Phase Problem in X‐ray Crystallography, and Its Solution

Abstract

X‐ray crystallography can provide detailed information about the structure of biological molecules if the ‘phase problem’ can be solved for the molecule under study. The phase problem arises because it is only possible to measure the amplitude of diffraction spots: information on the phase of the diffracted radiation is missing. Techniques are available to reconstruct this information.

Keywords: X‐ray diffraction; protein structure; phase problem; Patterson; crystallography

Figure 1.

The diffraction pattern from a crystal depends on the arrangement of atoms in the crystal. In (a) the scattered waves from atoms 1 and 2 have opposite phases and cancel out, so the scattered beam is weak along that direction. In (b) the scattered waves from atoms 3 and 4 combine to give a strong scattered beam.

Figure 2.

A simulation of a two‐dimensional crystal and its diffraction pattern. Note that the lattice repeat in the crystal gives rise to a pattern of spots in the diffraction pattern, and that the lattice directions in the crystal are orthogonal to the lattice directions in the diffraction pattern.

Figure 3.

Each reflection in the diffraction pattern can be described as a wave with a certain magnitude and phase. The magnitude determines the size of the wave (a), and the phase determines where the peaks occur (b).

Figure 4.

MIR allows estimation of phases when heavy atoms are introduced in known positions. Fp represents the total scattering from the native crystal, shifted to the origin of the crystal coordinates. Fh represents the additional scattering from a heavy atom located at H. If the addition of the heavy atom leads to stronger scattering along some direction, the phase of Fp must match that of Fh (a). If the addition of the heavy atom leads to weaker scattering, the phase of Fp must be opposite to that of Fh (b).

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References

Bragg WH (1915) X‐rays and crystal structure. Philosophical Transactions of the Royal Society of London A215: 253.

Cochran W (1952) Acta Crystallographica 5: 65–67.

Green DW, Ingram VM and Perutz MF (1954) The structure determination of haemoglobin: sign determination by the isomorphous replacement method. Proceedings of the Royal Society of London A225: 287.

Hendrickson WA and Ogata CM (1997) Phase determination from multiwavelength anomalous diffraction measurement. Methods in Enzymology 276: 494–523.

Patterson AL (1934) A Fourier series method for the determination of the components of interatomic distances in crystals. Physical Review 46: 372.

Rossmann MG (1972) The Molecular Replacement Method. London: Gordon and Breach.

Wang BC (1985) Resolution of phase ambiguity in macromolecular crystallography. Methods in Enzymology 115: 90–112.

Further Reading

Drenth J (1994) Principles of Protein X‐ray Crystallography. New York: Springer‐Verlag.

Blundell TL and Johnson LN (1976) Protein Crystallography. New York: Academic Press.

Glusker JP and Trueblood KN (1985) Crystal Structure Analysis: A Primer. New York: Oxford University Press.

Rhodes G (1999) Crystallography Made Crystal Clear: A Guide for Users of Macromolecular Models. San Diego: Academic Press.

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How to Cite close
Cowtan, Kevin(May 2003) Phase Problem in X‐ray Crystallography, and Its Solution. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1038/npg.els.0002722]