15n residual dipolar couplings - embocwp.embo.org/wpc09-07/lecture/rdctheory.pdfnmr workshop,...

NMR workshop, Rosario November 20081

Residual dipolar couplings15N

1H

B0

Markus ZweckstetterDepartment for NMR-based Structural Biology,

Göttingen, Germany

Max Planck Institute For Biophysical Chemistry


Background material

Saupe A, Englert G (1963) Phys. Rev. Lett. 11: 462-464

BothnerBy AA. (1996) In Grant DM, Harris RK (eds.), Encyclopedia of Nuclear Magnetic Resonance. Wiley, Chichester: pp. 2932-2938

Tjandra N, Bax A (1997) Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium. Science 278: 1111-1114

Bax A, Kontaxis G, Tjandra N. (2001) Dipolar couplings in macromolecular structure determination. In Nuclear Magnetic Resonance of Biological Macromolecules, Pt B, Vol. 339, pp. 127-174

Prestegard JH, Al-Hashimi HM, Tolman JR (2000) NMR structures of biomolecules using field oriented media and residual dipolar couplings. Q. Rev. Biophys. 33: 371-424

Kramer F, Deshmukh MV, Kessler H, Glaser SJ (2004) Residual dipolar coupling constants: An elementary derivation of key equations. Concepts Magn. Reson. Part A 21A: 10-21


NMR structure determination

Chemical Shift Restraints

Assignment

Dihedral Restraints

J

ω

J − Coupling(E.COSY, DQ/ZQ, FIDS, quant.J)

Distance Restraints

NOE/ROE~1/r(NOESY, ROESY)

Structure Calculation(Simulated Annealing, Distance Geometry,

Molecular Dynamics)

1) Residual Dipolar Couplings2) N-H Relaxation Rates

φ

θ

ψ ωN

HN

H k+1N

C'

Nk+1Cαk

H αk

R

O

Cross Correlated Relaxation

ω

ΓcNH,CH

1) Dipole-Susceptibility Tensor2) Dipole-Mass Tensor

Projection Restraints1) Dipole-Dipole2) Dipole-CSA3) CSA-CSA

φ ψ ωN

HN

Ηk+1N

C'

Nk+1Cαk

Η αk

R

O

φ ψ ωN

HN

Ηk+1N

C'

Nk+1Cαk

Η αk

R

O

φψ ωN

HN

H k+1N

C'

Nk+1Cαk

H αk

O

R

φ ψN

HN

Cαk

Η αk

C'

R

k+1

3D-Structure

AssignmentSample13C,15N-Source

Bacteria

Multi-D-NMR


Why do we want to use dipolar couplings in solution NMR?

• all these parameters give essentially local information:distances <5Å; dihedral angles; intraresidual/sequential ϕ/ψ values, …

• long-range information is virtually non-existent

this leads to NMR-specific problems in structure determination:

• what is the exact angle between two non-parallel α-helices in a protein?

• is a long helical structure (a-helical protein, DNA) straight or bent?

• what is the relative orientation of two protein domains?

?


• Residual dipolar couplings (RDCs) can be observed in solution when a molecule is aligned with the magnetic field

• When alignment can be kept sufficiently weak• NMR spectra remain simple as in isotropic solution• quantitative measurement of a wide variety of RDCs

• Several dilute liquid crystalline media are now available

• RDC measurements and analysis are highly efficient

Residual dipolar couplings are a generally applicable tool for NMR structure determination

