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TEMPy: a Python library for assessment of three-dimensional electron microscopy density fits

aInstitute of Structural and Molecular Biology, Department of Biological Sciences, Birkbeck, University of London, Malet street, London WC1E 7HX, UK, bOxford Particle Imaging Centre, Division of Structural Biology, Wellcome Trust Centre for Human Genetics, University of Oxford, Oxford OX3 7BN, UK, and cScientific Computing Department, Science and Technology Facilities Council, Research Complex at Harwell, Didcot, Oxon OX11 0QX, UK
*Correspondence e-mail: m.topf@cryst.bbk.ac.uk

Edited by D. I. Svergun, European Molecular Biology Laboratory, Hamburg, Germany (Received 5 November 2014; accepted 24 May 2015; online 27 June 2015)

Three-dimensional electron microscopy is currently one of the most promising techniques used to study macromolecular assemblies. Rigid and flexible fitting of atomic models into density maps is often essential to gain further insights into the assemblies they represent. Currently, tools that facilitate the assessment of fitted atomic models and maps are needed. TEMPy (template and electron microscopy comparison using Python) is a toolkit designed for this purpose. The library includes a set of methods to assess density fits in intermediate-to-low resolution maps, both globally and locally. It also provides procedures for single-fit assessment, ensemble generation of fits, clustering, and multiple and consensus scoring, as well as plots and output files for visualization purposes to help the user in analysing rigid and flexible fits. The modular nature of TEMPy helps the integration of scoring and assessment of fits into large pipelines, making it a tool suitable for both novice and expert structural biologists.

1. Introduction

The integration of data derived from a variety of biophysical techniques at multiple levels of resolution, such as electron microscopy (EM), small-angle X-ray scattering, X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy, is becoming common in the structural determination of large macromolecular assemblies (Ward et al., 2013[Ward, A. B., Sali, A. & Wilson, I. A. (2013). Science, 339, 913-915.]; Lander et al., 2012[Lander, G. C., Saibil, H. R. & Nogales, E. (2012). Curr. Opin. Struct. Biol. 22, 627-635.]; Karaca & Bonvin, 2013[Karaca, E. & Bonvin, A. M. J. J. (2013). Acta Cryst. D69, 683-694.]). This combination, often aided by computational methods, allows scientists to gain further insights into the macromolecular assemblies they study. An example is the fitting of atomic structures into three-dimensional EM (3D EM) density maps. At the beginning of 2015, out of 2770 maps in the Electron Microscopy Data Bank (spanning a wide range of resolutions, mostly between 5 and 20 Å; Milne et al., 2013[Milne, J. L., Borgnia, M. J., Bartesaghi, A., Tran, E. E., Earl, L. A., Schauder, D. M., Lengyel, J., Pierson, J., Patwardhan, A. & Subramaniam, S. (2013). FEBS J. 280, 28-45.]; http://www.ebi.ac.uk/pdbe/emdb), a total of 653 entries were linked to fitted atomic models in the Protein Data Bank (PDB; http://www.rcsb.org/pdb). Density fitting depends on the amount of information in the experimental data, the accuracy of the starting model, the complexity of their representation and the scoring function representing the goodness-of-fit (Henderson et al., 2012[Henderson, R. et al. (2012). Structure, 20, 205-214.]; Thalassinos et al., 2013[Thalassinos, K., Pandurangan, A. P., Xu, M., Alber, F. & Topf, M. (2013). Structure, 21, 1500-1508.]). Currently, most 3D EM density maps do not allow for an unambiguous placement of individual atoms. The number of parameters to be solved is experimentally underdetermined and false-positive solutions are likely. To reduce the number of parameters, `rigid' fitting is often performed on a given structural unit (e.g. a whole protein or a domain), that is, without changing the relative positions of the individual atoms within the unit. A global search is performed in six degrees of freedom to find the position and orientation of the atomic model in the map that gives the best fit between the two (Esquivel-Rodríguez & Kihara, 2013[Esquivel-Rodríguez, J. & Kihara, D. (2013). J. Struct. Biol. 184, 93-102.]; Thalassinos et al., 2013[Thalassinos, K., Pandurangan, A. P., Xu, M., Alber, F. & Topf, M. (2013). Structure, 21, 1500-1508.]). However, rigid fitting can also be performed locally, if prior knowledge about the approximate position of the model in the map exists (Topf et al., 2005[Topf, M., Baker, M. L., John, B., Chiu, W. & Sali, A. (2005). J. Struct. Biol. 149, 191-203.]; Goddard et al., 2007[Goddard, T. D., Huang, C. C. & Ferrin, T. E. (2007). J. Struct. Biol. 157, 281-287.]). Furthermore, 3D EM maps often represent conformational states that differ from the initial conformation of the atomic model (Thalassinos et al., 2013[Thalassinos, K., Pandurangan, A. P., Xu, M., Alber, F. & Topf, M. (2013). Structure, 21, 1500-1508.]; Villa & Lasker, 2014[Villa, E. & Lasker, K. (2014). Curr. Opin. Struct. Biol. 25, 118-125.]). In such cases, to gain insight into the dynamic properties of the structure, flexible fitting is applied, by changing the conformation of the initial atomic model while improving the goodness-of-fit. However, here too, additional constraints have to be applied to reduce the probability of overfitting (Topf et al., 2008[Topf, M., Lasker, K., Webb, B., Wolfson, H., Chiu, W. & Sali, A. (2008). Structure, 16, 295-307.]). Increasingly, 3D EM density maps are achieving high resolution (∼3–4 Å), allowing de novo models to be generated and the use of tools adapted from the X-ray crystallography field (Brown et al., 2015[Brown, A., Long, F., Nicholls, R. A., Toots, J., Emsley, P. & Murshudov, G. (2015). Acta Cryst. D71, 136-153.]; Wang et al., 2014[Wang, Z., Hryc, C. F., Bammes, B., Afonine, P. V., Jakana, J., Chen, D. H., Liu, X., Baker, M. L., Kao, C., Ludtke, S. J., Schmid, M. F., Adams, P. D. & Chiu, W. (2014). Nat. Commun. 5, 4808.]).

