2ème école de RMN Cargèse 18-‐23 Mars 2013
Analysis of molecular motions by Nuclear Magnetic Resonance (Mostly high resolution liquid state)
Carine van Heijenoort CNRS-‐ICSN laboratoire de chimie et biologie structurales
[email protected]‐gif.fr 0169823794
1
Multiplicity of proteins states
Cargèse 2013
« lock & key » induced Eit
3D structure α ↔ β
conformational switch
order → disorder
virus/pathogen penetration membrane insertion Nucléosome activation
Folding
Sequence
“Non folding” Elexible linkers display of sites entropic bristles, springs and clocks
Elexible ensemble
disorder → order molecular recognition virus/phages assembly stepping motors Dunker et al., Journal of Molecular Graphics and Modelling 19, 26–59, 2001 Dobson, C., Nature 426, 18-‐25, 2003 Carine van Heijenoort -‐ RMN et mouvements moléculaires
2
Cargèse 2013
Different techniques for the analysis of proteins dynamics
X-‐ray cristallography
X-‐Ray, neutron scattering
size/shape modiSications
Doniach, Chem. Rev. 2001, 101 ; Zacai, science 2000, 288.
timescales (ps-‐ns) for 1H positions
Fluorescence
ensemble / single molecule cellular context
Weiss, Nat. Struct. Biol. 2000, 7 ; Yang, Science 2003, 302 ; Haustein, Curr. Opin. Struct. Biol. 2004, 14.
Mass Spectroscopy (HX MS) radical footprinting
B factors
time scales static disorder, crystal contacts, ...
probes
large molecular assemblies
Wales, Mass. Spectrom. Rev. 2006, 25 ; Busenlehner, Arch. Biochem. Biophys. 2005, 433. Guan, Trends. Biochem. Sci. 2005, 30.
Mössbauer, Raman, 2D infrared spectroscopy ForceSields ... Short timescales ...
Molecular dynamics NMR Boehr, Chem. Rev. 2006, 106, 3055. Palmer, Chem. Rev. 2004, 104, 3623.
➫ 10-‐12↔ 105 s ➫ Site-‐speciSic information ➫ multiple atomic probes 1H, 2H, 15N, 13C, 31P, ...
➫ isotope labeling ➫ quantities ➫ size limitation ➫ complexity of the method ?
➫ Simultaneous monitoring of probes ➫ kinetic & thermodynamic proSile of
dynamic processes
Carine van Heijenoort -‐ RMN et mouvements moléculaires
3
Cargèse 2013
How motions are « visible » in NMR ?
ü Molecular motions in/luence NMR parameters ‣ Motions timescales versus NMR timescales ? ü Three distinct timescales in NMR o Equilibrium constant time T1 / Signal lifetime T2 § NMR experiment perturbation of spins system § Typical timescale for (macro)molecules in solution : 100 ms -‐ s (T1) / 10ms-‐s (T2) § Determine the lowest frequency of motions that can be characterized during one NMR experiment.
o Spectral range : τ=1/Δν § Spectrum features : chemical shift range, couplings, … § Averaging if the interactions by motions that have higher frequencies § Perturbation of spectral appearance by motions/processes occuring around this timescale
o “Larmor” timescale: τ=1/ω0 § Precession frequency of the spins in the magnetic Sield B0=ω0/γ § EfSiciency of spins state transitions during the relaxation processes is determined by the spectral density of molecular motions around these frequencies.
Carine van Heijenoort -‐ RMN et mouvements moléculaires
4
Cargèse 2013
How motions are « visible » in NMR ? Three distinct typical timescales in NMR Return to equilibrium : T1 Signal lifetime : T2 Spectral range : τ=1/Δν Larmor precession : τ=1/ω0
s
Carine van Heijenoort -‐ RMN et mouvements moléculaires
ms
μs
ns
5
How motions are « visible » in NMR ?
Cargèse 2013
Functions
Folding ; order ↔ disorder Interactions Catalytic processes Regulation, signalization
Effect of motions on spins interaction
Types of motions
s
NMR parameters
ms
Internal motions
µs
ns
Macroscopic diffusion
ps
Molecular vibrations
Conformational exchange Molecular rotations Diffusion experiments
Dipolar Couplings averaging
Magnetization exchange Spin relaxation
Lineshape modiEications
averaging of non-‐secular interactions
Averaging of spectral components
T1, T2
1/Δω
1/ω0
Signal relaxation
frequencies differences
nutation frequencies
Carine van Heijenoort -‐ RMN et mouvements moléculaires
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Cargèse 2013
NMR timescales 1. Relaxation times
ü Longitudinal relaxation time constant T1 characterizes the time it takes to the spin system to return to equilibrium.
Dynamical processes slower than T1 «real time» kinetics folding/unfolding Interactions, exchange H/ D exchange ...
