residual dipolar couplings ;rdc

Residual Dipolar Couplings ;RDCCheng-Kun Tsai2005.05.14

Residual Dipolar CouplingIntroductionTheoreticalApplication

IntroductionNOE, Scalar J coupling --- local

TROSY, Protein labeling strategies --- larger macromolecules RDC --- distance (short, long), angleJ = JSI S I

TheoreticalMagnetic field:H(r) = S/r3 + 3(rS) r/r5

Dipolar coupling Hamiltonian:D = - IH(r) = ( IS/r3) 3( Ir)(Sr)/r5 = SISI {S I/r3 3(S r)(I r)/r5}SIr

If the spins I and S are heternuclearExpand the equation and drop secondary termsand

ThenIn the special frame of reference definedDefineP: probability tensor

DefineNote:

1. for example, in the static case

The principle z axis is parallel to the vector b 2. for a completely isotropically reorienting moleculethenthen

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

Define aligment tensor A

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

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

thenand

Define axial component Aa and rhombic component ArSaupe matrix (or order matrix) SR: rhombicity of alignment tensor : asymmetry parameterthenor

Generalized order parameter S (0S1) Maximum dipolar coupling Magnitude of the residual dipolar coupling tensorGeneralized degree of order (GDO)andmotion ~ millisecond time scale

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

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

Dab = (J+D) - J

2H 1D spectrum of water deuterons in5% bicelle prepared in D2O at 35oC (a) Isotropic spectrum 1JNH(b) 4.5% (w/v) bicelle(c) 8% bicelle

Alignment mediaLiquid crystals --- 1963, SaupeBicelles --- 1990s, BacteriophagePolyacrylamide gelsOther media

BicellesBacteriophage

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

Alignment must be sufficient, but not so largeAdjustment of media concentrationOverall charge and charge distribution of a protein, in an electrically charged mediumThe use of media-free, field-induced orientation of biomolecules. Paramagnetic ionsDiamagnetic anisotropyThe option of using several alignment mediaUsing multiple media, three reasons

Data refinementRMSD --- improvedRamachandran plot --- the most favored region improved

ApplicationsStructure refinement and domain orientations

DNA/RNA structure refinement

Conformation of small molecules and bound ligands

Structure refinement anddomain orientationsNMR structure and crystal structure NMR structure refined with RDCs (1) rat apo S100B(), Ca2+-binding (2) VEGF11-109 (3) Prp40

(1) rat apo S100B(), Ca2+-bindingDimeric apo S100BBlue, rat, NMR with RDC yellow, rat green, bovine

The third Helix

RMSD: 1.04A to 0.29ARamachandran Plot: 76 to 86%(the most favored region)

(2) Vascular endothelial growth factor, VEGF11-109VEGF11-109 + v107, peptide antagonists, v107(GGNECDAIRMWEWECFERL)N terminus of VEGF11-109RMSD: 0.60 to 0.37Agrey, solution structure red, NMR with RDCcyan, crystal structure red, NMR with RDC

(3) The yeast splicing factor pre-mRNA processing protein 40, Prp40WW1 domain, , Solution structure (b) WW2 domainStructure 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) Ca2+-ligated CaM (2) hemoglobin

Calmodulin / CaM, a ubiquitous Ca2+ binding proteinBlue, 1 crystal structure (1EXR)Red, Ca2+CaM solution structure with RDC

(2) hemoglobinCrystal structure:T, tense state; R, relaxed state ; R2, second conformation

dark, R crystalmedium, solution with RDClight, R2 crystal

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)X-ray structureNMR with RDC

(2) three fingers in TFIIIA, transcription factor IIIACyan: without dipolar restraints

Yellow: with dipolar restraints

Red: crystal structure refined with NOE and dipolar restraints.

(3) MalBP, maltodextrin-binding proteinapo-state (crystal)bound to -cyclodextrin (inactive ligand)bound to maltotriose (natural ligand)

(4) T4 lysozymeWT lysozyme X-ray M6I mutant X-ray Red , with RDC

DNA/RNA structure refinementNMR lack the elaborate tertiary structure , less proton denseX-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

(1) A-tract DNA curvature DNA sequence:d(CGCGAATCGCGAATTCGCG)2

Blue, NMR with RDCRed, X-ray

Note:b) is rotated by 90 around the helix axis relative to a)

(2) A-tract DNA both local and global structure10mer 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, Mg2+ (3) IRE

(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+

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 (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-3green ribbon, Solution structure of galectin-3C in the absence of ligand

magenta ribbon, compared to the X-ray crystal structure with LacNAc bound

Conclusions1. to obtain dipolar couplings on macromolecules in solution, the potential for refining protein structures was immediatelyobvious.

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 and