EMBO Global Exchange course, IHEP, Beijing April 28 - May 5, 2011

Introduction solution NMR

Alexandre Bonvin

Bijvoet Center for Biomolecular Research

with thanks to Dr. Klaartje Houben

2

NMR ‘journey ’

• Why use NMR for structural biology...?

• The very basics

• Multidimensional NMR

• Resonance assignment

• Structural parameters

• NMR relaxation & dynamics

3

Topics

Why use NMR.... ?

NMR & Structural biology

Dynamic activation of an allosteric regulatory protein Tzeng S-R & Kalodimos CG Nature (2009)

S2 (DS2) are unevenly distributed throughout the protein structure.More specifically, whereas most of the residues in DBD of eitherWT-CAP or CAP-S62F becomemore rigid on DNA binding, the majorityof the residues that makes up the cAMP-binding site exhibit signifi-cantly lower S2 values in CAP-S62F, indicating an enhancement inmotional freedom. It should be noted that, as indicated by chemicalshift analysis, DNA binding to CAP-S62F-cAMP2 reorganizes thecAMP-binding pocket (Supplementary Fig. 4b). The relaxation datashow that this reorganization results in enhanced flexibility of thecAMP-binding region, presumably by altering the local packingdensity21.

Order parameters values are indicative of the amplitude of spatialfluctuations experienced by a bond vector and, thus, can be related toconformational entropy19. Despite certain assumptions and limita-tions, this approach can provide reasonably accurate per-residueentropies22–27. By converting order parameters to conformationalentropy, –TDSconf, we estimate that DNA binding to WT-CAP-cAMP2 is accompanied by an unfavourable conformational entropychange (–TDSconf ,39 kcalmol21), whereas DNA binding to CAP-S62F-cAMP2 is accompanied by a favourable conformationalentropy change amounting to –TDSconf ,–22 kcalmol21 (Fig. 2b

and Supplementary Fig. 13). We conclude that the calorimetricallymeasured large entropy that drives the strong binding of CAP-S62F-cAMP2 to DNA is dominated by the favourable conformationalentropy change (Fig. 2a).

In the case ofDNAbinding toCAP-S62F-cAMP2 the calorimetricallydetermined energetics is the sum of two events: the first is the directbinding interaction between DNA and the protein molecules in theactive conformation, and the second is the population shift from theinactive to the active conformation (Fig. 4). The thermodynamics ofthe allosteric transition that results in activation can be extracted byusing CAP*-G141S, a constitutively active mutant9,28 (SupplementaryFig. 14), wherein DBD, as NMR spectra indeed demonstrate (Sup-plementary Fig. 14a), adopts largely the active conformation in theabsence of cAMP. cAMP binds to CAP*-G141S with two orders ofmagnitude higher affinity than to WT-CAP protein (SupplementaryFig. 14b). This energy difference corresponds to the energy spent bycAMP binding to elicit the active conformation to the wild-typeprotein. The combined data (Supplementary Fig. 14a–c) indicate thatthe allosteric transition of DBD from the inactive to the active con-formation requires ,3.0 kcalmol21 (DGactiv), with the process beingentropy driven (–TDSactiv5 –2.2 kcalmol21) but enthalpically opposed

WT-CAP-cAMP2

CAP-S62F-cAMP2

+0.3

!0.3

!S

2

Rigidity

Flexibility

+0.3

!0.3

!S

2

Rigidity

Flexibility

–T!Sconf = 39.2 kcal mol–1 –T!Sconf = –22.3 kcal mol–1

WT-CAP CAP-S62F

b

a

!20

!10

0

10

20

40!G !H –T!S –T!Sconf

0.0 0.5 1.0 1.5 2.0!25

!20

!15

!10

!5

0

5

Molar ratio

!G (k

cal m

ol–1

)

kcal

mol

–1

" "

Figure 2 | Energetics of CAP interaction with DNA. a, ITC bindingisotherms of the calorimetric titration of a specific DNA sequence to WT-CAP-cAMP2 (blue) and CAP-S62F-cAMP2 (magenta) and the associatedthermodynamic components (DG,DH andDS) displayed as bars. –TDSconf isthe conformational entropy as measured by NMR. b, Effect of DNA bindingon N-H bond order parameters of CAP. Changes in order parameters, DS2,for WT-CAP-cAMP2 (left) and CAP-S62F-cAMP2 (right) on DNA binding.

