant. Several ingenious experimental set-ups have been devised for initiating a reaction and then obtaining a cryo-fixed EM sample a few milliseconds later (e.g. Berriman and Unwin, 1994; Subramaniam and Henderson, 1999; White et al., 2003). However, these designs have tended to focus on capturing short-lived states, and problems potentially arise in the context of synchronization, i.e., (i) particles near the leading edge of a plunge-frozen grid will be immobilized by cryo-fixation slightly earlier than those at the trailing edge (Kasas et al., 2003), and a similar inequity applies to particles that are, respectively, near the surface or in the middle of the thin film of buffer, and (ii) even if a dynamic process is initiated at a given instant, the particles may not remain in synchrony but may diverge stochastically. Thus, processes that occur in one to a few milliseconds appear to be the fastest that can be directly tackled by time-resolved cryo-EM. An alternative approach is to slow the reaction down so that it unfolds over a much longer timescale. This is the only approach feasible for processes whose natural timescale is faster than a millisecond or so, and is also advantageous for processes in the millisecond range
because the prospects of capturing reaction intermediates are enhanced. Moreover, there is the practical advantage that if the reaction can be slowed down to occur over minutes to hours, it may be conveniently sampled by conventional cryo-EM grid preparation procedures. Slowing the reaction kinetics may be attempted either (as below) by adjusting the environmental parameters— ionic strength, temperature, etc.,—or by identifying and exploiting appropriate mutants, or by partially poisoning the reaction with chemical inhibitors. 2.2. Size of movements The main idea underlying this approach is that image classification procedures may be used to distinguish differences among a set of projections that arise from temporal changes in a given structure from those that reflect variations in viewing geometry. In this context, it is essential that the transitions of interest should involve changes that are large enough for such a separation to be feasible for images with the high noise levels typical of cryo-electron micrographs. Thus, the first step is to determine how many distinct structures are present in the complete data set and to calculate density maps for them. The second step is to order these maps into a temporal sequence. Here a further complication arises from the possibility of static structural heterogeneity. Such heterogeneity may arise from the presence of contaminants of roughly the same size; or damaged particles (e.g., complexes that have suffered proteolytic degradation or which have lost subunits); or intrinsic polymorphism. Heterogeneity from these sources may undermine achieving a coherent classification, i.e., the assumption that all the conformers visualized represent different dynamic states of the same complex. 2.3. Number of states and resolution For practical purposes, a further requirement is that the number of distinct states should be relatively small. The resolution to be achieved in a three-dimensional density map depends, among other factors, on the number of particles included. If N states are present and all are equally populated, for a given resolution to be achieved, the data set has to be at least N-fold larger than is needed for the same resolution with a single conformer. The expectation that all states be equally populated is an optimistic one and it seems more likely that states will, in general, be of different durations and thus have different occupancies in the population at large. For instance, a system undergoing simple harmonic motion in one dimension spends more time near the end-points of its cycle than near the mid-point. In consequence, the two end-points would be well (and equally) represented in a random sampling whereas positions at or near the mid-point would be relatively
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rare. In practice, the number of states is not known in advance but must be ascertained from the classification analysis. 2.4. Classification strategy An evolving system displays heterogeneity depending on the degree of synchronization and the nature of the transitions. With adequate synchronization and a relatively simple sequence of events, the data at each timepoint may be taken as approximately homogeneous, making it possible to reconstruct distinct states. Conversely, if synchronization is not well observed or the system is inherently complex, many states may coexist at any given time-point. A prudent approach is then to disregard the fact that the particle images come from different time-points, and to derive as many states as the data support. The resulting time distribution of particle images in each class—associated with a state— represents the temporal manifestation of that state in the sample. To estimate the mean lifetime of individual particles in that state, these data must be subjected to kinetic analysis.
