Supporting InformationLasker et al. 10.1073/pnas.1120559109SI Material and Methods.Sample Preparation, Cryo-EM, and XL/MS. Sample preparation, cryo-EM single particle analysis, and XL/MS were performed as de-scribed in ref. 1. In brief, 26S proteasomes were purified from3×FLAGRpn11 S. pombe cells and the vitrified sample was imagedusing a Tecnai F20 transmission electron microscope (FEI). From375,000 single particles, we computed an 8.4-Å resolution map(Fourier-Shell correlation, FSC ¼ 0.5) using XMIPP (2) (Fig. S1).The local resolution at each voxel was computed using the FSC oftwo reconstructions from each 50% of the particles within a sof-tened sphere (radius ¼ 22 Å) centered at the respective vox-el (Fig. 1B).

XL/MS. Purified 26S proteasomes from S. pombe and S. cerevisiaewere concentrated to 1 mg∕mL. 50 μL of sample were cross-linked with 1 mM DSS (H12∕D12, from Creative Molecules).The cross-linking reaction was quenched with 50 mM ammoniumbicarbonate, and proteins were reduced, alkylated and digestedwith 1 μg trypsin (Promega). Cross-linked peptides were enrichedusing peptide size exclusion chromatography and analyzed by LC-MS/MS using a Thermo LTQ Orbitrap XL mass spectrometer.

MS data were analyzed using xQuest (3). The xQuest searchwas performed against target and decoy databases of previouslyidentified proteasome proteins with a precursor mass tolerance of10 ppm. For matching of fragment ions, tolerances of 0.2 Da forcommon ions and 0.3 Da for cross-link ions were used. FDRswere estimated based on the decoy counts using the softwarexProphet. All cross-link identifications corresponding to anFDR <5% were accepted.

Comparative Modeling of the Rpn Subunits. For each Rpn subunit,HHpred (4) was used to search for homologous structures (tem-plates), followed by building multiple comparative models withMODELLER-9v8 (5), based on combinations of templates se-lected manually (Table S3); unaligned termini were truncated.The models were scored by TSVMod (6), a program for predict-ing the Cα root-mean-square error. Models with predicted Cα-rmsd errors lower than 8 Å were used for subsequent analyses.

Multiple Fitting of the PCI Subunits.MultiFit (7) was used to simul-taneously fit the PCI subunit comparative models into their un-

iquely localized regions. We ran MultiFit 54 times, each time witha different combination of comparative models, because we couldnot determine a priori which comparative model to use for eachof the PCI subunits. Because the relative orientation between thePCI domain and the α-solenoid domain of each PCI subunit var-ied widely among its comparative models, we allowed the two do-mains to move relative to each other as rigid bodies, restrained bya maximum allowed distance. We then clustered the two top-scor-ing models from all MultiFit runs (108 models in total) accordingto their PCI-domain centroids. The models clustered into 11groups. The PCI-domain configuration shared by the three lar-gest clusters (with 15,15, and 12 members, respectively) clearlyindicated that the PCI subunits interact via their PCI do-mains (Fig. S3).

Flexible Fitting of the PCI Subunits, the AAA-ATPase Hexamer, and theCP. We used MDFF (8) to fit available atomic models into thecryo-EM map. All MDFF runs were done with default para-meters, using implicit solvent and temperature annealing. Thecomparative models of the AAA-ATPase hexamer and the CPwere first rigidly fitted into the density and then flexibly fitted.To fit the PCI-domain-containing subunits, the PCI domains ofthe comparative models from the three main clusters found byMultiFit were refined first, while the α-solenoid domains wereinternally restrained to move as rigid bodies. Additional restraintsbetween PCI-domain β-sheets enforced contacts observed be-tween the PCI domains of Rpn6 monomers in the crystal(PDB ID code 3TXM). In the second step, the α-solenoid re-straints were released and the entire subunits were allowed tofit into the cryo-EM map. To prevent the Rpn12 α-solenoid he-lices from moving into neighboring areas for which no atomicmodels were available, distance restraints between α-helices wereimposed. The accuracy of the flexibly refined models strongly de-pends on the local resolution of the cryo-EM map (Fig. S1) andthe quality of the comparative models (Table S3).

