R-factor-fit R-factor-non-fit

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1 Supplementary Figures and Legends R-factor-fit R-factor-non-fit R-factor-non-fit (overall) Supplementary figure 1 The areas where the R-factor-fit and the R-factor-non-fit were calculated. The edges of diffraction in the radial direction and along the equator are 1/3.0 and 1/5.6 (=0.18) Å -1, respectively. The left and right halves are a calculated and an observed diffraction pattern, respectively. We introduced two R-factors against a diffraction pattern: an R-factor-fit against the fitted area (1/56-1/6.5 & 1/5.5-1/3.6 Å -1 radially and to 1/5.8 Å -1 along the equator) and an R-factor-non-fit against the non-fitted area (1/6.5-1/5.5 Å -1 radially and to 1/15 Å -1 along the equator), which is comparable to the free R-factor commonly used in crystallography 1,2. We also used an R-factor-non-fit (overall) against the area (1/6.5-1/5.5 Å -1 radially and to 1/5.8 Å -1 along the equator) to distinguish the validity of the converged models. White circles represent radii of 1/3.6, 1/5.5, and 1/6.5 Å

2 Supplementary figure 2 Stereo pairs to show the transition from the G-actin conformation to the flat conformation in F-actin. The top pair is the front-view, whereas the bottom pair is the side-view, corresponding to Figure 2a and 2b in the main text, respectively. Yellow is a crystal structure of TMR-ADP-actin and cyan is a structure of F-actin subunit. See the legends to figure 2 for more details. 2

3 Supplementary figure 3 Comparison of MreB with F-actin. The subunit structure in the MreB protofilament 3 (cyan) and that in our F-actin model (yellow) are superimposed on the actin core regions of subdomains 1 & 2 4. (a) Front-view. (b) Side-view, viewed from the left hand side of (a), as subdomains 3 & 4 are seen in front. Note that in MreB, the cleft is closed and the two major domains are untwisted as in our F-actin model, but not in G-actin. The nucleotide binding sites are also similar to each other (see Supplementary Fig. 6). (c) Interaction regions between the subunits in the MreB protofilament 3 are highlighted in the same manner as in Fig. 3b. The contact pattern is similar to the intra-strand contact pattern within F-actin (Fig. 3b). Note that the MreB structure in the monomeric state has not been determined. 3

4 FSC Resolution (Å -1 ) 13.8 Å -1 Supplementary figure 4 Comparison of our F-actin model and the previous models with the cryo EM map. The red line represents the Fourier shell correlation (FSC), a measure of the reliability of the structural details of a particular spatial frequency (a resolution), of the EM map (Supplementary Methods). The structural details are reliable (higher than 0.5) to the resolution of 13.8 Å. The green line represents the FSC, a measure of matching, between the EM map and our model (Supplementary Methods), while the blue, purple, and cyan lines represent those for the Lorenz model 5, the Holmes 2003 model 6 and the original Holmes model 7, respectively. Our model shows an FSC higher than 0.6 even at 13.8 Å resolution, which is higher than the threshold value (0.5) at the resolution limit of the EM map. This means that our model completely agrees with the EM map in the reliable resolution area of the EM map. Moreover, in the entire resolution range up to 13.8 Å, our model shows the highest agreement with the EM map. This indicates that our model is better than any previous model, at least up to this resolution. Since the Volkmann model 8 could not be fairly compared in the FSC, because of the lack of a nucleotide in their structure, a real space comparison is provided in Supplementary figure

5 a b Supplementary figure 5 Agreement of our F-actin model and previous models with the EM map. In (a) and (b), the electron density map was reconstructed from cryo-electron micrographs and filtered through a 13.8Å low-pass filter, and is indicated as the envelope enclosing 100% volume. (a) The Holmes 2003 model 6 (red) is compared with our model (blue). Although both appear to fit well to the EM envelope, the peptide chain of our model is almost completely within the envelope, while that of the Holmes 2003 model has some edges outside of the envelope. This suggests that either the subunit of the Holmes 2003 model is extended or the subunit orientation is somewhat different. This probably accounts for the low FCS value of the Holmes 2003 model (Supplementary figure 3). (b) Comparsion of the Volkmann et al. 8 model (pink) with our model (blue). Volkmann et al. modified the position of the C-terminus of the Holmes 2003 model to match their EM map of F-actin. However, the C-terminal helix projects out from our EM envelope (arrow), thus worsening the agreement with our EM map. Movies at which F-actins in panels (a) and (b) rotate are available (Supplementary Videos 1 & 2). 5