DS2 is given as S2 (afterDNAbinding) – S2 (beforeDNAbinding), so positiveDS2 values denote enhanced rigidity of the protein backbone on DNAbinding. The conformational entropy of DNA complex formation estimatedthrough DS2 values is unfavourable for WT-CAP-cAMP2(–TDSconf5 39.2 kcalmol21) and favourable for CAP-S62F-cAMP2(–TDSconf5 –22.3 kcalmol21). S2 plots for all WT-CAP and CAP-S62Fliganded states, including error bars, are provided in Supplementary Fig. 13.

LETTERS NATURE |Vol 462 | 19 November 2009

370 Macmillan Publishers Limited. All rights reserved©2009

use distinct thermodynamic strategies to interact strongly and specifi-cally with DNA.

To better understand the mechanism by which CAP-S62F-cAMP2manages to bind strongly to DNA while adopting the DNA-bindinginactive conformation, we performed a series of relaxation dispersionexperiments (Fig. 3a). These experiments have the capacity to detectand characterize low-populated conformations15,16. The results showthat on binding of cAMP to CAP-S62F, DBD resonances becomebroader, indicating the presence of exchange between conformationson the micro-to-millisecond (ms–ms) time scale. Data fitting (seeMethods) is indicative of a two-site exchange process, with the popu-lation of the excited state being ,2% (Fig. 3a). The additional linebroadening of NMR signals (Rex; Fig. 3c) caused by conformationalexchange between the ground (A) and an excited state (B) dependson the relative populations of the exchanging species (pA and pB) andthe chemical shift difference between the exchanging species(Dv)15,16. The absolute 15N Dv values of DBD residues measuredbetween the apo-CAP andWT-CAP-cAMP2 (Figs 1b and 3b) clearlycorrelate with the Dv values between the major and the minor con-formations of CAP-S62F-cAMP2 determined by relaxation disper-sion measurements (Dvdisp; Fig. 3d). Thus, the data provide strongevidence that the excited state that DBD transiently populates inCAP-S62F-cAMP2 closely resembles the active, DNA-binding com-patible conformation. Because the affinity of the active DBD con-formation for DNA (for example, in CAP-cAMP2) is many orders ofmagnitude higher than that of the inactive DBD conformation (forexample in apo-CAP), DNA will preferentially bind to the active

DBD conformation of CAP-S62F-cAMP2, despite being so poorlypopulated. Thus, the data indicate that DNA binding to CAP-S62F-cAMP2 proceeds with a population-shift mechanism17.

Despite adopting predominantly the inactive conformation andonly very poorly the active one (,2%), CAP-S62F-cAMP2 binds toDNA as tightly as WT-CAP-cAMP2, driven by a large favourablebinding entropy change, as measured experimentally by calorimetry(Fig. 2a). The amount of surface that becomes buried on binding ofDNA to WT-CAP-cAMP2 and CAP-S62F-cAMP2 is very similar,indicating that the hydrophobic effect is not the source of the largeentropy difference measured for the formation of the twoDNA com-plexes. To understand the origin of this large favourable change inentropy, we sought to determine the role of dynamics in the bindingprocess. To assess the contribution of protein motions to the con-formational entropy of the system18,19, we measured changes in N-Hbond order parameters for DNA binding to WT-CAP-cAMP2 andCAP-S62F-cAMP2 (Supplementary Figs 9–13). The order parameter,S2, is a measure of the amplitude of internal motions on the ps–nstimescale and may vary from S25 1, for a bond vector having nointernal motion, to S25 0, for a bond vector rapidly sampling mul-tiple orientations20.

DNA binding to WT-CAP-cAMP2 results in widespread increasein S2, indicating a global rigidification of the protein (Fig. 2b andSupplementary Fig. 13c). Notably, DNA binding to CAP-S62F-cAMP2 causes a large number of residues to increase their motionsas evidenced by the corresponding decrease in their S2 values (Fig. 2band Supplementary Fig. 13c). It is of interest to note that changes in

a

0.0

0.6

! !