Visualization. All figures were generated using Chimera (9) andVMD (10).

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Fig. S1. Resolution assessment of the S. pombe 26S proteasome cryo-EM map. The Fourier-Shell Correlation (FSC) coefficient decreases below 0.5 at a re-solution of approximately 8.4−1 Å−1.

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Fig. S2. Comparative modeling of the Rpn subunits. The sequence segments covered by atomic models are indicated. A representative model for each subunitis shown. The PCI domain is indicated in yellow.

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Fig. S3. Multiple fitting of the PCI-domain-containing subunits and flexible fitting. (A) Comparative models of the PCI-domain-containing subunits selectedfor fitting are indexed as in Table S3. (B) Fifty-four MultiFit runs, one for each comparative model combination. (C) Representatives of the three largest clustersamong 108 MultiFit models (two top ranking models for each of the 54 runs). The models were clustered according to their PCI-domain centroids. The PCI-domain centroids, the main principal direction of the α-solenoid domains, as well as the atomic model are shown for each of the three cluster representatives.(D) Best-scoring combination of comparative models (green) fitted as rigid bodies into the cryo-EMmap that is shown in gray (Left); models after flexible fittingby MDFF (8), colored according to the local cross-correlation coefficient of the density of the model and the cryo-EMmap (computed analogously as for Fig. 1B)shown with (Middle) and without the cryo-EM map (Right). The local cross-correlation coefficient (colorcode explained in legend) is an indicator for the localconfidence of the atomic models. The local correlation suggests that the accuracy of models is higher for the PCI domains than for the solenoid domains, inparticular those of Rpn3 and Rpn7 (second and third from the right, respectively). (E) Cross-correlation coefficients (CCC, computed by UCSF Chimera) (9) of PCI-domain-containing subunits and the AAA-ATPase hexamer (Fig. 5) before (red) and after flexible fitting (blue). For all subunits, with the exception of Rpn6,whose initial model based on the D. melanogaster Rpn6 crystal structure (PDB ID code 3TXM), the correlation coefficients improve notably.

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Fig. S4. Fitting of Rpn2, Rpn6, Rpn8, and Rpn10 into the cryo-EMmap. (A) An atomic model of the Rpn2 LRR domain (residues 309–712) (11) was fitted into theB-factor corrected density (B ¼ −1;000 Å2) using MOLMATCH (12). The first five local maxima of the local correlation function are plotted in descending order(I) and a slice of the correlation function is shown with its maximum indicated (II). Moreover, the atomic model (green) is superposed onto the density (gold)identified by the correlation maximum (III). (B) Same for the Rpn6 crystal structure (PDB ID code 3TXM), which is colored according to its B factor, ranging fromgreen to red in III. (C andD) Same for crystal structure of the Rpn8MPN domain (PDB ID code 2O95), and the vonWillenbrand factor A (VWA), domain of Rpn10(PDB ID code 2X5N). (E) The fitted subunits placed in the cryo-EM density, seen from two different views.

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Fig. S5. Cross-links in the atomic model of the 26S proteasome. (A–D) The cross-links (Table S1) are plotted in the resulting models, seen from four differentviews. The Cα atoms of the cross-linked residues pairs are displayed as spheres that are connected by cylinders. The coloring is chosen according to subunit type(nonATPases: green, ATPases: blue, CP: red). Accordingly, cylinders connecting residues from different subunit types have two colors. Of 55 cross-linked Cα pairs,only two are more than 40 Å apart from each other, involving Rpt4 and Rpn5 (48 Å), as well as Rpn9 and Rpt3 (77 Å). This would suggest a false-positive rate<4% in the cross-linking data, which is predicted to be better than 5%.Moreover, the Rpt4-Rpn5 cross-link could also be due to motion of the Rpt4/Rpt5 coiled-coil. (E) Histogram of Cα-Cα distances for the cross-links.

