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Restrains and constrains in Jana2006

Restrains and constrains in Jana2006 (when data are lacking resolution or when the structure is disordered). (sin θ / λ ) max =1.5 Å -1 , d=0.33 Å. (sin θ / λ ) max =1.191 Å -1 , d=0.42 Å . (sin θ / λ ) max =0.9449 Å -1 , d=0.53 Å . (sin θ / λ ) max =0.75 Å -1 , d=0.66 Å.

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Restrains and constrains in Jana2006

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  1. Restrains and constrains in Jana2006 (when data are lacking resolution or when the structure is disordered)

  2. (sinθ/λ)max=1.5 Å-1, d=0.33 Å

  3. (sinθ/λ)max=1.191 Å-1 , d=0.42 Å

  4. (sinθ/λ)max=0.9449 Å-1 , d=0.53 Å

  5. (sinθ/λ)max=0.75 Å-1 , d=0.66 Å

  6. (sinθ/λ)max=0.5953 Å-1 , d=0.84 Å

  7. (sinθ/λ)max=0.4725 Å-1 , d=1.06 Å

  8. (sinθ/λ)max=0.375 Å-1 , d=1.33 Å

  9. (sinθ/λ)max=0.2976 Å-1 , d=1.68 Å

  10. “normal” restrains and constrains

  11. ECM27 Bergen Restraints and constraints in Jana system Distance restraints (specific values or the same values) Angle restraints (specific values or the same values) Torsion angle restraints (specific values or the same values) Keep commands: hard restraints with correcting geometry after each refinement cycle Keep hydrogens tetrahedral/trigonal/apical Keep geometry planar Keep geometry rigid

  12. ECM27 Bergen Example: distance restraints Distance/angle/torsion angle restraints can be set to a specific value or they can define that the value is the same (but refined) for several groups of atoms The minor conformer cannot be reliably refined, thus it takes bond lengths from the major conformer a' b' a 0.16 b 0.84

  13. Keep commands These commands are keeping during the refinement either hydrogen geometry, a specific geometrical restrictions (plane, rigidity) or ADP parameters (riding model): For hydrogen atoms the keep commands are usually created automatically

  14. Restrictions • These commands make a connection between two or more atoms in the structure. Selected parameters (coordinates, ADP, modulation parameters, …) can be made identical or related by a local symmetry operation. Together with these restrictions we can apply also conditions for atom site occupancies: atoms may keep overall occupancy or they can be occupied complementary for modulated structure. • In this command we can also use different wild characters which define set of atoms to which the conditions are applied. • For example these commands can be used: • to make all ADP parameters of specified atoms identical • to restrict structural parameters occupying the same atomic position and keep their overall occupancy identical • to keep some symmetry relationships between atoms valid in the higher symmetrical phase.

  15. Restrictions and local symmetry

  16. Group-subgroup transformation can generate local symmetry commands Jana2006 program offers possibility to test if a lower symmetry description gives more realistic model. For this we have developed a utility to transform the structure to a “subgroup” structure. This procedure can also generate possible twinning matrices and local symmetry operators for applying them as restrict commands.

  17. ECM27 Bergen Example for local symmetry: Parts of the structure can be connected by a local symmetry. This saves parameters especially for cases when only part of the structure violates the higher symmetry. Example: refinement of a Schiff base complex in space group Pc The differently hatched atoms are related by local symmetry operation – inversion from the previously used space group P2/c. The disordered parts are refined in Pc as rigid body; the minor component is marked in yellow.

  18. Equation commands As each parameter in the Jana program has its own unique name, we can use them to write equations to keep some linear conditions between parameters. These equation are defined in “program language style”, which means that on the left side of equation stands a parameter which should be kept equal to a linear combination given on the right side: ai[Si1]=1-ai[Fe1] The user defined equations are added to those generated automatically by the program to account for a site symmetry of each atoms. This automatic routine can be switched off but then user should take care of local symmetry himself.