(p.p

.m.)

0.0

0.6

! !

(p.p

.m.)

apo-CAP CAP-cAMP2 CAP-cAMP2-DNA

CBD

DBD

F helices F helices

b c

Figure 1 | Conformational states of CAP and effect of cAMP bindingassessed by NMR. a, Structures of CAP in three ligation states: apo9,cAMP2-bound

10, and cAMP2-DNA-bound8. The CBD, DBD and hinge

region are coloured blue, magenta and yellow, respectively. cAMP and DNAare displayed as grey and green sticks, respectively. b, c, Effect of cAMP

binding on the structure of WT-CAP (b) and CAP-S62F (c) as assessed bychemical shift mapping (Supplementary Fig. S4). Chemical shift difference(Dv; p.p.m.) values are mapped by continuous-scale colour onto the WT-CAP-cAMP2 structure.

NATURE |Vol 462 | 19 November 2009 LETTERS

369 Macmillan Publishers Limited. All rights reserved©2009

5

...allows to study the dynamics of biomolecular systems...

NMR & Structural biology

High-resolution multidimensional NMR spectroscopy of proteins in human cells Inomata K. et al Nature (2009)

6

...structural studies in membrane and whole cells possible!

The Sample

• isotope labeling– unlabeled (peptides)– 15N labelled (small proteins < 10 kDa)– 15N & 13C labelled (larger proteins, up to 30-40 kDa)– 15N, 13C & 2H labelled (large proteins > 40 kDa)

• protein production (E.coli)– quite a lot & very pure & stable

• 500 uL of 0.5 mM solution -> ~ 5 mg per sample

– 13C labelling is costly, ~k! per sample– preferably low salt, low pH, no additives.

7

• Pros...– no need for crystal:

• no crystal packing artefacts, solution more native-like

– potential to study dynamics:• picosecond to seconds time scales, conformational averaging,

chemical reactions, folding...

– easy study of protein-protein, protein-DNA, protein-ligand interactions

• Cons...– NMR structure determination is a bit slow....– Need isotope labeling (13C, 15N)– solution NMR works best for MW < 50 kDa

8

Pros & cons of solution NMR in structural biology

The very basics of NMR

10

precession

E = µ B0

11

Nuclear spin12

Nuclear spin

(rad . T-1 . s-1)

m = -!

m = !

Larmor frequency

1H (I = 1/2)Larmor frequency

!H = "HB0 = 2#$H

13 14

Boltzman distribution

m = -!

m = !

1H (I = 1/2)

15

Net magnetization16

Chemical shieldingLocal magnetic field is influenced by electronic environment

17

Chemical shielding

( )!"

#$ %= 12

0B Chemical shielding • Chemical shift:– δσiso [Hz] = νobs - ν0

– δσiso [ppm] = (νobs - ν0)/(ν0.10-6)• ppm: parts per million

• ppm value is not field dependent

Chemical shift18

14 Tesla: !H = 600 MHz→ 1 ppm = 600 Hz (1H)

21 Tesla: !H = 900 MHz→ 1 ppm = 900 Hz (1H)

19

PulseObserve with the Lamor frequency

→ “rotating frame”

FID: analogue vs digital20

Free Induction Decay (FID)

time (ms)

Sig

nal

0 25 50 75 100 125

0

175150 200 freq. (s-1)

Sig

nal

0 5 10 15 20 25

0

30 35 40

FT

FT

21

Fourier Transform

• NMR Relaxation– Restoring Boltzmann equilibrium

• T2-relaxation– disappearance of transverse (x,y) magnetization– 1/T2 ~ signal line-width

• T1-relaxation– build-up of longitudinal (z) magnetization– determines how long you should wait for the next

experiment

22

Relaxation

23

NMR spectral quality

• Sensitivity– Signal to noise ratio (S/N)

• Sample concentration

• Field strength

• ..

• Resolution– Peak separation

• Line-width (T2)

• Field strength

• ..