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If the protease is absent or inactivated by mutation, procapsids accumulate and may be isolated from infected cells, although these particles are exceedingly labile (Newcomb et al., 1996). Alternatively, in vitro assembly of precursor proteins yields procapsids (Newcomb et al., 1999). In either event, with isolated procapsids maintained at moderate ionic strength and room temperature, spontaneous maturation takes place over a period of several days. This property allows convenient sampling of the preparation by conventional cryo-EM procedures. 3.2. Time-sampled cryo-EM data In one such experiment, cryo-micrographs were recorded at four time-points corresponding to 0, 24, 48, and 96 h, respectively (Heymann et al., 2003). The 0-h time-point represented the earliest time at which procapsid isolation could be completed. This was 12 h after HeLa cells were infected with the tsProt.A mutant which carries a temperature-sensitive mutation in the protease and 4 h after the infected cells were harvested. After digitization and particle picking, the data set consisted of 5000 particles from focal pair micrographs with similar numbers from each time-point.
3. Herpes simplex virus 1 procapsid maturation 3.3. MPA classification 3.1. Background The earliest HSV-1 precursor is a procapsid consisting of a spherical surface shell overlaid on a core or inner shell of scaffolding proteins, about 10% of which contain the maturational protease (VP4, 24 kDa) as a Nterminal extension (Homa and Brown, 1997; Steven and Spear, 1997). The surface shell is composed of 960 copies of the major capsid protein (VP5, 150 kDa) arranged as 150 hexamers and 12 pentamers, coordinated by 320 heterotrimers called triplexes. Each triplex has one copy of the triplex-a protein (VP19c, 50 kDa) and two copies of the triplex-b protein (VP23, 35 kDa). If the portal protein UL6 (75 kDa) is present, a single ring of UL6 subunits replaces one of the VP5 pentamers (Newcomb et al., 2001). The trigger for maturation is activation of the protease, which then cleaves the scaffolding protein near the site where it interacts with the surface shell. This event appears to prime the surface shell to undergo a spontaneous cooperative conformational change (maturation). The exact timescale on which maturation takes place in vivo is not known but it appears to be fairly rapid since procapsids are not seen in thin sections of infected cells unless the protease is inactivated (Preston et al., 1983): moreover, maturation is probably accelerated by DNA packaging, as in bacteriophages. Concomitant with surface lattice maturation, the cleaved scaffolding proteins are expelled but the protease is retained inside the capsid.
At the outset, representations of the initial and final states were available. Our strategy was to use linear combinations of these density maps2 to define a first set of references that were then used to sift out images of potential intermediates according to the scheme given in Fig. 1A. The data were sorted by correlation-based projection-matching with multiple references. After a first round of classification, a second set of references was calculated, and this process was iterated to convergence. At each iteration, classes with too few particles to produce an adequately defined density map were eliminated and their particles reassigned. Outliers—i.e., particles whose correlation coefficients with any model did not exceed a given threshold—were eliminated: this corresponded to about 35% of the total data. Finally, a set of 17 density maps were obtained (Fig. 2; Table 1). This strategy involves certain assumptions that were adopted for pragmatic reasons. In the first place, it assumes that the end-states represent the extreme structural differences exhibited by the maturing capsid and that intermediates are intermediate not only on the temporal pathway but also in terms of physical resemblance (expressed in terms of correlation coefficients). In fact, it is not ruled out a priori that there may be intermediates that are distinctly different from either 2 The term ‘‘density map’’ refers to the three-dimensional matrix of density values produced in a reconstruction.
