Effects of TLS parameters in Macromolecular Refinement

1. Effects of TLS parameters in Macromolecular Refinement • Martyn Winn • Daresbury Laboratory, U.K. • IUCr99 08/08/99

2. Overview • Background to the use of TLS tensors. • Details of TLS refinement. • Implementation in REFMAC: examples

3. Contributions to atomic U U = Ucrystal + UTLS + Uinternal + Uatom Ucrystal : overall anisotropic scale factor w.r.t. crystal axes. UTLS : rigid body displacements e.g. of a.s.u., molecules, domains, secondary structure elements, aromatic rings of side groups, etc. Uinternal : internal displacements of molecules, e.g. normal modes of vibration, torsions, etc. Uatom : anisotropy of individual atoms

4. TLS: small molecules • D.W.J.Cruikshank (1956) - TL analysis • G.S.Pawley (1964, 1966) - TL refinement • V.Schomaker & K.N.Trueblood (1968) - introduction of S in analysis of ADPs • J.D.Dunitz & D.N.J.White (1973) - inclusion of internal torsional motion of “attached rigid group”

5. TLS: macromolecules • S.R.Holbrook et al (1985) - duplex DNA dodecanucleatide, 1.9Å, 70 groups (phosphate, ribose, base), CORELS • B.Howlin et al (1989) - bovine Ribonuclease A, 1.45Å, RESTRAIN • G.W.Harris et al (1992) - papain, 1.6Å , RESTRAIN • Sali et al (1992) - endothiapepsin complex, 1.8Å, RESTRAIN

6. Rigid body motion • Linearise general displacement u of atom (mean position r) in rigid body: u = t + D.r  t +  x r • Corresponding dyad: uu = tt + t x r - r x t - r x  x r • Average over dynamic motion and static disorder gives atomic ADP: U  <uu> = T + ST x r - r x S - r x L x r • T,L andS describe mean square translation, libration and their correlation of rigid body.

7. TLS in refinement • Need to specify TLS groups for molecule of interest. • 6 + 6 + 8 = 20 parameters per group (trace of S is undetermined). • T and S (but not L) origin-dependent. S is symmetric if origin is Centre of Reaction. • Gradients of residual w.r.t. TLS parameters follow from gradients w.r.t. U’s via chain rule.

8. NCS • REFMAC applies restraints to B and U values of NCS-related molecules. • But different molecules in a.s.u. may have different overall thermal parameters. • Refine independent overall TLS tensors for each molecule before refining restrained individual parameters.

9. Choice of TLS groups • Choose TLS groups using: • chemical knowledge, e.g. aromatic side groups of amino acids, domains of macromolecules • fit to ADPs of test structure, e.g. Holbrook & Kim (1984) compared 7 rigid body models of CMP and used best as basis for partitioning other nucleic acids. • dynamic domains identified from similar structures, e.g. from apo and holo forms of alcohol dehydrogenase

10. Implementation in REFMAC • Refine TLS parameters against ML residual, using previously refined atomic coordinates and B factors. • TLS parameters held in TLSIN/TLSOUT files. • Analyse with TLSANL program.  libration axes, etc and ADPs To be implemented: • Allow TLS refinement prior to or simultaneously with refinement of other parameters.

11. E.g. 1 - GAPDH • Glyceraldehyde-3-phosphate dehydrogenase from Sulfolobus solfataricus (M.N.Isupov et al, JMB, in press) • P41212, 2.0Å, 2 molecules in a.s.u., each molecule has NAD-binding and catalytic domains.

12. E.g. 1 - GAPDH ScalingBisoTLS groupsR factorRfree Isotropic Refined 0 23.3 29.6 Anisotropic Refined 0 22.6 28.9 Isotropic Refined 1 21.0 26.4 Isotropic Refined 2 20.9 26.2 Isotropic Refined 4 20.8 26.1 Isotropic 35Ų 0 29.5 34.4 Isotropic 35Ų 1 26.6 32.1 Isotropic 35Ų 2 24.2 29.0 Isotropic 35Ų 4 23.8 28.4

13. E.g.1: axes of libration Refined Bs. Blue - chain O, NAD-binding domain Red - chain O, catalytic domain Green - chain Q, NAD-binding domain Yellow - chain Q, catalytic domain

14. E.g.1: axes of libration Constant Bs. Blue - chain O, NAD-binding domain Red - chain O, catalytic domain Green - chain Q, NAD-binding domain Yellow - chain Q, catalytic domain

15. E.g.2: ADH • horse liver alcohol dehydrogenase (S.Ramaswamy et al). • apo form: C2221, 2.0Å, single chain in a.s.u. • DYNDOM results from apo vs. holo forms. ScalingBisoTLS groupsR factorRfree Isotropic Refined 0 27.9 32.5 Anisotropic Refined 0 23.6 29.1 Isotropic Refined 1 22.5 27.4 Isotropic Refined 4 22.3 27.4 Isotropic Refined 6 22.2 27.6

16. E.g.2: dynamic domains Results from DYNDOM. Blue - first domain Red - second domain Green - hinge region

17. E.g.2: axes of libration TLS groups: Blue - first dynamic domain Red - second dynamic domain Green - hinge region Yellow - flexible loop

18. E.g. 3: lysozyme complex • Hen egg white lysozyme complexed withcamelid single-chain antibody (K. Decanniere et al). • C2, 2.1Å, single copy in a.s.u. ScalingBisoTLS groupsR factorRfree Isotropic Refined 0 20.2 24.3 Anisotropic Refined 0 20.0 24.0 Isotropic Refined 4 19.9 23.7 Isotropic Refined 4* 19.9 23.7

19. E.g.3: axes of libration Simple minimisation. Blue - antibody Red - CRD3 loop of antibody Green - lysozyme Yellow - lysozyme

20. E.g.3: axes of libration Minimisation with TLS constrained to be positive semi-definite Blue - antibody Red - CRD3 loop of antibody Green - lysozyme Yellow - lysozyme

21. Acknowledgements • CCP4 • BBSRC • Garib Murshudov (REFMAC) • Misha Isupov (GAPDH) • S Ramaswamy (ADH) • Klaas Decanniere (lysozyme complex)