1
Supplementary material
Image processing and 3D reconstruction
The image processing applied here was derived from the conventional single particle scheme modified for the particular requirements of helical filaments. A helical filament is not a true one dimensional crystal but displays a considerable amount of flexibility
S1
. Therefore it is advantageous to apply single particle techniques to short lengths of helical objects and to reconstruct these by back-projection methods.
A single helical repeat of the 28/13 helix was used as the basic unit for all alignment steps in three dimensions. Figure S1a shows a projection of two such repeats.
Therefore the ‘single particle’ is about 77 nm long and about 35 nm wide. Such projections were aligned and classified using conventional correlation techniques. Their particular symmetry allows the determination of two of the three Euler angles with high accuracy. The 3 rd angle (azimuthal rotation around the filament axis) could not be determined with an error of less than about +/- 12º, which prevents high resolution reconstruction. However, by using a low-resolution reconstruction to establish an initial model it is possible to apply multivariate statistical analysis to projections of this model at known azimuthal rotation. We used trajectories in a factor space formed by the model data to find the closest distance between experimental and model projections. The azimuthal rotation angle of the closest model projection was then assigned to the experimental image. A short description of this procedure is given in S2 , other examples of the use of trajectories are in
S3,4
.
Image processing and 3D reconstruction was performed in the following steps:
1 – quality assessment of defocus series,
2 – helical repeat selection,

2
3 – alignment of helical repeats and classification according to helical symmetry,
4 – calculation of individual 3D densities for each defocus by an approach based on axial tomography,
5 – merging of defocus densities (correction of contrast transfer function in phase and amplitude part).
6 - This preliminary reconstruction is still hampered in resolution by an azimuthal mis-alignment of the individual helical repeats. Therefore an iterative refinement was performed by using the preliminary model as reference to refine alignment of the images, and to determine the projection angle around the filament axis applying multivariate statistics.
7 - With this new angular alignment new 3D reconstructions of helical repeats from each individual exposure were calculated using the identical approach based on axial tomography (step 4). In this step each helical repeat was assigned its Eulerian projection angles, and a simple algorithm, based on axial tomographic projections with uneven distribution of angles, was used to calculate individual 3D densities for helical repeats picked from one exposure.
8 – The individual 3D densities from one defocus series were merged together correcting the density for the effects of the contrast transfer function CTF (corrected in phase and amplitude).
9 – Comparison and merging of the 3D densities of all defocus series.
Steps 6 – 9 again had to be repeated several times. The final density stabilized after
7 refinement runs.
To calculate the final 3D reconstruction from the aligned projections, we have consided the projection of a helix as one dimensional assembly of axial tomographic projections of the basic repeating unit of the helix. i.e. we take the cylindrical volume of one unit cell, which in our 28/13 helix is 2.75 nm thick at a radius of about 20nm. The

3 real space helix is formed by a simple rotation (for the 28/13 helix the rotational angle is
–167.143º) and translation (for 2.75nm) of the unit cell along the filament axis. The projection image can then be separated in 2.75nm wide stripes perpendicular to the filament axis with a known azimuthal angle increment of –167.143º. We write down the algebraic matrix of all projection equations, and solve them by diagonalised least squares, which circumvents the problem of inverting a multiply singular normal matrix by restricting the inversion to a sub-space in which the eigenvalues are larger than the error on the data (analogous to a Moore-Penrose generalized inverse). All high order terms are then set to zero. This truncation is equivalent to restricting the resolution. The method is closely analogous to back projection with radial sharpening in Fourier space but makes use of an expansion in orthonormal functions that are appropriate for the geometry. The right hand side of the least-squares formulation is the back projection.
Thus the inverse normal matrix is the correct filter for turning the back projection into the original object. The algorithm is robust and allows the combination of helical symmetry and particles lying on the grid with various azimuthal angles. Solutions are initially sought in a circle of radius 180Å using a grid spacing of 2.75Å (the order of the normal matrix is then ca. 18,000, whereas the effective rank is 2000-3000). In the final reconstruction a mask can be employed to confine the density function to regions of space where the object is known to exist. Because of the shape of decorated actin, the use of a mask leads to a considerable reduction in the order of the normal matrix and to a corresponding increase in the resolution of the map. Algebraic reconstructions were first discussed by
S5
. For an overview of this approach see
S6
.
Figure S1a shows a projection of the final reconstructed density. Its 28/13 helical periodicity is obvious; one helical repeat consists of two ‘arrow-heads’. The

