Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Fast and accurate conversion of atomic models into electron density maps

1 National Center of Biotechnology (CSIC), c/Darwin, 3, Campus Univ. Autónoma de Madrid, 28049 Cantoblanco, Madrid, Spain;
2 Bioengineering Lab., Escuela Politécnica Superior, Univ. San Pablo CEU, Campus Urb. Montepríncipe s/n, 28668, Boadilla del Monte, Madrid, Spain;
3 Escuela Politécnica Superior, Univ. Autónoma de Madrid, Campus Univ. Autónoma de Madrid, 28049 Cantoblanco, Madrid, Spain

Special Issue: Structural analysis of macromolecules using Cryo electron microscopy

New image processing methodologies and algorithms have greatly contributed to the signi cant progress in three-dimensional electron microscopy (3DEM) of biological complexes we have seen over the last decades. Naturally, the availability of accurate procedures for the objective testing of new algorithms is a crucial requirement for the further advancement of the eld. A good and accepted testing work ow involves the generation of realistic 3DEM-like maps of biological macromolecules from which some measure of ground truth can be derived, ideally because their 3D atomic structure is already known. In this work we propose a very accurate generation of maps using atomic form factors for electron scattering. We thoroughly review current approaches in the eld, quantitatively demonstrating the bene ts of the new methodology. Additionally, we study a concrete example of the use of this approach for hypothesis testing in 3D Electron Microscopy.
  Article Metrics

Keywords Atom models; Electron scattering; Filter design; Image formation; 3D signals; Electron microscopy

Citation: Carlos O.S. Sorzano, Javier Vargas, Joaquín Otón, Vahid Abrishami, José M. de la Rosa-Trevín, Sandra del Riego, Alejandro Fernández-Alderete, Carlos Martínez-Rey, Roberto Marabini, José M. Carazo. Fast and accurate conversion of atomic models into electron density maps. AIMS Biophysics, 2015, 2(1): 8-20. doi: 10.3934/biophy.2015.1.8