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Fig. S6. Ensemble analysis. To assess the redundancy of the restraints, we omitted one proteomics or residue-specific cross-linking restraint at a time andrecalculated 5 · 105 top-scoring solutions violating at most five restraints for each restraint subset. We then compared the resulting “jack-knife” ensembleswith the union of the refined representative models from each one of the three clusters computed from all restraints (union model). The rows of the matrixcorrespond to the individual omitted restraints and the columns correspond to the individual Rpn subunits. Each bin indicates the sensitivity of the subunitlocalization to the presence of a specific restraint, quantified by the average centroid distance between the union and jack-knife subunit models. Even afteromitting one restraint at a time, the jack-knife ensembles remain similar to the union model, with the maximum sensitivity of approximately 13.5 Å.

Fig. S7. Putative DNA binding by Rpn6. The transcription factor E2F-DP in complex with DNA (PDB ID code 1CF7) was structurally aligned to the winged helixmotif from Rpn6 (white) using MUSTANG (13). The bound DNA molecule (green) does not yield major clashes with surrounding subunits.

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Fig. S8. Analysis of the space accessible for the AAA-ATPase coiled coils pairs. The maximum opening angles of cones originating from the coiled-coil hingeresidues corresponding to Pro62 in PAN were computed so that the coiled coils do not penetrate neighboring densities (Rpns: gray, remaining AAA-domains:blue). The opening angles were approximately 40° for the Rpt1/2 coiled-coil, 15° for Rpt6/3, and 40° for Rpt4/5 (blue cylinders).

Table S1. Cross-linked lysine residues in the 26S proteasomes fromS. pombe and S. cerevisiae

Residue 1 Residue 2 Species

IntraCP (6 from S. pombe and 1 from S. cerevisiae)α1:102 α2:91 S. pombeα1:102 α2:98 S. pombeα1:57 α7:177 S. pombeα2:176 α3:54 S. pombeα2:176 α3:50 S. pombeα6:115 α7:89 S. pombeα1:102 α2:91 S. cerevisiaeCP-ATPase (4 from S. pombe and 2 from S. cerevisiae)α1:169 Rpt4:297 S. pombeα2:176 Rpt6:390 S. pombeα4:168 Rpt1:422 S. pombeα4:168 Rpt1:426 S. pombeα4:176 Rpt1:415 S. cerevisiaeα5:66 Rpt1:426 S. cerevisiaeIntra ATPase (32 from S. pombe and 8 from S. cerevisiae)Rpt1:422 Rpt2:357 S. pombeRpt1:426 Rpt2:357 S. pombeRpt1:68 Rpt2:93 S. pombeRpt1:124 Rpt3:207 S. pombeRpt1:112 Rpt4:38 S. pombeRpt1:120 Rpt4:205 S. pombeRpt1:102 Rpt5:172 S. pombeRpt1:124 Rpt5:124 S. pombeRpt1:124 Rpt5:172 S. pombeRpt1:207 Rpt5:413 S. pombeRpt1:344 Rpt5:432 S. pombeRpt2:264 Rpt6:84 S. pombeRpt2:264 Rpt6:90 S. pombeRpt2:45 Rpt6:90 S. pombeRpt3:378 Rpt4:297 S. pombeRpt3:207 Rpt5:124 S. pombeRpt3:299 Rpt6:357 S. pombeRpt3:299 Rpt6:390 S. pombeRpt4:10 Rpt5:51 S. pombeRpt4:10 Rpt5:54 S. pombeRpt4:71 Rpt5:124 S. pombeRpt4:47 Rpt5:77 S. pombeRpt4:196 Rpt5:217 S. pombeRpt4:196 Rpt5:350 S. pombeRpt4:205 Rpt5:124 S. pombeRpt4:24 Rpt5:64 S. pombeRpt4:297 Rpt5:217 S. pombeRpt4:318 Rpt5:217 S. pombeRpt4:38 Rpt5:64 S. pombeRpt4:38 Rpt5:72 S. pombeRpt4:38 Rpt5:77 S. pombeRpt4:41 Rpt5:64 S. pombeRpt1:124 Rpt5:124 S. cerevisiaeRpt3:186 Rpt4:164 S. cerevisiaeRpt3:299 Rpt6:390 S. cerevisiaeRpt4:14 Rpt5:44 S. cerevisiaeRpt4:318 Rpt5:212 S. cerevisiaeRpt4:37 Rpt5:75 S. cerevisiaeRpt4:41 Rpt5:75 S. cerevisiaeRpt4:71 Rpt5:124 S. cerevisiae