4 corresponding power spectrum of the projection (figure S1b) shows the typical layer lines. For this reconstruction strong layer lines out to 18 Å were found (41 st
layer line); some weak intensities are visible at higher resolution (resolution of density cut-off with
Fermi-filter at 12Å). To test the signal at higher resolution we calculated Fourier shell coefficients (FSC, figure S2) between the 3D reconstructed density and a density model derived from the coordinates of actin and myosin docked into the density (see below).
The correlation function shows the improved aggreement for the stronger layer lines and breaks down at about 14 Å (lower than FSC value 0.5). Based on this behaviour we assign to our reconstruction a resolution of 14 Å.
Modified molecular model of F-actin
The actin filament structure was derived by fitting the crystal structure of monomeric actin (G-actin)
S7
to X-ray fibre diffraction patterns obtained from orientated gels of actin fibres (F-actin)
S7-10
. Since a substantial conformational change is involved in going from G- to F-actin, the G-actin structure has to be deformed in some way to fit the F-actin diffraction pattern. The nature of this deformation is not clear. Given the limited (6Å) resolution of the fibre diffraction pattern only a limited number of parameters can be determined by this procedure. Various attempts at generating the Factin structure used various methods of defining these parameters and ended up with related solutions which differ from each other enough to make them an unsatisfactory basis for the interpretation of a high resolution EM density map. The method of Lorenz et a.l
S10
produced a perfect fit to the fibre diffraction pattern but some damage to the stereochemistry of G-actin. Actin is made up from four sub-domains
S7
, which we have now allowed to move as independent solid bodies so as to minimize the difference between the calculated fibre diffraction pattern and the observed fibre diffraction pattern
S9
. Using an iterative non-linear least-squares procedure we obtain an excellent

5 fit to the X-ray fibre diffraction pattern with 22 parameters. As starting structure we used the structure of G-actin given by Otterbein et al
S11
but with sub-domain 4 rotated inwards about 15˚ as in the Lorenz structure (without this initial rotation the least squares procedure does not reach the best solution). The result is shown in Figure S3.
Defining the upper 50K domain
Inspection of the structure yields a definition of the upper 50K domain. The upper
50K domain is linked to the body of the motor domain by four ‘loops’, including the disordered trypsin sensitive sequences that delineate the 50K domain (loops 1 and 2), a short segment around residue 449 (skeletal chicken sequence numbers) that is disordered in smooth muscle
S12
, and the strut sequence of Sutoh et al .
S13
. Mutational analysis shows the strut to be important in controlling actin binding. In addition, there are two putative hinge points at 270 and 246 where the upper 50K domain is connected onto the 7-stranded

-sheet that is the backbone of the motor domain (a recent publication
S14
shows that this section of the

-sheet can bend).
The switch 1 sequence, which forms part of the nucleotide binding site is an integral part of the upper 50K domain. It forms the end strand of a small 4-stranded

sheet.
Fitting F-actin, the body, and the upper 50K domain by least-squares.
Coordinates for the actin helix were produced as described. Coordinates for the myosin cross-bridge (S1) were taken from Rayment et al.
S15
(PDB code 2MYS). The missing side chain coordinates for the light chains were constructed with CNS
S16
. The cross-bridge was broken into two pieces, the upper 50K domain and the rest, referred to as the ‘body’ (see above). An iterative least square refinement was carried out in the following way: The actin helix was taken as a solid body with two free parameters: z