RDCs today


The dipolar coupling


The classical dipolar interaction

Nuclear spin magnetic dipole μ magnetic field

( ) ( ) ( )05 3

4 rμμπ

= −⎡ ⎤⎣ ⎦B r μr r rr μ

2nd nuclear spin magnetic moment in Bμ interaction energy

( ) ( )( )1 2

012 2 1 2 1 12 2 123 21

12 12

1 34

Er rμ μ μ

μπ

⎡ ⎤= − = −⎢ ⎥

⎣ ⎦B r μ μ μ μ r μ r

Within strong external magnetic field B0 alignment

1 12 12 1/ | | cosμ θ=μ r r

1 2

201 23

12

1 1 3cos4

Erμ μ

μ μ μ θπ

⎡ ⎤= −⎣ ⎦


The classical dipolar interaction

1 2

201 23

12

1 1 3cos4

Erμ μ

μ μ μ θπ

⎡ ⎤= −⎣ ⎦

( )2

0

1 3cos sin 0dπ

θ θ θ− =∫

molecular reorientation

15N

1H

B0

isotropic

magic angle ~ 54°


Quantum mechanical picture

Iγ=μ Ihspin I

3 30 0

1 23 3, 1 , 1

1 3 34 4

j ji I S iD i ij j i ij j

i j i j

x xx xH I Sr r r r r r

μ γ γ μμ δ μ δπ π= =

⎛ ⎞ ⎛ ⎞= − − = − −⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠∑ ∑h

2

2

2

2

2

: 3 1

: 3

: 3

: 3

z z

x z z x

y z z y

x y y x

zI Sr

xzI S I SryzI S I SrxyI S I Sr

−

+

+

+

2

2

2

2

2 2 2 2 2 2 2 2 2

2 2 2

: 3 1

: 3 1

3 3 2 2 2 2 3 1: 3 12 2 2

x x

y y

x x y y

xI SryI Sr

x y x y z z x y zI S I Sr r r

⎫− ⎪⎪

⎬⎪− ⎪⎭

⎛ ⎞+ − − − − + ++ = − −⎜ ⎟

⎝ ⎠


Quantum mechanical picture

( )

( ) ( )

( ) ( ) ( )

2

2

03 2 2

2 2

2 2

1 3 12

3 34

33

2

z z x x y y

I SD x z z x y z z y

x y y x x x y y

zI S I S I Sr

xz yzH I S I S I S I Sr r r

x yxyI S I S I S I Sr r

γ γ μπ

⎧ ⎫⎛ ⎞⎡ ⎤⎪ ⎪− + − +⎜ ⎟⎢ ⎥⎪ ⎪⎣ ⎦ ⎝ ⎠⎪ ⎪

⎪ ⎪⎡ ⎤= − + + + +⎨ ⎬⎢ ⎥⎣ ⎦⎪ ⎪⎪ ⎪⎡ ⎤−⎪ ⎪⎢ ⎥+ + +⎪ ⎪⎢ ⎥⎣ ⎦⎩ ⎭

h

sin cos ; sin sin ; cosx y zr r r

θ φ θ φ θ= = =spherical coordinates

( ) ( )2 21 ,m m mD

mH F Tθ φ −= −∑ 1

20

2 23

244 5

m mI SF Yr

γ γ μ ππ

⎛ ⎞= − ⎜ ⎟⎝ ⎠

hwhere

coordinates spin operators


Spherical harmonics

component ( )2 ,mY θ φ 2mT −

0m = ( )12 25 1 3cos 1

4 2θ

π⎛ ⎞ −⎜ ⎟⎝ ⎠

( )1 126 z z x x y yI S I S I S⎛ ⎞ ⎡ ⎤− +⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠

