Examples of order-disorder in macromolecular crystals

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1 Examples of order-disorder in macromolecular crystals Andrey Lebedev York Structural Biology Laboratory University of York 1

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4 !"#$#%&'()#$*"$+#,&*)$ Rye et al. (2007). Acta Cryst. D63, Molecule: L-2-haloacid dehalogenase from Sulfolobus tokodaii Spacegroup: C2 Unit cell: a = 127.6, b = 58.1, c = 51.2 Å,! = 97.2 Resolution = 1.9 Å R-sym = 9.5% (16%) Asymmetric unit: dimer Method: MR Initial refinement: R = 0.21 R-free = 0.27 The electron density for protein atoms is defined, but it is poor for solvent structure. 4

5 8"/(#275"$5<$,=#$6&>#0/5"$'&($ w v=0 u C2 crystal There are series of non-origin peaks. Their heights are up to 0.2 of the origin peak height.?"&)@/*/$5<$20@/,&)$(&2:*";$ There is no NCS by translation However: z x C2 crystal is formed by layers with diperiodic symmetry C22(2). crystal with defect Defects preserving bilayers (i.e. contacts between layers) are possible. z x Defective layer would be shifted from the "correct" position by 13Å. This is the distance between neighbouring peaks in the Patterson map. The crystal must have been a twinned crystal. 5

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9 -#,3*""*";$ I T1 = (1 -! ) I 1 +! q 12 I 2 q 12 = q(h) I 1 = I 2 $ %& $.$&"$5C/#09#+$*",#"/*,@$<05'$,3*""#+$20@/,&)S$ $ & $&"+$$ ' $.$*",#"/*7#/$<05'$+*A#0#",$+5'&*"/S$ ( &' $.$59#0)&($C#,3##"$,3*"$0#)&,#+$0#J#275"/S$ )*.$,=#$,3*""*";$<0&275"+* 8"$&++*75"4$3#$:"53$,=&,$5")@$0#J#275"/$3*,=$,=#$/&'#$ #$2&"$59#0)&($&"+$,=&,$,=#$59#0)&($*/$*"+#(#"+#",$5"$!$ &"+$"E$ 8"$&++*75"4$3#$:"53$,=&,$59#0)&((*";$0#J#275"/$ =&9#$2)5/#$*",#"/*7#/E$ I T1 = (1 -! +! q(h)) I 1?),5;#,=#0B$+#.,3*""*";$*/$0#+12#+$,5$ +#'5+1)&75"S$,=#$'5+1)&75"$*/$+#D"#+$C@$5"#. +*'#"/*5"&)$(#0*5+*2$<1"275"E$$ I T1 = q'(h) I 1 G5"2*/#$<50'B$,=#0#$*/$"5$"##+$,5$+#,#0'*"#$,=#$,3*""*";$<0&275"$)E$ 9

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11 11

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13 Acta Cryst. (1961). 14, 167 On the Theory of Order-Disorder (OD) Structures BY K. DORNBERGER-SC~TFF AND H. GREzL-NIEMANN Institut fiir Stru]cturforschung der Deutschen A lcademie der Wissenschaften zu Berlin, Germany (Received 4 January 1960 and in revised form 17 March 1960) OD-structures consisting of equivalent layers are first characterized as having pairs of adjacent layers which are all equivalent. Then a slightly more general condition--the 'vicinity condition'-- is formulated which is satisfied not only by all ordered structures but also by all OD-structures. Partial operations (POs) are seen to be of fundamental importance for characterizing the symmetry properties of OD-structures and the set of POs of a certain structure is called an OD-groupoid. OD-structures of the same substance, built of the same kind of layers with the same kinds of pairs of adjacent layers are said to belong to the same family, the corresponding OD-groupoids to the same OD-groupoid family. Twins of one particular type are described as special members of families of OD-structures. A report on the deduction of a complete list of OD-groupoid families is given, and the resulting numbers of such families with different symmetry characteristics are listed in tables. There are 333 in all. 1. Introduction In earlier papers (Dornberger-Schiff, 1956,1957,1959c) one of us has described some examples of what we propose to call OD-structures. In such structures equivalent parts lie in equivalent vicinities but there need not be perfect long-range order. repeating operation under consideration may be described by a PO or by combinations of POs. A PO is fully characterized by (a) the transformation of space, and (b) the layer which is to be transformed. 13

OD-structure Stacking vector!-./,012,10#/$ An OD-structure is composed of geometrically identical layers. All pairs of contacting layers are equivalent, but triplets may differ.

