The Structural Biology
Programme
European Molecular Biology
Laboratory
Meyerhofstrasse 1
D-69012 Heidelberg, Federal
Republic of Germany
*Structural Studies
Department of
Biological Sciences
Lilly Hall of Life Sciences
Purdue
University
West Lafayette
Indiana 47907,
U.S.A
The advent of cryo-electron microscopy has allowed the imaging of isolated symmetric particles in the absence of stain and under conditions which preserve their symmetry. The image of a field of randomly oriented, symmetric particles can be processed to yield a three dimensional structure by determining the relative positions of the symmetry elements. This approach has been most powerful when applied to icosahedral particles because of their very high symmetry symmetry (point group 532 - 6 five fold axes, 10 three fold axes and 15 two fold axes for a total of 60 symmetry elements). This high symmetry eases the determination of the positions of the symmetry elements in individual images. It also decreases the number of images required to determine a three dimensional structure completely to a given resolution.
Icosahedral reconstruction from cryo-electron micrographs nicely complements X-ray crystallographic structure determinations. Orientation of the high resolution structure of the virus capsid or an isolated protein within the reconstructed density yields an atomic model (Cheng et al., 1995; Cheng et al., 1994; Grimes et al., 1995; Ilag et al., 1995; Olson et al., 1993; Smith et al., 1993; Smith et al., 1993; Stewart et al., 1993) . This approach provides a functional context for the X-ray structures of isolated proteins and allows more precise identification of molecular interactions. Cryo- electron microscopy in combination with image reconstruction also extends X-ray crystallographic studies because it can be applied to dynamic processes (Fuller et al., 1995) and heterogeneous populations (Vnien-Bryan & Fuller, 1994) which would otherwise be inaccessible to structural study.
This discussion focuses on the modifications to the icosahedral reconstruction programs made over the past decade to allow their use for cryo-electron micrographs. We will not repeat the original description of the algorithms (Crowther, 1971) .
The central problem in performing an icosahedral reconstruction is the reliable determination of the orientation of the individual particles. A particle of unknown structure is oriented on the basis of its icosahedral symmetry (Figure 1 - steps 1,2). Once putative orientations are determined for several particles, their transforms can be compared (Figure 1 step 3) and the correct relative hand determined. These orientations are then used to combine the particle transforms to generate a symmetric three- dimensional transform and a symmetrized density (Figure 1 - step 4). This density can then be used as a model to generate more reliable orientations for other particles in the input data (Figure 1 - step 5).
The determination of the orientation of a novel icosahedral particle is based on the symmetry elements. We use a polar coordinate system system to describe the orientations (Figure 1) in which a two fold axis lies along z, the adjacent three folds along the x axis and the adjacent five folds along y. One three-fold view is (Theta=69.09o,Phi=0”) in these coordinates. A third angle, OMEGA, indicates the rotation of the view in the plane of projection. Our standard icosahedral asymmetric unit is the one sixtieth of orientation space shown in Figure 1 which is bounded by two five folds (for example 90o,31.717o and 90”,- 31.717o) and an adjacent three fold (69.09o, 0o). A particle viewed down, for example, the three-fold symmetry axis can be readily identified by the three-fold symmetry of the projection. The same symmetry is seen in the Fourier transform of the projection which is a central section of the three dimensional transform (DeRosier & Klug, 1968) taken normal to the direction of projection.
The common lines arise when the symmetry axis is not along the direction of view. Applying a symmetry operation around this symmetry axis to the Fourier transform of the projection (Figure 2a) gives rise to a second, identical plane which intersects the original plane along a line (Figure 2b). Application of the inverse of this symmetry operation generates a third identical plane which also intersects the original and the second (Figure 2c). These lines of intersection are common to the three symmetry-related planes of the transform and so have identical values. The construction in Figure 2c shows the relative positions of the three planes in space for a three fold axis, and the three common lines. Only two lines of intersection are visible in the transform of the original plane of projection.