1m = ± ( )1215 sin cos exp

8iθ θ φ

π⎛ ⎞− ±⎜ ⎟⎝ ⎠

[ ]12 z zI S I S± ±± +

2m = ± ( )12 215 1 sin exp 2

2 4iθ φ

π⎛ ⎞ ±⎜ ⎟⎝ ⎠

12

I S± ±

( )x yI I iI+ = + ( )x yI I iI− = −

( )exp cos sini iφ φ φ= +


Secular approximation

( ) ( )203

13cos 14 4I S

D z zH I S I S I Sr

γ γ μ θπ + − − +

⎡ ⎤= − − − +⎢ ⎥⎣ ⎦h

( )12 x x y yI S I S I S I S+ − − ++ = +

034

I S

rγ γ μ

πh

r = 1.04 1D(N,H) = 21.7 kHz

( )203 3cos 1

4I S

D z zH I Sr

γ γ μ θπ

= − −h

heteronuclear case


( ) ( ) ( )0 023

2 , , cos4 4

P QPQD P F d dr

γ γ μβ γ θ φ β γ

π π= − ∫

h

molecular tumbling/internal motion

( )0 23

1 3cos 14 2

P QPQDr

γ γ μθ

π= − −

h

sampled orientations


Molecular alignment and RDCs



( ) ( ) ( ) ( )( )2

2 cos cos cos3 1cos cos cos cos2 2xx y zy zt t tP β βαθ α αβ= + + −

x

y

z

P

Q

βx (t)

βz(t)βy (t)

αx

αy

αz

B0θ

( ) ( )

( )( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

2

2 0 0

20

20 0 0 0

02

3cos 12

3 1, ,2 2

T

x x y x zx

x y z x y y y z y

zx z y z z

P

C t C t C t C t C t rr r r C t C t C t C t C t r

rC t C t C t C t C t

θ = −

⎧ ⎫⎛ ⎞⎛ ⎞⎪ ⎪⎜ ⎟⎜ ⎟⎪ ⎪⎜ ⎟= −⎨ ⎬⎜ ⎟⎜ ⎟

⎪ ⎪⎜ ⎟⎜ ⎟⎝ ⎠⎪ ⎪⎜ ⎟⎝ ⎠⎩ ⎭

b r

orientational probability distribution

( ) ( )cos ii t tC β= cosi ic α=

( )( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

22 22 2 2

23 1cos2 22 2 2

x x y y z z

x y x y x z x z y z y z

C t c C t c C t cP

C t C t c c C t C t c c C t C t c cθ

⎡ ⎤+ + +⎢ ⎥= −⎢ ⎥+ +⎣ ⎦

and



( ) ( ) ( ) ( )3/ 2 cos cos 1/ 2 3/ 2 1/ 2ij i j ij i j ijS t t C t C tβ β δ δ= − = −

x; Sxxd

y; Syyd

z; Szzd

P

QθPQ

φPQ

( ); cos ; sin cos ; sin sinPQ z z PQ x PQ PQ y PQ PQc c cθ α θ θ φ θ φ= = = =

22 2 1x y zC C C+ + = i j j iC C C C= S is real, traceless, symmetric5 independent elements

( ) { }22 22 2 2max

3, , 12

PQ PQx y z x x y y z zD D C c C c C cα α α ⎡ ⎤= + + −⎢ ⎥⎣ ⎦

principal alignment frame, i.e. diagonalization of S Sd

( ){ }

2, , ,

cos cos cosij i ji j x y z

P Sθ α α=

= ∑

2 1/ 3i ijC A= + ( ) 2 2 2 2 2max

3, , cos sin cos sin sin2

PQ PQx y z PQ zz PQ PQ xx PQ PQ yyD D A A Aα α α θ θ φ θ φ⎡ ⎤= + +⎣ ⎦

( ) ( ) ( )2max 2

3 1, cos sin cos 22 2

PQ PQPQ PQ PQ zz PQ PQ xx yyD D P A A Aθ φ θ θ φ⎡ ⎤= + −⎢ ⎥⎣ ⎦


Generalized degree of order (GDO): Euclidean norm ϑ = (2/3

4/5 π ∑i,j Sij2)1/2

( ) ( )0 2 22 3

3, 3cos 1 sin cos 224

P QPQPQ PQ LS PQ PQ PQ

PQ

D S Rr

γ γ μθ φ θ θ φ

π⎡ ⎤= − − +⎢ ⎥⎣ ⎦

h

Aa=3/2Azz=Szzd, Ar=(Axx-Ayy)=2/3 (Sxx

d - Syyd)

( ) ( )

( ) ( )