24

Scalar coupling / J-coupling

H3C - CH2 - Br

3JHH

Multidimensional NMR

• multidimensional NMR experiments– resolve overlapping signals

• enables assignment of all signals

– encode structural and/or dynamical information• enables structure determination

• enables study of dynamics

26

Why multidimensional NMR

27

2D NMR28

3D NMR

1D

single FID of N points

FID

t1

2D N FIDs of N pointst2

FIDt1 mixing

29

nD experiment

3D NxN FIDs of N points

t2t1 mixingt3

mixingFID

direct dimension

indirect dimensions

• mixing/magnetization transfer

spin-spin interactions

precession

E = µ B0

precession

E = µ B0????

proton A proton B

Encoding information30

• magnetic dipole interaction (NOE)– Nuclear Overhauser Effect– through space– distance dependent (1/r6)– NOESY -> distance restraints

• J-coupling interaction– through 3-4 bonds max.– chemical connectivities– assignment– also conformation dependent

31

Magnetization transfer

t2

FID

t1NOESY

tm

magnetic dipole interactioncrosspeak intensity ~1/r6

up to 5 Å

COSYt2

FID

t1 J-coupling interactiontransfer over one J-coupling, i.e. max. 3-4 bonds

TOCSYt2

FID

t1J-coupling interactiontransfer over several J-couplings, i.e. multiple steps over max. 3-4 bonds

mlev

32

homonuclear NMR

t2

FIDt1

NOESYtm

A A (ωA) A

B

A (ωA)

B (ωB)

F1

F2

ωA

ωA ωB

precession

E = µ B0

precession

E = µ B0

proton A proton B

~Å

33

homonuclear NMR

(F1,F2) = ωA, ωA

(F1,F2) = ωA, ωB

Diagonal

Cross-peak

2D TOCSY

2D COSY & TOCSY34

HN

Hα

Hβ

2D COSY

HN

Hα

Hβ

– measure frequencies of different nuclei; e.g. 1H, 15N, 13C– no diagonal peaks– mixing not possible using NOE, only via J

35

precession

E = µ B0

precession

E = µ B0

1H 15N

heteronuclear NMR!"# $%&'("#)*+,-.%/0'.%',1*23.%0

36

J coupling constants

1JCaCb = 35 Hz

1JCaC’ =

55 Hz

2JCaN = 7 Hz

1JNC’ =-15 Hz

1JCaN =-11 Hz

1JHN = -92 Hz

1JCaHa = 140 Hz

2JNC’ < 1 Hz

1JCbCg = 35 Hz

1JCbHb = 130 Hz

!"# $%&'("#)*+,-.%/0'.%',1*23.%037

J coupling constants

1JHN = -92 Hz

HSQC (heteronuclear single quantum coherence)

t2

FID

t1

1H

DEC15N

1H 15N (ω15N)1JNH 1JNH

(F1,F2) = ω15N, ω1H

J-mix block

38

heteronuclear NMR

J-mix block

1H (ω1H)

1H-15N HSQC: ‘protein fingerprint’39

note that spectrum is decoupled: no NH J-coupling

1H-15N HSQC: ‘protein fingerprint’40

!"# $%&'("#)*+,-.%/0'.%',1*23.%041

J coupling constants

1JHN = -92 Hz

2JCaN = 7 Hz

1JCaN = -11 Hz

HNCA

t3

FID

t2

1H

DEC15N

(F1,F2,F3)= (ω13Ca(i), ω15N(i), ω1H(i)) & (ω13Ca(i-1), ω15N(i), ω1H(i))

t113C

1H 15N1JNH 1JNCa(i)

2JNCa(i-1)

42

Triple resonance NMR

J-mix block

J-mix block

15N (ω15N)13C (ω13C) 1H (ω1H)

J-mix block

1JNCa(i)

2JNCa(i-1)

1JNH

J-mix block

Resonance assignment Structural parameters

a few months or more...

Structural study by NMR

• Sample preparation (months)

• Acquisition of NMR spectra (~1 month)

• Chemical shift assignments– Backbone (days)– Side-chains (days)

• Analysis of NOESY spectra (weeks)• Structure calculations (days)

• Functional studies with NMR– Interaction with partner

RESTRAINTS! dihedral angles! distances between

atoms! orientation between

bond vectors

Sources of structural information46

– long-range NOEs

– residual dipolar couplings

– H / D exchange

– effects of pH / T

– effects of interacting partners

– relaxation rates

– .....

