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| '''Multiple isomorphous replacement''' or '''MIR''' is, historically speaking, the most common approach to solving the [[phase problem]] in [[X-ray crystallography]]. 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 should not affect the crystal formation or [[unit cell]] dimensions in comparison to its native form, hence, they should be [[Isomorphism (crystallography)|isomorphic]].
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| Data sets from the native and heavy-atom derivative of the sample are first collected. Then the interpretation of the [[Patterson function|Patterson difference map]] reveals the heavy atom's location in the unit cell. This allows both the [[amplitude]] and the [[Phase (waves)|phase]] of the atom to be determined. Since the [[structure factor]] of the heavy atom derivative ('''F'''<sub>ph</sub>) of the crystal is the vector sum of the lone heavy atom ('''F'''<sub>h</sub>) and the native crystal ('''F'''<sub>p</sub>) then the phase of the native '''F'''<sub>p</sub> and '''F'''<sub>ph</sub> vectors can be solved geometrically.
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| :<math>\mathbf F_{ph} = \mathbf F_p + \mathbf F_h</math>
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| At least two isomorphous derivatives must be evaluated since using only one will give two possible phases.
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| ==Examples==
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| Some examples of heavy atoms used in protein MIR:
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| *[[Mercury (element)|Hg]]<sup>2+</sup> ions bind to [[thiol]] groups.
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| *[[Uranyl]] salts ([[Uranium dioxide|UO<sub>2</sub>]] + [[Nitrate|NO<sub>3</sub>]]) bind between [[carboxyl]] groups in [[Aspartic acid|Asp]] and [[Glutamic acid|Glu]]
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| *[[Lead|Pb]] bind to [[Cysteine|Cys]]
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| *[[Platinum(IV) chloride|PtCl<sub>4</sub><sup>2-</sup>]] ([[ion]]) bind to [[Histidine|His]]
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| == See also ==
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| === Anomalous Dispersion ===
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| * [[Multi-wavelength anomalous dispersion]] (MAD)
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| * [[Single wavelength anomalous dispersion]] (SAD)
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| === Isomorphous Replacement ===
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| Two methods for providing the needed phasing information by introducing heavy atoms into isomorphous crystals:
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| * Multiple isomorphous replacement (MIR); and
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| * [[Single isomorphous replacement with anomalous signal]] (SIRAS)
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| ===Other===
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| *[[Patterson map]]
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| == References ==
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| {{reflist}}
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| ===Further reading===
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| *{{cite journal |author=Hendrickson WA |year=1985 |title=Analysis of Protein Structure from Diffraction Measurement at Multiple Wavelengths |journal=Trans. ACA |volume=21}}
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| *{{cite journal |author=Karle J |year=1980 |title=Some Developments in Anomalous Dispersion for the Structural Investigation of Macromolecular Systems in Biology |journal=International Journal of Quantum Chemistry: Quantum Biology Symposium |volume=7 |pages=357–367}}
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| *{{cite journal |author=Karle J |year=1989 |title=Linear Algebraic Analyses of Structures with One Predominant Type of Anomalous Scatterer |journal=Acta Cryst. |volume=A45 |pages=303–307}}
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| *{{cite journal |author=Pahler A, Smith JL, Hendrickson WA |year=1990 |title=A Probability Representation for Phase Information from Multiwavelength Anomalous Dispersion |journal=Acta Cryst. |volume=A46 |pages=537–540}}
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| *{{cite journal |author=Terwilliger TC |year=1994 |title=MAD Phasing: Bayesian Estimates of FA |journal=Acta Cryst. |volume=D50 |pages=11–16}}