2max 2

2 2

3, cos sin cos 243, 3cos 1 sin cos 22

PQ PQPQ PQ PQ a r PQ PQ

PQ PQPQ PQ a PQ PQ PQ

D D P A A

D D R

θ φ θ θ φ

θ φ θ θ φ

⎡ ⎤= +⎢ ⎥⎣ ⎦⎡ ⎤= − +⎢ ⎥⎣ ⎦

DaPQ = ½ DPQ

max Aa : magnitude of alignment tensor (Aa=10-3 DaNH ~ 10 Hz)

R = Aa/Ar: rhombicity of alignment tensor; R ∈ [0; 2/3]

use only a very slight orientational preference ("partial alignment"), i.e., only ca. 1 out of 1000 solute molecules


How to Get Alignment


Partial Alignment

• dipolar couplings are LARGE in solids (~22 kHz for 1DHN !), but• fortunately average out for isotropically fast tumbling (solution NMR)

⇒ full dipolar couplings are not desirable in high-resolution NMR

Can we get orientational information WITHOUT messing up our nice NMR spectra ?

YES!• use only a very slight orientational preference ("partial alignment"), i.e.,

only ca. 1 out of 1000 solute molecules

result: dipolar coupling from the (0.1%) non-isotropic fraction is scaled down to residual dipolar couplings (RDCs) of ± 20 Hz max.! (0.1% of ±20 kHz)


Alignment – Anisotropic Tumbling

To extract dipolar coupling data, the molecule must behave anisotropically!

1) large magnetic susceptibility anisotropy• diamagnetic systems such as DNA (small anisotropy in each base) • metalloproteins with paramagnetic centers• lanthanide-binding tags

field-dependent alignment of molecules

2) anisotropic environment• oriented liquid-crystalline phase• anisotropically compresed gel

field-independent alignment


Alignment media

Requirements

• liquid crystalline at < 10% w/v order of biomolecules: ~ 0.002

• aqueous

• uniform anisotropy over the whole sample volume,

• stable at different ionic strength, pH, temperature

• not too strongly charged < 0.5 e/nm2,

• solute should not bind (significantly) to medium


Bicelles

• Diskshaped particles made from DMPC and DHPC (q = 3:1)

• concentration usually 5% (w/v)

• degree of protein alignment can be “tuned” by adjusting the bicelle concentration

• alignment is temperature dependent (liquid crystal > 37°C)

• aligning with their normal perpendicular to the direction of the magnetic field

• degree of alignment can be determined by measuring the 2H quadrupolar splitting in the HDO resonance.


Bicelles (2)

• Isotropic bicelles (q ~ 0.5) for solubilization of integral membrane proteins solution-state NMR

• Anisotropic bicelles for solid-state NMR and X-ray crystallography

Disadvantages:

• unstable in the presence of certain proteins

• offers only a limited temperature and pH range


Alignment media - Toolbox

• bicelles

• alkyl poly(ethylene glycol) based media

• filamentous phage (Pf1,fd; -0.47 e/nm2)

• polyacrylamide gel (charged, uncharged)

• cellulose crystallites

• purple membrane fragments

• cetylpyrimidinium-based media, ...


Alignment of Membrane Proteins

DNA nanotubes

Douglas et al.

PNAS, 2007

Acrylamide gels G-tetrad DNA

Lorieau et al.

JACS, 2008


Modulation of alignment tensor


The problem: Orientational degeneracy

Ramirez & Bax

JACS, 1998

DPQ = DaPQ [(3 cos2 θ –1) + 3/2 R sin2 θ cos(2φ)]


Strategies for Modulation of Alignment

• Alignment media with different properties (steric/electrostatic)

• Charged bicelles: doping with small charged amphiphiles to alter their charge

Positive: CTAB / Negative: SDS

• Charged gels

• variation of pH, ionic strength

• mutation (introduction of charged residues)

• paramagnetic alignment (different tags/lanthanides)


