Multiple isomorphous replacement

Multiple isomorphous replacement (MIR) is historically the most common approach to solving the phase problem in X-ray crystallography studies of proteins. For protein crystals this method is conducted by soaking the crystal of a sample to be analyzed with a heavy atom solution or co-crystallization with the heavy atom. The addition of the heavy atom (or ion) to the structure should not affect the crystal formation or unit cell dimensions in comparison to its native form, hence, they should be isomorphic.

Data sets from the native and heavy-atom derivative of the sample are first collected. Then the interpretation of the Patterson difference map reveals the heavy atom's location in the unit cell. This allows both the amplitude and the phase of the heavy-atom contribution to be determined. Since the structure factor of the heavy atom derivative (F_ph) of the crystal is the vector sum of the lone heavy atom (F_h) and the native crystal (F_p) then the phase of the native F_p and F_ph vectors can be solved geometrically.

\( {\displaystyle \mathbf {F} _{ph}=\mathbf {F} _{p}+\mathbf {F} _{h}} \)

At least two isomorphous derivatives must be evaluated since using only one will give two possible phases.

Development
Single Isomorphous Replacement (SIR)

Early demonstrations of isomorphous replacement in crystallography come from Cork,^[1] John Monteath Robertson,^[2] and others. An early demonstration of isomorphous replacement in crystallography came in 1927 with a paper reporting the x-ray crystal structures of a series of alum compounds from James M. Cork.^[1] The alum compounds studied had the general formula A^.B^.(SO₄)₂^.12H₂O, where A was a monovalent metallic ion (NH4⁺, K⁺, Rb⁺, Cs⁺, or Tl⁺), B was a trivalent metallic ion (Al³⁺, Cr³⁺, or Fe³⁺) and S was usually sulfur, but could also be selenium or tellurium. Because the alum crystals were largely isomorphous when the heavy atoms were changed out, they could be phased by isomorphous replacement. Fourier analysis was used to find the heavy atom positions.

The first demonstration of isomorphous replacement in protein crystallography was in 1954 with a paper from David W. Green, Vernon Ingram, and Max Perutz.^[3]

Multiple Isomorphous Replacement (MIR)
Examples

Some examples of heavy atoms used in protein MIR:

Hg2+ ions bind to thiol groups.
Uranyl salts (UO2 + NO3) bind between carboxyl groups in Asp and Glu
Lead binds to Cys residues.
PtCl42− (ion) bind to His

See also
Anomalous dispersion

Multi-wavelength anomalous dispersion (MAD)
Single wavelength anomalous dispersion (SAD)

Isomorphous replacement

Two methods for providing the needed phasing information by introducing heavy atoms into isomorphous crystals:

Multiple isomorphous replacement (MIR); and
Single isomorphous replacement with anomalous signal (SIRAS)

Other

Patterson map

References

Cork, J.M. (October 1927). "LX. The crystal structure of some of the alums". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 4 (23): 688–698. doi:10.1080/14786441008564371. ISSN 1941-5982.
Robertson, J Monteath (1937-01-01). "X-ray analysis and application of fourier series methods to molecular structures". Reports on Progress in Physics. 4 (1): 332–367. doi:10.1088/0034-4885/4/1/324. ISSN 0034-4885.

Green, D. W.; Ingram, Vernon Martin; Perutz, Max Ferdinand; Bragg, William Lawrence (1954-09-14). "The structure of haemoglobin - IV. Sign determination by the isomorphous replacement method". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 225 (1162): 287–307. doi:10.1098/rspa.1954.0203. S2CID 96889917.