6
(helix axis) and

the azimuthal angle. The upper 50K domain and the body were each given six parameters (three translation + three rotation around the centre of gravity).
The least-squares procedure was based on equating the calculated density with the observed density. The calculated density was evaluated by folding each atom with a
Gaussian of the appropriate width to reduce the resolution to that of the observed density. The target-factor was
R
2
=

(
 calc
–
 obs
)
2
/
 obs
2
(1)
The least-squares procedure converged in about 10 cycles to an R
2
-factor of 11% for the case of actin + body + upper 50K domain. The reduced

was 0.186 on 1900 degrees of freedom.
Accuracy of the parameters
Variances of the parameters were established by binning the data. The 15 defocus series were reconstructed independently and scaled as described by Fox & Holmes
S17
(The reconstructed density as evaluated and shown in all the figures corresponds to a ttest 99% confidence level). The least squares analysis was applied to each of the data sets independently and the resulting parameter values were pooled to obtain estimates of the variance. The estimated variances were then used to scale the statistical analysis of the fitting process. The analysis is a generalized least squares problem since the input data, i.e. the individual voxels of the reconstructed 3D density, are not independent.
Therefore the number of degrees of freedom is not equal to the number of voxels. Using standard methods (see e.g.
S18
) we calculated the generalized least squares estimator
(GLS) and thus the standard deviations of the individual fitting parameters. The estimated number of degrees of freedom was 1900. Thus the analysis is well determined.

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Figure S4 shows the coordinate system used for the atomic modelling and fitting
(x, y, z coordinate system). The least squares analysis was applied to three different models:
1 – actin (see above) plus the unmodified myosin model as derived from the crystal structure;
2 – actin and myosin as above but half-weight regulatory light chain (RLC);
3 – actin and myosin as in 2 but split into a body part and a small upper 50kD domain refining separately from the body.
These cases use one shift and one rotational parameter for actin (along or around the filament axis) and three shift and three angle parameters for each myosin part (total of 8 or 14 parameters). The number of parameters is thus very much smaller than the number of degrees of freedom.
Table 1 gives the standard R-factors and least squares for the stable fit of the three models discussed above; table 2 gives the deviations of the fit parameters as derived from the generalized least squares analysis. Figure S4 also shows the axis of rotation of the upper 50kD domain as found from the conformational change between fits of the crystallographic myosin and of the myosin separated into body and upper 50kD domain.

Table 1 R-Factor and least squares of fit for different atomic models
R
2
-factor reduced

2 original model original model
(2 nd light chain modified) modified model
0.184
0.133
0.108
0.379
0.274
0.186
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Table 2 Standard deviations of fitted orientational parameters
Standard deviations of shifts [Å] and rotations [degrees] for actin, myosin, and myosin parts as fitted into 15 independently reconstructed volumes.
Euler angles of rotation axis (in “x-convention”, see e.g. Goldstein (1960, pp.145-148)
Actin Myosin
Shift [ Å] rotation shift [Å] rotation z-coordinate (
 around axis[º]) x,y,z (Euler 
,

,
 º 
) original model 1.7 3.7 0.8
0.8
0.7 original model
(2 nd light chain modified)
1.4 2.9 0.7
0.7
0.8
1.5
1.0
1.2
1.4
1.1
1.2
body modified model 1.3
(2 nd light chain modified and upper 50 kD domain free to move)
2.6 0.7
0.6
0.7
1.5
1.1
1.3 upper 50kD domain
1.4 7.5
1.1
1.2
4.6
4.9
9

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Table 3 Orientation of rotation axis
Euler angles of rotation axis (in “x-convention”, see e.g. Goldstein (1960, pp.145-148)
  