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Second, it was assumed that maturing particles continue to observe icosahedral symmetry for most of the time, i.e., the maturation pathway consists of a succession of rapid transitions between relatively long-lived intermediates that are themselves icosahedrally symmetric. That this assumption is not necessarily valid is suggested by observations on maturing bacteriophage T4 giant capsids of a wave-like propagation of the transition front over their surface lattice (Steven and Carrascosa, 1979). If the assumption of icosahedral symmetry were to be significantly in error, correlation coefficients would be lower than expected, as would the resolution of reconstructions. Table 1 illustrates that the long-lived states at the extremes (maps 1–4 and 14–17) show higher resolutions than the shorter-lived intermediates. The lower numbers of numbers of particles obtained for the short-lived states contribute to the lower resolutions of these maps. The rejected low-scoring images may be in non-icosahedral transition states, or permanently damaged or distorted. However, the fact that the resolutions achieved were similar to those obtained with comparable numbers of homogeneous particles (data not shown) suggests that the transitions are strongly cooperative, i.e., maturation consists of a succession of rapid subtransitions through relatively longlived intermediate states. In such a state, the particle observes icosahedral symmetry to a good approximation, while in a subtransition it may depart from this symmetry (Heymann et al., 2003). For capsid maturation studies, the assumption of icosahedral symmetry may be more appropriate for portal-lacking mutants, as observations in the T4 (Steven and Carrascosa, 1979) and T7 (Cerritelli et al., 2003) systems suggest that the structural transformation may initiate in the portal vertex. 3.4. Comparing density maps
Fig. 1. Classification strategies for (A) maturing HSV-1 capsids and (B) maturing HK97 capsids.
end-state, and such intermediates may not be captured in such an analysis. Nevertheless, the nature of the competitive classification used here emphasizes differences between particles and should provide a reasonable representation of specimen heterogeneity. The main requirement is that the particles must resemble the reference maps to some extent. In support of this notion, acceptable orientations for procapsid particles were found using the mature capsid as reference (data not shown). If there were grossly different major states, they would probably be detected early in the analysis, e.g., during particle-picking.
An important requirement in MPA is for distance measures between density maps. These measures are needed for several purposes: to assess whether two maps are sufficiently similar to represent the same structure; conversely whether they represent significantly different states; and to assess relative proximity among multiple states. While recognizing that there is scope for further work to define more discriminating distance measures and to take into account the effects of noise, we have used a Euclidean distance-like measure, based on crystallographic R-factors, but defined in real-space as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P u 2 ðpi pj Þ u Ri;j ¼ tqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2; P 2P ðpi hpi iÞ ðpj pj Þ where the sums are over all voxels in a pair of maps (pi , pj ).
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Fig. 2. Procapsid and mature HSV-1 capsid maps (from Heymann et al., 2003). The main differences are angularization of the capsid and formation outward shift of the pentons (darker blue), and molecular rotations affecting hexon subunits. Blue: of the continuous floor, resulting from a 20 A VP5; Green: Triplex.
A small distance between two maps denotes close resemblance between them. If, in the present context, we equate closeness with temporal proximity, such measures may be used to order a set of maps (in our case, 17) sequentially. For this purpose, we converted the R-factor-based measure as follows: Di;j ¼ lnð1 Ri;j Þ:
The latter measure, Di;j , was found to be almost additive such that the distance between two maps was approximately equal to the sum of the distances between all intervening maps. An exhaustive permutation algorithm was implemented to find the order of maps that minimized the difference between the measure distances and the sums of distances of intervening adjacent maps:
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Table 1 Final set of HSV-1 capsid density maps Map (n)
Particles
Average CCa
b Resolution (A)
Time constant (h)c (transition n
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
521 252 183 153 81 81 83 79 76 71 68 62 57 152 194 283 636
0.275 0.273 0.275 0.263 0.259 0.258 0.258 0.255 0.259 0.263 0.268 0.272 0.276 0.280 0.314 0.318 0.323
23 24 24 25 25 25 26 27 26 26 25 25 24 24 23 22 21
16.9 7.8 6.7 6.0 3.0 2.9 2.8 2.6 2.4 2.3 2.3 2.1 2.0 6.2 9.4 17.9
n þ 1)
The resolution achieved reflects both the number of particles and quality as given by the average correlation coefficient. The first order time constants derived from the particle distributions at each time-point are inversely related to the numbers of particles in each map. a Average correlation coefficient for particles used in the reconstruction. b Fourier shell correlation, 0.5 cutoff. c First order time constant.
