objects. The EM maps were therefore represented as ensembles of spheres (‘‘virtual atoms’’) that can be easily rotated and translated. The spheres fill the objects’ envelopes at the selected electron density cutoff values. The representation of the EM objects is governed by the parameter w, which determines the extension of the surface layer of the object and its outer shape. This parameter is likely to be affected by the resolution of the EM map and the density cutoff; its optimization was executed by matching several EM structures, each to its copy (self-matching). We chose to match symmetrical or pseudo-symmetrical EM structures expecting several correct matches (the actual number depends on the symmetry) some of which are identity matches and other are approximate either because the symmetry of the structure is not perfect or because the symmetry operation does not comply with the rotational step employed in the scan and only nearby orientations are sampled. Self-matching of EM maps Nine EM structures determined at different resolutions (from 11.2 to 42.2 A˚) and obtained using different experimental procedures were selected for this test (see Table 1). EM maps were taken from the Macromolecular Structure Database (EMDB) at http://www.ebi.ac.uk/msd-srv/emsearch. The electron density cutoffs were obtained from the investigators in most cases; in other cases the cutoffs were manually approximated to reproduce the published EM objects. Several rotation-translation matching scans were preformed for each structure in the benchmark, employing different w values. The rotations interval was fixed at 12u in these tests. The highest score in each scan was either that of the identity match (no rotation; translation within 3 grid steps of the expected position) or of an exact symmetry related match. Matches that deviate by ,6u (half the rotation step) from a correct position (identity or Matching & Docking EM Maps symmetry related) were ranked after the exact symmetry matches and were followed by matches that deviate by ,12u (the rotations grid interval). In only one case, the SV40 T antigen, a false match, rotated by 180u about an axis perpendicular to the C6 symmetry axis, was ranked among the matches with ,12u deviation; this is a false match because the SV40 T antigen does not have D6 symmetry even at the low resolution of 29 A˚. The score of this false match is however only 54% of the score of the top ranked correct match. The optimal w for each map was chosen based on 2 criteria: the first was good tolerance of deviations up to 6u from a correct position, thus the scores of such matches were close to the score of the identity match ($80%). The second criterion was that deviations of 12u were tolerated yet were distinct from the correct matches; hence the scores of these matches were positive but dropped to ,15%–70% of the score of the identity match. It appears that ranges of w comply with these criteria for each system (see Table 2), which is indicative of only moderate sensitivity of the matching results to w. However, the w ranges vary considerably between systems and w is negatively correlated with the EM map grid interval (R2 = 0.85 for the central values of the w ranges) and with the resolution (R2 = 0.78; see Figure 1). This is expected, because the optimal w were chosen to confer limited tolerance of structural mismatches the extent of which depends on the experimental resolution and the grid interval. In contrast, w is not correlated with the density cutoff (R2 = 0.16). This is also expected, because the density cutoff used to produce the molecular envelope depends on the molecular volume and on the background scattering of the electrons beam hence on the EM method and the experimental conditions [21,24]. Unlike w, the virtual atoms radii (determined by w and g, see Methods) are not correlated with the resolution (see Table 2). The average virtual atoms radius calculated with the central values of Table 1. Benchmark of EM structures used in the optimization of w, the parameter that determines the width and shape of the surface layer of object A. EMDB code EM method/complex symmetry Optimal w Resolutiona (A˚ ) range System ATP-TClpB mutant [10] TET1 peptidase [42] apo-TClpB [10] TIP48/TIP49 complex [43] GroES-ADP7-GroEL-ATP7 [27] MCM helicase [44] SV40 T antigen [45] DnaB [25] DnaB.DnaC complex [25] DnaB.DnaC complex at two resolutions [25,26] 1023/1017 GroES-ADP7-GroEL-ATP7 and GroES-ATP7- 1046/1180 GroEL [27,28] ATP-TClpB mutant and ADP-TClpB [10] AMPPNP-TClpB and ADP-TClpB [10] 1244/1242 1243/1242 GroES-ADP7-GroEL-ATP7 and GroEL-ATP7 1046/1047 [27] 1244 1188 1241 1317 1046 1134 1024 1022 1023 cryo–EM/tetrahedral 12-mer uranyl acetate negative staining/C6 uranyl acetate negative staining/C6 uranyl acetate negative staining/C6 cryo-EM/C6 cryo-EM/C6 cryo EM/C7 cryo-EM/C3 cryo-EM/C3 cryo-EM/C3 cryo EM/C7 cryo-EM/C6 cryo-EM/C6 cryo-EM/C7 11.2 14 17.7 20 23.5 25 29 34.5 42.2 34.1 15.6 14.0 14.4 19.2 3.2–3.6 2.6–3.0 3.0–3.4 2.0–2.2 1.8–2.2 1.8–2.2 1.8 1.4 1.6–2.0 1.8–2.0 2.2–2.6 2.6–3.0 3.0–3.4 2.6–3.0 R1b 9.4 10.4 9.2 9.9 8.1 10.1 10.3 10.3 8.8 10.4 6.7 8.2 9.4 8.4 R2c 8.6 10.6 8.0 11.3 9.0 10.9 11.0 9.7 7.9 9.5 7.8 8.4 8.4 8.1 aThe resolution quoted here is the value in the EMDB; average resolution is given for the pairs of related structures. bR1 is the virtual atoms radius calculated with the central values of the w ranges in column 5. cR2 is the virtual atoms radius calculated with w values derived from the linear dependency of w on the resolution (Figure 1). doi:10.1371/journal.pone.0003594.t001 PLoS ONE | www.plosone.org 2 October 2008 | Volume 3 | Issue 10 | e3594