Anisotropy in macromolecular crystal structures. Andrea Thorn July 19 th, 2012

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1 Anisotropy in macromolecular crystal structures Andrea Thorn July 19 th, 2012

2 Motivation Courtesy of M. Sawaya

3 Motivation Crystal structures are inherently anisotropic. X-ray diffraction reflects this fact and hence it is necessary to account for it: Anisotropic atomic displacement parameters (ADPs) TLS (+ isotropic B factor) refinement Anisotropic scaling

4 Anisotropic scaling a) before structure solution: Data quality improvement prior to phasing Local average intensities are made independent of the direction in reciprocal space In cases of severe anisotropy, an ellipsoidal rather than spherical boundary for the reflections can be used. b) after structure solution; model known: Refinement of up to six anisotropic parameters (depending on crystal system). In SHELXL, the parameters are restrained to zero to prevent instabilities in full-matrix refinement. Sheriff & Hendrickson (1987). Acta Cryst. A43, Strong et al. (2010). Comp. Cryst. Newsletter 1,

5 TLS A typical choice at medium resolution: TLS + isotropic B factors Translation, libration and screw motion (TLS) rigid molecular domain in a crystal lattice 20 independent parameters T tensor and B factors are interdependent: no unique solution Calculation leads to same anisotropic ADPs in PDB Omission of diagonal T tensor term resolves dependence (Ian Tickle, personal communication)

6 TLS ADPs are then dominated by the isotropic contributions which compensate for unequal occupancies.

7 Anisotropic refinement Anisotropic refinement at very good resolution: Six U ij parameters per atom are refined.

8 Rigid-bond restraints Hirshfield criterion for small molecule structure validation: The mean-square displacement amplitudes of bonded atoms are equal in the direction of the bond joining them. ΔU zz = 0 z y x Hirshfeld, F. L. (1976). Acta Cryst. A32,

9 Rigid-bond restraints Rollett (1970): Rigid-bond restraints DELU in SHELXL; RBON in REFMAC. Improvement of the data/parameter ratio; enables anisotropic refinement at relatively good resolution. Standard deviation usually Å 2 Provides about one restraint per atom. If applied to 1,3-distances as well: about two restraints per atom Rollett (1970). Cryst. Computing, Copenhagen: Munksgaard.

10 Similar-U restraints Similar U restraints: All six U ij values of two bonded atoms should be as equal as possible. SIMU in SHELX Large estimated standard deviations Much less justified by theory and experimental evidence

11 Enhanced rigid-bond restraints If a bond between two atoms is really rigid, the relative motion of the two atoms should be perpendicular to the bond! ΔU zz = 0 ΔU zz = 0 ΔU yz = 0; ΔU xz = 0 Three restraints per atom; if applied to 1,3-distances: Approximately 6 restraints per atom! z y x Thorn, Dittrich, Sheldrick. (2012) Acta Cryst. A68,

12 Verification at high resolution Refinement of a cyclic hexapeptide Å; 100 K Cut to 0.84 Å IAM ,2 IAM 1,2 XD 1,2 IAM ,3 IAM 1,3 XD 1,3 r.m.s. ΔU ZZ [Å 2 ] r.m.s. ΔU XZ&YZ [Å 2 ] r.m.s. ΔU XY [Å 2 ] r.m.s. ΔU XX&YY [Å 2 ] IAM = Independent atom refinement XD = XD multipole refinement

13 Standard deviations Usage as restraint: p 2 +Ueq,A +Ueq,B σ p p 2 +Ueq,A +Ueq,B σ d p A and B are the two atoms U eq equivalent isotropic displacement parameter d is the distance between atoms A and B σ and p are user-supplied parameters (0.004 Å 2 and p = 0.5 gave good results) ADPs are not allowed to be non-positive definite.

14 Test set Test set: Eight well-refined protein structures * Å residues minor components of disordered residues removed water molecules refined isotropically structures shaken by random shifts (mean of 0.5 Å) * 1b0y, 1lu0, 1ok0, 1rqw, 1us0, 2cm5, 2fdn and 2vb1

15 Tests 1.4 Å resolution

16 Tests 1.7 Å resolution

17 Tests 2.0 Å resolution

18 Tests PDB 1us0 at 1.7 Å

19 Conclusion Both anisotropic scaling as well as TLS can significantly lower R(free) values and improve electron density maps. Their interdependencies cannot be resolved completely. The new rigid-bond restraints are an enhancement to the established rigid-bond restraints and may pose an alternative to TLS + isotropic B factors at medium to good resolution. They cannot account for occupancies dropping along sidechains; on the other hand, the enhanced rigid-bond model should be better able to expose defects, especially those involving previously undetected alternative conformations or chemical inhomogeneity.

20 Acknowledgements George M. Sheldrick Birger Dittrich David Watkin & Richard Cooper Michael Sawaya

What's new in SHELXL-2013?

Bruker Webinar What's new in SHELXL-2013? Andrea Thorn 12 th September, 2013 Michael Ruf & Bruce C. Noll Welcome Dr. Michael Ruf Product Manager, SC-XRD Bruker AXS Inc. Madison, WI, USA Andrea Thorn Crystallographic