6 Supplementary figure 6 Comparison of the ATPase site structures between MreB, G-actin and F-actin. (a) The location of the focused region in the G-actin molecule is highlighted in red. (b) G-actin (yellow) versus MreB (pink). The two structures are superimposed on the β-sheet that forms the core of subdomains 3 & 4 4. This clearly shows that the ATPase site structures are distinct in G-actin and MreB. The side-chain of Gln 131 (at the equivalent position of Gln 137 of actin) is closer to the γ-p in MreB, as compared to G-actin. (c) Our F-actin subunit (cyan) versus MreB (pink). The two structures are similar, including the position of the side chain of Gln137 (Gln131). (d) G-actin (yellow) versus our F-actin subunit (cyan). This comparison suggests that the relative rotation of the two major domains moves Gln 137 to the vicinity of γ-p. The MreB crystal structure, with its similar flat conformation to our F-actin, suggests that the global structural change is probably associated with the ATPase, although the detailed mechanism of the ATPase remains obscure. The conformations of the amino acid side chains and the ADP include ambiguity. This is because the bound ADP contacts 6 discontinuous segments in the actin molecule, and thus slight shifts of these segments greatly affect the conformation of ADP. Conformation of side-chain of Gln137 was determined by the contact with Thr106 rather than data. 6

7 Supplementary figure 7 Side chain rearrangements at the boundary between the two major domains associated with the G- to F-actin conformational transition (a back-view). (a) TMR-ADP-G-actin (PDB 1J6Z) 9. (b) Our F-actin subunit. In both, the loops and (orange) of subdomain 1 connect the two major domains. However, only in our F-actin model, but not in G-actin, Arg206, Glu72, Arg183, Asp187, MeHis73, Asp179 and Arg177 form a concatenation of salt bridges. Moreover, in F-actin, Pro109 and Leu110 (pink) of loop of subdomain 1 detach from Val163 and Ile175 (yellow) of the core of subdomain

8 T S P Wild-type D286R D288R Supplementary figure 8 Polymerization activities of the recombinant D286R and D288R mutants of actin. The wild-type actin was prepared by the method described previously 10. D286R and D288R actins were also prepared by the same method, but without the polymerization and depolymerization cycle. Those actins were stored in G-buffer (10 mm Tris-HCl, ph 8.0, 0.2 mm CaCl 2, 0.5 mm ATP, and 1 mm DTT). Polymerization was initiated by the addition of a 20-fold concentrated polymerization solution, to make final concentrations of 100 mm KCl, 2 mm MgCl 2, and 0.5 mm ATP, in the actin solution (5 µm). After an overnight incubation at room temperature, the mixture was centrifuged at 100,000 x g for 30 min at 25 C to pellet the F-actin. The total mixture before centrifugation (T), the supernatant (S) and the pellet (P) fractions after centrifugation were analyzed by SDS-PAGE. After centrifugation, almost all of the wild-type actin was found in the pellet, whereas the D286R and D288R mutants were predominantly found in the supernatant, indicating that the polymerization activity is impaired in the D286R and D288R mutants. In the presence of phalloidin, the D286R and D288R mutants polymerized, and 70 % of the total actin was pelleted at 100,000 x g. This suggests that the loss of polymerizability is not due to the misfolding of the entire molecule, but instead is due to the local effects of the replaced residues. 8

9 Supplementary figure 9 Comparison of intra-strand contacts between the helical polymer constructed by computer modeling, the crystal contacts in 2HMP 11 and our F-actin. (a) Intra-strand contacts between the subunits within the virtual helical polymer. The polymer was made by twisting the two-stranded non-helical polymer in Fig. 4a, i.e., by azimuthally rotating each subunit about the helix axis, according to the helical symmetry of F-actin. (b) Crystal contacts in the 2HMP crystal. Through these contacts, the single stranded twisted polymer can be traced in the crystal, although the twist between the subunits is not identical to that of F-actin. (c) F-actin model (in the same orientation as Fig.3b). 9

10 References 1 Brunger, A. T. Assessment of phase accuracy by cross validation: the free R value Methods and applications. Acta Crystallogr D Biol Crystallogr 49, (1993). Wu, Y. & Ma, J. Refinement of F-actin model against fiber diffraction data by long-range normal modes. Biophys J 86, (2004). van den Ent, F., Amos, L. A., & Lowe, J. Prokaryotic origin of the actin cytoskeleton. Nature 413, (2001). Page, R., Lindberg, U., & Schutt, C. E. Domain motions in actin. J Mol Biol 280, (1998). 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, (1993). Holmes, K. C. et al. Electron cryo-microscopy shows how strong binding of myosin to actin releases nucleotide. Nature 425, (2003). Holmes, K. C., Popp, D., Gebhard, W., & Kabsch, W. Atomic model of the actin filament. Nature 347, (1990). Volkmann, N. et al. The structural basis of myosin V processive movement as revealed by electron cryomicroscopy. Mol Cell 19, (2005). Otterbein, L. R., Graceffa, P., & Dominguez, R. The crystal structure of uncomplexed actin in the ADP state. Science 293, (2001). Iwasa, M. et al. Dual roles of Q137 of actin revealed by recombinant human cardiac muscle alpha -actin mutants. J Biol Chem 283, (2008). Klenchin, V. A., Khaitlina, S. Y., & Rayment, I. Crystal structure of polymerization-competent actin. J Mol Biol 362, (2006). 10