Each symmetry operation and its inverse about an axis generates a pair of common lines which lie to either side of the projection of the axis (Figure 3). The existence of a symmetry axis at a particular position can be found by testing for equal values in the transform along the lines which would be generated by that axis. This would be a very weak test, easily satisfied for a single symmetry axis. The power of this approach for icosahedral objects comes from the fact that the high symmetry of the icosahedron gives rise to 37 pairs of common lines: each of the 6 five folds gives rise to two pairs (from 2p/5,-2p/5 and 4p/5,-4p/5), each of the 10 three-folds generates 1 pair (2p/3,-2p/3) and each of the 15 two folds a further pair (p,-p) which lie along the projection of the two-fold symmetry axis. The "pair" of common lines generated by a two fold axis are colinear, and force this line to be centrosymmetric (r (x, y) = r (-x, -y)) or equivalently forces the phases along this line in the transform to be 0 or p.
The existence of common lines is independent of the details of the structure, however, their usefulness in orientation is dependent on the presence of angular variation in the projection. The projections of a smooth object will show little angular variation and so the correct orientation will yield common lines which agree only slightly better with the projection than incorrect orientations. Experience with cryo-electron micrographs indicates that this angular variation can be maximized by selecting particular resolution ranges in the analysis.
The test for agreement between common lines is the calculation of a phase residual between the transform values which lie on the pairs of lines. The simplest form of the orientation search is then the calculation of the sum of the phase residuals between the 37 pairs of common lines in one degree steps for each of the orientations in the asymmetric unit (132480 distinct orientations corresponding to 736 values of Theta and Phi ((69.09”,0”), (70”, -1”),.., (90”, 31), (90”, 31.717”)) times 180 values of OMEGA). The orientation which generates common line positions with the lowest sum of phase residuals is taken as the correct one.
This approach of calculating the simple sum of phase residuals seems reasonable but does not take into account the degeneracy of the common lines. Ths simple approach works most effectively for comparison of putative orientations near the center of the asymmetric unit (such as 80”,11”) which have well spread common lines (Figure 3). It does not work equally well for other orientations. When a view is along (69”,0”) or near to (89”,-1”) a symmetry axis, the common lines are not well separated and a low residual is less significant because it results from fewer independent values of the transform (Figure 3). This degeneracy is particularly serious for cryo-images which have a relatively low signal to noise ratio. A weighting scheme is used to compensate for this degeneracy in the program emicofv. Orientations with the same Theta and Phi but different values of Omega have the same spread of common lines. A reduced chi-squared statistic in which the number of degrees of freedom is the number of independent transform values used in the calculation of the distribution of residuals for a given theta and phi as a function of omega is used to determine the probability of the lowest residual for that Theta and F. This probability is used to weight the residual for comparison between different values of q and Phi (Fuller, 1987) . This chi-squared weighting scheme is far from perfect but it has been sufficient to serve as the first step in the reconstruction of several dozen virus structures.
Common lines are used in two other places in the reconstruction process. One is in the refinement of the phase origin . The calculation of the phase residual described above assumes that the center of the transform lies at the center of symmetry of the particle. Initially this is taken as the center of mass of the projection and determined by cross correlation with a circularly symmetrized average projection. This origin is usually adequate for the first attempt at an orientation search. Once this initial orientation search yields a putative orientation, a refined phase origin can be determined by minimizing the common lines residual for that orientation using the program emicoorg1 for sets of particles or emicoorg for a single particle. This refined origin is used for further orientation searches. The cycle of orientation search and origin refinement is continued until consistent values of Q, F, W, x and y have been determined for several particles.
The third use of common lines in the reconstruction process comes in the comparison of transforms of different particles. Once the orientations of the projections of two particles have been determined, the position of the common line between the two projections can be calculated. Further, one can generate a set of 59 other intersections (one for each symmetry element) between the symmetry-related planes generated from these projections. This gives rise to 60 pairs of cross common lines, i.e. lines which should have matching values in the two transforms. The sum of the phase residual over these pairs of lines is a measure of the degree to which the two transforms represent projections of the same structure at the given orientations. This residual is calculated between particles is the basis of the refinement performed by simplex. Calculation of the sum of the cross common lines residuals over the entire set of particles identifies those particles which agree poorly with the rest of the set. These particles may truly differ or may simply have incorrectly determined orientations. Once these outliers have been excluded, the orientations of the remaining particles can be refined by altering the orientation and origin parameters to minimize the cross common lines phase residual over the whole set of particles (Table I). Experience shows that this refinement is slow, extremely sensitive to noise and only successful if the particles in the set have values close to the correct ones.
