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

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

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

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”

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

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  = T + S T x r - r x S - r x L x r T, L and S describe mean square translation, libration and their correlation of rigid body.

TLS in refinement Need to specify TLS groups for molecule of interest = 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.

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.

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

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.

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

E.g. 1 - GAPDH ScalingBisoTLS groupsR factorR free IsotropicRefined AnisotropicRefined IsotropicRefined IsotropicRefined IsotropicRefined Isotropic35Ų Isotropic35Ų Isotropic35Ų Isotropic35Ų

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

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

E.g.2: ADH horse liver alcohol dehydrogenase (S.Ramaswamy et al). apo form: C222 1, 2.0Å, single chain in a.s.u. DYNDOM results from apo vs. holo forms. ScalingBisoTLS groupsR factorR free IsotropicRefined AnisotropicRefined IsotropicRefined IsotropicRefined IsotropicRefined

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

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

E.g. 3: lysozyme complex Hen egg white lysozyme complexed with camelid single-chain antibody (K. Decanniere et al). C2, 2.1Å, single copy in a.s.u. ScalingBisoTLS groupsR factorR free IsotropicRefined AnisotropicRefined IsotropicRefined IsotropicRefined 4*

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

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

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