1. Residual Dipolar Couplings ;RDC Cheng-Kun Tsai 2005.05.14 Cheng-Kun Tsai 2005.05.14

2. Residual Dipolar Coupling  Introduction  Theoretical  Application  Introduction  Theoretical  Application

3. Introduction  NOE, Scalar J coupling --- local  TROSY, Protein labeling strategies --- larger macromolecules   RDC --- distance (short, long), angle  NOE, Scalar J coupling --- local  TROSY, Protein labeling strategies --- larger macromolecules   RDC --- distance (short, long), angle Ξ J = J SI S ‧ I

4. Theoretical Magnetic field: H(r) = ﹣ μ S /r 3 + 3(r ． μ S ) ． r/r 5 Dipolar coupling Hamiltonian: Ξ D = - μ I ． H(r) = ( μ I ． μ S /r 3 ) – 3( μ I ． r)(μ S ． r)/r 5 = γ S γ I β S β I {S ． I/r 3 – 3(S ． r)(I ． r)/r 5 } S Ir

5. If the spins I and S are heternuclear Expand the equation and drop secondary terms and

6. Then In the “special” frame of reference defined Define P: “probability tensor”

7. Define Note:

8. 1. for example, in the static case The principle z axis is parallel to the vector b 2. for a completely isotropically reorienting molecule then

9. A. P x = P y = 0.25 and P z = 0.5 B. P x = 0.2, P y = 0.3 and P z = 0.5 C. P x = P y = P z = 1/3 P x 2 + P y 2 + P z 2 = 1 P: “probability tensor”

10. Define “aligment tensor” A

11. A x + A y + A z = 0 A. A x = A y = -1/12, A z =1/6 B. A x = -2/15, A y = -1/30, A z = 1/6 C. A x = A y = A z =0

12. The calculation of the RDC constant D are expressed in various more or less complicated forms found in literature and

13. then and

14. Define axial component Aa and rhombic component Ar Saupe matrix (or order matrix) S R: rhombicity of alignment tensor η : asymmetry parameter then or

15. ※ Generalized order parameter S (0 ≦ S ≦ 1) ※ Maximum dipolar coupling ※ Magnitude of the residual dipolar coupling tensor ※ Generalized degree of order (GDO) and motion ~ millisecond time scale

16. Dynamics: = b x (t) ． r x (t) + b y (t) ． r y (t) + b z (t) ． r z (t), θ = θ (t) then

17. anisotropies  Residual dipolar couplings  Complementary observables 1. chemical shift anisotropy (CSA) 2. pseudocontact shifts in paramagnetic systems 3. cross-correlated relaxation  Residual dipolar couplings  Complementary observables 1. chemical shift anisotropy (CSA) 2. pseudocontact shifts in paramagnetic systems 3. cross-correlated relaxation

18. D ab = (J+D) - J

19. 2 H 1D spectrum of water deuterons in 5% bicelle prepared in D 2 O at 35 o C (a) Isotropic spectrum 1 J NH (b) 4.5% (w/v) bicelle (c) 8% bicelle

20. Alignment media  Liquid crystals --- 1963, Saupe  Bicelles --- 1990s,  Bacteriophage  Polyacrylamide gels  Other media  Liquid crystals --- 1963, Saupe  Bicelles --- 1990s,  Bacteriophage  Polyacrylamide gels  Other media

21. BicellesBacteriophage

22. Ref. RDC in structure determination of biomolecules, Chem. Rev. 2004, 104, 3519-3540

23.  Alignment must be sufficient, but not so large  Adjustment of media concentration  Overall charge and charge distribution of a protein, in an electrically charged medium  The use of media-free, field-induced orientation of biomolecules. Paramagnetic ions  Diamagnetic anisotropy  The option of using several alignment media  Using multiple media, three reasons  Alignment must be sufficient, but not so large  Adjustment of media concentration  Overall charge and charge distribution of a protein, in an electrically charged medium  The use of media-free, field-induced orientation of biomolecules. Paramagnetic ions  Diamagnetic anisotropy  The option of using several alignment media  Using multiple media, three reasons

24. Data refinement  RMSD --- improved  Ramachandran plot --- the most favored region improved  RMSD --- improved  Ramachandran plot --- the most favored region improved

25. Applications  Structure refinement and domain orientations  DNA/RNA structure refinement  Conformation of small molecules and bound ligands  Structure refinement and domain orientations  DNA/RNA structure refinement  Conformation of small molecules and bound ligands

26. Structure refinement and domain orientations  NMR structure and crystal structure  NMR structure refined with RDCs (1) rat apo S100B(ββ), Ca 2+ -binding (2) VEGF 11-109 (3) Prp40  NMR structure and crystal structure  NMR structure refined with RDCs (1) rat apo S100B(ββ), Ca 2+ -binding (2) VEGF 11-109 (3) Prp40