" min
X i;j
Di;j
j1 X
!# Dk;kþ1
:
k¼i
Once this order was determined, we found it useful to reduce the noise level in each map (thus rendering them more uniform in quality) for the next cycle of classification by adding fractions of the preceding and succeeding maps to each with weights (0.5, 1.0, and 0.5). No such averaging was performed after the last round of classification.
same views) of the procapsid and the mature capsid by the same measure and obtained an average value of 0.599 0.037. These data imply that the differences between maps, although less pronounced than differences in viewing geometry, are quite strongly expressed. Because the orientation selection is stronger than the conformational discrimination, it is unlikely that a wrong view assignment would be confused with a different conformation of the HSV-1 capsid. 3.6. Classification
3.5. Differences among projections: viewing geometry versus intrinsic conformational variability Time-resolved processing of 2D images requires a distinction between assigning particle images to particular orientations (i.e., viewing geometry), and classifying them with respect to different reference maps (i.e., intrinsic variability). In order to make an overall assessment of this distinction, we performed the following experiment. For a given density map, a set of projections covering the asymmetric unit was generated and pairwise correlation coefficients calculated between them, excluding self-comparisons which have a correlation coefficient of unity. The coefficient used was an average of the three calculated in the PFT program (Baker and Cheng, 1996). For the procapsid (map 1), we obtained a value of 0.413 0.056 (SD) and for the mature capsid (map 17), 0.399 0.060. These figures, typical of the correlation coefficients between projections from different views, afford a baseline for incorrect comparisons. Next we compared corresponding projections (i.e., the
At the outset, we assumed that the number of distinct states would be manageably small. Otherwise, there would be insufficient particles in each class to produce resolution range, well-defined density maps in the 20 A for which we estimate that 100–200 particles are needed for a capsid of this size. Based on these considerations, we chose to start with 21 models. The number of particles eventually assigned to a given structural state would reflect its longevity. To maximize the discriminatory power of the projection-matching protocol, we considered which spatial frequencies should be emphasized. For instance, the strong low-frequency components of the images would be essentially the same for each image; on the other hand, the highest frequencies are very noisy and therefore error-prone for classification purposes. To determine an appropriate frequency band, we calculated a Fourier shell correlation between the procapsid and mature capsid maps (Fig. 3). It shows low correlations (and hence marked differences) in the frequency range of
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yielding time constants indicative of the life-times of transition states (Table 1). It is noteworthy that that starting procapsid preparation was not homogeneous (t ¼ 0; Fig. 5), suggesting that conformational heterogeneity has been a limiting factor on the resolution of procapsid reconstructions to date (Newcomb et al., 1999; Trus et al., 1996). The numbers of particles in states 8–10, when the major transition is taking place, are never high, indicating that this switch is relatively fast and consequently is relatively poorly perceived.