An important aspect of refinement is the determination of a consistent hand for the particles. The projection of a particle will have an identical common lines residual for the orientation Q,F, Omega and Q,F, W+p. These two orientations (unflipped and flipped) correspond to viewing the same particle from opposite directions or to the projections arising from the particle and its enantiomorph. Although the common lines residual for an individual particle is the same for these two orientations, the cross common lines residual between the particle and another of fixed orientation will be different (Table I). Particles which exhibit strong enantiomorphic features at resolutions as low as 50 such as the papovaviruses (which have a handed triangulation number, T=7d) show dramatic differences and allow a consistent set of orientations to be established quickly (Baker et al., 1985; Baker et al., 1991) . Particles such as herpes virus (T=16) (Baker et al., 1990; Booy et al., 1991) , adenovirus (T=25) (Stewart et al., 1991) or Semliki Forest virus (T=4) (Vnien-Bryan & Fuller, 1994) for which only the structural unit shows handedness, show the difference only at higher resolutions (35A or finer). The proper hand for such a structure must be selected by trying all possible combinations of flipped and unflipped particles for the set. Since correct refinement is dependent on the selection of the proper hand for each particle, this hand selection must be repeated at each step of the refinement of the orientations. This is fairly compute intensive. A dynamic algorithm is used to speed the search for the best combination of orientations. The set of hand choices for a subset of particles is extended by including all possible orientations of an additional particle in each round and retaining only those sets which could generate a residual comparable to the best observed in previous rounds (Stewart et al., 1991) . For larger sets of particles a simulated annealing approach is used (Metropolis et al., 1953) in which the probability of flipping a particle in a cycle is an exponential function of the difference in residual between the flipped and unflipped orientation. Annealing is continued until further cycles result in no decrease in residual.
The refinement process is continued until a consistent hand has been established for all particles and the values of the common lines residual are acceptable for all the particles to the desired resolution. Sufficiently persistent refinement will result in improved residuals even for poor data sets. One can overcome this tendency to refine beyond the quality of the data by monitoring the free residual (Fuller et al., 1995) . Refinement of the data set is performed with a randomly selected subset of the cross common lines. Once the refinement is completed for the subset, the values of the residuals are calculated for all of the common lines and compared to the those for the refined subset. If the refinement is proceeding properly, the orientations determined by refinement will also decrease the residual for the data left free during the refinement (Figure 4).
The calculation of the reconstruction itself is the portion of the process which has changed least since its original description (Crowther, 1971) . The reconstruction is performed by determining the coefficients of a Fourier-Bessel expansion of the transform over a series of functions with 52 symmetry.:
F(R,F,Z) = Sn Gn (R,Z) exp(in(F+p/2))
where the Z axis now corresponds to the position of the five fold. This five fold symmetry axis is imposed by including only those Gn(R, Z) for which n is a multiple of 5. This method of imposing 52 symmetry is computationally efficient. The expansion coefficients Gn(R, Z) are determined separately for each annulus of radius, R and height, Z in the transform. The orientation of each particle is used to determine the positions of the fifty nine planes equivalent to the original one. For all orientations but the five fold, each of these sixty planes will intersect an R, Z annulus at two positions (F1,F2). Combining the data from all sixty planes for all of the images gives a series of unevenly spaced sample points along each annulus. The sampling is performed by emicomat. The coefficients of the expansion for each annulus are determined from the sample points by solving the linear equations:
Fj = F(R,Fj,Z) = Sn Bjn Gn (R,Z)
where the Bjn express the azimuthal dependence
(Bjn = exp(in(Fj + p/2))
for Gn(R,Z). The program emicobg solves the set of linear equations to produce the coefficients. The number and spacing of the sample points limit the quality of the solution. This can be seen quantitatively in the eigenvalues of the least squares solution (Figure 5). A low inverse eigenvalue indicates that many, well-spaced samples have been averaged to generate the coefficient while a high one indicates that only a few sample points were used so that the coefficient is more susceptible to noise. The eigenvalue spectrum provides an answer to the question of how many images are necessary to determine a reconstruction to a given resolution. Since the eigenvalues are only determined by the spacing and number of the sample points, the eigenvalue spectrum is not affected by the signal to noise in the data or the reliability of the orientations. This information is seen from the resolution dependence of the phase residual seen during refinement.
