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77:
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22:
524:
In the translation function, the now correctly oriented known model can be correctly positioned by translating it to the correct co-ordinates within the asymmetric unit. This is accomplished by moving the model, calculating a new
Patterson map, and comparing it to the unknown-derived Patterson map.
472:
for the intensities, which is an interatomic vector map created by squaring the structure factor amplitudes and setting all phases to zero. This vector map contains a peak for each atom related to every other atom, with a large peak at 0,0,0, where vectors relating atoms to themselves "pile up".
473:
Such a map is far too noisy to derive any high resolution structural information—however if we generate
Patterson maps for the data derived from our unknown structure, and from the structure of a previously solved homologue, in the correct orientation and position within the
384:
560:
Following this, we should have correctly oriented and translated phasing models, from which we can derive phases which are (hopefully) accurate enough to derive electron density maps. These can be used to build and refine an atomic model of our unknown structure.
477:, the two Patterson maps should be closely correlated. This principle lies at the heart of MR, and can allow us to infer information about the orientation and location of an unknown molecule with its unit cell.
1502:
1497:
201:
1553:
508:-based algorithms. The highest correlation (and therefore scores) are obtained when the two structures (known and unknown) are in similar orientation(s)—these can then be output in
184:. MR relies upon the existence of a previously solved protein structure which is similar to our unknown structure from which the diffraction data is derived. This could come from a
426:
40:
496:
In the rotation function, our unknown
Patterson map is compared to Patterson maps derived from our known homologue structure in different orientations. Historically
460:) to real-space electron density, into which the atomic model is built. MR tries to find the model which fits best experimental intensities among known structures.
446:
501:
525:
This brute-force search is computationally expensive and fast translation functions are now more commonly used. Positions with high correlations are output in
1371:
704:
640:
Jin, Shikai; Miller, Mitchell D.; Chen, Mingchen; Schafer, Nicholas P.; Lin, Xingcheng; Chen, Xun; Phillips, George N.; Wolynes, Peter G. (1 November 2020).
548:, many protocols including MR-Rosetta, QUARK, AWSEM-Suite and I-TASSER-MR can generate a lot of native-like decoy structures that are useful to solve the
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The first goal of the crystallographer is to obtain an electron density map, density being related with diffracted wave as follows:
160:
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58:
379:{\displaystyle \rho (x,y,z)={\frac {1}{V}}\sum _{h}\sum _{k}\sum _{\ell }|F_{hk\ell }|\exp(2\pi i(hx+ky+\ell z)+i\Phi (hk\ell )).}
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Ramelot, TA; Raman, S; Kuzin, AP; Xiao, R; Ma, LC; Acton, TB; Hunt, JF; Montelione, GT; Baker, D; Kennedy, MA (April 2009).
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Due to historic limitations in computing power, an MR search is typically divided into two steps:
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593:"Improving NMR protein structure quality by Rosetta refinement: a molecular replacement study"
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642:"Molecular-replacement phasing using predicted protein structures from AWSEM-Suite"
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448:) is lost. Then, in the absence of phases (Φ), we are unable to complete the shown
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were used to score the rotation function, however, modern programs use
694:
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697:– One of the most commonly used molecular replacement programmes.
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70:
15:
577:
Ch 10 in "Principles of
Protein X-ray Crystallography", by
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is being measured, and all the information about phase (
36:
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716:– A helpful public domain introduction to the topic.
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Principles of
Patterson-based molecular replacement
101:. Unsourced material may be challenged and removed.
31:
may be too technical for most readers to understand
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537:predicted structures in molecular replacement
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161:Learn how and when to remove this message
59:Learn how and when to remove this message
43:, without removing the technical details.
703:– Molecular replacement package within
570:
188:protein, or from the lower-resolution
41:make it understandable to non-experts
7:
1636:
976:Phase transformation crystallography
452:relating the experimental data from
99:adding citations to reliable sources
1483:Journal of Chemical Crystallography
389:With usual detectors the intensity
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14:
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192:structure of the same protein.
86:needs additional citations for
1425:Bilbao Crystallographic Server
421:{\displaystyle I=F\cdot F^{*}}
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1:
546:protein structure prediction
1473:Crystal Growth & Design
765:Timeline of crystallography
176:is a method of solving the
1680:
1284:Nuclear magnetic resonance
552:by molecular replacement.
