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!