  19. Rigid body Rigid body approach “Model molecule” is a fragment, which is placed arbitrarily and does not contribute to structure factors Model molecule is transformed to “Actual positions” by translation vector and three rotation angles: xm is position in the model moleculexo is a reference point Reference point determines the symmetry Rotations can be combined with an inversion Molecule can have its own local symmetry

  20. Actual position #1 Model molecule The parameters of atoms of the model molecule (coordinates, ADP …) can be refined. Thus the model molecule is less rigid then an object fixed by “Keep geometry rigid” Actual position #2

  21. Actual position #1 Model molecule Actual position #2

  22. Actual position #1 Model molecule Actual position #2

  23. Actual position #1 Model molecule Actual position #2

  24. Actual position #1 Model molecule Actual position #2

  25. Actual position #1 Model molecule TLS tensors Instead of individual ADP of the model molecule we can assume that all atoms have amplitudes appropriate to a rigid body and that all atoms are moving in phase. Then we can refine TLS tensors (20 parameters) for each actual position. Symmetry restrictions will be done according to the reference point. Actual position #2

  26. Rigid body approach applied to structure of cyclodextrin β-Cyclodextrin duplex connected by two disulfide bondsChem. Eur. J. 2012, in print, DOI: 10.1002/chem.201201239 a=b=21.04 Å, c=26.69 Å, α=β=γ=90°V=11833 Å3 Symmetry I4

  27. Some of glucose units are disordered, the others not. The disordered part could not be described reliably by splitting of atoms because of low data quality. Fixing geometry by restraints would be extremely laborious.

  28. One of not disordered glucose units was taken as a model molecule. The model molecule is indicated in yellow and suffix “a”. O1, O2 and C1a were refined freely.

  29. The model molecule enters to ten actual positions. The pairs g-f, h-I, e-d describe disordered glucose units, with total occupancy 1. Because all actual position have common geometry refined only for the model molecule, disorder can be reliably refined. Introduction of rigid bodies did not affect R value. This is a prove that the glucose unit is the same in all position within our data precision. Advantages for visualization: minor actual position can be easily removed.

  30. Parameters -> molecules Examples in Cookbook, where local symmetry and local coordinate system must be defined: Terbut (8.1)Dinitros (8.2)

  31. cell 13 13 13 90 90 90 pgroup C1 scdist C-C 1.3 C1+ 1 1 1.000000 0.000000 0.050000 0.242705 0 C2+ 1 1 1.000000 0.000000-0.050000 0.242705 0 C3+ 1 1 1.000000 0.080902 0.100000 0.211803 0 C4+ 1 1 1.000000 0.080902-0.100000 0.211803 0 C5+ 1 1 1.000000-0.080902 0.100000 0.211803 0 C6+ 1 1 1.000000-0.080902-0.100000 0.211803 0 C7+ 1 1 1.000000 0.161803 0.050000 0.180902 0 C8+ 1 1 1.000000 0.161803-0.050000 0.180902 0 C9+ 1 1 1.000000-0.161803 0.050000 0.180902 0 C10+ 1 1 1.000000-0.161803-0.050000 0.180902 0 C11+ 1 1 1.000000 0.050000 0.180901 0.161803 0 C12+ 1 1 1.000000 0.050000-0.180902 0.161803 0 C13+ 1 1 1.000000-0.050000 0.180901 0.161803 0 C14+ 1 1 1.000000-0.050000-0.180901 0.161803 0 C15+ 1 1 1.000000 0.211803 0.080902 0.100000 0 C16+ 1 1 1.000000 0.211803-0.080902 0.100000 0 C17+ 1 1 1.000000-0.211803 0.080902 0.100000 0 C18+ 1 1 1.000000-0.211803-0.080902 0.100000 0 C19+ 1 1 1.000000 0.100000-0.211803 0.080902 0 C20+ 1 1 1.000000 0.100000 0.211803 0.080902 0 C21+ 1 1 1.000000-0.100000 0.211803 0.080902 0 C22+ 1 1 1.000000-0.100000-0.211803 0.080902 0 C23+ 1 1 1.000000 0.180902 0.161803 0.050000 0 C24+ 1 1 1.000000 0.180902-0.161803 0.050000 0 C25+ 1 1 1.000000-0.180902 0.161803 0.050000 0 C26+ 1 1 1.000000-0.180902-0.161803 0.050000 0 C27+ 1 1 1.000000 0.242705 0.000000 0.050000 0 C28+ 1 1 1.000000-0.242705 0.000000 0.050000 0 C29 1 1 1.000000 0.050000 0.242705 0.000000 0 C30 1 1 1.000000 0.050000-0.242705 0.000000 0 C31 1 1 1.000000-0.050000 0.242705 0.000000 0 C32 1 1 1.000000-0.050000-0.242705 0.000000 0 C1- 1 1 1.000000 0.000000 0.050000-0.242705 0 C2- 1 1 1.000000 0.000000-0.050000-0.242705 0 C3- 1 1 1.000000 0.080902 0.100000-0.211803 0 C4- 1 1 1.000000 0.080902-0.100000-0.211803 0 . . . . Rigid body templates (M45) Example: C60