Secondary structure

Tertiary structure

• OBSERVABLES– chemical shifts (1H, 15N, 13C,

31P)– J-couplings, e.g. J(HN,Hα)

φ

ω ~ 180º

N NC C C C

C C

O O

φ

ψ ω

RESTRAINTS: dihedral angles47

φ

anti-parallel β-strand α-helix

RESTRAINTS: dihedral angles48

φ ψ

ψ

φ

+180

ψ

-180

-180 φ +180

α-helix

β-strand

Ramachandran plot49

φ -130 -60

ψ 125 -45

β-strand α-helix

• 13Cα and 13Cβ chemical shifts– sensitive to dihedral angles– report on secondary structure elements

OBSERVABLE: chemical shift50

KarplusJ = A.cos2(φ) + B.cos (φ) + C

measured 3J(HNHα)

reports on φ

φ!

OBSERVABLE: homonuclear J-couplings

51

φ!

RESTRAINT: distances52

• 1H-1H NOEs (2D NOESY, 3D NOESY-HSQC)– signal intensity proportional to 1/r6

– reports on distance between protons• distance restraints

OBSERVABLE: NOE53

Hx

Hy

Cross-peak between Hx and Hy

• 1H-1H NOEs– signal intensity proportional to 1/r6

– reports on distance between protons• distance restraints

Sequential & medium range NOEs - SECONDARY STRUCTURE

Sequential

A B C D Z• • • • Intra-residue

(used for identifying spin-systems)

Medium range

OBSERVABLE: NOE54

r =

r =

NOEs in secondary structure elements

55

A B C D Z• • • •

Sequential

Intra-residue(used for identifying

spin-systems)

Medium range

Long range NOEs - TERTIARY STRUCTURE

OBSERVABLE: NOE56

Longe range

• 1H-1H NOES– signal intensity proportional to 1/r6

– reports on distance between protons• distance restraints

• Tertiary information– distances < 5 Å– Important structural information

Long-range NOEs57

anti-parallel

RESTRAINT: Orientation58

OBSERVABLE: Residual dipolar couplings

59

No protein alignment

ISOTROPIC SYSTEMD = 0

B0

! "!

strand (aa 474-515) via which it is attached to the tetramerization domain of P (Figure 1). A

structural model of the disordered domain of pX was obtained on the basis of experimental

residual dipolar couplings [26]. The dipolar coupling Dij between two spins i and j is given by

[27]:

!

Dij = "# i# j!µ0

4$ 2r3

3cos2%(t) "1

2 (1)

where ! is the angle of the inter-nuclear vector relative to the direction of the static magnetic

field, "i and "j are the gyromagnetic ratios of spin i and j, respectively, and r is the inter-

nuclear distance. The brackets indicate an average over all conformations exchanging on

timescales faster than the millisecond. In solution NMR, the dipolar coupling between two

nuclei is effectively averaged to zero because all orientations of the protein molecule are

equally probable (isotropic solution). However, a small part of the dipolar coupling can be re-

introduced by partially aligning the protein molecules in the magnetic field for example using

an anisotropic solution [28] or exploiting the magnetic anisotropy of paramagnetic metal ions

[29]. These so-called residual dipolar couplings (RDCs) add to the experimentally measured

scalar coupling (J-couplings), and RDCs can therefore be obtained by comparing the coupling

splitting in the NMR spectra recorded in isotropic and anisotropic solutions. A variety of

anisotropic solutions exists for weakly aligning proteins in the magnetic field e.g. lipid

bicelles [28], filamentous phages [30-32], lyotropic ethylene glycol/alcohol phases [33] and

polyacrylamide gels that have been strained either laterally or longitudinally to produce

anisotropic cavities [34, 35]. Alignment results from a steric repulsion between the protein

and the medium or from a combination of electrostatic and steric interactions.