In addition to identifying an appropriate fitting method, it is important to assess the accuracy of the fitted model (the difference from the true structure) as well as its precision (the variability from other models consistent with the data that score similarly) (Alber et al., 2008[Alber, F., Förster, F., Korkin, D., Topf, M. & Sali, A. (2008). Annu. Rev. Biochem. 77, 443-477.]). Many tools exist for the assessment of structural models against geometric criteria, such as MolProbity (Chen et al., 2010[Chen, V. B., Arendall, W. B. 3rd, Headd, J. J., Keedy, D. A., Immormino, R. M., Kapral, G. J., Murray, L. W., Richardson, J. S. & Richardson, D. C. (2010). Acta Cryst. D66, 12-21.]) and WHAT_CHECK (Hooft et al., 1996[Hooft, R. W., Vriend, G., Sander, C. & Abola, E. E. (1996). Nature, 381, 272.]). Methods and tools to assess the quality of a model in the context of 3D EM maps are less common, although it is becoming clear that such validation approaches are needed (Henderson et al., 2012[Henderson, R. et al. (2012). Structure, 20, 205-214.]; Ludtke et al., 2012[Ludtke, S. J., Lawson, C. L., Kleywegt, G. J., Berman, H. & Chiu, W. (2012). Biopolymers, 97, 651-654.]). One approach is the use of confidence intervals and docking precision estimates in global rigid body fitting (Volkmann, 2009[Volkmann, N. (2009). Acta Cryst. D65, 679-689.]). This approach was used to assess the fit of the first 559 residues of the 2.5 MDa ryanodine receptor (RyR1) crystal structure within the cryo EM map of the entire complex at 9.6 Å (Tung et al., 2010[Tung, C. C., Lobo, P. A., Kimlicka, L. & Van Petegem, F. (2010). Nature, 468, 585-588.]; Garzón et al., 2007[Garzón, J. I., Kovacs, J., Abagyan, R. & Chacón, P. (2007). Bioinformatics, 23, 427-433.]; Wriggers & Birmanns, 2001[Wriggers, W. & Birmanns, S. (2001). J. Struct. Biol. 133, 193-202.]), which has recently been confirmed on the basis of higher resolution maps (Zalk et al., 2015[Zalk, R., Clarke, O. B., des Georges, A., Grassucci, R. A., Reiken, S., Mancia, F., Hendrickson, W. A., Frank, J. & Marks, A. R. (2015). Nature, 517, 44-49.]; Yan et al., 2015[Yan, Z., Bai, X. C., Yan, C., Wu, J., Li, Z., Xie, T., Peng, W., Yin, C. C., Li, X., Scheres, S. H., Shi, Y. & Yan, N. (2015). Nature, 517, 50-55.]). This higher resolution model is different from an earlier fit of a comparative model into the same map, which resulted from a local fitting procedure, relying on antibody labelling that constrained the sampling to an incorrect region of the map (Serysheva et al., 2008[Serysheva, I. I., Ludtke, S. J., Baker, M. L., Cong, Y., Topf, M., Eramian, D., Sali, A., Hamilton, S. L. & Chiu, W. (2008). Proc. Natl Acad. Sci. USA, 105, 9610-9615.]). Another validation approach that has been proven useful is the selection of the best-fitting model relative to alternative fits (Vasishtan & Topf, 2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]; Wriggers & Birmanns, 2001[Wriggers, W. & Birmanns, S. (2001). J. Struct. Biol. 133, 193-202.]; Roseman, 2000[Roseman, A. M. (2000). Acta Cryst. D56, 1332-1340.]). For instance, alternative models generated by protein structure prediction methods can be assessed by selecting the model that fits best into the map (Topf et al., 2005[Topf, M., Baker, M. L., John, B., Chiu, W. & Sali, A. (2005). J. Struct. Biol. 149, 191-203.]). Such an approach has been used in structure characterization of macromolecular assemblies, including eukaryotic ribosomes (Chandramouli et al., 2008[Chandramouli, P., Topf, M., Ménétret, J. F., Eswar, N., Cannone, J. J., Gutell, R. R., Sali, A. & Akey, C. W. (2008). Structure, 16, 535-548.]; Taylor et al., 2009[Taylor, D. J., Devkota, B., Huang, A. D., Topf, M., Narayanan, E., Sali, A., Harvey, S. C. & Frank, J. (2009). Structure, 17, 1591-1604.]) and herpesviruses capsids (Baker et al., 2005[Baker, M. L., Jiang, W., Rixon, F. J. & Chiu, W. (2005). J. Virol. 79, 14967-14970.]). Interestingly, for structural characterization of a tobacco mosaic virus map at 4.4 Å resolution, four models generated by real-space mol­ecular dynamics were suggested in order to provide a better representation of the data (Sachse et al., 2007[Sachse, C., Chen, J. Z., Coureux, P. D., Stroupe, M. E., Fändrich, M. & Grigorieff, N. (2007). J. Mol. Biol. 371, 812-835.]). In the context of lower resolution maps it has been suggested to use much larger ensembles to describe coordinate uncertainty in certain regions of the map (Lukoyanova et al., 2015[Lukoyanova, N. et al. (2015). PLoS Biol. 13, e1002049.]; Goulet et al., 2014[Goulet, A., Major, J., Jun, Y., Gross, S. P., Rosenfeld, S. S. & Moores, C. A. (2014). Proc. Natl Acad. Sci. USA, 111, 1837-1842.]). For example, for the three intermediates of a membrane attack complex/perforin-like protein (pleurotolysin) at resolutions of 14–17 Å, 20 models generated by angular sweeps were suggested (and deposited in the PDB; Lukoyanova et al., 2015[Lukoyanova, N. et al. (2015). PLoS Biol. 13, e1002049.]).

Another validation approach, in the context of flexible fitting, is the use of multiple flexible fitting methods in order to reach a consensus fit and measure the local fit reliability using root-mean-square fluctuations and local correlation (Ahmed et al., 2012[Ahmed, A., Whitford, P. C., Sanbonmatsu, K. Y. & Tama, F. (2012). J. Struct. Biol. 177, 561-570.]; Ahmed & Tama, 2013[Ahmed, A. & Tama, F. (2013). J. Struct. Biol. 182, 67-77.]; Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]). This approach has helped in the refinement of the coxsackievirus A7 capsid in subnanometre resolution cryo EM maps representing two conformations (Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]).

Finally, cross-validation methods have also been used to identify the optimally fitted model of cyclic nucleotide-modulated ion channels (MloK1) in a large density map at 16 Å resolution (Schröder et al., 2010[Schröder, G. F., Levitt, M. & Brunger, A. T. (2010). Nature, 464, 1218-1222.]; Kowal et al., 2014[Kowal, J., Chami, M., Baumgartner, P., Arheit, M., Chiu, P. L., Rangl, M., Scheuring, S., Schröder, G. F., Nimigean, C. M. & Stahlberg, H. (2014). Nat. Commun. 5, 3106.]) and to validate an all-atom de novo model of the brome mosaic virus obtained from a 3.8 Å resolution map (Wang et al., 2014[Wang, Z., Hryc, C. F., Bammes, B., Afonine, P. V., Jakana, J., Chen, D. H., Liu, X., Baker, M. L., Kao, C., Ludtke, S. J., Schmid, M. F., Adams, P. D. & Chiu, W. (2014). Nat. Commun. 5, 4808.]; DiMaio et al., 2013[DiMaio, F., Zhang, J., Chiu, W. & Baker, D. (2013). Protein Sci. 22, 865-868.]).

Previously, we proposed that a useful way of assessing models is the use of a variety of goodness-of-fit scores (Vasishtan & Topf, 2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]). Although a number of scoring methods have been developed, different scores have specific advantages. Thus, their combination could be proven useful in different scenarios. These include the most commonly used cross-correlation coefficient and its variations (e.g. Laplacian-filtered cross-correlation coefficient; Wriggers & Chacón, 2001[Wriggers, W. & Chacón, P. (2001). Structure, 9, 779-788.]), a mutual information-based score, and edge-based scores (Vasishtan & Topf, 2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]). The scoring in most programs for rigid and flexible fitting (which are available either independently or as part of image processing packages; Heymann, 2001[Heymann, J. B. (2001). J. Struct. Biol. 133, 156-169.]; Ludtke et al., 1999[Ludtke, S. J., Baldwin, P. R. & Chiu, W. (1999). J. Struct. Biol. 128, 82-97.]; Villa & Lasker, 2014[Villa, E. & Lasker, K. (2014). Curr. Opin. Struct. Biol. 25, 118-125.]) is based primarily on cross-correlation methods. However, there are currently no tools that allow the assessment of fit quality using a large selection of scoring methods either independently or as a means of consensus in the same platform.