  • 1. H. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. Bhat, H. Weissig, I. Shindyalov and P. Bourne, The protein data bank, Nucleic Acids Research, 28 (2000), 235-242.
  • 2. J. R. Bilbao-Castro, C. O. S. Sorzano, I. García and J. J. Fernández, Phan3D: design of biological phantoms in 3D electron microscopy, Bioinformatics, 20 (2004), 3286-3288.
  • 3. K. Braig, Z. Otwinowski, R. Hegde, D. C. Boisvert, A. Joachimiak, A. L. Horwich and P. B. Sigler, The crystal structure of the bacterial chaperonin GroEL at 2.8Á, Nature, 371 (1994), 578-86.
  • 4. C. T. Chantler, Detailed tabulation of atomic form factors, photoelectric absorption and scattering cross section, and mass attenuation coe cients in the vicinity of absorption edges in the soft x-rays (z=30-36, z=60-89, e=0.1kev-10kev), addressing convergence issues of earlier work, J. Phys. Chem. Ref. Data, 29 (2000), 597-1048.
  • 5. M. S. Chapman, A. Trzynka and B. K. Chapman, Atomic modeling of cryo-electron microscopy reconstructions - joint re nement of model and imaging parameters., J. Structural Biology, 182 (2013), 10-21, URL http://dx.doi.org/10.1016/j.jsb.2013.01.003.
  • 6. Collaborative computational project no. 4, The CCP4 Suite: Programs for Protein Crystallography, Acta Crystallo- graphica, D50 (1994), 760-763.
  • 7. H. A. David and H. N. Nagaraja, Order statistics, John Wiley and Sons, 2003.
  • 8. W. R. Dillon and M. Goldstein, Multivariate analysis: Methods and applications, John Wiley, New York, USA, 1984.
  • 9. J. Frank, Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State, Oxford Univ. Press, New York, USA, 2006.
  • 10. J. Frank, M. Radermacher, P. Penczek, J. Zhu, Y. Li, M. Ladjadj and A. Leith, SPIDER and WEB: Processing and visualization of images in 3D electron microscopy and related elds., J. Structural Biology, 116 (1996), 190-9.
  • 11. P. Ge and Z. H. Zhou, Hydrogen-bonding networks and rna bases revealed by cryo electron microscopy suggest a triggering mechanism for calcium switches., Proc. Natl. Acad. Sci. USA, 108 (2011), 9637-9642.
  • 12. G. Harauz and M. van Heel, Exact lters for general geometry three dimensional reconstruction, Optik, 73 (1986),146-156.
  • 13. R. Henderson, A. Sali, M. L. Baker, B. Carragher, B. Devkota, K. H. Downing, E. H. Egelman, Z. Feng, J. Frank, N. Grigorieff, W. Jiang, S. J. Ludtke, O. Medalia, P. A. Penczek, P. B. Rosenthal, M. G. Rossmann, M. F. Schmid, G. F. SchrÃüder, A. C. Steven, D. L. Stokes, J. D. Westbrook, W. Wriggers, H. Yang, J. Young, H. M. Berman, W. Chiu, G. J. Kleywegt and C. L. Lawson, Outcome of the rst electron microscopy validation task force meeting., Structure, 20 (2012), 205-214.
  • 14. B. Heymann and D. Belnap, Bsoft: Image processing and molecular modeling for electron microscopy, J. Structural Biology, 157 (2007), 3-18.
  • 15. S. Jonic, C. O. S. Sorzano and N. Boisset, Comparison of single-particle analysis and electron tomography approaches: an overview, J. Microscopy, 232 (2008), 562-579.
  • 16. D. C. Joy, Monte Carlo Modeling for Electron Microscopy and Microanalysis, Oxford Univ. Press, London, England,1995.
  • 17. E. Kirkland, Advanced computing in electron microscopy, Plenum press, New York, USA, 1998.
  • 18. C. L. Lawson, M. L. Baker, C. Best, C. Bi, M. Dougherty, P. Feng, G. van Ginkel, B. Devkota, I. Lagerstedt, S. J. Ludtke, R. H. Newman, T. J. Old eld, I. Rees, G. Sahni, R. Sala, S. Velankar, J. Warren, J. D. Westbrook, K. Henrick, G. J. Kleywegt, H. M. Berman and W. Chiu, Emdatabank.org: uni ed data resource for cryoem., Nucleic Acids Res,39 (2011), D456-D464.
  • 19. R. M. Lewitt, Alternatives to voxels for image representation in iterative reconstruction algorithms, Physics in Medicine & Biology, 37 (1992), 705-716.
  • 20. H. Lilliefors, On the kolmogorov-smirnov test for normality with mean and variance unknown, J. American Statistical Association, 62 (1967), 399-402.
  • 21. S. J. Ludtke, P. R. Baldwin and W. Chiu, EMAN: Semiautomated software for high-resolution single-particle reconstructions, J. Structural Biology, 128 (1999), 82-97.
  • 22. A. Oppenheim, R. Schafer and J. Buck, Discrete-time signal processing, 2nd edition, Prentice-Hall, 1999.
  • 23. L. M. Peng, Electron atomic scattering factors, debye-waller factors and the optical potential for high-energy electron diffraction, J. Electron Microscopy, 54 (2005), 199-207.
  • 24. L. M. Peng, G. Ren, S. L. Dudarev and M. J. Whelan, Robust parameterization of elastic and absorptive electron atomic scattering factors, Acta Crystallographica, A52 (1996), 257-276.
  • 25. P. W. Rose, B. Beran, C. Bi, W. F. Bluhm, D. Dimitropoulos, D. S. Goodsell, A. Prlic, M. Quesada, G. B. Quinn, J. D. Westbrook, J. Young, B. Yukich, C. Zardecki, H. M. Berman and P. E. Bourne, The rcsb protein data bank: redesigned web site and web services., Nucleic Acids Res, 39 (2011), D392-D401.
  • 26. H. Rullgård, L.-G. Ofverstedt, S. Masich, B. Daneholt and O. Oktem, Simulation of transmission electron microscope images of biological specimens., J Microsc, 243 (2011), 234-256, URL http://dx.doi.org/10.1111/j.1365-2818.2011.03497.x.
  • 27. S. H. W. Scheres, A Bayesian view on cryo-EM structure determination., J. Molecular Biology, 415 (2012), 406-418.
  • 28. G. H. Smith and R. E. Burge, The analytical representation of atomic scattering amplitudes for electrons, Acta Crystallographica, 15 (1962), 182-186.
  • 29. C. O. S. Sorzano, S. Jonic, M. Cottevieille, E. Larquet, N. Boisset and S. Marco, 3D electron microscopy of biological nanomachines: principles and applications, European Biophysics Journal, 36 (2007), 995-1013.
  • 30. C. O. S. Sorzano, R. Marabini, , J. Velázquez-Muriel, J. R. Bilbao-Castro, S. H. W. Scheres, J. M. Carazo and A. Pascual-Montano, XMIPP: A new generation of an open-source image processing package for electron microscopy, J. Structural Biology, 148 (2004), 194-204.
  • 31. C. O. S. Sorzano, R. Marabini, N. Boisset, E. Rietzel, R. Schröder, G. T. Herman and J. M. Carazo, The effect of overabundant projection directions on 3D reconstruction algorithms, J. Structural Biology, 133 (2001), 108-118.
  • 32. J. C. H. Spence, On the accurate measurement of structure-factor amplitudes and phases by electron diffraction, Acta Crystallographica, A49 (1993), 231-260.
  • 33. P. A. Stadelmann, EMS - a software package for electron diffraction analysis and HREM image simulation in materials science, Ultramicroscopy, 21 (1987), 131-146.
  • 34. S. M. Stagg, J. Pulokas, D. Fellmann, A. Cheng, J. D. Quispe, S. P. Mallick, R. M. Avila, B. Carragher and C. S. Potter, Automated cryoem data acquisition and analysis of 284,742 particles of groel, Nature, 439 (2006), 234-238.
  • 35. F. Tama, O. Miyashita and C. L. Brooks, Flexible multi-scale tting of atomic structures into low-resolution electron density maps with elastic network normal mode analysis., J Mol Biol, 337 (2004), 985-999.
  • 36. F. Tama, O. Miyashita and C. L. Brooks III, Normal mode based exible tting of high-resolution structure into low-resolution experimental data from cryo-EM, J. Structural Biology, 147 (2004), 315-326.
  • 37. E. Tjioe, K. Lasker, B. Webb, H. J. Wolfson and A. Sali, Multi t: a web server for tting multiple protein structures into their electron microscopy density map., Nucleic Acids Res, 39 (2011), W167-W170.
  • 38. M. Topf, K. Lasker, B. Webb, H. Wolfson, W. Chiu and A. Sali, Protein structure tting and re nement guided by cryo-em density., Structure, 16 (2008), 295-307.
  • 39. L. G. Trabuco, E. Villa, K. Mitra, J. Frank and K. Schulten, Flexible tting of atomic structures into electron microscopy maps using molecular dynamics., Structure, 16 (2008), 673-683.
  • 40. M. Unser, A. Aldroubi and M. Eden, B-Spline signal processing: Part I - theory, IEEE Trans. Signal Processing, 41 (1993), 821-832.
  • 41. M. Unser, A. Aldroubi and M. Eden, B-Spline signal processing: Part II-E cient design and applications, IEEE Trans. Signal Processing, 41 (1993), 834-848.
  • 42. M. van Heel, G. Harauz, E. V. Orlova, R. Schmidt and M. Schatz, A new generation of the IMAGIC image processing system, J. Structural Biology, 116 (1996), 17-24.
  • 43. M. Vulović, R. B. G. Ravelli, L. J. van Vliet, A. J. Koster, I. Lazić, U. Lücken, H. Rullgård, O. Öktem and B. Rieger, Image formation modeling in cryo-electron microscopy., J Struct Biol, 183 (2013), 19-32, URL http://dx.doi.org/10.1016/j.jsb.2013.05.008.
  • 44. A. J. C. Wilson (ed.), International tables for crystallography, 500, Kluwer Academics Publisher, 1995.
  • 45. W. Wriggers, Using situs for the integration of multi-resolution structures., Biophys Rev, 2 (2010), 21-27.
  • 46. W. Wriggers, R. A. Milligan and J. A. McCammon, Situs: A package for docking crystal structures into low-resolution maps from electron microscopy, J. Structural Biology, 125 (1999), 185-195.
  • 47. X. Zhang, L. Jin, Q. Fang, W. H. Hui and Z. H. Zhou, 3.3 a cryo-em structure of a nonenveloped virus reveals a priming mechanism for cell entry., Cell, 141 (2010), 472-482.