11 Supplementary Methods Collection of X-ray fiber diffraction data from F-actin sols Preparation of well-oriented F-actin sols Actin was prepared from rabbit skeletal muscle acetone powder 1. Gelsolin was prepared from bovine serum 2. Well-oriented F-actin sols were prepared as previously described 3. Gelsolin was added to a purified G-actin solution, typically at a molar ratio of 1:400 or 1:200 to control the filament length, and then KCl was added to the solution to a final concentration of 60 mm. The F-actin solution was dialyzed against a solution containing 30 mm KCl, 1 mm CaCl 2, 0.5 mm ATP, 1 mm NaN 3 1mM β-mercaptoethanol and 10mM Tris-acetate (ph 8.0). The F-actin was then collected by low speed centrifugation for a long period, typically 10,000g for ca. 30 hours, and the F-pellet was sucked into a quartz capillary. The capillary-packed F-actin sol was further concentrated by low speed centrifugation, and then was placed within a strong magnetic field of 13.5 or 18 Tesla, to further improve the orientation of F-actin. Recording and processing of X-ray diffraction patterns X-ray diffraction patterns from well-oriented F-actin sols were recorded on cm imaging plates (R-Axis 4 detector, Rigaku) by the use of synchrotron radiation at a wavelength of 1.0 Å at the beam-line BL40B2 or BL41XU, and at a wavelength of 0.9 Å at beam-line BL45XU-SAXS of SPring-8. The specimen-to-film distance, the exposure time, and the beam size were ca. 78 cm, 5 seconds, and mm, respectively, at BL41XU, and ca. 40 cm, 120 seconds, and mm, respectively, at BL40B2. The imaging plates were scanned at a 11

12 pixel size of mm. The recorded patterns were converted into reciprocal space, and the four-quadrants were averaged. Furthermore, five or ten of the four-quadrant-averaged diffraction patterns from the same sols were averaged, and finally the circular background was subtracted. From the processed patterns, the disorientation of the filaments in the sols, the pitch of the basic helix, and the most plausible helical symmetry were determined, in which the positions and the widths of the 51 & 59 Å layer-lines were defined. By the use of these parameters, layer-line intensity profiles were extracted at intervals of Å -1 by deconvoluting the processed patterns, using the software package developed by K.Hasegawa & K.Namba. Several sets of extracted layer-line intensities were averaged. Supplementary method Figure 1. Diffraction pattern from a well-oriented F-actin sol with optimal quality. The diffraction pattern was recorded at BL41XU at SPring-8. The edge of resolution is 8 Å. Grouped layer-line intensities The analysis of the diffraction patterns gave rise to the most plausible helical symmetry of

13 subunits in 153 turns of the left handed basic helix (u = 331, t = -153). The pitch of the basic helix is 59.7 Å, and the structure repeats every 9135 Å. The layer-lines are indexed as l =-153n+331m, where l is the order of the layer-line, n is the order of the Bessel term that contributes the layer-line, and m is an integer. However, the layer-lines indexed by a spacing of 9135 Å were not individually visible, and the layer-lines were fused to form several layer-lines, with a distribution very close to that obtained by the helical symmetry specified by u = 13 and t = -6. Therefore, we used the extracted layer-line intensities as the grouped layer-line intensities, indexed as l=-6n+13m. After the structure factor ( i.e. G-functions defined by Klug 4 ) was calculated by the use of a helical symmetry of 331/-153 (subunits/turns) and a repeat of 9135 Å, the structure factors were summed up in each group: I clac ( l, R) = l ' = 153n+ 331m for 2 Gn, l ' ( R) ( n, m) in l = 6n+ 13m and were used for comparisons between the extracted and calculated layer-line intensities. 13