Fig. 3. Resolution dependence of the consistency between density maps of the HSV-1 procapsid and the mature capsid. Consistency was assessed by the FSC (solid line) and DPR (dotted line) measures. The range in which there is relatively strong signal and in which the two was used for classification. states differ most (25–60 A)
1 to (60 A) 1 . Accordingly, this range was used (25 A) throughout the classification process. To illustrate the discrimination occurring in classification of the original data, we compare in Fig. 4A two particles with the corresponding reprojections of 7 of the 17 density maps. The particle in the top row is viewed close to a twofold axis, and its Euler angles were consistently determined by all 7 models (see Fig. 4 legend): however, the correlation coefficients reveal the marked distinction between procapsid-like states (maps 1 and 7) and mature capsid-like states (maps 9, 10, 11, and 17), with the major switch occurring between maps 7 and 8 (Heymann et al., 2003). The capsid in the second row is a relatively mature particle viewed close to a fivefold axis. Accordingly it appears round in projection even though the particle is quite polyhedral. In this case, the procapsidlike maps (1, 7, and 8) with correlation coefficients of 0.2 consistently misidentify the projection whereas the mature capsid-like maps (9, 10, 11, and 17) with correlation coefficients of 0.35 assign the same (correct) Euler angles. According to relatively small margins in the correlation coefficient, this particle was assigned to class 11. 3.7. Ordering into a time series Although the starting references followed a logical order in relation to the initial and final states, there was no guarantee that the 17 distinct maps finally realized would be time-ordered. We explored this aspect in two ways. First we ordered them according to a ‘‘minimum difference between successive states’’ criterion (see Section 3.5). However, a more conclusive ordering was obtained by studying the kinetics of the time series, i.e., the percentage of particles assigned to each class at each time-point were tabulated, and their kinetics (Fig. 5) confirmed the inferred ordering. This process was then modeled as a succession of first order kinetic transitions,
4. Bacteriophage HK97 capsid maturation 4.1. Background Prohead I, the HK97 procapsid, has a T ¼ 7 icosahedral shell of 60 hexamers and 11 pentamers of a single 42 kDa protein with the portal protein, ring at the twelfth vertex. It also contains 50 copies of the maturational protease (Hendrix and Duda, 1998). Neither the protease nor the portal is required to produce correctly formed particles, but these proteins are needed for maturation and DNA packaging to ensue. Prohead I is converted to Prohead II by excision of the amino-terminal 11 kDa of the capsid protein. Prohead II is metastable and may be transformed to the larger, thin-walled, flat-faceted Head. In vivo, this transition is promoted by DNA packaging: in vitro it may be triggered by any of several chemical stimuli (Conway et al., 1995; Duda et al., 1995). In Head II, stabilizing covalent cross-links are formed between neighboring subunits (Wikoff et al., 2000). 4.2. Time-sampled cryo-EM data Acidic conditions promote maturation of Prohead II and slight variations in pH around the value of 4 strongly influence the rate at which this reaction proceeds (Lata et al., 2000). A preparation of purified portal-less Prohead II was set to pH 4.18 and sampled for cryo-EM thirteen times at unequal intervals over the following 20 h. From visual inspection of the micrographs, it was apparent that Prohead II rapidly increased in size by about 50% of its final expansion and then converted more slowly to a spherical thin-walled state. Upon reversion to neutral pH, the latter particle rapidly converted to the polyhedral Head II morphology. 4.3. MPA classification Since the primary feature of HK97 maturation is the large size change (ÔexpansionÕ) and it was apparent that early intermediates were 10% bigger than Prohead II, size was used as the initial arbiter and a set of reference models was generated as versions of Prohead II enlarged
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Fig. 4. Projection matching of two images of (A) maturing HSV-1 capsids with 7 of the 17 models, and (B and C) maturing HK97 capsids with the 5 models. The top particle is viewed near a 2-fold axis and the bottom particle near a 5-fold axis, in each case. The corresponding correlation coefficients are given. For the HSV-1 capsid, the orientations for the 2-fold view particle were consistent for all maps (h : 89:0 89:5, / : 3:0 0:0, x : 158:6 158:9). The orientations for the 5-fold view particle showed a distinction between procapsid-like maps (maps 1–8: h, 81.0; /, 9.6; and x; 253:5 253:8) and mature capsid-like maps (maps 9–17: h, 89.0; /, 25.5; and x, 139.6).