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Residue 1 Residue 2 Species

nonATPase-ATPase (12 S. pombe, 6 S. cerevisiae)Rpn10:30 Rpt5:54 S. pombeRpn11:246 Rpt3:49 S. pombeRpn11:276 Rpt3:49 S. pombeRpn11:276 Rpt3:94 S. pombeRpn11:281 Rpt3:49 S. pombeRpn2:806 Rpt2:93 S. pombeRpn2:703 Rpt6:78 S. pombeRpn2:703 Rpt6:80 S. pombeRpn5:170 Rpt4:153 S. pombeRpn5:200 Rpt4:153 S. pombeRpn5:204 Rpt4:153 S. pombeRpn6:272 Rpt4:164 S. pombeRpn11:153 Rpt6:56 S. cerevisiaeRpn2:703 Rpt2:104 S. cerevisiaeRpn2:703 Rpt6:79 S. cerevisiaeRpn5:203 Rpt4:153 S. cerevisiaeRpn6:185 Rpt3:193 S. cerevisiaeRpn9:74 Rpt5:44 S. cerevisiaeintra nonATPase (3 S. pombe, 5 S. cerevisiae)Rpn11:281 Rpn3:465 S. pombeRpn3:314 Rpn7:397 S. pombeRpn3:318 Rpn7:69 S. pombeRpn2:625 Rpn3:463 S. cerevisiaeRpn2:925 Rpn5:7 S. cerevisiaeRpn2:178 Rpn9:111 S. cerevisiaeRpn3:277 Rpn7:397 S. cerevisiaeRpn5:286 Rpn9:135 S. cerevisiae

For each pair of cross-linked lysines, the subunit name and the residueindices in the respective subunit from S. pombe are listed. ATPase refersto the AAA-ATPase hexamer.

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Table S2. Protein interactions in the RP involving six or less subunits

Subcomplex Technique References Species

Rpt1, Rpt2 IVB, x-link (14–17) sc,hRpt1, Rpt3 x-link (14) hRpt1, Rpt2, Rpt3, Rpt6 IVB (15) hRpt1, Rpt2, Rpt5, Rpn1 IVPD (18) scRpt1, Rpn1 IVB (17, 19) hRpt1, Rpt2, Rpn1 IVB (17, 20) hRpt2, Rpt6 x-link (14) hRpt2, Rpn1 IVPD, 2h, IVB (17, 21–23) hRpt2, alpha4 IVPD, 2h (22, 24) hRpt2, Rpn12, Rpn2, Rpt1, Rpn13, Rpn8 IVPD (25) scRpt3, Rpt4 2h (22, 26, 27) scRpt3, Rpt5 2h, x-link (14, 26–29) sc,hRpt3, Rpt6 2h, IVB, IVPD (15, 22, 26, 28, 30) sc,hRpt3, Rpn11, Rpt6, Rpn8 IVPD (31) scRpt4, Rpt5 2h, IVB, x-link, IVPD (14, 15, 20, 23, 28, 29) w,sc,hRpt4, Rpt6 Y2h, x-link (14, 22, 32) sc,hRpt4, alpha4 Y2h (22, 23) sc,wRpt4, alpha6 x-link (14) hRpt6, alpha2 x-link (33) pRpt6, Rpn1 IVB (34) scRpt6, Rpn2 x-link (14) hRpn1, Rpn10 IVB (19, 35) scRpn1, Ubp6 IVB (36) spRpn2, Rpn13 2h, IVPD (29, 37, 38) dm,sc,spRpn3, Rpn5 x-link (39) scRpn3, Rpn5, Rpn8 x-link (39) scRpn3, Rpn5, Rpn8, Rpn9 x-link (39) scRpn3, Rpn5, Rpn7, Rpn9, Rpn11 x-link (39) scRpn3, Rpn7 2h (23, 28, 29) sc,w,hRpn3, Rpn11 IVB (40) scRpn3, Rpn12 2h (22, 28, 41) scRpn3, Rpn15 x-link (39) scRpn5, Rpn6 2h (22, 29, 42) scRpn5, Rpn6, Rpn8 WCMS (39) scRpn5, Rpn6, Rpn8, Rpn9 WCMS (39) scRpn5, Rpn8, Rpn9 WCMS (39) scRpn5, Rpn8 IVPD (43) hRpn5, Rpn9 2h (28, 37) sc,dmRpn6, Rpn7 IVB (44) dmRpn6, Rpn8, Rpn9 WCMS (39) scRpn7, Rpn15 x-link (39) scRpn8, Rpn9 2h (22, 23) scRpn8, Rpn11 2h (23, 26, 28, 37) sc,dmRpn9, Rpn11 2h (23, 28) scRpn10, UCH37 IVPD (36) spRpn12, UCH37 IVB, 2h (45) hRpn13, UCH37 IVPD, IVB (38, 43) sp