14 Modeling the F-actin structure by X-ray fiber diffraction The outline of our procedure for modeling the F-actin structure is shown in the following Fig.2. Starting models for the subunit in F-actin 3 crystal structures + 7 orientations Rigid-body search for orientation and radial position of the subunit Normal mode-based search for the conformation of the subunit Calculation of elastic normal modes of the subunit Minimization of the target function F Molecular dynamics refinement of the subunit in F-actin MD with empirical energy including the low angle reflection term ( Å) at 400K for 3000 steps Decreasing the temperature during the following (400->10K) MD including the low reflection term ( Å) MD including the high reflection term ( Å) Final refinement by minimization of empirical energy Modification of some defects in the chain with reference to the TMR-actin crystal structure and the OMIT map Minimization including the low reflection term Minimization including the high reflection term Acceptance or rejection of the modification was judged by the R- factor-non-fit. Refined models of F-actin Supplementary method Figure 2. Outline of the procedure for F-actin modeling 14

15 1. R-factor-fit and R-factor-non-fit To check the plausibility of the refined model, we defined the un-weighted R-factors against an X-ray pattern of the fitted area and of the non-fitted area, as follows: I obs ( Ri, ϕ i ) ki calc ( Ri, ϕi ) S i / I obs ( Ri, ϕi ) i i R = where k is a scaling factor. I obs (R i,ϕ ) ι and I calc (R i,ϕ ) ι are the intensities of the pixels in the observed and calculated diffraction patterns at the polar coordinate position (R i,ϕ ), ι respectively. S i is a square element of the polar pixel. The R-factor-fit is against the fitted area (the area radially 1/56-1/6.5 Å -1 & 1/5.5-1/3.6 Å -1 and laterally from the meridian to 1/5.8 Å -1 ) and the R-factor-non-fit is against the non-fitted area (the area radially 1/6.5-1/5.5 Å -1 and laterally from meridian to 1/15 Å -1 ). The R-factor-non-fit is similar to the free R-factor in the bio-crystallography 5,6 (Supplementary Fig. 1). S i 2. Starting models The starting models for modeling F-actin were made from the straight actin polymer of the actin-formin-crystal (Fig 3a; PDB 1Y64) 7 ; the geometry of the actin subunits relative to the helix axis in F-actin was set to be the same as that in the straight polymer. The subunit was then replaced by one from the three crystal structures. The three crystal structures used were the closed conformation with (PDB 1J6Z: TMR-actin) 8 and without (PDB 2BTF) 9 the α-helical D-loop (DNase I-binding loop), and the open conformation (PDB 1HLU) 10. The crystal structure of the open conformation has several stereo-chemical defects and a large difference between the R-factor and the free R-factor. Nevertheless, we included this structure in our starting structures. This is partly because our purpose was to make our search for the subunit conformation as wide as possible and partly because Egelman s group had reported that the open conformation fit well with their EM map of F-actin 11,12. The D-loop was also started from 15

16 three different conformations, to ensure a wide search for the conformations. The coordinates 2BTF and 1HLU are structures of β-actin, in which the specific residues were replaced by the corresponding residues of α-actin. Complementation of the missing regions was also performed by the use of the Holmes model 13 for the F-actin structure. We assumed that the bound nucleotide was ADP, and we removed the γ-phosphate in 2BTF and 1HLU. We also used two ADP conformations for the open conformation: the original ADP in the open conformation and the ADP in the closed conformation. We then added 6 variations in the subunit orientation around the original one in the straight polymer. The six orientations were generated by +10 o rotations of the subunit about each of the three orthogonal axes passing through the mass center of the subunit. 3. Rigid-body search and Normal mode-based search 3-1. Elastic network of Cα atoms and normal mode analysis 14,15 The neighboring Cα atoms that lay within given standard distances were connected by imaginary springs with a common spring constant, irrespective of the real connection of the chain. As the standard distances for the Cα atom connections, four distances (8, 10, 12 and 14 Å) were tested. The mass of each amino acid residue was placed at the position of the Cα atom. To simulate the situation of ADP binding, we added the C4 position of ADP to the elastic network and placed the mass of the bound ADP on the position. The elastic network was expressed by the orthogonal mass-weighted coordinates. The potential energy (V) is: V = k / 2 i j ( ( x i x ) j 2 + ( y i y ) j 2 + ( z i z ) j 2 l ij ) 2 where k is the common spring constant and l ij is the distance between the Cα atoms of the i-th and j-th residues. The standard classical mechanics theory was used to obtain the normal modes of the elastic network derived from the actin coordinates. In the analysis, the second derivatives matrix 16