(In general case operation relating neighbouring layers includes rotation or reflection) S 1 S 2 S 1 S 1 OD-family Single crystal OD-twin Allotwin Disordered OD-structure All (putative or real)

14 OD-structure Stacking vector!-./,012,10#/$ An OD-structure is composed of geometrically identical layers. All pairs of contacting layers are equivalent, but triplets may differ. Stacking vector relates two neighbouring layers. There are two possible stacking vectors in the discussed example, S 1 and S 2. (In general case operation relating neighbouring layers includes rotation or reflection) S 1 S 2 S 1 S 1 OD-family Single crystal OD-twin Allotwin Disordered OD-structure All (putative or real) structures built of the same layers with the same interfaces form a family of OD-structures. Regular sequences of stacking vectors: S 1 S 1 S 1... or S 1 S 1 S 2 S 1 S 1 S 2... etc. represent single crystals. S 1 S 1 S 1 S 1 S 2 S 2 S 2 S 2... Two individuals have the same symmetry. S 1 S 1 S 1 S 1 S 2 S 1 S 2 S 1 S 2 S 1 S 2... Two individuals have different symmetries. S 1 S 1 S 2 S 1 S 1 S 2 S 2 S 2 S 1... Irregular sequence of stacking vectors. 14

15 Y5";.0&";#$50+#0$*"$!-./,012,10#/$ C2 single crystal C222 1 single crystal C2 C222 1 OD-twin Allotwin Disordered OD-structure C2 C2 C2 C

16 G)&//*D2&75"B$!-./,012,10#/$,-+$,3*"/$ OD-structures: Single crystals allotwin OD-twin (partially) disordered OD-structure Twinning: by merohedry by pseudomerohedry by reticular (pseudo)merohedry... This is structure based classification of a specific class of structures This is geometry based classification accounting for crystal and lattice symmetries. 16

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c%&'()#$5<$&))5,3*"$ 6-b$25+#$KdL,$ 6-b$25+#$KdL9$ Dauter et al. (2005). Acta Cryst. D61, 967-975.

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23 c%&'()#$5<$&))5,3*"$ 6-b$25+#$KdL,$ 6-b$25+#$KdL9$ Dauter et al. (2005). Acta Cryst. D61, Crystal of Lon protease Resolution 3Å G)#&0$+#'5"/,0&75"$ 5<$,=#$(0#/#"2#$5<$,35$)&I2#/$ P &$i$$gfew$j$ C$i$$eLEf$j$ 2$i$K]gEL$j$ P2 1 &$i$$]geu$j$ C$i$$gfEW$j$ 2$i$KWgEL$j$ k$i$ehewn$!-$)&@#0b$ $ $ $6H K H K OHP$ F=#$2)5/#/,$ <1))@$50+#0#+$/,012,10#B $6H K H K H$ 23

c%&'()#$5<$&))5,3*"$ Dauter et al. (2005). Acta Cryst. D61, 967-975.

24 c%&'()#$5<$&))5,3*"$ Dauter et al. (2005). Acta Cryst. D61, P2 1 R / R-free = 0.21 / 0.31 P R / R-free = 0.19 /

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6&07&))@$+*/50+#0#+$!-./,012,10#$ Wang et al. (2005). Acta Cryst. D61, 67-74.

31 Wang et al. (2005). Acta Cryst. D61, l$crystals of DNA polymerase from phage ϕ29 l$resolution 2.2Å l$refinement against corrected data: R=0.28 a* The translation symmetry is perturbed in the direction a*. The diffraction pattern is characterised by the presence of the diffuse streaks along a* for odd l. 2 Sep (5/#+$'5+#)$ ECM 31

32 Wang et al. (2005). Acta Cryst. D61, l$f=#$/,012,10#$3&/$/5)9#+$1/*";$#%(#0*'#",&)$(=&/*";$o25'c*"&75"$5<$ h8qth?-p$&"+$+#'5+1)&,#+$+&,&$ 32

33 6&07&)$+*/50+#0$3*,=$/#9#0&)$/,&2:*";$9#2,50/$ Trame, C. B. & McKay, D. B. (2001). ActaCryst. D57, '()#%#/$ '5+#)$5<$6HHH K $ /*";)#$20@/,&)$ '5+#)$5<$ +*/50+#0#+$20@/,&)$ Z#9#0&)$20@/,&)$<50'/4$ &))$(&07&))@$+*/50+#0#+$!-$ C#)5";*";$,5$+*A#0#",$!-.<&'*)*#/E$ -&,&B$ Q#/5)175" $ $ $ $HEWj$ 6052#//#+$*" $ $ $ $6fHH$ &$i$kklef4$$$2$i$wwueg$ F=#$"&79#$20@/,&)$*/$/=53"$!-$)&@#0B$ $ $ $ $6OfPHH$ R1))@$50+#0#+$/,012,10#B $ $6fHH$ 33

6&07&)$+*/50+#0$3*,=$/#9#0&)$/,&2:*";$9#2,50/$ Trame, C. B. & McKay, D. B. (2001). ActaCryst. D57, 1079 1090.

34 6&07&)$+*/50+#0$3*,=$/#9#0&)$/,&2:*";$9#2,50/$ Trame, C. B. & McKay, D. B. (2001). ActaCryst. D57, #'5+1)&75"$5<$+&,&$,5$;#,$+&,&$ 5"#$+5+#2&'#0$(#0$1"*,$2#))$$ '#&"$".5++$,5$'#&"$".#9#"$ /5)*+B $#%(#0*'#",&)$+&,&$ +&/=#+B $*",#0<#0#"2#$,#0'$ "&79#$+&,&$ 6&>#0/5"$'&(4$3iLEU$ +#'5+1)&,#+$+&,&$ Figure 3 34

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Twinning and other pathologies

Twinning and other pathologies Andrey Lebedev CCP4 OD- structures Twinning by (pseudo)merohedry StaAsAcs of one observaaon StaAsAcs of two observaaons Twinning tests summary Space group validaaon June