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Residual Dipolar Couplings ;RDC

Residual Dipolar Couplings ;RDC. Cheng-Kun Tsai 2005.05.14. Residual Dipolar Coupling. Introduction Theoretical Application. Introduction. NOE, Scalar J coupling --- local TROSY, Protein labeling strategies --- larger macromolecules  RDC --- distance (short, long), angle.

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Residual Dipolar Couplings ;RDC

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

  2. Residual Dipolar Coupling • Introduction • Theoretical • Application

  3. Introduction • NOE, Scalar J coupling --- local • TROSY, Protein labeling strategies --- larger macromolecules •  RDC --- distance (short, long), angle ΞJ = JSIS‧I

  4. Theoretical Magnetic field: H(r) = ﹣μS/r3 + 3(r．μS) ．r/r5 Dipolar coupling Hamiltonian: ΞD = - μI．H(r) = ( μI．μS/r3) – 3( μI．r)(μS．r)/r5 = γSγIβSβI {S．I/r3 – 3(S．r)(I．r)/r5} r I S

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

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

  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 then

  9. A. Px = Py = 0.25 and Pz = 0.5 B. Px = 0.2, Py = 0.3 and Pz = 0.5 C. Px = Py = Pz = 1/3 Px2 + Py2 + Pz2 = 1 P: “probability tensor”

  10. Define “aligment tensor” A

  11. A. Ax = Ay = -1/12, Az=1/6 B. Ax = -2/15, Ay = -1/30, Az = 1/6 C. Ax = Ay = Az =0 Ax + Ay + Az = 0

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

  13. and then

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

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

  16. Dynamics: = bx(t)．rx(t) + by(t) ． ry(t) + bz(t) ．rz (t) then , θ = θ (t)

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

  18. Dab = (J+D) - J

  19. 2H 1D spectrum of water deuterons in 5% bicelle prepared in D2O at 35oC (a) Isotropic spectrum 1JNH (b) 4.5% (w/v) bicelle (c) 8% bicelle

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

  21. Bicelles Bacteriophage

  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

  24. Data refinement • 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

  26. Structure refinement anddomain orientations • NMR structure and crystal structure  NMR structure refined with RDCs (1) rat apo S100B(ββ), Ca2+-binding (2) VEGF11-109 (3) Prp40

  27. (1) rat apo S100B(ββ), Ca2+-binding • Dimeric apo S100B • 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, VEGF11-109 • grey, solution structure • red, NMR with RDC • cyan, crystal structure • red, NMR with RDC VEGF11-109 + v107 , peptide antagonists, v107 (GGNECDAIRMWEWECFERL) N terminus of VEGF11-109 RMSD: 0.60 to 0.37A

  29. (3) The yeast splicing factorpre-mRNA processing protein 40, Prp40 • WW1 domain, • , Solution structure • (b) WW2 domain • 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) Ca2+-ligated CaM (2) hemoglobin

  31. 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

  34. (1) B and C domains of barley lection (BL) • X-ray structure • 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 • apo-state (crystal) • bound to β-cyclodextrin (inactive ligand) • bound to maltotriose (natural ligand)

  37. (4) T4 lysozyme • WT lysozyme X-ray • 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

  39. 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, Mg2+ (3) IRE

  43. (2) hammerhead ribozyme, Mg2+ (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

  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

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