17 of the potential energy was diagonalized, by the use of the LAPACK package Target function for rigid-body search and normal mode-based search The rigid-body search and the normal mode-based search were performed by minimizing the following target function F in the resolution range of 1/56-1/7.2 Å -1 : F = w( I ( l, R ) ki i, j obs i j calc ( l, R i j, q)) 2 where w and k are a weight factor and a scaling factor, respectively. I obs (l,r) and I calc (l,r,q) are the observed and calculated intensities at position R along the l-th layer-line, respectively. The variable q is a general fitting parameter. To correct the solvent contrast, we calculated I calc (l,r,q) by the use of the effective scattering factors of each atom, which is its normal electron scattering factor less the scattering from a sphere full of water with its atomic radii defined for the individual chemical groups 13. During the minimization, the following equation was solved for an increment of δa l by calculating the inverse matrix of a kl, using the LAPACK routine (SPOTRF SPOTRI): n l a kl 2 F δ al = β k, α kl =, q q k l β k F = q k A small shift in the direction of δa l was undertaken, and thereby the target function was iteratively minimized. The derivatives were numerically calculated Rigid-body search for the orientation and the radial position of the subunit in the filament We initially used three parameters for the subunit orientation around the mass center, one parameter for its radial distance measured from the helix axis and one fudge parameter for the solvent contrast 13, to minimize the target function. The R-factor-fit values of the convergent 17

18 models were around 0.34 (Supplementary method Fig. 4) Normal mode-based search for the conformation of the subunit We subsequently altered the subunit structure by twelve additional parameters for the amplitudes of the conformational changes along the vibration directions of the twelve lower elastic normal modes 17, to minimize the target function. This search repeated a procedure consisting of 2 steps: first, the normal modes of the actin molecule were calculated as described above, and then the target function was minimized by moving not only the Cα atom but also the entire residue along the vibration directions of the normal modes. The number of iterations was 60. The models thus obtained contained violations in the polypeptide stereo-chemistry, which were removed by minimizing the conformational energy with harmonic coordinate restraints (10 kcal/å 2 ) against the Cα atom positions. The model is referred to as the normal mode-based model in this supplement. Among the resulting convergent models with low R-factors (R-factor-fit ~ 0.27: Supplementary method Fig. 4), the orientations, radial positions and conformations of the subunits were alike, irrespective of the starting coordinates. The common characteristics were a closed nucleotide-binding cleft and the tilting of subdomains 3 & 4 with respect to the helix axis, by the relative rotation of the two major domains (Supplementary method Fig. 3b). The D-loops were similarly positioned, but their conformations substantially differed from each other (Supplementary method Fig. 3b). 4. Molecular dynamics refinement The molecular dynamics refinement and the minimization of the effective energy were performed by the use of the FX-plor software 18,19. The effective energy consists of the 18

19 conformational and non-bonded interaction energy terms, including contacts between neighboring subunits related by helical symmetry, and the reflection term. The default parameters for van der Waals interactions and the force field based on CHARMM version 19 for the refinement of the crystal structure were used. No water molecules were included. The weights of the reflection term were chosen so that the gradients of the reflection term upon minimization were comparable to those of the conformational energy terms. Layer-line intensities at the low resolution area 1/56 1/6.5 Å -1 were calculated by the use of the solvent contrast-corrected atomic scattering factors described in the preceding section, while the intensities at the high resolution area 1/6.5 1/3.3 Å -1 were calculated by the use of the atomic scattering factors in the international tables 20. Therefore, the two atomic scattering factors are discontinuous at 1/6.5 Å -1. The calculated layer-line intensities were independently scaled against the observed layer-line intensities on either side of 1/6.5 Å -1, which are areas with higher and lower resolutions. These correspond to the ranges for the MD refinement and the final minimization with the low reflection term or with the high reflection term described below Refinement by simulated annealing molecular dynamics The starting models for the MD refinement included not only the normal mode-based models described above, but also some modified models. The modified starting models were made by a partial extension of the hydrophobic plug or by a combination of two major domains in two different normal mode-based models. The total number of starting models for the MD refinement was 21: 9 models derived from the crystal structures, 6 models with the extended hydrophobic plug and 6 models obtained by a combination of the two major domains. The models with a partial extension of the hydrophobic plug were made as follows: when the normal mode based-search and the MD refinement were performed against the simulated intensities 19