by increments of 2% (Fig. 1B). Additional reference maps were taken as similar variants of a reconstruction calculated from all data at the 37 min time-point. Then each particle image was matched with reprojections from all maps to assign its orientation and size class. Reconstructions were calculated from each size class at each time. Similar maps from different time-points were combined to produce a new set of references and this process was iterated several times. Finally a conservative decision was made as to the number of distinct intermediates. Two, of the same size and with relatively subtle differences between them, were called Expansion Intermediates I and II. A third transition state, EI-III, was the end product at low pH. This particle is fully
expanded but spherical rather than polyhedral in shape. Finally, the five density maps—Prohead II, Head II, and the three Expansion Intermediates were used to produce movies by morphing (Lata et al., 2000). In retrospect, classification was facilitated by the apparent maintenance of icosahedral symmetry by the maturing capsids and the relatively large differences between all states except EI-I and EI-II (Fig. 4B). There may in fact be other similar states that a more exhaustive classification with higher resolution reference maps would distinguish. Of note and (these were at 25 A) some surprise in view of the convoluted surfaces of the starting models was the successful determination of a structure for the thin-walled, smooth-surfaced, and
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classes corresponding to relative scale factors of 0.90, 0.95, 1.0, 1.05, and 1.10. The variations were attributed to expansion and contraction of a flexible, Ôspring-likeÕ peptide that connects adjacent trimers in this particle. The size distribution was Gaussian-like indicating that, whatever the dynamics of this particle are, they do not represent simple harmonic pulsation in which case the largest and smallest particles would predominate. The comparable quality of the differently sized reconstructions was inferred to indicate cooperative dodecahedral motions. 5.2. Numbers of states and numbers of particles
Fig. 5. HSV-1 particle distributions as determined (A) in the initial classification, (B) after several iterations of classification and for the final 17 maps. The distributions show a preponderance of initial procapsid-like forms and forms close to the mature capsid, while the intermediate, short-lived forms are poorly represented.
spherical EI-III. The skew T ¼ 7 lattice of the HK97 capsid was probably a major factor for this result.
5. Discussion
Resolution in time (the number of states) and spatial resolution are inter-dependent and both parameters are limited by the amount of data available. Given higher spatial resolution in the reference maps, more subtle differences may be detected between states and consequently, better time resolution obtained. Given better time resolution, the models should identify classes of particles that are more internally consistent and hence yield higher resolution density maps. However, in practice, given a fixed amount of data, the question arises of how to choose an optimal number of states as a starting point for MPA. In the HSV-1 case, the initial choice of 21 reference maps was based on the maximum number of recon range at, structions that could be expected in the 20 A say, 150–200 particles per reconstruction, allowing for a certain fraction of non-classifiable rejects. For particles of lower symmetry, the number per particle would be correspondingly higher by a factor of approximately (60.Dp )/(Np .DHSV ), where Np is the order of symmetry
5.1. Equilibrium and non-equilibrium systems In a non-equilibrium situation, as in time-course experiments with an evolving system, each time-point samples a different distribution of states. For a dynamic system in equilibrium, on the other hand, the distribution of states remains constant over time. Dynamics of the latter kind were observed for the pyruvate dehydrogenase complex (PDC) of Saccharomyces cerevisiae on the basis of large size variations, ranging between +/ ) 10%, detected by cryo-EM (Zhou et al., 2001). PDC has an dodecahedral core of 60 E2 (dihydrolipoamide acetyltransferase) subunits. The observed size variations were well beyond the 1–2% range of magnification variations across or between micrographs (Aldroubi et al., 1992), and were interpreted as exhibiting dynamic properties of PDC related to its function. A first reconstruction was calculated from a small set via the common of particles to a resolution of 25 A lines approach. The particles were then classified by size and finally reconstructions were calculated for five size
Fig. 6. Relatedness between the 17 different maturation states determined for the HSV-1 capsid. Relatedness is expressed in terms of the resolution of pairwise comparisons according to the differential phase residual (DPR) criterion. This measure reveals a sharp distinction between procapsid-like and mature capsid-like maps. Scale: Resolution based on the 45° cutoff of the DPR curve.