Here, we implement such a platform, called TEMPy (template and EM comparison using Python). The software is useful for density map and atomic structure processing and for fit assessment (model-to-map and map-to-map), especially in the intermediate-to-low resolution range. It provides a selection of scoring functions that allow the user to assess the reliability of density fits, which can be used in conjunction with ensemble generation of alternative fits and clustering, as well as consensus scoring. Additionally, the capability to provide local fit assessment based on any user-defined structure segment (e.g. a protein domain or a secondary structure element) can be useful in flexible fitting, particularly at subnanometre resolution (Pandurangan & Topf, 2012[Pandurangan, A. P. & Topf, M. (2012). J. Struct. Biol. 177, 520-531.]). TEMPy can also provide plots and output files for visualization purposes that can further help the user in analysing the results. The software has already been used for fit assessment of multiple conformers of coxsackievirus A7 (Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]), microtubule-bound kinesins 1 and 3 (Atherton et al., 2014[Atherton, J., Farabella, I., Yu, I. M., Rosenfeld, S. S., Houdusse, A., Topf, M. & Moores, C. A. (2014). eLife, 3, e03680.]), and pleurotolysin (Lukoyanova et al., 2015[Lukoyanova, N. et al. (2015). PLoS Biol. 13, e1002049.]).

2. Software design and implementation

TEMPy is a cross-platform package implemented in the Python programming language, which uses the NumPy and SciPy libraries (Jones et al., 2001[Jones, E., Oliphant, T., Peterson, P. et al. (2001). SciPy, http://www.scipy.org.]), making it computationally efficient. Additionally, it uses Biopython for handling atomic coordinate files (Hamelryck & Manderick, 2003[Hamelryck, T. & Manderick, B. (2003). Bioinformatics, 19, 2308-2310.]). The program is flexible, allowing the users to build customized functions. The modular organization of the software supports its integration into large modular pipelines or into larger software suites, such as CCP-EM (Wood et al., 2015[Wood, C., Burnley, T., Patwardhan, A., Scheres, S., Topf, M., Roseman, A. & Winn, M. (2015). Acta Cryst. D71, 123-126.]).

2.1. Input/output

TEMPy currently supports reading and writing of density maps in CCP4/MRC format and atomic structures in PDB or mmCIF format. It can parse subsets of atomic structures (rigid bodies) as simple text files (for example RIBFIND output files; Pandurangan & Topf, 2012[Pandurangan, A. P. & Topf, M. (2012). J. Struct. Biol. 177, 520-531.]). It can also generate Chimera (Pettersen et al., 2004[Pettersen, E. F., Goddard, T. D., Huang, C. C., Couch, G. S., Greenblatt, D. M., Meng, E. C. & Ferrin, T. E. (2004). J. Comput. Chem. 25, 1605-1612.]) input files for visualization of fits, as well as high-quality plots using the Python library Matplotlib (Hunter, 2007[Hunter, J. D. (2007). Comput. Sci. Eng. 9, 90-95.]), to help the user with the interpretation of the results using a colour gradient.

2.2. Core modules

TEMPy consists of a number of core Python modules, including the Map module (EMMap.py) for processing density maps; the Structure module (ProtRep.py) for processing atomic structures; the Structure Blurrer module (StructureBlurrer.py) for creating density maps from atomic structures; the Scoring Functions module (ScoringFunctions.py) that contains a variety of methods for scoring density fits; and the Ensemble Generation module (EnsembleGeneration.py) for generating ensembles of fits. The program can also load alternative fits or ensembles generated by other programs based on approaches such as density fitting combined with molecular docking (Lasker et al., 2010[Lasker, K., Sali, A. & Wolfson, H. J. (2010). Proteins, 78, 3205-3211.]; Esquivel-Rodríguez & Kihara, 2012[Esquivel-Rodríguez, J. & Kihara, D. (2012). J. Phys. Chem. B, 116, 6854-6861.]), normal mode analysis (Tama et al., 2002[Tama, F., Wriggers, W. & Brooks, C. L. 3rd (2002). J. Mol. Biol. 321, 297-305.]), molecular dynamics (Trabuco et al., 2008[Trabuco, L. G., Villa, E., Mitra, K., Frank, J. & Schulten, K. (2008). Structure, 16, 673-683.]), comparative modelling (Topf et al., 2005[Topf, M., Baker, M. L., John, B., Chiu, W. & Sali, A. (2005). J. Struct. Biol. 149, 191-203.]) and loop modelling (Goulet et al., 2014[Goulet, A., Major, J., Jun, Y., Gross, S. P., Rosenfeld, S. S. & Moores, C. A. (2014). Proc. Natl Acad. Sci. USA, 111, 1837-1842.]). These ensembles can be analysed using the Clustering module (Cluster.py) and the Consensus Scoring module (Consensus.py), which can be useful in estimating precision and, in some cases, accuracy.

2.3. Algorithms

2.3.1. Scoring functions

TEMPy offers a selection of scoring methods for the assessment of fit quality on a single platform (Table 1[link]). The cross-correlation coefficient (CCC) is expressed by the following formula (Roseman, 2000[Roseman, A. M. (2000). Acta Cryst. D56, 1332-1340.]):

[{\rm{CCC}} = {{ \sum \nolimits_{i \in M} \left ({\rho _i^{\rm P} - {{\bar \rho }^{\rm P}}} \right)\left ({\rho _i^{\rm T} - {{\bar \rho }^{\rm T}}} \right)} \over {\left[ {\sum \nolimits_{i \in M} {{\left ({\rho _i^{\rm P} - {{\bar \rho }^{\rm P}}} \right)}^2} \sum \nolimits_{i \in M} {{\left ({\rho _i^{\rm T} - {{\bar \rho }^{\rm T}}} \right)}^2}}\right]^{1/2} }}, \eqno(1)]

where M represents all the voxels in the density grid of the map target, [{\rho }_{i}^{\rm P}] and [\rho _i^{\rm T}] represent the intensities at points i in the probe map and target map, respectively, and [{ \bar{\rho }}_{i}^{\rm P}] and [\bar \rho _i^{\rm T}] are the respective mean intensities. Different variations on the CCC, such as Laplacian-filtered CCC (LAP) (Wriggers & Chacon, 2001[Wriggers, W. & Chacón, P. (2001). Structure, 9, 779-788.]) and the segment-based cross correlation (SCCC) (Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]), are also implemented.

Table 1
Guidelines to the scores currently available in TEMPy

Score Name Reference Note
Cross-correlation coefficient CCC Roseman (2000[Roseman, A. M. (2000). Acta Cryst. D56, 1332-1340.])
Segment-based CCC SCCC Pandurangan et al. (2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]) Useful for comparing specific regions in multiple fits (Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]; Atherton et al., 2014[Atherton, J., Farabella, I., Yu, I. M., Rosenfeld, S. S., Houdusse, A., Topf, M. & Moores, C. A. (2014). eLife, 3, e03680.]; Lukoyanova et al., 2015[Lukoyanova, N. et al. (2015). PLoS Biol. 13, e1002049.]).
Laplacian-filtered CCC LAP Wriggers & Chacón (2001[Wriggers, W. & Chacón, P. (2001). Structure, 9, 779-788.]) Useful for resolutions worse than 10–15 Å.
Mutual information score MI Vasishtan & Topf (2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.])
Segment-based MI SMI Useful for comparing specific regions in multiple fits.
Envelope score ENV Vasishtan & Topf (2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]) Useful at high resolution. Very fast to calculate and therefore useful in screening fits in large assemblies.
Normal vector score NV Vasishtan & Topf (2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]), Ceulemans & Russell (2004[Ceulemans, H. & Russell, R. B. (2004). J. Mol. Biol. 338, 783-793.]) Sensitive to edge detection.
Normal vector score with Sobel filter NV-S
Chamfer distance CD Vasishtan & Topf (2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]) Highly sensitive to edge detection. Not recommended for segmented maps.

The mutual information score (MI) is an entropy-based concept given by the relative entropy between the joint distribution p(x, y) and the product distribution p(x)p(y):

[{\rm{MI}}\left({X;Y} \right) = \mathop \sum \limits_{x \in X} \mathop \sum \limits_{y \in Y} p\left({x,y} \right){\rm{log}}{{p\left({x,y} \right)} \over {p\left(x \right)p\left(y \right)}}, \eqno(2)]

where X and Y correspond to the density values of the voxels in the probe and target maps. p(x) and p(y) are given by the percentage of voxels with density values equal to x and y, respectively. p(x, y) is given by the percentage of aligned voxels with value x in the probe map and y in the target map. Since the density values in an EM map take a wide range of values and are typically noisy, it is necessary to bin the map into a limited number of values (typically 20; Shatsky et al., 2009[Shatsky, M., Hall, R. J., Brenner, S. E. & Glaeser, R. M. (2009). J. Struct. Biol. 166, 67-78.]). A segment-based variation of this score (SMI) is also available in TEMPy and is implemented in a manner similar to the SCCC score (Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]).

The envelope score (ENV) attempts to describe how much of the density map is filled with atoms and penalizes both protrusions from the surface (`envelope') and empty spaces in the map. First, all the pixels in the target map are given binary values, based on whether they are higher or lower than a given density threshold. Then, for each atom in the probe structure, the nearest density point in the target map is found and is down- or up-weighted taking into account the binary values of the target map. The sum of all of these values gives the ENV score, which can take any integer value, with the largest values denoting the best fits.

The normal vector score and Chamfer distance are both based on the comparison of the surfaces of the atomic structure and EM map (Vasishtan & Topf, 2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]).

The normal vector (NV) score is a calculation of the difference in angle between the normal vectors of the surfaces of the target and probe maps, in which the vectors are calculated using a variation of the method developed in the 3SOM algorithm (Ceulemans & Russell, 2004[Ceulemans, H. & Russell, R. B. (2004). J. Mol. Biol. 338, 783-793.]). The NV score gives non-negative output values and it is expressed as

[{\rm{NV}} = {1 \over n}\mathop \sum \limits_{i \in v} {{{{\bf N}_i^{\rm{T}}} \times {{\bf N}_i^{\rm{P}}} } \over {\left| {{{\bf N}_i^{\rm{T}}} } \right|\left| { {{\bf N}_i^{\rm{P}}} } \right|}},\eqno(3)]

where n is the number of normal vectors calculated in the target map, [{{\bf N}_i^{\rm{T}}}] and [{{\bf N}_{i}^{\rm P}}] are the normal vectors of the target and probe map, respectively, at point i on the surface, and v is the set of surface points within the volume threshold. The vertical bars denote the vector magnitude. The score is ranged between 0 and π, where 0 is the best score, i.e. there is no difference in the direction of all corresponding normal vectors between the target and probe maps.

The Chamfer distance (CD) is a pattern matching score used successfully in video tracking (Knossow et al., 2007[Knossow, D., Ronfard, R. & Horaud, R. (2007). Int. J. Comput. Vis. 79, 247-269.]; Chen et al., 2007[Chen, Z., Husz, Z. L., Wallace, I. & Wallace, A. M. (2007). IEEE Int. Conf. Image Process. 3, 357-360.]) that has been used recently for assessing 3D EM fits (Vasishtan & Topf, 2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]). The CD between two sets of points, X and Y, on the surfaces of the target and probe maps, is given by calculating the distance of every point in X from its nearest neighbour in Y and taking the average of all these values. It is expressed as

[{\rm{CD}}({X,Y} ) = {1 \over n} \sum \limits_{x \in X} {\rm inf} \,{{d}}({x,Y} ),\eqno(4)]

where n is the number of points of X, d(x,Y ) is the set of Euclidean distances between x and every point in Y, and inf is the infimum. The CD score, like the NV score, gives non-negative values. Zero is the best score, given when all surface voxels in the probe map are perfectly superimposed on the surface voxels in the target map.

Previously, we have used a volume-based threshold method to define the surface (Vasishtan & Topf, 2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]). Here, to improve surface detection within this threshold we implement the Sobel filter (using Scipy) (Duda & Hart, 1973[Duda, R. O. & Hart, P. E. (1973). Pattern Classification and Scene Analysis. New York: John Wiley.]), which has been used in image processing (Pinidiyaarachchi et al., 2009[Pinidiyaarachchi, A., Zieba, A., Allalou, A., Pardali, K. & Wählby, C. (2009). Cytometry, 75A, 319-328.]; Wahlby et al., 2004[Wahlby, C., Sintorn, I. M., Erlandsson, F., Borgefors, G. & Bengtsson, E. (2004). J. Microsc. 215, 67-76.]). It approximates the gradient of voxel density by convolution of the filter kernel along the axis. The filter kernel consists of averaging (Sa) and differentiation (Ha) kernels:

[{S}_{\rm a} = \left(\matrix{1\cr 2\cr 1}\right), \quad {H}_{\rm a} = (\matrix{-1 & 0 & 1}).\eqno(5)]

The convolution filter kernels along the three axis directions are separable as

[H_x^1 = {H_x}{S_y}{S_z}, \quad H_y^1 = {H_y}{S_z}{S_x}, \quad H_z^1 = {H_z}{S_y}{S_x}.\eqno(6)]

The filtered map A1 is obtained as

[{A}^{1} = \left[{{\left({H}_{x}^{1}*A\right)}^{2}+ {\left({H}_{y}^{1}*A\right)}^{2}+ {\left({H}_{z}^{1}*A\right)}^{2}}\right]^{1/2},\eqno(7)]

where A is the original map and * is the convolution operator.

