Residual Dipolar Couplings ;RDC Cheng-Kun Tsai Cheng-Kun Tsai

Residual Dipolar Coupling  Introduction  Theoretical  Application  Introduction  Theoretical  Application

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

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

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

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

Define Note:

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

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”

Define “aligment tensor” A

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

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

then and

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

※ 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

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

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

D ab = (J+D) - J

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

Alignment media  Liquid crystals , Saupe  Bicelles s,  Bacteriophage  Polyacrylamide gels  Other media  Liquid crystals , Saupe  Bicelles s,  Bacteriophage  Polyacrylamide gels  Other media

BicellesBacteriophage

Ref. RDC in structure determination of biomolecules, Chem. Rev. 2004, 104,

 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

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

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

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 (3) Prp40  NMR structure and crystal structure  NMR structure refined with RDCs (1) rat apo S100B(ββ), Ca 2+ -binding (2) VEGF (3) Prp40

(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)

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

(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

 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

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

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

 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

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

(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.

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

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

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

 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

(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)

(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

 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

(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+

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

(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.

(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

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