Skip to main content

Phasing in crystallography: a modern perspective

Abstract

Phasing by crystallographic methods dramatically contributed to the development of the modern Sciences. As effect of their application, hundreds of thousands structures have been deposited in appropriate databases, a mine of information for chemistry, physics, geosciences and biology, so far only partially exploited. In this paper the historical development of the phasing approaches and the connected scientific paradigms are discussed. A short presentation of the state of the art is also given, together with short term perspectives.

This is a preview of subscription content, access via your institution.

References

  • Altomare A, Caliandro R, Camalli M, Cuocci C, da Silva I, Giacovazzo C, Moliterni AGG, Rizzi R (2004) Automatic structure determination from powder data with EXPO2004. J Appl Cryst 37:1025–1028

    Article  CAS  Google Scholar 

  • Baggio R, Woolfson MM, Declercq JP, Germain G (1978) On the application of phase relationships to complex structures: XVI. A random approach to structure determination. Acta Cryst A34:883–892

    CAS  Google Scholar 

  • Blow DM, Crick FHC (1959) The treatment of errors in isomorphous replacement method. Acta Cryst 12:794–802

    Article  CAS  Google Scholar 

  • Bragg WL, Perutz MF (1954) The structure of haemoglobin: VI. Fourier projections on the 010 plane. Proc R Soc London Ser A 225:315–329

    Article  CAS  Google Scholar 

  • Burla MC, Caliandro R, Camalli M, Carrozzini B, Cascarano GL, De Caro L, Giacovazzo C, Polidori G, Spagna R (2005) SIR2004: an improved tool for crystal structure determination and refinement. J Appl Cryst 38:381–388

    Article  CAS  Google Scholar 

  • Burla MC, Carrozzini B, Cascarano GL, Giacovazzo C, Polidori G (2011) Advances in the VLD algorithm. J Appl Cryst 44:1143–1151

    Article  CAS  Google Scholar 

  • Caliandro R, Carrozzini B, Cascarano GL, De Caro L, Giacovazzo C, Mazzone A, Siliqi D (2008) Ab initio phasing of proteins with heavy atoms at non-atomic resolution: pushing the size limit of solvable structures up to 7890 non-H atoms in the asymmetric unit. J Appl Cryst 41:548–553

    Article  CAS  Google Scholar 

  • Caliandro R, Carrozzini B, Cascarano GL, Giacovazzo C, Mazzone A, Siliqi D (2009) Molecular replacement: the probabilistic approach of the program REMO09 and its applications. Acta Cryst A65:512–527

    Google Scholar 

  • Cochran W (1955) Relations between the phases of structure factors. Acta Cryst 8:473–478

    Article  CAS  Google Scholar 

  • Giacovazzo C (1977) A general approach to phase relationships: the method of representations. Acta Cryst A33:933–944

    Google Scholar 

  • Giacovazzo C (1980) The method of representations of structure seminvariants: II. New theoretical and practical aspects. Acta Cryst A36:362–372

    CAS  Google Scholar 

  • Giacovazzo C, Siliqi D (2002) The method of joint probability distribution functions applied to SIR–MIR and to SIRAS-MIRAS cases. Acta Cryst A58:590–597

    CAS  Google Scholar 

  • Giacovazzo C, Siliqi D (2004) Phasing via SAD/MAD data: the method of the joint probability distribution functions. Acta Cryst D60:73–82

    CAS  Google Scholar 

  • Green DW, Ingram VM, Perutz MF (1954) The structure of haemoglobin: IV. Sign determination by the isomorphous replacement method. Proc R Soc London Ser A 225:287–307

    Article  CAS  Google Scholar 

  • Hauptman H (1975) A new method in the probabilistic theory of the structure invariants. Acta Cryst A31:680–687

    Google Scholar 

  • Hauptman H, Karle J (1953) Solution of the phase problem: I. The centrosymmetrical crystal, American Crystallography Association Monograph No. 3. Polycrystal Book Service, Dayton, Ohio

  • Hauptman H, Karle J (1956) Structure invariants and seminvariants for non-centrosymmetric space groups. Acta Cryst 9:45–55