2.3.2. Clustering

TEMPy provides a procedure for clustering different sets of density fits to identify the best fits (using the Clustering module), for example, by hierarchical root-mean-square deviation (RMSD) clustering. The analysis is accompanied by plots and output files that are readable in Chimera, allowing the visualization of the top-scoring fits coloured by clusters in the context of the map (Plot.py). This approach helps the user to decide in a more systematic and objective fashion if any one of the fits stands out. In cases where it is not possible to identify a single accurate and/or precise fit (as is often the case in low resolution EM density maps), to better represent the experimental data one could suggest multiple solutions based on the set of good-scoring fits. The variability among this set of solutions represents the precision of the suggested model and/or the lower bound on its accuracy (Schneidman-Duhovny et al., 2014[Schneidman-Duhovny, D., Pellarin, R. & Sali, A. (2014). Curr. Opin. Struct. Biol. 28, 96-104.]).

2.3.3. Consensus Scoring

TEMPy provides a consensus scoring (using the Consensus module). We implemented this option based on the Borda count: a preference method-based voting system that has been used to compute consensus in networks (Brush et al., 2013[Brush, E. R., Krakauer, D. C. & Flack, J. C. (2013). PLoS Comput. Biol. 9, e1003109.]) and in ligand-based docking (Ahmed et al., 2014[Ahmed, A., Saeed, F., Salim, N. & Abdo, A. (2014). J. Cheminf. 6, 19.]). Each fit in an ensemble of N fits is ranked on the basis of a list of S different scores (S > 1, any given combination of scores can be chosen). Given a score i, a ranking score (r) is assigned to each fit according to its positional order in the ensemble. The Borda score is defined as

[{\rm{Borda}} = \textstyle \sum \limits_{i = 1}^S \left({N - r} \right).\eqno(8)]

TEMPy also offers the possibility to visualize the ranked fits (with the support of a colour-coded interpretation of the results), which can help the user to interpret the consensus among the scoring metrics chosen.

3. Application examples

TEMPy provides procedures for single-fit assessment, ensemble generation of fits, clustering, multiple scoring and consensus scoring (Fig. 1[link]). In principle, any type of set of fits (model-to-map and map-to-map) can be assessed both globally and/or locally in a map using the entire structure or just parts of it. Below we describe a set of test cases to highlight some of these capabilities.

[Figure 1]
Figure 1
Workflow in TEMPy for assessing atomic models fitted in 3D EM density maps.

3.1. Assessment of ensemble of fits

Different strategies to detect the most appropriate solution within a set of alternative fits, such as hierarchical clustering and consensus scoring protocols, are implemented in TEMPy. To show how these strategies can be employed to identify a fit that stands out among a set of alternative solutions, we provide four different types of examples that cover a fair range of expected fitting scenarios in maps at intermediate-to-low resolution. In the first two examples we used TEMPy to generate an ensemble of alternative fits around a given initial fit (local search) using 12 simulated maps (Example 1, §3.1.1[link]) and one experimental map (Example 2, §3.1.2[link]). In the third and fourth examples we used as an input to TEMPy ensembles generated elsewhere: by collecting different conformations (from the PDB) of a given initial fit into an experimental map (Example 3, §3.1.3[link]); and from a global search performed by another fitting program (Example 4, §3.1.4[link]). In each case, we used the Ensemble module, Scoring Function module, Clustering module, and/or Consensus and Plotting modules for assessment. The snippet of code in Fig. S1A in the supporting information shows a few Python code lines that are needed to generate an ensemble of fits, rank them on the basis of a chosen score, hierarchically cluster them on the basis of Cα-RMSD and then visualize the cluster dendrograms of the fits.

3.1.1. Simulated benchmark: assessment of a local search ensemble and score performance

A total of 12 maps were simulated at 5, 10, 15 and 20 Å resolution from three known X-ray structures: the ligand-free glutamine-binding protein (PDB code 1ggg; Hsiao et al.,1996[Hsiao, C.-D., Sun, Y.-J., Rose, J. & Wang, B.-C. (1996). J. Mol. Biol. 262, 225-242.]); the ligand-bound maltodextrin binding protein (PDB code 1anf; Quiocho et al., 1997[Quiocho, F. A., Spurlino, J. C. & Rodseth, L. E. (1997). Structure, 5, 997-1015.]); and the ligand-free D-ribose-binding protein (PDB code 1urp; Björkman & Mowbray, 1998[Björkman, A. J. & Mowbray, S. L. (1998). J. Mol. Biol. 279, 651-664.]). The maps were produced with the molmap command in Chimera (Goddard et al., 2007[Goddard, T. D., Huang, C. C. & Ferrin, T. E. (2007). J. Struct. Biol. 157, 281-287.]) using the default sigma factor of 0.225 (setting the maximal grid spacing to 3.5 Å per pixel). For each example a random ensemble of 200 alternative fits was generated with TEMPy (0 ≤ ΔT ≤ 10 Å and 0 ≤ ΔΦ ≤ 60°).

All fits were scored using four different scores: CCC, MI and NV score, with and without the Sobel filter (NV-S, applied to any densities above the threshold). If the best fits are similar, different scoring methods will typically result in a slightly different ranking. Here, we show how clustering those fits can guide the user to identify the best fit. The 20 top-scoring fits based on each score were hierarchically clustered by Cα-RMSD (using the mean Cα-RMSD of the top 20 fits for each score as a cutoff). Examination of the resulting clusters underlines the performance of each score (i.e. the separation between the top fit and the alternative ones) (Figs. S2–S4).

As expected, the starting fit (model 0, which was used to simulate the map) is highlighted by all four scores to be the top-scoring fit within the top-scoring non-singleton cluster. Only in the case of 1urp does some ambiguity arise between model 0 and an alternative fit (model 154) at low resolutions (15 and 20 Å) for all four scores and at higher resolutions (5 and 10 Å) for CCC (Fig. S4). However, the Cα-RMSD between the models is very small (0.32 Å). At 20 Å resolution, using the Sobel filter with the NV score (NV-S) improves the discrimination between the top fits for both 1anf and 1urp. Independent of the target map resolution, in all the test cases the MI score allows better discrimination between alternative solutions.

To show the usability of the consensus approach in the context of EM fits we used the three simulated test cases presented above. Each of the 200 random alternative fits was scored using CCC, MI and NV-S (because of the improved performance over the NV score). The Borda score was then used to re-rank the ensemble of alternative solutions (Tables S1–S12). In the case of 1urp, the ambiguity in the top-ranking solution (due to NV-S ranking model 0 second) is overcome by re-ranking with the Borda score.