20 calculated from the Lorenz model 21, the hydrophobic plug was partially extended. After we aligned the models onto residues & residues of the normal mode-based models, the partially extended plugs were substituted for the hydrophobic plugs of the normal mode-based models. The models to connect the two major domains in two different normal mode-based models were made as follows: after the subunits of the normal mode based-models were aligned by azimuthally rotating them around the F-actin helical axis, the peptide chains forming the two major domains in the two models were exchanged at the residues where the Cα atoms overlap: for example, we exchanged the two major domains of the models arising from the open and the closed starting models at residue 135 and residue 331. To remove the clash of the side-chains that occurred upon the exchange of the peptide chains, we minimized the conformational energy with harmonic coordinate restraints against the Cα atom positions. Subsequent MD refinement of these modified models did not provide a low R-factor-non-fit. Therefore, these modified models were rejected for the MD process. (Supplementary method Figs. 3 & 4). We performed five or ten sessions of MD for each model. Initially, we added the reflection term against the layer-line amplitudes of the lower resolution area 1/56 1/6.5 Å -1. The MD with the reflection term was performed at an interval of 0.001ns for 3000 steps at 400K. The thermal energy of 400K is about 0.8 kcal/mol, while the bonding energy per hydrogen bond is 3-4 kcal/mol, which maintained the secondary structures in the protein at 400K; consequently, the hydrogen bonds would sometimes be broken, but the secondary structures of actin would be maintained. Next, we repeatedly performed the MD with the reflection term against the amplitudes of the higher resolution area 1/5.5 1/3.3 Å -1 (with lateral coordinates from 0 to 1/5.5 Å -1 ) for 100 steps, and the MD against the amplitude of the lower resolution area 1/56 1/6.5 Å -1 for 100 steps. While iterating the two kinds of MD 20 times, we decreased the temperature gradually from 400 K to 10K. Finally, we minimized the 20

21 effective energy with the high resolution reflection term, by the conjugate gradient method. We found two models that provided substantially lower R-factor-non-fit values than the others in 128 MD trials (Supplementary method Fig. 4; R-factor-fit ~ 0.14, R-factor-non-fit ~ 0.30); the two models had the common characteristics of a closed nucleotide-binding cleft, an extended D-loop and a round hydrophobic plug (Supplementary method Fig. 3c). These models were derived from the starting models with the open conformation. However, the nucleotide-binding cleft closed at the stage of the normal mode-based search, and the D-loop conformation fit to a groove of the upper subunit at the molecular dynamics refinement stage. The R-factor-non-fit values of the models refined from the Lorenz model 21 were higher than those of the two models (Supplementary method Fig. 4) Final refinement by minimization of the empirical energy In the two models, some of the hydrogen bonds of the α-helix and the β-sheets in the core region of the molecule were disrupted. The Ramachandran plot of the models showed worse stereo-chemistry in these regions of the models. We modified the models, by considering the stereo-chemistry in the crystal structure of TMR-actin 8. We subsequently iterated two kinds of energy minimization, with the low resolution reflection term (1/56 1/7.2 Å -1 ) and with the high resolution reflection term (1/5.5 1/3.3 Å -1 ) times, and checked the R-factor-fit and the R-factor-non-fit. At this step, the weights of reflection terms were reduced to one-half or two-thirds of the value from the molecular dynamics refinement process, to restore the stereochemistry of the protein. When the R-factor-non-fit decreased, the modification was basically accepted. To refine some parts of the resulting models, we made an OMIT refined map 22 by the use of the layer-line intensities within the resolution of 1/56 1/7.2 Å -1. We set the 21

22 occupancy of the atoms to omit in the model to zero, and refined the model by using the same procedure as in the MD refinement. The OMIT refined maps were made from the amplitudes of 6fo-5fc and the model phase. In the omit map of residues 39-50, an extra peak near Val45 was detected. In the omit map of residues and , there are 2 extra masses that extend to residues and to the main chain part near residue 39 from the plug. After we slightly modified the conformation form of the hydrophobic plug according to the OMIT map, we performed the energy minimization and checked the R-factor-fit and the R-factor-non-fit. In the end, we selected the F-actin structural model that provided the lowest R-factor-non-fit (Fig. 1). The overall similarities between the calculated and observed intensities are satisfactory, even in the non-fitted area: R-factor-fit = 0.143, R-factor-non-fit = and R-factor-non-fit (overall) = (Fig. 1). 5. Contribution of the diffraction to the structural determination We examined the contribution of the reflection term to the determination of the F-actin structure. We calculated R-factor-fit and R-factor-non-fit after we shifted a segment (2, 4 or 6 successive amino acid residues) from the plausible position in our F-actin atomic model in the direction of the helix axis (z) or in the two directions perpendicular to the helix axis (x & y) by -3 to 3 Å. We selected 19 segments at random. In several shifts, we observed that R-factor-fit and R-factor-non-fit slightly decreased, although the conformational energy increased. Supplementary method Figure 5 shows the average of the individual R-factors for the shifts of 19 segments versus the shift size. A two residue shift along the helix axis by 2 Å caused the R-factor-non-fit to increase by 5%. The R-factor is sensitive to a shift of residues in the direction of the helix axis. On the other hand, a six residue shift in the plane perpendicular to the helix axis by 3Å gave rise to a 5 % increase in an R-factor-non-fit. The R-factor is insensitive to the shift of residues in the plane perpendicular to the helix axis. Therefore, in our modeling, the 22

