Residual Dipolar Couplings ;RDCResidual Dipolar Couplings ;RDC

Cheng-Kun Tsai2005.05.14

Cheng-Kun Tsai2005.05.14

Residual Dipolar CouplingResidual Dipolar Coupling

Introduction Theoretical Application

Introduction Theoretical Application

IntroductionIntroduction

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

ΞJ = JSI S ‧ I

TheoreticalTheoretical

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}

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 then

A. Px = Py = 0.25 and Pz = 0.5B. Px = 0.2, Py = 0.3 and Pz = 0.5C. Px = Py = Pz = 1/3

Px2 + Py

2 + Pz2 = 1

P: “probability tensor”

Define “aligment tensor” A

Ax + Ay + Az = 0

A. 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 literature

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:

= bx(t) ． rx(t) + by(t) ． ry(t)

+ bz(t) ． rz (t)

, θ = θ (t)

then

anisotropies 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

Dab = (J+D) - JDab = (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 mediaAlignment media

Liquid crystals --- 1963, Saupe Bicelles --- 1990s, Bacteriophage Polyacrylamide gels Other media

Liquid crystals --- 1963, Saupe Bicelles --- 1990s, Bacteriophage Polyacrylamide gels Other media

Bicelles Bacteriophage

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

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 refinementData refinement

RMSD

--- improved Ramachandran plot

--- the most favored region improved

RMSD

--- improved Ramachandran plot

--- the most favored region improved

ApplicationsApplications

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 anddomain orientations

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

NMR structure and crystal structure

NMR structure refined with RDCs

(1) rat apo S100B(ββ), Ca2+-binding

(2) VEGF11-109

(3) Prp40

(1) rat apo S100B(ββ), Ca2+-binding(1) rat apo S100B(ββ), Ca2+-binding

A. Dimeric apo S100BB. Blue, 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, VEGF11-109(2) Vascular endothelial growth factor, VEGF11-109

VEGF11-109 + v107, peptide antagonists, v107(GGNECDAIRMWEWECFERL)N terminus of VEGF11-109RMSD: 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

(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) Ca2+-ligated CaM

(2) hemoglobin

No solution structure a homologous structure

, a closely related molecule

, a crystal structure

fitting of RDCs

(1) Ca2+-ligated CaM

(2) hemoglobin

(1) Calmodulin / CaM, a ubiquitous Ca2+ binding protein(1) Calmodulin / CaM, a ubiquitous Ca2+ binding protein

Blue, 1 Å crystal structure (1EXR)Red, Ca2+–CaM solution structure with RDC

(2) hemoglobin(2) hemoglobin

Crystal 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

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)(1) B and C domains of barley lection (BL)

A. X-ray structureB. NMR with RDC

(2) three fingers in TFIIIA, transcription factor IIIA(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(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(4) T4 lysozyme

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

DNA/RNA structure refinementDNA/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 (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 structure (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, Mg2+

(3) IRE

RDCs from RNA molecules

(1) RNA and tRNA

(2) hammerhead ribozyme, Mg2+

(3) IRE

(2) hammerhead ribozyme, Mg2+(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

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)

(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(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

ConclusionsConclusions

1. 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 θ and ψ