Protein–protein interactions were compiled from two-hybrid screens (2h), chemical cross-linking (x-link), invitro binding assays (IVB), different in vivo pull-down experiments (IVPD), and whole complex massspectrometry (WCMS). The data were obtained from 26S proteasomes of Homo sapiens (h),Saccharomyces cerevisiae (sc), Schizomycetes pombe (sp), Sus barbatus (p), Drosophila melanogaster (dm),and Caenorhabditis elegans (w).

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Table S3. Comparative modeling of the PCI-domain-containing subunits Rpn3/5/6/7/9/12

Model, used formultiple fitting (Y/N)

Templates(PDB code, chain id, region,aligned region on target)

Modeled region (Residuerange), Coverage (%)

TSVMod PredictedCα rmsd (Å) (33)

TSVMod Predicted nativeoverlap at 3.5 Å (%)

Rpn3Rpn3_1, N 1hz4, A, 1–373, 50–453 67–448, 77% 9.2 41Rpn3_2, N 1hz4, A, 1–373, 50–453 59–448, 78% 11.0 33

3q15, A, 4–376, 51–4111qqe, A, 2–288, 73–3692ifu, A, 2–307, 67–4023u4t, A, 1–268, 73–368

Rpn3_3, Y 3txm, A, 87–353, 167–426 124–425, 60% 5.3 571qqe, A, 37–265, 125–347

Rpn3_4, Y 3txm, A, 87–353, 167–426 124–427, 60% 6.0 601qqe, A , 37–265, 125–3473chm,A, 26–158, 292–427

Rpn3_5, Y 3txm, A, 87–353, 167–426 128–424, 60% 5.5 603chm, A, 26–158, 292–4271hz4, A, 55–287, 129–353

Rpn5Rpn5_1, N 2y4t, A, 41–446, 2–432 1–423, 95% 14.2 11Rpn5_2, N 2y4t, A, 41–446, 2–432 1–423, 95% 14.8 8

1hz4, A, 2–373, 1–3541qqe, A, 1–292, 10–3233q15, A, 69–375, 1–255

Rpn5_3, N 3txm, A, 3–352, 45–399 23–399, 85% 11.0 132ifu, A, 2–231, 23–248

Rpn5_4, Y 3txm, A, 3–352, 45–399 24–398, 85% 7.2 571ufm, A, 5–78, 329–4023chm, A, 4–158, 225–4012ifu, A, 2–231, 23–248

1qqe, A, 43–228, 58–241Rpn5_5, N 3txm, A, 3–352, 45–399 24–398, 85% 8.9 34

1ufm, A, 5–78, 329–4022ifu, A, 2–231, 23–248

Rpn7Rpn7_1, N 1qqe, A, 2–288, 39–318 39–356, 77% 13.7 30Rpn7_2, N 1qqe, A, 2–288, 39–318 22–356, 82% 14.8 8

3gw4, A, 2–202, 17–2731elr, A, 1–129,1 07–2563gyz, A, 2–150, 75–2392xcb, A, 1–142, 86–2461ufm, A, 6–84, 304–382

Rpn7_3, Y 3txm, 90–352, 112–373 37–356, 78% 6.2 623chm, A, 25–161, 230–3782ifu, A, 53–259,3 9–256