When there is insufficient data to complete the solution of the linear equations to the degree defined by the eigenvalue limit, the program recycles to a lower number of parameters. In practice this means that some of the coefficients of the BG expansion will not be calculated. Since the BG expansion is over cylindrical rather than icosahedral coordinates, the resulting map will NOT have exact icosahedral symmetry and, in extreme cases, will resemble a badly distorted bowler hat. This can be corrected by symmetrizing the result so that starting bowler hat density now looks like an icosahedrally arranged bowler hat chimera. This does not increase the biological significance of the result. Recycling is not a bug but a warning that you should be less optimistic about your ability to extract silk purses from sow's ears or 2A structures from 50A data.
Naturally when you are attempting a single particle reconstruction you will always get this error and you will always ignore it and you will NEVER completely believe the result and are honor bound not to try to publish it!!!!
Once the coefficients of the expansion of the transform are determined, the program emicolg used to calculate the corresponding coefficients of the expansion in real space
and the density in polar coordinates .
This polar expansion is then interpolated onto a Cartesian system to complete the reconstruction process byt the program emicofb.
The symmetry of the expansion functions is 52 and hence the three fold symmetry elements of icosahedral (or 532) symmetry are not imposed on the reconstruction. Sixty icosahedrally related planes of data are extracted from each transform so that the presence of the three-fold symmetry in the reconstruction signals agreement between the data from different particles. Full icosahedral symmetry can be imposed by real space averaging of the map by the program symmetrize This averaging increases the signal-to- noise within the map.
In the early stages of a project, it is often useful to calculate a low resolution, three dimensional reconstruction from a single particle. The icosahedral sampling of the data forces such a reconstruction to be icosahedral but the eigenvalue spectrum will indicate that it is poorly determined and artifact rich as a result. Such a reconstruction can never serve as evidence for the icosahedral nature of the particle, but it can be useful in classifying particles or generating models for further orientation searches.
The reader who has never attempted to determine orientations by the use of common lines will have no appreciation of its difficulty or the lack of certainty which plagues plagues the early steps in the reconstruction process. The development of a model- based orientation search method for icosahedral particles allows one to use a first, possibly noisy, reconstruction to check and refine orientations independently of the common lines approach (Cheng et al., 1994) . The algorithm is implemented in the program *empftref1. In the early stages of the reconstruction, the comparison of the two methods allows one to gain confidence in the correct orientations and discard incorrect orientations quickly. Once a structure has been established from a subset of data, the use of model-based refinement allows rapid screening for other additional particles and expansion of the data set.
The model-based refinement algorithm used in the icosahedral programs is based on a polar Fourier transform (pft) (Cheng et al., 1994) . A three dimensional structure which has usually been symmetrized and radially cropped to increase its signal to noise ratio is used to generate projections for each value of Theta and Phi throughout the asymmetric unit (Fig 6a). Each model projection r(x,y) is then sampled onto polar coordinates r(r,g) - (Fig 6b). The density for each r is then Fourier transformed to produce the pft which is an array of one dimensional Fourier transforms along g (Fig 6c). These pftÕs are used to select the projection which most closely matches the particle image. The conversion to pftÕs allows comparison which is independent of W. Each particle image is first centered by cross correlation with the circularly averaged projection of the model and then converted to a pft. The best match between the model and the image is found by multiplication of the pftÕs to calculate the one dimensional cross correlation. The model orientation which gives the highest cross correlation is selected. Once the best match of projection to image has been found, the best value of Omega is determined by interpolation in the polar cross correlation function. Hence, omega is estimated by a parabolic fit to the peak of the one-dimensional cross correlation function which maps to a rotation since this is a polar Fourier transform. The hand is selected by cross correlating the image with the unflipped and flipped model projections. The center of the image is then refined by using this model projection. The values of the new orientation and origin are then written out in a format which can be used by cross common lines refinement or by a further round of model-based orientation search.