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of the particle, Dp is its diameter, and DHSV is that of the However, this number (21) was HSV-1 capsid (1250 A). never deemed fixed. Relationships between classes were assessed by pairwise comparisons, allowing for combining two classes when their maps were clearly much more closely related than other pairs. In the end, 17 maps were obtained. We have compared them pairwise in Fig. 6 according to the differential phase residual criterion which illustrates the property that the first 7–8 are essentially procapsid-like and the final 7–8 are mature capsid-like. In the absence of a more rigorous criterion that they are all independent, the strongest argument in favor of this conclusion is that they could be interpreted in a self-consistent manner as sequential movements of the capsid building blocks (Heymann et al., 2003). 5.3. Starting models for multiple particle analysis A general problem to be confronted in analyses of this kind is how to define the reference maps to be used in the initial stages of MPA by projection-matching. Subsequently, it is expected that the data will take over and home in on a final set of models that is maximally consistent—by some quantitative criterion—with the full data set. In the two procapsid maturation studies, rather different strategies were followed, both of which have advantages. The HK97 analysis (Lata et al., 2000) made the initial assumption that at each time-point the population was homogeneous, apart from the visually evident distinction between spherical thin-walled EI-III and the 10% smaller thicker-walled EI-I- and EI-II-like particles. This assumption was then relaxed by allowing each particle to move up or down by one time-point/ class at each iteration. Eventually, a conservative decision was made—largely by visual criteria—as to the number of distinct classes—taken to be two, EI-I and EIII. If, in another system, fewer time-points were taken and more models needed, they could be generated by say, averaging maps N and N þ 1 to obtain another proto-intermediate. In the HSV-1 system, end-point maps were again available and were used in linear combinations to generate a set of proto-intermediates. Alternatively and perhaps better, stepwise morphing could have been used for this purpose. The number of classes detected at the end of this analysis was considerably larger—17 as compared with 5 for HK97; but conversely, the number of major transitions is larger for HK97 than HSV-1— three (Prohead II to EI-I; EI-II to EI-III; and EI-III to Head II) as compared to one (the big switch between states 8 and 9). However, there is an explanation for the proliferation of microstates in the HSV-1 system. This capsid has a larger triangulation number and hence a larger number of quasi-equivalent variants of each interaction. Thus, the incremental changes among the
procapsid-like states and the mature capsid-like states represent, to a large extent, the staggering of the same local switching events between different quasi-equivalent sites (Heymann et al., 2003). In the absence of end-states, how does one define appropriately diverse starting models? One plan would be first to define a single majority-species model by SPA that accounts for a certain percentage of the data according to some threshold on correlation coefficients. The data rejected by this criterion may then be analyzed for a second majority-species model, and so on. An alternative approach would be to perform classification and class-averaging of cryo-tomograms (Nitsch et al., 1998). With tomograms, the problem of orientation-dependent variations in projections does not arise. However, because each tomogram stems from only one particle, the noise-levels are relatively high and averaging is desirable. Despite the risks that the classification may be biased by clustering particles whose resolution anisotropy is in the same orientation relative to the particle; and individual tomograms may not convey enough detail to be effective in discriminating subtle differences when applied to high resolution zero-tilt projection data, this appears to be a very promising approach. 5.4. Prospects: the art of the possible From the foregoing appraisal, it emerges that the application of cryo-EM for time-resolved studies by MPA is limited to transitions that are naturally slow (s 1 ms) or may be slowed down, are large in scale, and take place in large complexes (>250 kDa and preferably >1 MDa). Although conformational changes appear widespread in many contexts such as mechanoenzymes; macromolecular assembly and activation; virus maturation, etc., it remains to be seen how many are amenable to this approach. On the other hand, there has not previously been an experimental approach that is applicable to slow transitions of large complexes and they may be quite common. Despite the intimidatingly large data sets that such studies will require, particularly for particles of lower symmetry, the ongoing progress in cryo-EM data acquisition and image processing resources offers a strong incentive to explore this approach further.
Acknowledgments We thank Benes Trus, Ramani Lata, and Jack Johnson for insightful discussions of time-resolved imaging; Naiqian Cheng for superb cryo-microscopy; and William Newcomb and Jay Brown (HSV) and Robert Duda and Roger Hendrix (HK97) for providing excellent preparations of purified capsids.
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