Euler angles 350.6º 4.1º 19.1º
From these data we can estimate the positional accuracy of certain residues. The rotation around the x-axis has the largest error, but the upper 50kD domain also shows its smallest radius around this axis (see figure S4). Thus the standard deviation of 7.9º in this parameter converts into an error of 1 Å at the ‘surface’ of the upper 50kD domain.
The same is true for the other two axes; the smaller standard deviation in angle needs then to be applied to residues at higher radius (because of elongated shape of the upper domain), again resulting in about 1 Å standard deviation in position. The accuracy of the current study is of the order of 1-2 Å for positional localizations.
Additional material visualizing the model fit (movies)
Six movies are provided. The first set of four shows the fit of the original crystallographic myosin into the density (solid and transparent surface) with part of the upper 50kD domain (red ribbon model) protruding out of the density, versus the

modified fit (moved upper 50kD domain) with all of the macromolecular model contained inside the density.
11
Movie 1 – fit of original model thumbnail
thumbnail Movie 2 – fit of original model
Movie 3 - fit of modified model
Movie 4 - fit of modified model
thumbnail
thumbnail

12
The second set of movies shows real space difference maps between reconstructed density and density derived from the fitted model structures reduced to 14Å resolution.
Movie 5 uses the original crystallographic protein-data-bank data (2Mys) with a regulatory light chain (RLC) with its full density. In the difference map (model – reconstruction = red density) the RLC shows up clearly as negative density. Note that this difference density is very much located at the RLC, indicating the discussed partial loss of this light chain during biochemical preparation. Other effects such as disorder of the sample or rotational misalignment during image processing can be excluded, since such problems would also affect the essential light chain adjacent to the RLC.
Movie 5 – difference maps: red –> crystal structure model – reconstructed density blue -> reconstructed density – crystal structure model
thumbnail
Movie 6 illustrates (a) the good fit of the RLC density if we assume a 50% loss of RLC and (b) the necessity for a further modification of the crystallographic myosin structure to fit the reconstructed density. At the surface of the actin filament the red and blue density differences are visible indicating the movement of protein from the red to the blue location. At the distal part of the upper 50 kD domain (red ribbon) additional red

13 density is present, this represents the opening nucleotide binding tunnel. These observed density movements illustrate the need for the rotation of the upper 50kD domain.
Movie 6 - difference maps: red –> crystal structure model (50% RLC) – reconstructed density blue -> reconstructed density – crystal structure model (50% RLC)
thumbnail
Model data and reconstructed density
For further reference the following data are provided: a – em reconstructed density in brix-format (em_density.brix) b – pdb models of actin (3actin.pdb), the myosin body domain (motor_domain.pdb), the rotation axis of the myosin upper domain movement (axis.pdb), and the upper 50kD domain in its crystallographic position (original_upper_50K_domain.pdb) and its modified position
(upper_50K_domain.pdb).

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References for supplementary material
S1 Egelmann, E. H. A robust algorithm for the reconstruction of helical filaments using single particle methods. Ultramicroscopy , 85 , 225-234 (2000).
S2 Schroeder, R. R., Angert, I., Frank, J. & Holmes, K. C. Multivariate statistical analysis and tomographic processing of helical objects. Proc. ICEM, 15 , 443-
444 (2002).
S3 Bellon, P. L., Cantele, F. & Lanzavecchia, S. Correspondence analysis of sinogram lines. Sinogram trajectories in factor space replace raw images in the orientation of projections of macromolecular assemblies. Ultramicroscopy , 88 ,
187-197 (2001).
S4 Bellon, P. L., Cantele, F., DeCarlo, S. & Lanzavecchia, S. A trajectory-based algorithm to determine and refine Euler angles of projections in threedimensional microscopy. Improvements and tests. Ultramicroscopy , 93 , 111-121
(2002).
S5 Crowther, R. A., DeRosier, D. J. & Klug, A. The reconstruction of a threedimensional structure from projections and its application to electron microscopy. Proceedings of the Royal Society of London Series A Mathematical
& Physical Sciences , 317 , 319-40 (1972).
S6 Herman, G. T. & Kuba, A. Discrete Tomography (Birkhäuser, Boston, 1999).
S7 Kabsch, W., Mannherz, H. G., Suck, D., Pai, E. F. & Holmes, K. C. Atomic structure of the actin:DNase I complex. Nature , 347 , 37-44 (1990).