The icosahedral reconstruction programs described above have their origin in a set of FORTRAN routines written by R. A. Crowther at the MRC LMB that have been modified and extended by a continuous interchange between the groups at EMBL and Purdue. The EMBL and Purdue versions are functionally equivalent but utilize different data formats and program names. Both run under VMS on AXP and VAX architectures. The EMBL version utilizes the MRC image, map and fft formats and has been ported to IRIX 6.0.1. An architecture stamp on the files allows their reading on either UNIX or VMS machines in the same manner that CCP4 files can be exchanged between architectures. The Purdue version utilizes a packed image format in which many images are stored in a single file. This helps minimize 'bookkeeping' of files and reduces the overhead of many file openings. Only image data is stored. The fft is calculated within each program as it is needed.
Future prospects
The programs now available cover a comprehensive set of manipulations for icosahedral reconstructions. The future holds the promise of increased resolution. Instrumental improvements such as the use of higher voltage electron microscopes and field emission guns are obviously one way to achieve this. However, as the resolution is increased, the number of particles used for averaging and the accuracy with which the particles need to be aligned also need to increase. These are computationally intensive tasks and are candidates for parallel computing algorithms. One recent important lesson is that improved image quality and larger data sets do indeed lead to higher resolution structures. It is clear that the limit has not been reached and that the intrinsic order of the particles will support even higher resolution.
Baker, T.S., Drak, J. and Bina, M. (1985). The structure of SV40 virus by electron microscopy of unstained frozen hydrated suspensions and negatively stained crystalline arrays Biophys. J. 47, 50a.
Baker, T.S., Newcomb, W.W., Booy, F.P., Brown, J.C. and Steven, A.C. (1990). Three-dimensional structures of maturable and abortive capsids of equine herpesvirus 1 from cryoelectron microscopy J. Virol. 64, 563-573.
Baker, T.S., Newcomb, W.W., Olson, N.H., Cowsert, L.M., Olson, C. and Brown, J.C. (1991). Structures of bovine and human papilloma viruses: Analysis by cryoelectron microscopy and three-dimensional image reconstruction Biophys. J. 60, 1445-1456.
Booy, F.P., Newcomb, W.W., Trus, B.L., Brown, J.C., Baker, T.S. and Steven, A.C. (1991). Liquid-crystalline, phage-like packing of encapsidated DNA in herpes simplex virus Cell 64, 1007-1015.
Cheng, R.H., Kuhn, R.J., Olson, N.H., Rossmann, M.G., Choi, H.-K., Smith, T.J. and Baker, T.S. (1995). Nucleocapsid and glycoprotein organization in an enveloped virus Cell 80, 621-630.
Cheng, R.H., Reddy, V.S., Olson, N.H., Fisher, A.J., Baker, T.S. and Johnson, J.E. (1994). Functional implications of quasi-equivalence in a T = 3 icosahedral animal virus established by cryo-electron microscopy and X-ray crystallography Structure 2, 271-82.
Crowther, R.A. (1971). Procedures for three-dimensional reconstruction of spherical viruses by Fourier synthesis from electron micrographs Phil. Trans. R. Soc. Lond. B. 261, 221-230.
DeRosier, D.J. and Klug, A. (1968). Reconstruction of three dimensional structures from electron micrographs Nature (London) 217, 130-134.
Fuller, S.D. (1987). The T=4 Envelope of Sindbis virus is organized by complementary interactions with a T=3 icosahedral capsid. Cell 48, 923-934.
Fuller, S.D., Berriman, J., Butcher, S.J. and Gowen, B.E. (1995). Low pH induces swivelling of the glycoprotein heterodimers in the Semliki Forest virus spike complex. Cell 85, 215-225.