3.1.2. Experimental benchmark: assessment of a local search ensemble and score performance

We applied the ensemble clustering approach to an experimental case using the X-ray structure of the bacterial chaperonin apo-GroEL (PDB code 1oel; Braig et al., 1995[Braig, K., Adams, P. D. & Brunger, A. T. (1995). Nat. Struct. Mol. Biol. 2, 1083-1094.]) and a cryo EM density map of apo-GroEL at 11.5 Å resolution (EMD code 1080; Ludtke et al., 2001[Ludtke, S. J., Jakana, J., Song, J. L., Chuang, D. T. & Chiu, W. (2001). J. Mol. Biol. 314, 253-262.]). First, the structure was fitted using the cross-correlation score implemented in Chimera's fit_in_map tool (Goddard et al., 2007[Goddard, T. D., Huang, C. C. & Ferrin, T. E. (2007). J. Struct. Biol. 157, 281-287.]). Then, the density map was segmented around a single subunit with a large box using Chimera. Next, a random ensemble of 1000 alternative fits was generated with TEMPy using 0 ≤ ΔT ≤ 5 Å and 0 ≤ ΔΦ ≤ 60° to explore the immediate neighbourhood of fits. The fits were then scored as before using CCC, MI, NV and NV-S. The 20 top-scoring fits based on each score were hierarchically clustered by Cα-RMSD (Fig. 2[link]). The analysis of the 20 top-scoring fits based on the Cα-RMSD clustering resulted in a similar trend to the simulated data. The starting Chimera fit is the top-scoring fit within the top-scoring non-singleton cluster. The MI is again the most discriminatory score and the NV-S more discriminatory than the NV. Here too, we applied the consensus scoring approach. Calculating the Borda score over 1000 alternative fits using CCC, MI and NV-S clearly resulted in model 0 as the best model (Table S13).

[Figure 2]
Figure 2
Clustering an ensemble of rigid fits. The 20 top-scoring fits of a single GroEL subunit (PDB code 1oel; Braig et al., 1995[Braig, K., Adams, P. D. & Brunger, A. T. (1995). Nat. Struct. Mol. Biol. 2, 1083-1094.]) within the 11.5 Å resolution density map of GroEL (EMD code 1080; Ludtke et al., 2001[Ludtke, S. J., Jakana, J., Song, J. L., Chuang, D. T. & Chiu, W. (2001). J. Mol. Biol. 314, 253-262.]) (in grey) are shown based on four different scores: CCC (a), MI (b), NV (c) and NV with Sobel filter (NV-S) (d). Left column: the fitted models are shown in the context of the map. Right column: the cluster dendrograms of the fits. The colour bars represent the score of each fit from white (lowest score) to blue (best score). Each cluster is coloured differently and the average Cα-RMSD value is reported below.
3.1.3. Assessment of an ensemble of conformations from the PDB

Using an ensemble generated from actin PDB structures, we applied the ensemble clustering approach to identify a model that best fits into the actin filament map at 8.9 Å resolution (EMD code 1990; Behrmann et al., 2012[Behrmann, E., Müller, M., Penczek, P. A., Mannherz, H. G., Manstein, D. J. & Raunser, S. (2012). Cell, 150, 327-338.]). We generated the ensemble based on sequence and structure similarity to an F-actin subunit model (PDB code 3mfp; Fujii et al., 2010[Fujii, T., Iwane, A. H., Yanagida, T. & Namba, K. (2010). Nature, 467, 724-728.]) via the DALI server (Holm & Rosenström, 2010[Holm, L. & Rosenström, P. (2010). Nucleic Acids Res. 38, W545-W549.]), using the following criteria: sequence id > 90%, all-against-all Cα-RMSD ≤ 3.5 Å, removal of incomplete structures and use of a single representative for identical chains. This resulted in 84 structures in total. An actin subunit consists of four subdomains (D1–D4) that are arranged by twist-and-scissors rotation angle (Cong et al., 2008[Cong, Y., Topf, M., Sali, A., Matsudaira, P., Dougherty, M., Chiu, W. & Schmid, M. F. (2008). J. Mol. Biol. 375, 331-336.]). Although the overall organization is similar within the structures in the ensemble, RMSD analysis with TEMPy showed that differences occur between the subdomains, with the most prominent difference occurring in subdomain D2 (the mean Cα-RMSDs are D1 2.1 Å, D2 4.8 Å, D3 2.1 Å and D4 2.5 Å). Each actin subunit in the ensemble was rigidly fitted into the actin filament map, which was first segmented around a single subunit using Chimera (Fig. 3[link]a). The obtained fitted ensemble was then used as an input into TEMPy and scored using the ensemble clustering protocol with CCC and MI. With both scores, several actin structures fit equally well in the map. Hierarchical Cα-RMSD clustering analysis on the complete ensemble resulted in the majority of these top-scoring fits belonging to the same non-singleton cluster [Fig. 3[link](b) for the CCC analysis]. To better represent the heterogeneity of the experimental map we chose the top 10% scoring fits based on each score (resulting in a total of ten fits) (Fig. 3[link]c).

[Figure 3]
Figure 3
Assessment of an ensemble of conformations from the PDB. (a) An ensemble generated from 84 different actin structures (taken from the PDB) is shown (in light blue) within an actin monomer density map [segmented from an 8.9 Å resolution actin filament (EMD code 1990; Behrmann et al., 2012[Behrmann, E., Müller, M., Penczek, P. A., Mannherz, H. G., Manstein, D. J. & Raunser, S. (2012). Cell, 150, 327-338.]), in grey]. (b) The cluster dendrogram of the fits is shown alongside, with the colour bars representing the CCC score of each fit (from white to blue, low to high score). Each cluster is coloured differently. (c) The top 10% scoring fits of the actin monomer from (a), selected on the basis of the CCC and MI ranking (data not shown), are shown (in dark blue) within an actin monomer density map [as in (a)]. The subdomains 1–4 (D1, D2, D3 and D4, respectively) and the DNase-I loop are labelled.
3.1.4. Simulated test case: assessment of a global search ensemble

We use TEMPy to assess the outcome of a global rigid fitting of a protein into the density map of a complex (a typical scenario, especially when the atomic structure of some of the other components is unknown). Several automated rigid-body fitting programs are available to globally fit either single or multiple component structures into EM density maps (Villa & Lasker, 2014[Villa, E. & Lasker, K. (2014). Curr. Opin. Struct. Biol. 25, 118-125.]). Assessing the accuracy of the placement of the components given as the top-ranking solutions by these programs is fundamental to gain insight into the native configuration of the multicomponent system. Here we use the X-ray structure of the Arp2/3 seven-subunit complex with ATP and Ca2+ (PDB code 1tyq; Nolen et al., 2004[Nolen, B. J., Littlefield, R. S. & Pollard, T. D. (2004). Proc. Natl Acad. Sci. USA, 101, 15627-15632.]) as a test case (Fig. 4[link]a). A 20 Å resolution simulated map was obtained using Chimera as described above. A global search of the seven-bladed beta-propeller ARCP1 subunit (chain C) was performed automatically using ADP_EM (Garzón et al., 2007[Garzón, J. I., Kovacs, J., Abagyan, R. & Chacón, P. (2007). Bioinformatics, 23, 427-433.]) without any a priori assumptions. The top-ten solutions ranked by ADP_EM (out of 100) placed chain C in two distinct areas of the EM density map (Fig. 4[link]b). To examine if a clearer solution can be identified, we re-ranked the entire ADP_EM ensemble using the SCCC, NV-S and SMI scores and hierarchically clustered it by Cα-RMSD (data not shown). According to our ranking, the majority of the top-scoring fits belong to the same cluster, suggesting that it may represent the correct placement of the subunit.