23 reflection term must have restricted the positions of the residues within 2Å, whereas the conformational energy term must have determined the structure of finer details of the structure. 23

24 Initial models in the straight polymer After the normal mode-based search After the MD refinement Supplementary method Figure 3 Changes of the actin subunit structure in F-actin after each modeling step. The left, middle and right panels are the side-view of subdomains 3 & 4 alone, and the front-view and the side-view of subdomains 1 & 2 alone, respectively (a) Superposition of three structures of the starting models the open conformation (red), and the closed conformation with (green) and without the helical D-loop (blue). Each structure is oriented relative to the helix axis, as in the straight polymer in the formin-actin crystal (PDB:1Y64). (b) Superposition of three convergent structures that originating from the three structures in (a) after the normal mode-based search (these correspond to the three blue points in the nine blue models in Supplementary method Fig. 4). The color code is the same as in (a). (c) Superposition of two structures with lower R-factor-non-fit values after the molecular dynamics simulation refinement (corresponding to the two points circled in Supplementary method Fig. 4). 24

25 R-factor-non-fit R-factor-fit Supplementary method Figure 4 R-factor-non-fit (radially 1/6.5-1/5.5 Å -1 and laterally to 1/15 Å -1 ) versus R-factor-fit (radially 1/56-1/6.5 & 1/5.5-1/3.6 Å -1 and laterally to 1/5.8 Å -1 ). Points were plotted for the individual models after the rigid-body search (green), after the normal mode-based search (blue), after the molecular dynamics simulation refinement (red), and for the models refined from the Lorenz model (black). The rigid-body search and the normal mode-based search were performed against data to 1/56-1/7.2 Å -1. However, we computed the R-factor-fit including the high resolution area, 1/ Å -1, and therefore the R-factor-fit is somewhat high. Points in the blue circle indicate the two MD converged models with lower R-factor-non-fit values. The figure shows that the R-factor-fit decreased from ~0.36, via ~0.27, to ~0.14 as we in turn performed the rigid-body search, the normal mode-based search and the MD refinement. The figure also shows that the models providing the low R-factor-fit are not necessarily good: the R-factor-fit could be vastly reduced in exchange for a slight increase in the R-factor-non-fit. 25

26 X Y Z (helix axis) Shift of 2 successive residues R-factor-fit R-factor-non-fit Shift (Å) 0.20 Shift of 4 succesive residues Shift (Å) X Y Z (helix axis) 0.24 R-factor-fit R-factor-non-fit X Y Z (helix axis) Shift (Å) 0.20 Shift of 6 successive residues Shift (Å) R-factor-fit R-factor-non-fit Shift (Å) Shift (Å) Supplementary method Figure 5 R-factor versus shift size. See text for details. 26

27 EM reconstruction Structure determination The cryo grids were prepared with the same solution conditions described previously 23. Electron micrographs were obtained and digitized as described 23. The phase of the contrast transfer function (CTF) was corrected and the image analysis was performed as described (step 1 in the published procedure 24 ). The starting model for the reconstruction was the Lorenz model 21. After the structure was determined, the amplitude of the CTF was corrected as described 24. The final reconstruction was achieved from actin filament images, including 80,145 actin monomers. All of the image analysis was performed on Eos 25. Evaluation of the resolution We divided the images of the actin filaments into two groups and reconstructed two 3D maps 26, which were compared by Fourier Shell Correlation 27. The resolution was estimated to be 13.8 Å, with a threshold of 0.5 (Supplementary Fig. 3). Comparison with atomic models Each non-hydrogen atom in the atomic model was replaced by a Gaussian density distribution with a radius of 1 Å (= r o ), ρ(r) = exp(-r 2 /r 2 o ), and a 3D density map with a pixel size of 3.4 Å was generated. This approximation of atom density scarcely affected the comparison result in the corresponding resolution range. The 200 % volume contour in the EM map was defined as zero, and the pixels with negative values in the EM map were set to zero. The Fourier Shell Correlation 27 was then calculated between the EM map and the map from the atomic model (Supplementary Fig. 3). 27