27. (1) rat apo S100B(ββ), Ca 2+ -binding A.Dimeric apo S100B B.Blue, rat, NMR with RDC yellow, rat green, bovine The third Helix RMSD: 1.04A to 0.29A Ramachandran Plot: 76 to 86% (the most favored region)

28. (2) Vascular endothelial growth factor, VEGF 11-109 VEGF 11-109 + v107, peptide antagonists, v107 (GGNECDAIRMWEWECFERL) N terminus of VEGF11-109 RMSD: 0.60 to 0.37A (a)grey, solution structure red, NMR with RDC (b)cyan, crystal structure red, NMR with RDC

29. (3) The yeast splicing factor pre-mRNA processing protein 40, Prp40 (a)WW1 domain,, Solution structure (b) WW2 domain (e)Structure with RDC RMSD: 1.14 to 0.55A

30.  No solution structure  a homologous structure, a closely related molecule, a crystal structure   fitting of RDCs (1) Ca 2+ -ligated CaM (2) hemoglobin  No solution structure  a homologous structure, a closely related molecule, a crystal structure   fitting of RDCs (1) Ca 2+ -ligated CaM (2) hemoglobin

31. (1)Calmodulin / CaM, a ubiquitous Ca2+ binding protein Blue, 1 Å crystal structure (1EXR) Red, Ca2+–CaM solution structure with RDC

32. (2) hemoglobin Crystal structure: T, tense state ; R, relaxed state ; R2, second conformation dark, R crystal medium, solution with RDC light, R2 crystal

33.  Relative domain orientations (1) B and C domains of BL (2) three fingers in TFIIIA (3) MalBP (4) T4 lysozyme  Relative domain orientations (1) B and C domains of BL (2) three fingers in TFIIIA (3) MalBP (4) T4 lysozyme

34. (1) B and C domains of barley lection (BL) A.X-ray structure B.NMR with RDC

35. (2) three fingers in TFIIIA, transcription factor IIIA Cyan: without dipolar restraints Yellow: with dipolar restraints Red: crystal structure refined with NOE and dipolar restraints.

36. (3) MalBP, maltodextrin-binding protein (a)apo-state (crystal) (b)bound to β-cyclodextrin (inactive ligand) (c)bound to maltotriose (natural ligand)

37. (4) T4 lysozyme (a)WT lysozyme X-ray (b)M6I mutant X-ray Red, with RDC

38. DNA/RNA structure refinement  NMR – lack the elaborate tertiary structure, less proton dense  X-ray – misinterpretations of the global feature   RDCs  NMR – lack the elaborate tertiary structure, less proton dense  X-ray – misinterpretations of the global feature   RDCs

39.  RDCs from RNA molecules (1) A-tract DNA – curvature (2) A-tract DNA -- both local and global structure  RDCs from RNA molecules (1) A-tract DNA – curvature (2) A-tract DNA -- both local and global structure

40. (1) A-tract DNA – curvature DNA sequence: d(CGCGAATCGCGAATTCGCG) 2 Blue, NMR with RDC Red, X-ray Note: b) is rotated by 90° around the helix axis relative to a)

41. (2) A-tract DNA – both local and global structure 10mer DNA strcture (GCGAAAAAAC) (a) only NOE and sugar pucker constraints (b) NOE, sugar pucker, and RDC constraints (c) NOE, sugar pucker, backbone torsion angle, and RDC constraints

42.  RDCs from RNA molecules (1) RNA and tRNA (2) hammerhead ribozyme, Mg 2+ (3) IRE  RDCs from RNA molecules (1) RNA and tRNA (2) hammerhead ribozyme, Mg 2+ (3) IRE

43. (2) hammerhead ribozyme, Mg 2+ (A) Solution conformation derived from dipolar coupling data in the absence of Mg2+. (B) X-ray structure in the presence of Mg2+

44. Conformation of small molecules and bound ligands  (1) AMM bound to ManBPA  (2) LacNAc binds to lectin protein Galectin-3  (3) trimannoside at the glycosidic linkages  (1) AMM bound to ManBPA  (2) LacNAc binds to lectin protein Galectin-3  (3) trimannoside at the glycosidic linkages

45. (1) AMM (a-methyl mannoside) bound to ManBPA (mannose-binding protein-A) Yellow spheres correspond to Ca2. Black and red shperes to carbon and oxygen, respectively, of AMM, and MBP is represented by ribbon diagram.

46. (2) LacNAc binds to lectin protein Galectin-3 green ribbon, Solution structure of galectin-3C in the absence of ligand magenta ribbon, compared to the X-ray crystal structure with LacNAc bound

47. Conclusions 1. to obtain dipolar couplings on macromolecules in solution, the potential for refining protein structures was immediately obvious. 2. focused on the structural applications, researchers are also beginning to exploit RDCs in solution NMR for their dynamics information content. 3. have established a framework to determine interfragment motion, to calculate amplitudes of interdomain motion, and to separate the dynamic contribution to the measured RDC to determine the effective values of θ and ψ