Rpn7_4, N 3txm, A, 90–352, 112–373 39–373, 82% 9.7 281ufm, A, 12–79, 310–3771qqe, A, 57–275, 92–3052ifu, A, 53–259, 39–256

Rpn7_5, Y 3txm, A, 90–352, 112–373 87–346, 64% 4.1 741ufm, A, 12–79, 310–3773chm, A, 25–161, 230–3781qqe, A, 57–275, 92–3052ifu, A, 53–259, 39–256

Rpn9Rpn9_1, N 2ifu, A, 30–307, 1–278 1–324, 85% 9.0 35

1wi9, A, 4–72, 274–346Rpn9_2, N 2ifu, A, 30–307, 1–278 1–342, 87% 10.6 34

3chm, A, 2–169, 170–3533edt, B, 19–282, 1–2633as5, A, 2–185, 1–2002fo7, A, 1–136, 25–1921wi9, A, 4–72, 274–3461ufm_A, 4–84, 260–349

Rpn9_3, Y 3chm, A, 24–169, 201–353 1–339, 89% 6.5 583txm, A, 25–352, 20–3403edt, B, 22–199, 4–189

Rpn9_4, Y 3txm, A, 25–352, 20–340 1–339, 89% 4.5 701ufm, A, 14–78, 270–3432ifu, A, 83–261, 85–267

Rpn9_5, Y 3chm, A, 24–169, 201–353 1–399, 89% 6.8 57

Lasker et al. www.pnas.org/cgi/doi/10.1073/pnas.1120559109 11 of 14

Model, used formultiple fitting (Y/N)

Templates(PDB code, chain id, region,aligned region on target)

Modeled region (Residuerange), Coverage (%)

TSVMod PredictedCα rmsd (Å) (33)

TSVMod Predicted nativeoverlap at 3.5 Å (%)

3txm, A, 25–352, 20–3401ufm, A, 14–78, 270–3432ifu, A, 83–261, 85–2673edt, B, 22–199, 4–189

Rpn12Rpn12_1, N 1rz4, A, 1–222, 1–269 18–262, 90% 9.6 37Rpn12_2, Y 1rz4, A, 1–222, 1–269 51–221, 63% 5.4 65

3txm, A, 172–351, 52–2221umf, A, 11–79, 166–227

Rpn12_3, Y 1rz4, A, 1–222, 1–269 51–211, 59% 3.7 783txm, 172–351, 52–222

Rpn12_4, Y 3txm, 172–351, 52–222 53–221, 63% 3.6 791umf, A, 11–79, 166–227

In addition, we used a comparative model of the AAA-ATPase hexamer based on the PAN structures (PDB ID codes 3H43 and 3H4M).Comparative models for Rpn1/2/8/11 were also built but not used here. The comparative model for Rpn6 was calculated in a previous study(44). Coverage indicates the percentage of target residues in the modeled region. The TSVmod program was used to predict modelaccuracies in terms of the Cα rmsd and native overlap at 3.5-Å cutoff (33).

Table S4. Representation of the S. pombe 26S proteasome RP subunits

Subunit No. of residues Coarse-grained representation Atomic representationName, UniProt code,

UniProt nameNo. of beads (50 residues per bead),

Rigid (R)/Flexible (F), No. of sampled localizationsFirst–last residue

in a segment

Rpt1, O42931, PRS7_SCHPO 438 9, R, 1 77–427Rpt2, P36612, PRS4_SCHPO 448 9, R, 1 96–441Rpt3, O74894, PRS6B_SCHPO 389 8, R, 1 36–380Rpt4, O74445, PRS10_SCHPO 388 8, R, 1 68–433Rpt5, O14126, PRS6A_SCHPO 438 9, R, 1 38–383Rpt6, P41836, PRS8_SCHPO 403 8, R, 1 49–394Rpn1, P87048, RPN1_SCHPO 891 18, F, 39,269 NoneRpn2, O74762, RPN2_SCHPO 965 19, F, 68,261 309–712Rpn3, O42897, RPN3_SCHPO 497 10, F, 31,456 124–425Rpn5, Q9UTM3, RPN5_SCHPO 443 9, F, 12,994 24–398Rpn6, Q9P7S2, RPN6_SCHPO 421 8, R, 1 1–374Rpn7, Q10335, RPN7_SCHPO 409 8, F, 157 87–346Rpn8, O74440, RPN8_SCHPO 324 6, F, 5,023 15–186Rpn9, Q9US13, RPN9_SCHPO 381 8, F, 39,230 1–399Rpn10, O94444, RPN10_SCHPO 243 5, F, 1 2–190Rpn11, P41878, RPN11_SCHPO 308 6, F, 2,044 NoneRpn12, P50524, RPN12_SCHPO 270 5, F, 5,955 53–221Rpn13, Q9USM1, ADRM1_SCHPO 388 8, R, 1 None