28 References Spudich, J. A. & Watt, S. The regulation of rabbit skeletal muscle contraction. I. Biochemical studies of the interaction of the tropomyosin-troponin complex with actin and the proteolytic fragments of myosin. J Biol Chem 246, (1971). Kurokawa, H. et al. Simple and rapid purification of brevin. Biochem Biophys Res Commun 168, (1990). Oda, T. et al. Effect of the length and effective diameter of F-actin on the filament orientation in liquid crystalline sols measured by x-ray fiber diffraction. Biophys J 75, (1998). Klug, A., Crick, F. H., & Wyckoff, H. W Diffraction by helical structure. Acta Cryst 11, (1958). Brunger, A. T. Assessment of phase accuracy by cross validation: the free R value. Methods and applications. Acta Crystallogr D Biol Crystallogr 49, (1993). Wu, Y. & Ma, J. Refinement of F-actin model against fiber diffraction data by long-range normal modes. Biophys J 86, (2004). Otomo, T. et al. Structural basis of actin filament nucleation and processive capping by a formin homology 2 domain. Nature 433, (2005). Otterbein, L. R., Graceffa, P., & Dominguez, R. The crystal structure of uncomplexed actin in the ADP state. Science 293, (2001). Schutt, C. E. et al. The structure of crystalline profilin-beta-actin. Nature 365, (1993). Chik, J. K., Lindberg, U., & Schutt, C. E. The structure of an open state of beta-actin at 2.65 Å resolution. J Mol Biol 263, (1996). Belmont, L. D., Orlova, A., Drubin, D. G., & Egelman, E. H. A change in actin conformation associated with filament instability after Pi release. Proc Natl Acad Sci U S A 96, (1999). Galkin, V. E., VanLoock, M. S., Orlova, A., & Egelman, E. H. A new internal mode in F-actin helps explain the remarkable evolutionary conservation of actin's sequence and structure. Curr Biol 12, (2002). Holmes, K. C., Popp, D., Gebhard, W., & Kabsch, W. Atomic model of the actin filament. Nature 347, (1990). Bahar, I., Atilgan, A. R., & Erman, B. Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. Fold Des 2, (1997). 28

29 Tama, F. & Sanejouand, Y. H. Conformational change of proteins arising from normal mode calculations. Protein Eng 14, 1-6 (2001). E. Anderson et al. LAPACK Users' Guide Third Edition. (1999). Tirion, M. M., ben-avraham, D., Lorenz, M., & Holmes, K. C. Normal modes as refinement parameters for the F-actin model. Biophys J 68, 5-12 (1995). Wang, H. & Stubbs, G. Molecular dynamics in refinement against fiber diffraction data. Acta Crystallogr A 49, (1993). Brunger, A. T. X-PLOR, version 3.1. A system for X-ray crystallography and NMR. (Yale University Press, New Haven, CT, 1992). Brown, P.J. et al. in International Tables for Crystallography, Vol.C, edited by A.J.C. Wilson & E. Prince (Springer / IUCr, 2006), pp 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, (1993). Namba, K. & Stubbs, G. Difference Fourier syntheses in fiber diffraction. Acta Cryst. A43, (1987). Narita, A., Takeda, S., Yamashita, A., & Maeda, Y. Structural basis of actin filament capping at the barbed-end: a cryo-electron microscopy study. Embo J 25, (2006). Narita, A. & Maeda, Y. Molecular determination by electron microscopy of the actin filament end structure. J Mol Biol 365, (2007). Yasunaga, T. & Wakabayashi, T. Extensible and object-oriented system Eos supplies a new environment for image analysis of electron micrographs of macromolecules. J Struct Biol 116, (1996). Frank, J. Single-particle imaging of macromolecules by cryo-electron microscopy. Annu Rev Biophys Biomol Struct 31, (2002). van Heel, M. Similarity measures between images. Ultramicroscopy 21, (1987). 29

30 Supplementary Video Legends Supplementary Video 1 Comparison of our F-actin model and the Holmes 2003 model with the EM map. The Holmes 2003 model 1 (red) is compared with our model (blue). Although both appear to fit well to the EM envelope, the peptide chain of our model is almost completely within the envelope, while that of the Holmes 2003 model has some edges outside of the envelope. This video is made by rotating of Supplementary Figure 5a. Supplementary Video 2 Comparsion of our F-actin model and the Volkmann model with the EM map. Volkmann et al. 2 model (pink) is compared with our model (blue). Volkmann et al. modified the position of the C-terminus of the Holmes 2003 model to match their EM map of F-actin. This video is made by rotating of Supplementary Figure 5b. 1 2 Holmes, K. C. et al. Electron cryo-microscopy shows how strong binding of myosin to actin releases nucleotide. Nature 425, (2003). Volkmann, N. et al. The structural basis of myosin V processive movement as revealed by electron cryomicroscopy. Mol Cell 19, (2005). 30