[Figure 4]
Figure 4
Assessment of a global search ensemble. (a) The X-ray atomic structure of the Arp2/3 seven-subunit complex with ATP and Ca2+ (PDB code 1tyq; Nolen et al., 2004[Nolen, B. J., Littlefield, R. S. & Pollard, T. D. (2004). Proc. Natl Acad. Sci. USA, 101, 15627-15632.]) is shown (in light grey) within a corresponding 20 Å resolution simulated map (in grey), with chain C (the seven-bladed beta-propeller ARCP1 subunit) highlighted (in yellow). (b) The top-ten-ranked solutions resulting from global fitting of chain C within the 20 Å resolution map based on ADP_EM (in light blue) are shown within the density map (in grey). The native chain C is shown as reference in yellow [as in (a)]. (c) The top-ten-scoring fits (in dark blue) based on re-ranking of the 100 ADP-EM fits using the Borda score (calculated from the SCCC, NV-S and SMI scores) are placed accurately within the 20 Å resolution map (shown in grey). The native chain C is shown as reference in yellow [as in (a)].

Additionally, we applied the consensus scoring to the global ensemble. Calculating the Borda score confirmed that the top-ranked model obtained with ADP_EM is the one that stands out more. Visual inspection of the re-ranked ten top-scoring fits (Fig. 4[link]c) revealed that all of them are placed accurately within the same region of the map (with the centre of mass within 4.9 Å of that of the native structure). Thus, re-ranking with TEMPy helped to identify the correct placement of the protein in the map by selecting near-native solutions from an ensemble of solutions (i.e. reduce overfitting).

3.2. Local assessment of structure segments in single fits

Local assessment of structure segments of a single fit can provide a better way to evaluate specific regions of a single model in different scenarios (Atherton et al., 2014[Atherton, J., Farabella, I., Yu, I. M., Rosenfeld, S. S., Houdusse, A., Topf, M. & Moores, C. A. (2014). eLife, 3, e03680.]; Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]). This capability of TEMPy can be useful in the context of flexible fitting. To demonstrate this, we present two examples using six simulated maps (Example 1) and one experimental (Example 2). We show how to assess the quality of individual secondary structure elements before, after and during the refinement procedure. In each case, as before, we have used the basic functionalities of TEMPy, with the Scoring Function module and the Plotting module for assessment. The snippet of code in Fig. S1B shows how to select a set of individual secondary structure elements from a single fitted model, score them with SCCC and generate Chimera attribute files (more detailed examples are available online in the TEMPy documentation).

3.2.1. Example 1: simulated benchmark

We assessed three different test cases comprising a protein in two conformations within maps at two different resolutions (5 and 10 Å). The assessment was performed on previously calculated fitted models resulting from flexible fitting by Flex-EM/RIBFIND (Pandurangan & Topf, 2012[Pandurangan, A. P. & Topf, M. (2012). J. Struct. Biol. 177, 520-531.]) of (i) the ligand-bound conformation of the glutamine-binding protein (PDB code 1wdn; Sun et al., 1998[Sun, Y.-J., Rose, J., Wang, B.-C. & Hsiao, C.-D. (1998). J. Mol. Biol. 278, 219-229.]) in the density maps simulated from the ligand-free conformation (PDB code 1ggg); (ii) the ligand-free maltodextrin binding protein (PDB code 1omp; Sharff et al., 1992[Sharff, A. J., Rodseth, L. E., Spurlino, J. C. & Quiocho, F. A. (1992). Biochemistry, 31, 10657-10663.]) in the maps simulated from the ligand-bound conformation (PDB code 1anf); and (iii) the ligand-bound D-ribose-binding protein (PDB code 2dri; Björkman et al., 1994[Björkman, A. J., Binnie, R. A., Zhang, H., Cole, L. B., Hermodson, M. A. & Mowbray, S. L. (1994). J. Biol. Chem. 269, 30206-30211.]) in the maps simulated from the ligand-free conformation (PDB code 1urp). Here, we used the SCCC score to assess the fit quality of individual secondary structure elements (as determined by DSSP; Kabsch & Sander, 1983[Kabsch, W. & Sander, C. (1983). Biopolymers, 22, 2577-2637.]) of the initial and final models (Fig. S4). As previously shown, this analysis is useful in finding the consensus between multiple flexible fitting methods and thus can help to identify regions with high variability (that may result from overfitting or local errors in the starting models) (Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]). Furthermore, using SCCC we examined the quality of the fit after each Flex-EM simulated annealing cycle of the refinement procedure (Topf et al., 2008[Topf, M., Lasker, K., Webb, B., Wolfson, H., Chiu, W. & Sali, A. (2008). Structure, 16, 295-307.]) (Fig. S5). Visualizing the progression of the refinement process in this manner can help in detecting which regions of the structure are more dynamic.

3.2.2. Example 2: Actin

We also compared, using the segment-based assessment of a single fit, two models: (i) the published model of the F-actin subunit (PDB code 3mfp) refined in the 6.6 Å resolution map of actin filament (EMD code 5168; Fujii et al., 2010[Fujii, T., Iwane, A. H., Yanagida, T. & Namba, K. (2010). Nature, 467, 724-728.]) and (ii) the crystal structure of a unbound G-actin monomer in the ADP state (PDB code 1j6z; Otterbein et al., 2001[Otterbein, L. R., Graceffa, P. & Dominguez, R. (2001). Science, 293, 708-711.]), which was used as a starting model. The initial model was rigidly fitted into the actin filament map using Chimera's fit_in_map tool. Here too we used the SCCC score to assess the fit quality of individual secondary structure elements (as determined by DSSP) of the initial and final models (Fig. 5[link]). This type of analysis helps to highlight specific regions where the fit has improved more significantly. As discussed above, an actin subunit consists of four subdomains, with D3 being the most similar in most actin crystal structures (Cong et al., 2008[Cong, Y., Topf, M., Sali, A., Matsudaira, P., Dougherty, M., Chiu, W. & Schmid, M. F. (2008). J. Mol. Biol. 375, 331-336.]). This feature is clearly captured by our local assessment having similar quality of fit in the initial and final models (Fig. 5[link]). On the other end, in D1 our analysis captures subtle changes that could have not been observed using a global analysis approach (i.e. scoring the entire model).

[Figure 5]
Figure 5
Local assessment of structure segments after refinement of a single fit. Comparison between an actin monomer (initial fit; PDB code 1j6z; Otterbein et al., 2001[Otterbein, L. R., Graceffa, P. & Dominguez, R. (2001). Science, 293, 708-711.]) rigidly fitted in an actin monomer density map (segmented from 6.6 Å resolution actin filament; EMD code 5168; Fujii et al., 2010[Fujii, T., Iwane, A. H., Yanagida, T. & Namba, K. (2010). Nature, 467, 724-728.]) and the final model resulting from flexible fitting in the same map (final fit; PDB code 3mfp; Fujii et al., 2010[Fujii, T., Iwane, A. H., Yanagida, T. & Namba, K. (2010). Nature, 467, 724-728.]). Both models are shown within the actin monomer density (in grey). The two models are colour coded according to the SCCC score for each individual secondary structure element (as defined by DSSP). Subdomains 1–4 (D1, D2, D3 and D4, respectively) and the DNase-I loop are labelled.