    Article  CAS  Google Scholar 

  • Hendrickson W (1985) Analysis of protein structure from diffraction measurements at multiple wavelengths. Trans Am Crystallogr Assoc 21:11–21

    CAS  Google Scholar 

  • Hoppe W (1957) Die Faltmolekülmethode-eine neue Methode zur Bestimmung der Kristallstruktur bei ganz oder teilweise bekannter Molekülstruktur. Acta Cryst 10:750–751

    Google Scholar 

  • Hoppe W, Gassmann J (1968) Phase correction, a new method to solve partially known structures. Acta Cryst B24:97–107

    Google Scholar 

  • Hoppe W, Jakubowski U (1975) The determination of phases of erythrocruorin using the two wavelength method with iron as anomalous scatterer. In: Ramaseshan S, Abrahams SC (eds) Anomalous scattering. Munksgaard, Copenhagen, pp 3–11

    Google Scholar 

  • McCoy AJ (2007) Solving structures of protein complexes by molecular replacement with Phaser. Acta Cryst D63:32–41

    Google Scholar 

  • McCoy AJ, Grosse-Kunstleve RW, Adams PD, Winn MD, Storoni LC, Read RJ (2007) Phaser crystallographic software. J Appl Cryst 40:658–674

    Article  CAS  Google Scholar 

  • Okaya Y, Pepinski R (1956) New formulation and solution of the phase problem in X-ray analysis of noncentric crystals containing anomalous scattering. Phys Rev 103:1645–1647

    Article  CAS  Google Scholar 

  • Oszlányi G, Suto A (2007) Ab initio neutron crystallography by the charge flipping method. Acta Cryst A63:156–163

    Google Scholar 

  • Palatinus L, Chapuis G (2007) SUPERFLIP—a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions. J Appl Cryst 40:786–790

    Article  CAS  Google Scholar 

  • Patterson AL (1934) A Fourier series representation of the average distribution of scattering power in crystals. Phys Rev 45:763

    Google Scholar 

  • Perrakis A, Sixma TK, Wilson KS, Lamzin VS (1997) wARP: improvement and extension of crystallographic phases by weighted averaging of multiple-refined dummy atomic models. Acta Cryst D53:448–455

    CAS  Google Scholar 

  • Rossmann MG, Blow DM (1962) The detection of sub-units within the crystallographic asymmetric unit. Acta Cryst 15:24–31

    Article  CAS  Google Scholar 

  • Sheldrick G (1997) Direct methods for solving macromolecular structures. NATO Advanced Study Institute, Erice

    Google Scholar 

  • Vainshtein BK (1964) Structure analysis by electron diffraction. Pergamon Press, Oxford

    Google Scholar 

  • Vincent R, Migdley PA (1994) Double conical beam-rocking system for measurement of integrated electron diffraction intensities. Ultramicroscopy 53:271–282

    Article  CAS  Google Scholar 

  • Weeks CM, de Titta GT, Hauptman HA, Thuman P, Miller R (1994) Structure solution by minimal-function phase refinement and Fourier filtering: II. implementation and applications. Acta Cryst A50:210–220

    CAS  Google Scholar 

  • Winn MD, Ballard CC, Cowtan KD, Dodson EJ, Emsley P, Evans PR, Keegan RM, Krissinel EB, Leslie AGW, McCoy A, McNicholas SJ, Murshudov GN, Pannu NS, Potterton EA, Powell HR, Read RJ, Vagin A, Wilson KS (2011) Overview of the CCP4 suite and current developments. Acta Cryst D67:235–242

    Google Scholar 

  • Yao J, Woolfson MM, Wilson KS, Dodson EJ (2005) A modified ACORN to solve protein structures at resolutions of 1.7 Å or better. Acta Cryst D61:1465–1475

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carmelo Giacovazzo.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Giacovazzo, C. Phasing in crystallography: a modern perspective. Rend. Fis. Acc. Lincei 24 (Suppl 1), 71–76 (2013). https://doi.org/10.1007/s12210-012-0209-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12210-012-0209-x

Keywords

  • Crystallographic methods
  • The phase problem
  • History of phasing techniques