Further reading

Hendrickson WA (1985). "Analysis of Protein Structure from Diffraction Measurement at Multiple Wavelengths". Trans. ACA. 21.
Karle J (1980). "Some Developments in Anomalous Dispersion for the Structural Investigation of Macromolecular Systems in Biology". International Journal of Quantum Chemistry: Quantum Biology Symposium. 7: 357–367.
Karle J (1989). "Linear Algebraic Analyses of Structures with One Predominant Type of Anomalous Scatterer". Acta Crystallogr. A. 45 (4): 303–307. doi:10.1107/s0108767388013042. PMID 2559755.
Pahler A, Smith JL, Hendrickson WA (1990). "A Probability Representation for Phase Information from Multiwavelength Anomalous Dispersion". Acta Crystallogr. A. 46 (7): 537–540. doi:10.1107/s0108767390002379. PMID 2206480.
Terwilliger TC (1994). "MAD Phasing: Bayesian Estimates of FA". Acta Crystallogr. D. 50: 11–16. doi:10.1107/s0907444993008224. PMID 15299471.
Terwilliger TC (1994). "MAD Phasing: Treatment of Dispersive Differences as Isomorphous Replacement Information". Acta Crystallogr. D. 50 (Pt 1): 17–23. doi:10.1107/s0907444993008236. PMID 15299472.
Fourme R, Shepard W, Kahn R, l'Hermite G, de La Sierra IL (1995). "The Multiwavelength Anomalous Solvent Contrast (MASC) Method in Macrocolecular Crystallography". J. Synchrotron Rad. 2 (Pt 1): 36–48. doi:10.1107/S0909049594006680. PMID 16714785.
de la Fortelle E, Bricogne G (1997). Maximum-Likelihood Heavy-Atom Parameter Refinement for Multiple Isomorphous Replacement and Multiwavelength Anomalous Diffraction Methods. Methods in Enzymology. 276. pp. 472–494. doi:10.1016/S0076-6879(97)76073-7. ISBN 978-0-12-182177-7. PMID 27799110.
Hendrickson WA, Ogata CM (1997). Phase Determination from Multiwavelength Anomalous Diffraction Measurements. Methods in Enzymology. 276. pp. 494–523. doi:10.1016/S0076-6879(97)76074-9. ISBN 978-0-12-182177-7. PMID 27799111.
Bella J, Rossmann MG (1998). "A General Phasing Algorithm for Multiple MAD and MIR Data". Acta Crystallogr. D. 54 (2): 159–174. doi:10.1107/s0907444997010469. PMID 9761882.
Guss JM, Merritt EA, Phizackerley RP, Hedman B, Murata M, Hodgson KO, Freeman HC (1989). "Phase determination by multiple-wavelength X-ray diffraction: crystal structure of a basic blue copper protein from cucumbers". Science. 241 (4867): 806–811. Bibcode:1988Sci...241..806G. doi:10.1126/science.3406739. PMID 3406739.

External links

MAD phasing — an in depth tutorial with examples, illustrations, and references.

Computer programs

The SSRL Absorption Package — Brennan S, Cowan PL (1992). "A suite of programs for calculating x-ray absorption, reflection and diffraction performance for a variety of materials at arbitrary wavelengths". Rev. Sci. Instrum. 63 (1): 850. Bibcode:1992RScI...63..850B. doi:10.1063/1.1142625.
CHOOCH — Evans G, Pettifer RF (2001). "CHOOCH: a program for deriving anomalous-scattering factors from X-ray fluorescence spectra". J. Appl. Cryst. 34: 82–86. doi:10.1107/S0021889800014655.
Shake-and-Bake (SnB) — Smith GD, Nagar B, Rini JM, Hauptman HA, Blessing RH (1998). "The use of Snb to determine an anomalous scattering substructure". Acta Crystallogr D. 54 (Pt 5): 799–804. doi:10.1107/S0907444997018805. PMID 9757093.
SHELX — Sheldrick GM (1998). "SHELX: applications to macromolecules". In S Fortier (ed.). Direct methods for solving macromolecular structures. Dordrecht: Kluwer Academic Publishers. pp. 401–411. ISBN 0-7923-4949-0.

Tutorials and examples
Evans, Gwyndaf (October 1994). "The method of Multiple wavelength Anomalous Diffraction using Synchrotron Radiation at optimal X-ray energies: Application to Protein Crystallography". PhD Thesis. University of Warwick.

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