Attenuation of alignment strength by increasing the ionic strength

ubiquitin at 450 mM NaClin 20 mg/ml Pf1

450 mM NaCl

150 mM NaCl20 mg/ml Pf1

7.08.09.0 ppm


Modulation of alignment tensor orientation by ionic strength changes

GB1


Liquid crystal theory


Liquid crystal theory

B2cp > caB2 = π Deff L2/4

25 Hz

Onsager (1949): concentration at which a solution undergoes a spontaneous first order phase transition from an isotropic to a chiral nematic phase

first-order transition coexistence region cp ∈ [ci, ca]

for semi-flexible rods

ci = 0.3588 [(1-√x)B2]-1 ca = 0.3588 [(x-√x)B2]-1


Onsager theory

effective increase in rod diameter Deff = D + κ-1 (ln ω + 0.7704)

B2cp > ca

contact potential ω = 2π Z2 [β γ x0 K1(x0)]-2 Q κ-1 exp(-2 x0)contribution of the polyions to the ionic strength κ = 8πQ(cs + Γzpcp)

B2 = π Deff L2/4


Liquid crystal theorydensity of most nematogens is higher than for the solvent

average density of the nematic region is higher than for the isotropic region gravity causes it to occupy the bottom region of the sample

Pf1 (12 mg/ml)

0.5M

B2cp > 4.19 and B2cp > 5.51


Paranematic phase of Pf1 phage

• 600 MHz□ 800 MHz

Qcc(2H) = 0.886 cPf1

cPf1 [mg/ml]

For a fully nematic phase, the degree of alignment is independent of field strength above a typically very low threshold

paranematic


Measurement of RDCs


NOESY HSQC


1JHN [1]: IPAP-HSQC, DSSE-HSQC, 3D HNCO1JC‘Cα [5]: 3D HNCO (CSA(C‘) ~ 500 MHz optimum)1JC‘N & 2JC‘HN [8.3]: 2D HSQC, 3D TROSY-HNCO1JCαHα [0.5]: 2D JCH-modulated HSQC, (HA)CANH, HN(CO)CA1JCH (side-chain): 2D JCH-mod. HSQC, CCH-COSY, SPITZE-HSQC1H-1H: COSY, CT-COSY, HNHA, 3D SS-HMQC2 (long-range)

Accuracy of measured splitting: ΔJ = LW/SN

required accuracy < 5% * Da

Bax, Kontaxis & Tjandra Method Enzymol. 339, 127-174, 2001;

Chou & Bax JBNMR, 2001; Delaglio et al. JMR 2001; Wu & Bax, JACS, 2002;


RDC measurement: J splitting (1JHN)

IPAP-HSQC

Ottiger et al. JMR, 1998


RDC measurement: Quantitative J correlation (1JC‘N)

Chou & BaxJBNMR, 2001


Determination of a MolecularAlignment Tensor


Four Methods

1) RDC distribution analysis

2) Back-calculation of alignment tensor

3) Prediction of alignment from structure

4) Prediction of alignment from structure and charge distribution


1) Estimate for alignment tensor

DzzPQ = 2 Da

PQ

DyyPQ = –Da

PQ (1 + 1.5 R)Dxx

PQ = –DaPQ (1 – 1.5 R)

with DiiPQ = DPQ

max Siid no structure necessary !

Cou

nt

-40 -20 0 200

10

20

30

1d(NH) [Hz]

-20 0 20

A B

D [Hz]aNH

-20 -150

0.1

0.2

R

Dzz

Dyy

Dxx

log( L( d1…nPQ| Da

PQ , R)) = ∑i=1,..,N log (P(diPQ))


2) Back-calculation of alignment tensor

• singular value decomposition (SVD)

very stable & with a minimumof five RDCs possible

• iterative least squares procedure (Levenberg-Marquardt minimization) χ2 = ∑i=1,..,N [di

PQ(exp) – diPQ(calc)]2/(σi

PQ)2

fixing of alignment parameters (e.g. rhombic component zero due to three-fold or higher symmetry)

2 GLN HN 2 GLN N -8.170 1.000 1.003 ILE HN 3 ILE N 8.271 1.000 1.004 PHE HN 4 PHE N 10.489 1.000 1.005 VAL HN 5 VAL N 9.871 1.000 1.006 LYS HN 6 LYS N 9.152 1.000 1.007 THR HN 7 THR N 3.700 1.000 1.008 LEU HN 8 LEU N 6.461 1.000 1.00

10 GLY HN 10 GLY N 7.634 1.000 1.0011 LYS HN 11 LYS N -7.528 1.000 1.00

if well-defined structure available


Evaluation of uncertainty in back-calculated alignment tensors (I)

Can you trust a back-calculated alignment tensor?