This article has been cited by

  • 1. Joan Segura, Ruben Sanchez-Garcia, Daniel Tabas-Madrid, Jesus Cuenca-Alba, Carlos Oscar S. Sorzano, Jose Maria Carazo, 3DIANA: 3D Domain Interaction Analysis: A Toolbox for Quaternary Structure Modeling, Biophysical Journal, 2016, 10.1016/j.bpj.2015.11.3519
  • 2. Slavica Jonic, Carlos Oscar Sanchez Sorzano, Coarse-Graining of Volumes for Modeling of Structure and Dynamics in Electron Microscopy: Algorithm to Automatically Control Accuracy of Approximation, IEEE Journal of Selected Topics in Signal Processing, 2016, 10, 1, 161, 10.1109/JSTSP.2015.2489186
  • 3. Tejal Bhamre, Teng Zhang, Amit Singer, Denoising and covariance estimation of single particle cryo-EM images, Journal of Structural Biology, 2016, 10.1016/j.jsb.2016.04.013
  • 4. C.O.S. Sorzano, J. Vargas, J. Otón, V. Abrishami, J.M. de la Rosa-Trevín, J. Gómez-Blanco, J.L. Vilas, R. Marabini, J.M. Carazo, A review of resolution measures and related aspects in 3D Electron Microscopy, Progress in Biophysics and Molecular Biology, 2016, 10.1016/j.pbiomolbio.2016.09.005
  • 5. S. Jonić, J. Vargas, R. Melero, J. Gómez-Blanco, J.M. Carazo, C.O.S. Sorzano, Denoising of high-resolution single-particle electron-microscopy density maps by their approximation using three-dimensional Gaussian functions, Journal of Structural Biology, 2016, 194, 3, 423, 10.1016/j.jsb.2016.04.007

Reader Comments

your name: *   your email: *  

Copyright Info: © 2015, Carlos O.S. Sorzano, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved