Model and data. An X-ray structure solution requires a model.

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2 Model and data An X-ray structure solution requires a model. This model has to be consistent with: The findings of Chemistry Reflection positions and intensities Structure refinement = Model fitting by parameter adjustment

3 Data/parameter ratio The fewer parameters there are, the better they can be determined by a given number of data. More Parameters than measurements: No unique solution. To make the data/parameter ratio bigger, constraints and restraints are applied.

4 Constraints Certain values or dependencies which have to be fulfilled. Example: Result: Riding hydrogen positions Less independent parameters

5 Restraints Dependencies which have not be exactly fulfilled. Like data, they have a target value and a standard uncertainty (s.u.). Example: Result: To bond lengths should be equal within a certain s.u. More data

6 Atomic displacement Vibrations, Disorder and lattice defects Isotropic or anisotropic: Isotropic: Anisotropic: 4N parameters 9N parameters N Number of Atoms in the asymmetric unit Atomic displacement is described as Gaussian function(s).

7 Isotropic refinement

8 Anisotropic refinement

9 Restraints for atomic displacement There are several common restraints in SHELXL: DELU: Anisotropic displacement shall be equal along a bond direction between two atoms. SIMU : Displacement shall be similar between two atoms in several directions. ISOR : Anisotropic displacement shall be similar in all directions within one atom.

10 ADP restraints in SHELXL

11 TLS Rigid body (Rosenfield et al., 1978) Domain definition 20 Parameters per domain: 6 symmetric tensor of translation movement 6 symmetric tensor of libration movement 8 asymmetric tensor of screw motion (quadratic correlation between T and L) Works mostly well in macromolecules REFMAC: Additional isotropic displacement parameter for each atom.

12 TLS anisotropic refinement

13 Problems Domain definition: Often arbitrary No atom can be in more than one domain Insufficient modeling of high displacement in loose regions, like loops Does the rigid bond criterion really hold? One component of translation is dependent on isotropic displacement: Refinement of dependent parameters Constraints: No deviation is allowed.

14 Rigid bond restraints Flexible alternative (Rollett 1970). Rosenfield, Trueblood & Dunitz, 1978: Hold well for C, N and O atoms in precise small molecule structures. All atoms in a certain area are restrained. Components of the anisotropic displacements along the line joining two atoms are restrained to be equal (similar to DELU) Didisheim & Schwarzenbach, 1987: If it is applied tightly, it asymptotes TLS

15 Rigid-bond refinement

16 Test conditions Restraint sphere: 8 Å radius. S.u. proportional to the square root of the distance d Weighting of s.u. with a factor s Macromolecule only Only within the same chain Isotropic water molecules Implementation in a betatest version of SHELXL-2018

17 Advantages Domains appear naturally Deviations are allowed Adjustable Good data/parameter ratio High displacement in looser regions

18 Test results: Good resolution (<2Å) Isotropic component of displacement Short range DELU restraints with a s.u. of 0.05 Å Lower free R than obtained by SHELXL isotropic or anisotropic refinement Lower number of non-positive definite (NPD) atoms Smaller gap between the free R and R1

19 Test structures at 1.8 Å Squash Trypsin 2 Cocavalin 3 Glucose Isomerase 4 High Potential Iron Protein H42Q 5 Thaumatin

20 Test results: Resolution range Additional isotropic refinement Additional standard DELU restraints Equal or lower free R than standard (SIMU) restrained isotropic refinement over a wide resolution range

21 Concanavalin

22 Test results: Low resolution No isotropic compound Anisotropic refinement only, with strong dependency of all displacement factors In the limit of tight restraints only 20 thermal parameters per domain No additional short range DELU restraints Better free R values than isotropic refinement as normal

23 Thaumatin

24 Rigid-bond refinement

25 Conclusion The new TLSR restraints have a wide range of applicability. They are part of a project to make SHELXL more suitable for the refinement of macromolecules at modest resolution.

26 Acknowledgements Prof. George M. Sheldrick Christian Große and Tobias Beck Iñaki Martinez de Ilarduya Muñoz Everyone from my working group Thank you for this great week!

27 Literature Didisheim, J.J. & Schwarzenbach, D. (1987). Acta Cryst. A43, Massa, W. (2007) Kristallstrukturbestimmung, Teubner, Wiesbaden. Rollett, J.S. (1970). Crystallographic Computing, edited by F.R. Ahmed, S.R. Hall & C.P.Huber, pp Copenhagen: Munksgaard. Rosenfield, R.E., Trueblood, K.N. & Dunitz, J.D. (1978). Acta Cryst. A34, Schomaker, V. & Trueblood, K.N. (1968). Acta Cryst. B24, Sheldrick. G.M. (2008). Acta Cryst. A64, Winn, M.D., Isupov, M.N. & Murshudov, G.N. (2001). Acta Cryst. D57,