In the coarse-grained representation, each RP subunit was represented as a string of beads, each bead corresponding to an approximately 50-residue fragment. If the atomic structure of a subunit was reliably predicted by comparative modeling, the beads were positioned rigidly (R) tomimic the shape of the atomic model, otherwise, the string of beads was allowed to flex (F). In the atomic representation, atomic coordinateswere used for segments with available comparative models.

Lasker et al. www.pnas.org/cgi/doi/10.1073/pnas.1120559109 12 of 14

Table

S5.Restraintdescription

Inform

ation

Restraint

Description

Restraintparam

eters

Violationcu

toff

Samplin

gstag

e

8.4-Å

cryo

-EM

den

sity

map

ofthe

S.pombe26

Sproteasome,

Fig.1

Quality-of-fitinto

aden

sity

map

Thefitofamodel

into

anassembly

den

sity

map

was

quan

tified

byacross-correlationmea

sure

betwee

ntheassembly

den

sity

andthemodel

smoothed

totheresolutionofthemap

(46).

Gau

ssianke

rnel

σof4.2Å

N/A

Subunit

fitting

Chem

ical

cross-links

from

XL/MS,

Table

S1

Intersubunit

residue–

residuedistance

restraint

Intheco

arse-grained

representation,ea

chresidue–

residueproximityis

tran

slated

into

subunit–subunit

proximityusingthe

subomplexco

nnectivity

restraint.

Inthe

atomic

representation,ea

chresidue-residue

proximityis

enco

ded

asapairw

isedistance

restraintbetwee

nthecross-linke

datoms.

Adistance

restraintisdefined

asalower

boundharmonic

restraintbetwee

npairs

of

bea

dswiththefollo

wing

param

eters:

fis

thesphere

distance

(surface-to-surface

distance)betwee

nthetw

obea

ds,f 0

issetto

20Åto

allow

forlonglin

kers,a

ndKissetto

0.02

36,co

rrespondingto

the

stan

darddev

iationof5Å.

Arestraintis

violatedwhen

itsva

lueis

exceed

s1.18

,co

rrespondingto

two

stan

darddev

iationsofthe

upper

bound.Th

emax

imal

number

of

allowed

violationsis

five

.

Subunit

localiz

ation

andsubunit

fitting

Proteomicsdata,

Table

S2Su

bco

mplexco

nnectivity

Each

directinteractionorproximitybetwee

nsubunitsis

enco

ded

asagraphofnodes

connectedbyed

ges.Ea

chnoderepresents

abea

dofasubunit,a

ndea

ched

gerepresents

apossible

interactionbetwee

nbea

ds.Ed

ges

are

gen

erated

forallpossible

interactionsthat

mightbeim

plie

dbytheco

rresponding

experim

entan

dforpairs

ofbea

ds

representingsequen

tial

frag

men

tsofthe

samesubunit.Aned

geim

posesaputative

distance

restraint,scoringwellw

hen

thetw

opotentially

interactingbea

dsareactually

interactingin

theassessed

assembly

configuration,an

dscoringpoorlywhen

the

bea

dsaretoofarap

artto

interact.Fo

rea

chphysical

interactiongraph,thebest-scoring

setofed

ges

nee

ded

toco

nnectallnodes

isch

osenbycalculatingaminim

alspan

ningtree

(MST

)ontheco

mposite

graph.Th

eva

lueof

therestraintis

thesum

ofalled

gedistance

restraints

intheMST.