174:Molecular replacement (MR)
1619:
1488:Journal of Crystal Growth
1228:
659:10.1107/S2052252520013494
581:(2nd Edn.) Springer, 1999
1354:Single particle analysis
1212:Hermann–Mauguin notation
541:With the improvement of
502:correlation coefficients
1478:Crystallography Reviews
1322:Isomorphous replacement
1116:Lomer–Cottrell junction
110:"Molecular replacement"
991:Spinodal decomposition
442:
422:
380:
1664:X-ray crystallography
1531:Gregori Aminoff Prize
1327:Molecular replacement
527:Cartesian coordinates
454:X-ray crystallography
443:
441:{\displaystyle \Phi }
423:
381:
182:X-ray crystallography
837:Structure prediction
520:Translation function
432:
393:
202:
95:improve this article
1101:Cottrell atmosphere
1081:Partial dislocation
825:Restriction theorem
1521:Carl Hermann Medal
1332:Molecular dynamics
1179:Defects in diamond
1174:Stone–Wales defect
820:Reciprocal lattice
782:Biocrystallography
609:10.1002/prot.22229
506:maximum likelihood
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1222:Thermal ellipsoid
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1096:Frank–Read source
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922:Aperiodic crystal
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770:Crystallographers
492:Rotation function
450:Fourier transform
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1493:Kristallografija
1347:Gerchberg–Saxton
1242:Characterisation
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1217:Structure factor
1021:
1006:Ostwald ripening
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652:(6): 1168–1178.
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468:We can derive a
458:reciprocal space
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1382:CrystalExplorer
1358:
1342:Phase retrieval
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1183:
1162:Schottky defect
1061:Perfect crystal
1052:
1048:Abnormal growth
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996:Supersaturation
959:Miscibility gap
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805:Bravais lattice
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751:Crystallography
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832:Periodic table
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710:Phaser article
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689:External links
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1337:Patterson map
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1207:Friedel's law
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1150:Wigner effect
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981:Precipitation
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949:Phase diagram
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603:(1): 147–67.
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556:The next step
555:
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550:phase problem
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470:Patterson map
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178:phase problem
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112: –
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106:Find sources:
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84:This article
82:
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73:
72:
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60:
52:
42:
38:
32:
29:This article
27:
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1640:
1628:
1573:Associations
1541:Organisation
1326:
1033:Disclination
964:Polymorphism
927:Quasicrystal
870:Orthorhombic
810:Miller index
758:Key concepts
649:
645:
635:
600:
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586:
573:
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510:Euler angles
495:
479:
467:
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173:
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105:
93:Please help
88:verification
85:
55:
46:
30:
1526:Ewald Prize
1294:Diffraction
1272:Diffraction
1255:Diffraction
1197:Bragg plane
1192:Bragg's law
1071:Dislocation
986:Segregation
898:Crystallite
815:Point group
486:translation
190:protein NMR
1310:Algorithms
1299:Scattering
1277:Scattering
1260:Scattering
1128:Slip bands
1091:Cross slip
941:transition
875:Tetragonal
865:Monoclinic
777:Metallurgy
579:Jan Drenth
565:References
186:homologous
151:April 2019
121:newspapers
1417:Databases
880:Triclinic
860:Hexagonal
800:Unit cell
792:Structure
498:r-factors
475:unit cell
436:Φ
414:∗
406:⋅
365:ℓ
353:Φ
338:ℓ
311:π
302:
289:ℓ
268:ℓ
264:∑
254:∑
244:∑
206:ρ
1658:Category
1630:Category
1465:Journals
1397:OctaDist
1392:JANA2020
1364:Software
1250:Electron
1167:F-center
954:Eutectic
915:Fiveling
910:Twinning
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678:33209327
627:18816799
597:Proteins
516:angles.
482:rotation
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1642:Commons
1590:Germany
1267:Neutron
1157:Vacancy
1016:Defects
1001:GP-zone
847:Systems
669:7642774
618:3612016
543:de novo
535:de novo
500:and/or
135:scholar
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893:Growth
701:Molrep
695:Phaser
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142:JSTOR
128:books
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1123:Slip
1086:Kink
714:PDBe
705:CCP4
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484:and
456:(in
114:news
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1559:RAS
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1440:COD
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1111:GND
1038:CSL
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664:PMC
654:doi
613:PMC
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512:or
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