Monte-Carlo type approach (RDC noise)´

repeat SVD calculation many times (~1000 times)each time add different Gaussian noise to experimental RDCsaccept only those solutions for which all back-calculated RDCs are within

a given margin of the original experimental dipolar couplings

error in the data is dominated by the random measurement error in the dipolar couplings

indirectly take into account uncertainties in the structureset the amplitude of the added noise two to three times higher than the measurement uncertainty


Evaluation of uncertainty in back-calculated alignment tensors (II)

Structural noise Monte-Carlo type approachrepeat SVD calculation many times (~1000 times)

each time add different Gaussian noise to the original structure (match the RMSD between the experimental and back-calculated RDCs)

spread in alignment parameters obtained for these noise-corrupted structures, when using the coupling constants calculated for the original structure (i.e., yielding a perfect fit if no structural noise were added)


3) Prediction of alignment from structure

no RDCs necessary !


Computer experiment: PALES

Sij=1/2 <3cosΘi cos Θj - δij> (i,j=x,y,z)

Periodic boundary conditionsr < d/(2 Vf) (wall model), or r < d/(4Vf)1/2 (cylinder)

Smol linear average over all non-excluded S matrices


Shape prediction of magnitude and orientation of alignment

1DNHmeasured [Hz]

1 DN

Hpr

edic

ted

[Hz]

Protein alignment in bicelles is sterically induced


Weak alignment in Pf1 bacteriophage

http://www.asla-biotech.com/asla-phage.htm


4) Prediction of alignment from structure and charge distribution

p = 0 p = 1p = 1

steric

pB = exp[ -ΔGel(r,Ω)/kBT]

ΔGel(r,Ω) = ∑i qi φ[ri(r,Ω)]

Sijmol = ∫ Sij pB(r,Ω) dr dΩ / ∫ pB(r,Ω) dr dΩ

B0


How to calculate the electrostatic energy?

• Continuum electrostatic theory (Debye and Hueckel 1923): protein embedded in a dielectric medium containing excess ions

• non-linear Poisson-Boltzmann equation (Chapman 1913; Gouy 1910)

• Further simplification: Protein = a particle in the external field of the liquid crystal many approximations !

• protein = charges of their ionizable residues• static dielectric constant of water ε = 78.29• average surface charge of phages: -0.47 e/nm2


0.5

rela

tive

G

0distance from Pf1 [nm]

-4

-2

0

Bφ

[kT/

e]

10 20

Electrostatic potential0


Experiment versus PALES prediction

ubiquitin

DinI

GB3

GB1

DNA

steric

Zweckstetter et al.,

Biophys. J. 2004

electrostatic + steric


ubiquitin

DinI

GB3

GB1

Ionic strength dependence

DNA

orientationmagnitude


Weak alignment in surfactant liquid crystalline phases

3 nm Lα

10-20 nm

+

+

++

++

+

B0

PALES


Residual dipolar couplings in cetylpyridinium bromide/hexanol/sodium

bromide Zweckstetter,

submitted

steric and electrostatic interactions dominate weak alignment of biomolecules

in polar liquid crystalline media


Partial alignment at pH 3

pH 3

pH 7

Barrientos et al., JMR 2001

pH 3

pH 7

Zweckstetter, Eur. Biophys. J. 2005


PH dependence of alignment

NMR workshop, Rosario November 200860Zweckstetter et al., Biophys. J. 2004

RDCs are a sensitive probe of proteinelectrostatics

DinI (PDB code: 1GHH)