Grimes, J., Basak, A.K., Roy, P. and Stuart, D. (1995). The crystal structure of bluetongue virus VP7 Nature 373, 167-170.
Ilag, L.L., Olson, N.H., Dokland, T., Music, C.L., Cheng, R.H., Bowen, Z., McKenna, R., Rossmann, M.G., Baker, T.S. and Incardona, N.L. (1995). DNA packaging intermediates of bacteriophage phiX174 Structure 3, 353- 363.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. and Teller, E. (1953). Equation of state calculations by fast computing machines J. Chem. Physics 21, 1087-1092.
Olson, N.H., Kolatkar, P.R., Oliveira, M.A., Cheng, R.H., Greve, J.M., McClelland, A., Baker, T.S. and Rossmann, M.G. (1993). Structure of a human rhinovirus complexed with its receptor molecule Proc. Nat. Acad. Sci. USA 90, 507-511.
Smith, T.J., Olson, N.H., Cheng, R.H., Chase, E.S. and Baker, T.S. (1993). Structure of a human rhinovirus-bivalently bound antibody complex: Implications for viral neutralization and antibody flexibility Proc. Nat. Acad. Sci. USA 90, 7015-7018.
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The coordinate system used for describing orientations is shown in the second line of the figure. Capital letters are used to denote reciprocal space variables (Q,F,W) and small letters (x,y) are used to denote real space coordinates. The asymmetric unit triangle is bounded by two five fold axes (90”, ±31.717”) and a three fold axis (69.09”,0”) and is shown in a planar representation with the symmetry axes marked by pentagons and a triangle and on the surface of an icosahedron to show its relationship to the Cartesian axes. The two fold axis (90”,0”) between the five folds is shown with the standard crystallographic symbol. Refinement of the phase origin corresponds to changing the center of the area used to calculate the transform and hence is described in the real space coordinates (x,y). Orientation searches are done using the transform of the projection and hence the orientation is described in terms of the reciprocal space angles (Q,F,W) which are numerically identical to their real space counterparts.
The Purdue and EMBL versions of the
icosahedral reconstruction program suite use different settings of the
icosahedral axes. The EMBL setting is described in the text. The Purdue
setting generates an equivalent asymmetric unit which is bounded by
two five folds Q,F = (31.717”, ± 90”) and the three-fold at (20.91”,0”) and
the two fold at (0”,0”) however this is transparent to the user of eitherprogram set.
The positions of the common lines are indicated for
three orientations of an icosahedral particle. The situation
corresponding to Figure 2 is illustrated by the top panel (Theta=89”,Phi=-1”).
The positions of the pair of common lines generated by the three fold is
marked with a large 3. The positions of the two pairs of common lines
generated by a single five fold axis is marked by a large 5. In each case
the symmetry axis lies between the pairs. All thirty-seven pairs of
common lines are indicated for the three orientations. The common
lines generated by the 15 two fold axes are shown as dashed lines since
the two lines of the "pair" are colinear but oppositely
directed. The Friedel symmetry of the transform forces the values along
such a line to have phases of 0 or p. The change in the distribution and
independence of the common lines for different orientations can be
seen easily by comparison of the distribution near a two fold (Theta=89”,F=-
1”) or a three fold (Theta=69”,Phi=0”) to that in the center of the asymmetric
unit (Theta=80”,Phi=11”). The positions of the common lines for different
values of Omega are simply generated by rotating the positions for
Omega=0 in the
plane. Hence the spacings of the lines for the same Theta and Phi but
different Omega are similar.
Data from ten particles of the SQL mutant of Semliki Forest virus were refined in Theta, Phi and Omega with SIMPLEX for 10 cycles with a random quarter of the common lines excluded from the residual used for refinement. After refinement the average phase residual was calculated from the included lines (closed squares) and from the complete set of common lines (closed diamonds). The number of comparisons used for each resolution range is also shownfor the included lines (closed triangles) and the complete set (open circles). The inclusion of the "free" data causes a slight drop in the average phase residual indicating the refinement has found a better orientation for this data as well as the included data.