Experimentally measured RDCs report on orientations of inter-nuclear bond vectors (e.g N-

HN, C#-H#, C#-C’ and HN-C’) that can be usefully expressed with respect to a second rank

tensor describing the overall alignment of the protein molecule in the magnetic field:

!

Dij = "# i# j!µ0

8$ 2r3Aa (3cos

2% "1) +3

2Ar sin

2% cos(2&)'

( ) *

+ , (2)

Here, Aa and Ar are the axial and rhombic components of the alignment tensor, and (!, ")

represents the orientation of the inter-nuclear vector with respect to the alignment tensor.

RDCs have been used extensively in determination of the structure of folded proteins [36-39]

and for determining the relative orientation of proteins involved in protein-protein complexes

Dipolar coupling

Ω

OBSERVABLE: Residual dipolar couplings

60

No protein alignment

ISOTROPIC SYSTEMD = 0

B0

! "!

strand (aa 474-515) via which it is attached to the tetramerization domain of P (Figure 1). A

structural model of the disordered domain of pX was obtained on the basis of experimental

residual dipolar couplings [26]. The dipolar coupling Dij between two spins i and j is given by

[27]:

!

Dij = "# i# j!µ0

4$ 2r3

3cos2%(t) "1

2 (1)

where ! is the angle of the inter-nuclear vector relative to the direction of the static magnetic

field, "i and "j are the gyromagnetic ratios of spin i and j, respectively, and r is the inter-

nuclear distance. The brackets indicate an average over all conformations exchanging on

timescales faster than the millisecond. In solution NMR, the dipolar coupling between two

nuclei is effectively averaged to zero because all orientations of the protein molecule are

equally probable (isotropic solution). However, a small part of the dipolar coupling can be re-

introduced by partially aligning the protein molecules in the magnetic field for example using

an anisotropic solution [28] or exploiting the magnetic anisotropy of paramagnetic metal ions

[29]. These so-called residual dipolar couplings (RDCs) add to the experimentally measured

scalar coupling (J-couplings), and RDCs can therefore be obtained by comparing the coupling

splitting in the NMR spectra recorded in isotropic and anisotropic solutions. A variety of

anisotropic solutions exists for weakly aligning proteins in the magnetic field e.g. lipid

bicelles [28], filamentous phages [30-32], lyotropic ethylene glycol/alcohol phases [33] and

polyacrylamide gels that have been strained either laterally or longitudinally to produce

anisotropic cavities [34, 35]. Alignment results from a steric repulsion between the protein

and the medium or from a combination of electrostatic and steric interactions.

Experimentally measured RDCs report on orientations of inter-nuclear bond vectors (e.g N-

HN, C#-H#, C#-C’ and HN-C’) that can be usefully expressed with respect to a second rank

tensor describing the overall alignment of the protein molecule in the magnetic field:

!

Dij = "# i# j!µ0

8$ 2r3Aa (3cos

2% "1) +3

2Ar sin

2% cos(2&)'

( ) *

+ , (2)

Here, Aa and Ar are the axial and rhombic components of the alignment tensor, and (!, ")

represents the orientation of the inter-nuclear vector with respect to the alignment tensor.

RDCs have been used extensively in determination of the structure of folded proteins [36-39]

and for determining the relative orientation of proteins involved in protein-protein complexes

Dipolar coupling

Protein alignment

ANISOTROPIC SYSTEMD ≠ 0

OBSERVABLE: Residual dipolar couplings

61

JNH

ISOTROPIC

JNH + DNHJNH

ANISOTROPIC

⇒ Difference gives RDC DNH

B

• RDC reports on orientation of bond-vector – orientation of bond-vector within an alignment tensor

(defined by Aa and Ar) with respect to the magnetic field

– i.e. orientation of bond vector with respect to other bonds

Residual dipolar coupling62

Long range orientational restraint - TERTIARY STRUCTURE

Dij = "# i# j!µ0

8$ 2r3Aa (3cos

2% "1) +3

2Ar sin

2% cos(2&)'

( ) *

+,

• Exchange 1H by D (2H)– peaks disappear in time– accessibility of sites– stability of secondary structure elements