Charge/Shape prediction: applications• differentiation of monomeric and homodimeric states (Zweckstetter and Bax 2000)

• conformational analysis of dynamic systems such as oligosaccharides (Azurmendi and Bush 2002)

• refinement of nucleic acid structures (Warren and Moore, 2001)

• determination of the relative orientation of protein domains (Bewley and Clore 2000)

• validation of structures of protein complexes(Bewley 2001)

• classify protein fold families on the basis of unassigned NMR data(Valafar and Prestegard 2003)

• Probing surface electrostatics of proteins and nucleic acids,refinement of side chain orientations in proteins, …


RDCs in Structure Calculation


RDC-based refinement of structures

PROBLEM:Potential energy surface is very rough many local/false minima

convergence problem

RDC-based refinement of starting structures

kdip force constant adjust such that dipolar RMS is equal to measurement error)


Crititical PointsHow to use the structural information obtained from molecular alignment1. In order to use the information one needs to know the direction and the size of thetensor (susceptibility, alignment, etc). 2. Minimization of the deviation between the measured quantity and its calculatedvalue from a given structure and set of tensor parameters. 3. One has to be able to evaluate the outcome of the minimization.

Minimization procedure1. Get a good estimate on the tensor parameters (magnitude and rhombicity). 2. Define structural constraints with respect to the arbitrary tensor coordinate system. 3. Turn on the force constant for a particular alignment potential such that the final RMS between the measured and calculated values reflect the experimental error. 4. During the calculation the tensor orientation will be automatically determinedthrough global minimization with respect to the current structure. 5. Refine the initial estimate of the tensor parameters. This can be achieved througheither grid search method or built into the minimization itself.


Define axis system representing thealignment tensor


From PALES to XPLOR

rDC(NH) measured aligned - isotropic (PALES convention)(min(DC)=-16.2 Hz; max(DC)=12.7 Hz ==> estimated Da(NH)=-8.1*(-1) as correct measurement isotropic-aligned)

==> PALES gives: DATA Da -4.177638e-04 ==> get correct Da by multiplying -4.177638e-04*-21585.19 = 9.0 Hz (for XPLOR however use -9.0 Hz, i.e. sign of Szz/2)

rDC(NH) measured isotropic - aligned (SSIA convention)(min(DC)=-12.7 Hz; max(DC)=16.2 Hz ===> estimated Da(NH)=16.2/2=8.1

==> PALES gives: DATA Da 4.177638e-04 ==> get correct Da by multiplying 4.177638e-04*21585.19 = 9.0 Hz (for XPLOR however use -9.0 Hz, i.e. (-1)*sign of Szz/2)


1. The final dipolar RMS between measured .vs. calculated values

2. Consistency between dipolar coupling data and NOE data(decrease in non-RDC energy terms)

3. If one has more than one class of dipolar couplings: cross validation withquality factor

4. Use programs such as Procheck to look at the overall quality of the structure(distribution in Ramchandran plot should improve)

5. In most cases where one obtains a high degree of consistency one would also gain in the overall RMSD of the family of calculated structures.

rms (Dobs - Dcalc)rms (Dobs) Q =

How to evaluate structures produced byminimizing against alignment data


Quality measure of calculated/simulated RDCs

• use only for RDCs not included in structure determination !

• no translational validation

Q ~ 17% ≈ 1.8 Å X-rayO ~ 11% ≈ 1.1 Å X-ray

1DNHmeasured [Hz]

1 DN

Hpr

edic

ted

[Hz]

rms (Dobs - Dcalc)rms (Dobs) Q =

rms(Dobs)= [2 (Danorm)2 (4 + 3R2)/5]1/2


a) without rdcb) with rdc

Zhou et al. Biopolymers (1999-2000) 52, 168.

Impact of RDC refinement

15n residual dipolar couplings - embocwp.embo.org/wpc09-07/lecture/rdctheory.pdfnmr workshop,...

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