  32. cell 13 13 13 90 90 90 pgroupIh scdist C-C 1.3 C1+ 1 1 0.500000 0.000000 0.050000 0.242705 0 C2+ 1 1 0.500000 0.000000-0.050000 0.242705 1 C3+ 1 1 0.500000 0.080902 0.100000 0.211803 1 C4+ 1 1 0.500000 0.080902-0.100000 0.211803 1 C5+ 1 1 0.500000-0.080902 0.100000 0.211803 1 C6+ 1 1 0.500000-0.080902-0.100000 0.211803 1 C7+ 1 1 0.500000 0.161803 0.050000 0.180902 1 C8+ 1 1 0.500000 0.161803-0.050000 0.180902 1 C9+ 1 1 0.500000-0.161803 0.050000 0.180902 1 C10+ 1 1 0.500000-0.161803-0.050000 0.180902 1 C11+ 1 1 0.500000 0.050000 0.180901 0.161803 1 C12+ 1 1 0.500000 0.050000-0.180902 0.161803 1 C13+ 1 1 0.500000-0.050000 0.180901 0.161803 1 C14+ 1 1 0.500000-0.050000-0.180901 0.161803 1 C15+ 1 1 0.500000 0.211803 0.080902 0.100000 1 C16+ 1 1 0.500000 0.211803-0.080902 0.100000 1 C17+ 1 1 0.500000-0.211803 0.080902 0.100000 1 C18+ 1 1 0.500000-0.211803-0.080902 0.100000 1 C19+ 1 1 0.500000 0.100000-0.211803 0.080902 1 C20+ 1 1 0.500000 0.100000 0.211803 0.080902 1 C21+ 1 1 0.500000-0.100000 0.211803 0.080902 1 C22+ 1 1 0.500000-0.100000-0.211803 0.080902 1 C23+ 1 1 0.500000 0.180902 0.161803 0.050000 1 C24+ 1 1 0.500000 0.180902-0.161803 0.050000 1 C25+ 1 1 0.500000-0.180902 0.161803 0.050000 1 C26+ 1 1 0.500000-0.180902-0.161803 0.050000 1 C27+ 1 1 0.500000 0.242705 0.000000 0.050000 1 C28+ 1 1 0.500000-0.242705 0.000000 0.050000 1 C29 1 1 0.500000 0.050000 0.242705 0.000000 1 C30 1 1 0.500000 0.050000-0.242705 0.000000 1 C31 1 1 0.500000-0.050000 0.242705 0.000000 1 C32 1 1 0.500000-0.050000-0.242705 0.000000 1 C1- 1 1 0.500000 0.000000 0.050000-0.242705 1 C2- 1 1 0.500000 0.000000-0.050000-0.242705 1 C3- 1 1 0.500000 0.080902 0.100000-0.211803 1 . . . . Example: C60 with symmetry Ih

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