• H-bonds

OBSERVABLE: H/D exchange rates63

!1

!2

!3

increasing HN protection

N !H " " "O = C

kopen# $ # # kclose% # # #

N !H kint# $ # N !D

• Titration– add in steps an interacting molecule (ligand / protein /

DNA)– observe changes in chemical shift

• map interaction site

OBSERVABLE: chemical shift changes64

H17.08.09.0

N15

106.0

111.0

116.0

121.0

126.0

H17.08.09.0

N15

106.0

111.0

116.0

121.0

126.0

• Titration– add in steps an interacting molecule (ligand / protein /

DNA)– observe changes in chemical shift

• map interaction site

OBSERVABLE: chemical shift changes

65

Key concepts structural parameters

• OBSERVABLES– chemical shifts (1H, 15N, 13C, 31P)– J-couplings, e.g. 3J(HN,Hα)– medium-range NOEs

– long-range NOEs– residual dipolar couplings (RDCs)

– H / D exchange– effects of interacting partners– .....

66

• RESTRAINTS– dihedral angles– dihedral angles– medium range distances

– long-range distances– orientations bond-vectors

– accessibility / H-bonds– interaction surface– .....

Relaxation & dynamics

17

Introduction

ps ns s ms s

RDC

H/D exchange

relaxation dispersionR1,R

2,NOE

fs

bond vibrations overall tumbling enzyme catalysis; allosterics

loop motions

domain motions

side chain motions

protein folding

real time NMR

J-couplingsp

rote

in d

yn

am

ics

NM

R

68

NMR time scales

• Fast motion– Locally induced magnetic field changes– Causes relaxation

Binduced

B0

69

Local fluctuating magnetic fields

• Return to equilibrium– Longitudinal relaxation → T1

relaxation• Return to z-axis

– Transversal relaxation → T2 relaxation• Dephasing of magnetization in the x/y

plane

Relaxation70

B0

B0

B1

B1

71

Relaxation

• relaxation time is related to rate of motion

R1 = 1/T1

R2 = 1/T2

72

FAST (ps-ns): rotation correlation time

72

Chapter 5.

0 2 4 6

J(0) ns/rad

10

20

30

40

J(0

.87

H)

ps/r

ad

0 2 4 6

J(0) ns/rad

0

0.05

0.1

0.15

0.2

0.25

0.3

J(

N)

ns/r

ad

I IIIIIa

IIIb

I

II

IIIa

IIIb

(b)(a)

tail

loop

13

N

C

(d)(c)

0 500 10000

10

20

30

40

50

R2

,eff (

s-1

)

0 500 1000

CPMG (Hz)CPMG (Hz)

kex

L169

turn 1/ 2

N244

tail kex = 1.30.103; pb = 0.92 %

kex = 2.29.103; pb = 1.20 %0

6

(ppm)

80

Chapter 5.

148 155 163 171 179 187 195 203 211 219 227

2-

1-

0

1

2

3

4

5

6

7

U-f

acto

r / R

am

achandra

n Z

-score

residue number

s-Z tolp nardnahcamaR laniF

erocs-U

eroc

R1 (

s-1

)

0

0.4

0.8

1.2

1.6

2

0

5

10

15

20

25

30

157

residue number

-1

-0.5

0

0.5

1

NO

E

residue number

0

5

10

15

R1

(s

-1)

R1

/R1

177 197 217 237 157 177 197 217 237

73

FAST (ps-ns): protein flexibility

R2 /R

1

17

Introduction

ps ns s ms s

RDC

H/D exchange

relaxation dispersionR1,R

2,NOE

fs

bond vibrations overall tumbling enzyme catalysis; allosterics

loop motions

domain motions

side chain motions

protein folding

real time NMR

J-couplings

pro

tein

dyn

am

ics

NM

R

74

NMR time scales

75

SLOW (µs-ms): conformational exchange

76

SLOW (µs-ms): conformational exchange

• Causes line-broadening– Makes T2 relaxation faster

• wide range of time scales

• fluctuating magnetic fields

• rotational correlation time (ns)

• fast time scale flexibility (ps-ns)

• slow time scale (μs-ms): conformational exchange

77

Key concepts relaxation

The End

Thank you for your attention!