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| *{{cite journal |author=Terwilliger TC |year=1994 |title=MAD Phasing: Treatment of Dispersive Differences as Isomorphous Replacement Information |journal=Acta Cryst. |volume=D50 |pages=17–23}}
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| *{{cite journal |author=Fourme R, Shepard W, Kahn R, l'Hermite G, de La Sierra IL |year=1995 |title=The Multiwavelength Anomalous Solvent Contrast (MASC) Method in Macrocolecular Crystallography |journal=J. Synchrotron Rad. |volume=2 |pages=36–48 |doi=10.1107/S0909049594006680}}
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| *{{cite journal |author=de la Fortelle E, Bricogne G |year=1997 |title=Maximum-Likelihood Heavy-Atom Parameter Refinement for Multiple Isomorphous Replacement and Multiwavelength Anomalous Diffraction Methods |journal=Methods in Enzymology |volume=276 |pages=472–494 |doi=10.1016/S0076-6879(97)76073-7 |series=Methods in Enzymology |isbn=978-0-12-182177-7}}
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| *{{cite journal |author=Hendrickson WA, Ogata CM |year=1997 |title=Phase Determination from Multiwavelength Anomalous Diffraction Measurements |journal=Methods in Enzymology |volume=276 |pages=494–523 |doi=10.1016/S0076-6879(97)76074-9 |series=Methods in Enzymology |isbn=978-0-12-182177-7}}
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| *{{cite journal |author=Bella J, Rossmann MG |year=1998 |title=A General Phasing Algorithm for Multiple MAD and MIR Data |journal=Acta Cryst. |volume=D54 |pages=159–174}}
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| *{{cite journal |author=Guss JM, Merritt EA, Phizackerley RP, Hedman B, Murata M, [[Keith Hodgson|Hodgson KO]], [[Hans Freeman|Freeman HC]] |year=1989 |title=Phase determination by multiple-wavelength X-ray diffraction: crystal structure of a basic blue copper protein from cucumbers |journal=Science |volume=241 |pages=806–811 |pmid=3406739 |doi=10.1126/science.3406739 |issue=4867 |bibcode=1988Sci...241..806G}}
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| ==External links==
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| *[http://skuld.bmsc.washington.edu/scatter/MAD_1.html MAD phasing] — an in depth tutorial with examples, illustrations, and references.
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| ===Computer programs===
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| *[http://www-ssrl.slac.stanford.edu/absorb.html The SSRL Absorption Package] — {{cite journal |author=Brennan S, Cowan PL |year=1992 |title=A suite of programs for calculating x-ray absorption, reflection and diffraction performance for a variety of materials at arbitrary wavelengths |journal=Rev. Sci. Instrum. |volume=63 |page=850 |doi=10.1063/1.1142625|bibcode = 1992RScI...63..850B }}
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| *[http://www.gwyndafevans.co.uk/chooch.html CHOOCH] — {{cite journal |author=Evans G, Pettifer RF |year=2001 |title=CHOOCH: a program for deriving anomalous-scattering factors from X-ray fluorescence spectra |journal=J. Appl. Cryst. |volume=34 |pages=82–86 |doi=10.1107/S0021889800014655}}
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| *[http://www.hwi.buffalo.edu/SnB/ ''Shake-and-Bake''] (''SnB'') — {{cite journal |author=Smith GD, Nagar B, Rini JM, Hauptman HA, Blessing RH |year=1998 |title=The use of Snb to determine an anomalous scattering substructure |journal=Acta Cryst D |volume=54 |pages=799–804 |pmid=9757093 |doi=10.1107/S0907444997018805 |issue=Pt 5}}
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| *[http://shelx.uni-ac.gwdg.de/SHELX/ SHELX] — {{cite book |author=Sheldrick GM |year=1998 |chapter=SHELX: applications to macromolecules |title=Direct methods for solving macromolecular structures |editor=S Fortier |pages=401–411 |publisher=Dordrecht: Kluwer Academic Publishers |isbn=0-7923-4949-0}}
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| ===Tutorials and examples===
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| *{{cite web |title=The method of Multiple wavelength Anomalous Diffraction using Synchrotron Radiation at optimal X-ray energies: Application to Protein Crystallography |first=Gwyndaf |last=Evans |work=PhD Thesis |date=October 1994 |publisher=University of Warwick |url=http://www.gwyndafevans.co.uk/thesis-html/thesis.html}}
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| [[Category:Crystallography]]
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| {{optics-stub}}
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