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S8 Tirion, M. M., ben-Avraham, D., Lorenz, M. & Holmes, K. C. Normal modes as refinement parameters for the F-actin model. Biophysical Journal , 68 , 5-12
(1995).
S9 Holmes, K. C., Popp, D., Gebhard, W. & Kabsch, W. Atomic model of the actin filament. Nature , 347 , 44-9 (1990).
S10 Lorenz, M., Popp, D. & Holmes, K. C. Refinement of the F-Actin Model against
X-Ray Fiber Diffraction Data by the Use of a Directed Mutation Algorithm. J.
Mol. Biol., 234 , 826-836 (1993).
S11 Otterbein, L. R., Graceffa, P. & Dominguez, R. The crystal structure of uncomplexed actin in the ADP state. Science , 293 , 708-11 (2001).
S12 Dominguez, R., Freyzon, Y., Trybus, K. M. & Cohen, C. Crystal structure of a vertebrate smooth muscle myosin motor domain and its complex with the essential light chain: visualization of the pre-power stroke state. Cell , 94 , 559-71
(1998).
S13 Sasaki, N., Ohkura, R. & Sutoh, K. Insertion or deletion of a single residue in the strut sequence of Dictyostelium myosin II abolishes strong binding to actin.
Journal of Biological Chemistry , 275 , 38705-38709 (2000).
S14 Reubold, T., Eschenburg, S., Becker, A., Kull, F. J. & Manstein, D. J. A structural model for actin-induced nucleotide release in myosin. Nature
Structural Biology . in press (2003).
S15 Rayment, I. et al. Three-dimensional structure of myosin subfragment-1: a molecular motor. Science , 261 , 50-8 (1993).
S16 Brunger, A. T. et al. Crystallography & NMR system: A new software suite for macromolecular structure determination. Acta Crystallographica Section D-
Biological Crystallography , 54 , 905-21 (1998).

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S17 Fox, G. C. & Holmes, K. C. An alternative method of solving the layer scaling quations of Hamilton, Rollett and Sparks. Acta Crystallographica , 20 , 886-891
(1966).
S18 Tomas, J.J
. An introduction to statistical analysis for economists , Weidenfeld and Nicolson, London, 1977.
Supplement Figure 1
(a) Projection of the reconstructed density of the helical complex of F-actin and myosin subfragment 1 (S1). Shown are two complete helical repeats of the
28/13 helix (154 nm).
(b) Power spectrum of projection shown in a. The resolution is limited to about
13Å by a Fermi-filter. Layer lines are clearly visible and indicate a strong signal out to the 41 st laye r line, (18 Å resolution) and some weaker signal extending to the resolution cut-off of the Fermi-filter ( cf . resolution comparison using Fourier shell coefficients shown in figure S2).
Supplement Figure 2
Fourier shell coefficients (FSCs) between the reconstructed density and a model density derived from the fitted molecular models. The correlation coefficients show a strong correlation at strong layer lines (cf. figure S1).
Beyond the resolution cut-off of the reconstruction by the Fermi-filter only a

17 noise correlation can be found (scattering around the zero correlation base).
The FSC falls below the 0.5 significance threshold at a resolution of about 14Å.
Supplement Figure 3
Modified F-actin structure as it is used in this study. Shown are 5 actin monomers in the same colour coding as in the figures of the main text.
Supplement Figure 4
Myosin subfragment 1 (chicken skeletal muscle myosin) as published by
Rayment 3 . The N-terminal domain is shown in green and the C-terminal lever arm is shown blue. The central 50kD domain of the myosin cross-bridge is split into two sub-domains (upper and lower) by the major cleft that connects the actin binding site with the nucleotide binding site. The two sub-domains have been allocated distinct colours, red (upper domain) and white (lower domain).
Often the parts in green, red and white together are referred to as the motor domain.
In addition the position of the atomic model coordinate system is indicated, as well as the rotation axis, which is calculated from the observed movement of the upper 50kD domain. The orientation of the rotation axis with respect to the coordinate system is given in Table 3.