Adistance

restraintisdefined

asalower

boundharmonic

restraintbetwee

npairs

of

bea

ds(oratoms)

withthe

follo

wingparam

eters:

fis

the

spheredistance

betwee

nthe

twobea

ds,f 0

issetto

10Å

for

directinteractionan

dto

10Å

plusmax

imal

linke

rlength

for

cross-links,an

dK

issetto

0.02

36,co

rrespondingto

the

stan

darddev

iationof5Å.

Arestraintis

violatedwhen

itsva

lueex

ceed

sðn

−1Þ�

m,wherenis

the

number

ofsubunits

restrained

andm

is1.18

;n−1is

thenumber

of

edges

intheMST.Th

emax

imal

number

of

allowed

violationsis

four.

Subunit

localiz

ation

andsubunit

fitting

Bioinform

atics

Rad

ius-of-gyration

(ROG)restraint

Aharmonic

upper

boundfunctionis

imposed

betwee

nthepredictedROG

ofthesubunit

(47)

andtheactual

ROG.Becau

seasubunit

may

adap

tanonglobulargeo

metry,the

predictedROG

isscaled

by1.6.

f 0is

thepredictedROG

multiplie

dby1.6,

fistheactual

ROG,an

dK

issetto

1.

Arestraintis

violatedif

its

valueex

ceed

s1.18

.Th

emax

imal

number

of

allowed

violationsis

0.

Subunit

localiz

ation

Lasker et al. www.pnas.org/cgi/doi/10.1073/pnas.1120559109 13 of 14

Inform

ation

Restraint

Description

Restraintparam

eters

Violationcu

toff

Samplin

gstag

e

Bioinform

atics

Excluded

volume

restraint

Toen

sure

asubunitdoes

notpen

etrate

another,

anex

cluded

volumerestraintis

applie

dto

pairs

ofsubunits.Th

erestraintisdefined

asa

sum

ofupper

bounddistance

restraints

betwee

nintersubunit

pairs

ofbea

ds.

Adistance

restraintisdefined

asan

upper

boundharmonic

restraintbetwee

npairs

of

bea

dswiththefollo

wing

param

eters:fis

thesphere

distance

betwee

nthetw

obea

ds,f 0

issetto

0Å,a

ndK

issetto

1.

Arestraintis

violatedwhen

itsva

lueex

ceed

sn1�n

2�r

�m,where

n1ðn

2Þi

sthenumber

of

bea

dsofthefirst(second)

subunit,r

isthefractionof

bea

dpairs

allowed

toove

rlap

,heresetto

0.1,

andm

1.18

.Th

emax

imal

number

ofallowed

violationsis

13.

Subunit

localiz

ation

Bioinform

atics

Geo

metric

complemen

tarity

restraint

AConnolly

surfaceis

calculatedforea

chco

mponen

t(48).Interactingsurfaces

were

scoredbysummingarewardforthenumber

ofsurfaceatom

pairs

within

adistance

cutoff

andapen

alty

forallclashingpairs

ofatoms

(7).

Defau

ltparam

eterswereused

(48),e

xcep

tfortheshellw

idths

that

weretw

iceas

wideto

allow

foruncertainty

inco

mparativemodels.

Arestraintis

violatedwhen

itsva

lueis

larger

than

1.Th

emax

imal

number

of

allowed

violationsis

5.

Subunit

fitting

Man

yoftherestraints,such

asthesubco

mplexco

nnectivity,rad

iusofgyration,a

ndintersubunitdistance

restraint,aredefined

asasum

ofharmonicfunctions,wherea

sother

restraints,such

asthequality-of-

fitan

dgeo

metricco

mplemen

tarity

restraints,a

redefined

asco

rrelationfunctions.Aharmonicfunctionis

1 2Kðf

−f 0Þ2 ,

wherefistherestrained

feature

andKistheparam

eter

that

determines

thestrength

ofthe

restraint.

Foran

upper

bound,thescore

is0forf<f 0;foralower

bound,thescore

is0forf>f 0.

Lasker et al. www.pnas.org/cgi/doi/10.1073/pnas.1120559109 14 of 14