4. Discussion

TEMPy is a modular library and it has been proven useful in assessing density fits in the context of EM reconstructions (Lukoyanova et al., 2015[Lukoyanova, N. et al. (2015). PLoS Biol. 13, e1002049.]; Atherton et al., 2014[Atherton, J., Farabella, I., Yu, I. M., Rosenfeld, S. S., Houdusse, A., Topf, M. & Moores, C. A. (2014). eLife, 3, e03680.]; Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]). It offers a number of distinctive features, in particular the use of multiple scores for the comparison and assessment of fits. In this paper, we introduce TEMPy's capability to assess an individual fit or an ensemble of fits with clustering and with multiple and consensus scoring.

With TEMPy, the user can generate a random ensemble or load ensembles that were generated with external software (based on local or global searches) in order to select the best-fitting model relative to alternative fits. Depending on the type of ensemble, this can be useful in assessing a fitted model in terms of accuracy and precision. The scoring function can be selected by the user taking into consideration the resolution and the quality of the EM map, as well as the information available about the fitting component(s) (Vasishtan & Topf, 2011[Vasishtan, D. & Topf, M. (2011). J. Struct. Biol. 174, 333-343.]).

The selection of the most appropriate fit from the gamut of alternative solutions could be based on different strategies. One strategy, widely used in computational biology, is to cluster a set of models on the basis of the RMSD values between each pair (Alber et al., 2008[Alber, F., Förster, F., Korkin, D., Topf, M. & Sali, A. (2008). Annu. Rev. Biochem. 77, 443-477.]). In TEMPy the user can cluster the fits and visualize the clusters and associated scores for the members of each cluster. This could help to identify the set of fits that score high by multiple methods. It has been shown, for example in small-molecule docking, that relying on the concept of consensus scoring schemes can help to balance errors and increase the ranking power within multiple solutions of docking poses (Kitchen et al., 2004[Kitchen, D. B., Decornez, H., Furr, J. R. & Bajorath, J. (2004). Nat. Rev. Drug Discov. 3, 935-949.]). Such an approach is also supported via the use of the Borda score.

Importantly, in cases where there is no clear single solution resulting from these protocols as the observation-to-parameter ratio is too small for a reliable fitting (owing, for example, to poor resolution, map defects, protein dynamics), multiple solutions can be proposed to better represent the experimental data. This approach is common practice in the NMR field, where atomic coordinates are proposed not only for regions that are well defined by the data but also for `ill defined' regions, which correspond to conformational dynamics and/or reflect incompleteness of the restraining data (Montelione et al., 2013[Montelione, G. T., Nilges, M., Bax, A., Güntert, P., Herrmann, T., Richardson, J. S., Schwieters, C. D., Vranken, W. F., Vuister, G. W., Wishart, D. S., Berman, H. M., Kleywegt, G. J. & Markley, J. L. (2013). Structure, 21, 1563-1570.]; Havel & Wüthrich, 1985[Havel, T. F. & Wüthrich, K. (1985). J. Mol. Biol. 182, 281-294.]). Consequently, each member of the NMR `ensemble' represents a single model that is consistent with the experimental data.

The variability of models across the ensemble provides insight into how well defined are different regions of the structure and the map. Using this strategy to represent EM data can help to describe coordinate uncertainty (Sachse et al., 2007[Sachse, C., Chen, J. Z., Coureux, P. D., Stroupe, M. E., Fändrich, M. & Grigorieff, N. (2007). J. Mol. Biol. 371, 812-835.]; Goulet et al., 2014[Goulet, A., Major, J., Jun, Y., Gross, S. P., Rosenfeld, S. S. & Moores, C. A. (2014). Proc. Natl Acad. Sci. USA, 111, 1837-1842.]; Lukoyanova et al., 2015[Lukoyanova, N. et al. (2015). PLoS Biol. 13, e1002049.]). The selection of the representative models depends on the different fitting scenarios. For example, if the majority of the top-scoring fits belong to the same non-singleton cluster, the fits in the cluster can be selected as the representative ensemble. Alternatively, depending on the nature of the ensemble, sometimes one can follow the common practice from the protein–protein docking field in which the top 10% of the ensemble (or the 10−20 top models) are chosen. It has been shown in protein–protein docking studies that the majority of the scoring functions routinely used in the field yield an acceptable solution in the majority of the ten top-scoring poses within different docking decoys (Moal et al., 2013[Moal, I. H., Torchala, M., Bates, P. A. & Fernández-Recio, J. (2013). BMC Bioinformatics, 14, 286.]).

Finally, TEMPy can also help in addressing the problem of overfitting in flexible fitting. Errors arising from overfitting can be reduced by applying constraints (for example, by grouping atoms together into rigid bodies) during the fitting process (Lopéz-Blanco & Chacón, 2013[Lopéz-Blanco, J. R. & Chacón, P. (2013). J. Struct. Biol. 184, 261-270.]; Topf et al., 2008[Topf, M., Lasker, K., Webb, B., Wolfson, H., Chiu, W. & Sali, A. (2008). Structure, 16, 295-307.]; Trabuco et al., 2008[Trabuco, L. G., Villa, E., Mitra, K., Frank, J. & Schulten, K. (2008). Structure, 16, 673-683.]; Pandurangan & Topf, 2012[Pandurangan, A. P. & Topf, M. (2012). J. Struct. Biol. 177, 520-531.]; Grubisic et al., 2010[Grubisic, I., Shokhirev, M. N., Orzechowski, M., Miyashita, O. & Tama, F. (2010). J. Struct. Biol. 169, 95-105.]) and can also be detected by means of consensus between multiple flexible fitting methods (Pandurangan et al., 2014[Pandurangan, A. P., Shakeel, S., Butcher, S. J. & Topf, M. (2014). J. Struct. Biol. 185, 427-439.]; Ahmed et al., 2012[Ahmed, A., Whitford, P. C., Sanbonmatsu, K. Y. & Tama, F. (2012). J. Struct. Biol. 177, 561-570.]; Ahmed & Tama, 2013[Ahmed, A. & Tama, F. (2013). J. Struct. Biol. 182, 67-77.]). TEMPy's local assessment of structure segments is a useful complementary tool to these approaches.

In conclusion, the modular nature of TEMPy makes it a unique platform that will help the user in a fair range of expected fitting scenarios in intermediate-to-low resolution maps. An additional advantage is that it includes the use of plots and output files for visualization purposes that can further help the user in analysing and interpreting density fits at various steps of the fitting process.

5. Availability

The stable release of the library is available for download under Public License from http://tempy.ismb.lon.ac.uk/. The TEMPy software package includes well organized documentation built with the Sphinx Python documentation generator (http://sphinx-doc.org) and a set of sample scripts that demonstrate usage of the package.

Supporting information


Acknowledgements

We thank Dr David Houldershaw for computer support, and Drs Martyn Winn, Ardan Patwardhan, Sony Malhotra, Ingvar Lagerstedt, Giulia Zanetti and Marta Carroni for helpful discussions. This work was mainly supported by BBSRC (BB/K01692X/1). We also thank MRC (G0600084), Leverhulme Trust (RPG-2012-519) and the European Commission within the Research Infrastructures of the FP7 Capacities Specific Programme (contract Biomedbridges No. 284209).

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