Panel A shows a histogram of the distribution of inverse eigenvalues for the determination of the real (cross hatched) and imaginary (filled) Gn for a reconstruction of bacteriophage PRD1 with 28 particles calculated to a resolution of 26. The resolution dependence of the mean fractional error for the real (R) and imaginary (I) Gn and the inverse eigenvalues (lambda) for their determination in the same reconstruction is shown in panel B.
The polar Fourier
transform is generated by projection of the model (a), radial sampling of
the projection (b) to produce r(r,g) and transformation of the radially
sampled projection along the angular direction (g) to produce a pft
which is a function of r and G (c). Multiplication of pft's corresponding
to the image and evenly spaced model projections allow rapid
identification of the most similar projection to the image and hence
yield an orientation for the image.
Before Refinement
| Particle | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|
| 13 | 80.6 | 91.3 | 79.9 | 70.0 | 92 .8 | 78.4 |
| 80.6 | 74.8 | 76.0 | 78.2 | 83.1 | 81.5 | |
| 14 | 91.3 | 99.5 | 94.3 | 86.4 | 96 .2 | 94.3 |
| 74.8 | 99.5 | 85.2 | 86.9 | 84.4 | 88.1 | |
| 15 | 79.9 | 94.3 | 69.7 | 80.6 | 80 .1 | 76.9 |
| 76.0 | 85.2 | 69.7 | 69.4 | 73.3 | 87.6 | |
| 16 | 70.0 | 86.4 | 80.6 | 62.9 | 86 .0 | 72.3 |
| 78.2 | 86.9 | 69.4 | 62.9 | 84.1 | 80.1 | |
| 17 | 92.8 | 96.2 | 80.1 | 86.0 | 80 .3 | 93.1 |
| 83.1 | 84.4 | 73.3 | 84.1 | 80.3 | 93.7 | |
| 18 | 78.4 | 94.3 | 76.9 | 72.3 | 93 .1 | 78.6 |
| 81.5 | 88.1 | 87.6 | 80.1 | 93.7 | 78.6 |
| Up | 73.9 | 83.6 | 75.3 | 71.7 | 92.6 | 84.3 |
|---|---|---|---|---|---|---|
| Flipped | 78.8 | 82.2 | 78.6 | 80.9 | 86.1 | 84.6 |
| Best | 71.4 | 79.8 | 72.7 | 70.6 | 84.9 | 81.8 |
| Particle | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|
| 13 | 80.0 | 66.3 | 72.4 | 63.8 | 78.4 | 60.4 |
| 80.0 | 86.3 | 85.1 | 78.9 | 101.7 | 76.0 | |
| 14 | 66.3 | 67.8 | 70.2 | 61.1 | 66.9 | 60.6 |
| 86.3 | 67.8 | 103.0 | 78.0 | 83. 1 | 81.8 | |
| 15 | 72.4 | 70.2 | 70.5 | 77.9 | 68.3 | 67.9 |
| 85.1 | 103.0 | 70.5 | 83.3 | 92. 7 | 75.4 | |
| 16 | 63.8 | 61.1 | 77.9 | 59.6 | 62.0 | 61.1 |
| 78.9 | 78.0 | 83.3 | 59.6 | 86.2 | 76.1 | |
| 17 | 78.4 | 66.9 | 68.3 | 62.0 | 65.8 | 66.1 |
| 101.7 | 83.1 | 92.7 | 86.2 | 65. 8 | 88.9 | |
| 18 | 60.4 | 60.6 | 67.9 | 61.1 | 66.1 | 63.0 |
| 76.0 | 81.8 | 75.4 | 76.1 | 88.9 | 63.0 |
| Up | 65.1 | 64.7 | 66.4 | 64.1 | 67.1 | 62.8 |
|---|---|---|---|---|---|---|
| Flipped | 82.1 | 80.2 | 81.2 | 79.9 | 82.2 | 76.6 |
| Best | 65.1 | 64.7 | 66.4 | 64.1 | 67.1 | 62.8 |
Author: Stephen Fuller
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