ü It determines the delay beteen two scans ü Motions slower than T1 can not be characterized by one NMR scan. ü NB. T1 depends on the magnetic Sield strength B0, the type of spin, the size of the molecule, the local dynamics of the system, the temperature, etc.
Wüthrich, « NMR of proteins and nucleic acids », Wiley Interscience, 1986 Carine van Heijenoort -‐ RMN et mouvements moléculaires
7
Cargèse 2013
NMR timescales 1. Relaxation times
ü Transversal relaxation time constant T2 characterizes the lifetime of the signal.
Mx (t) =
Meq sin(
0 t)exp(
t/T2 )
ü It determines the linewidth of the resonances ü Motions slower than T1 can not be characterized by one NMR scan. ü NB. T1 depends on the magnetic Sield strength B0, the type of spin, the size of the molecule, the local dynamics of the system, the temperature, etc.
1/(
0
Carine van Heijenoort -‐ RMN et mouvements moléculaires
/2
2)
/2 8
NMR timescales 1. Relaxation times
Cargèse 2013
ü Relaxation contants depends on the magnetic Sield strength B0, the type of spin, the size of the molecule, the local dynamics of the system, the temperature, etc.
Longitudinal relaxation time constant for a system of 2 proton spins with rHH=0.2nm
relaxation times (s)
100
10
T1 400,600,800MHz
1
0,1 10-12
10-11
10-10
τc(s)
Carine van Heijenoort -‐ RMN et mouvements moléculaires
10-9
10-8
9
How motions are « visible » in NMR ?
Cargèse 2013
Functions
Folding ; order ↔ disorder Interactions Catalytic processes Regulation, signalization
Effect of motions on spins interaction
Types of motions
s
NMR parameters
ms
Internal motions
µs
ns
Macroscopic diffusion
ps
Molecular vibrations
Conformational exchange Molecular rotations Diffusion experiments
Dipolar Couplings averaging
Magnetization exchange Spin relaxation
Lineshape modiEications
averaging of non-‐secular interactions
Averaging of spectral components
T1, T2
1/Δω
1/ω0
Signal relaxation
frequencies differences
nutation frequencies
Carine van Heijenoort -‐ RMN et mouvements moléculaires
10
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
ü Largest observable difference of resonance frequency (spectral width) ü Smallest observable difference of resonance frequency (resolution) ⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
⇤
B0 2⇡
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins. Carine van Heijenoort -‐ RMN et mouvements moléculaires
B0=14.1T
Δω=13ppm
B
Δν=7800Hz
0=
Δω=0,2ppm
22 .3T
B0=14.1T B
τspect~100μs Δν=12350Hz
Δν=120Hz
0=
22 .3T
τspect~5-‐10ms Δν=190Hz
11
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
ü Largest observable difference of resonance frequency (spectral width) ü Smallest observable difference of resonance frequency (resolution) ⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
⇤
B0 2⇡
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins. Carine van Heijenoort -‐ RMN et mouvements moléculaires
Δω(15Ν)=25ppm
Δω(1Η)=3,5ppm
B0=14,1T
Δν~1500Hz τspect~0,7ms
B0=14,1T
Δν~2000Hz τspect~0,5ms
12
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
ü Largest observable difference of resonance frequency (spectral width) ü Smallest observable difference of resonance frequency (resolution) ⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
⇤
B0 2⇡
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins. Carine van Heijenoort -‐ RMN et mouvements moléculaires
Δω(15Ν)=1,5ppm
Δω(1Η)=0,5ppm
B0=14,1T
Δν~100Hz τspect~10ms
B0=14,1T
Δν~300Hz τspect~3ms
Same nucleus ; two different conformations 13
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
( )
Δν Hz =
( ) ∗ 10
Δω ppm
−6
2π
τ spect =
∗ γB 0
1 Δν(Hz )
€
€
Δω(15Ν)=1,5ppm
Δω(1Η)=0,5ppm
B0=14,1T
Δν~100Hz τspect~10ms
B0=14,1T
Δν~300Hz τspect~3ms
Same nucleus ; two different conformations Carine van Heijenoort -‐ RMN et mouvements moléculaires
14
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
• Dipolar interaction between spins magnetic moment
ü Largest observable difference of resonance frequency (spectral width) DD Hˆ IS
ü Smallest observable difference of resonance frequency (resolution) ⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
B0 ⇤ 2⇡
(
)
E/ ≤ 104-‐105 Hz
€
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect € on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins. € Carine van Heijenoort -‐ RMN et mouvements moléculaires
µ 0γ I γ S ⎛ 3cos 2 θ IS −1⎞ ˆ ˆ ˆ ˆ =− ⎜ ⎟ 3 I z S z − I.S 3 2 4 πrIS ⎝ ⎠
• Chemical shift anisotropy c −c Hˆ ICSA = −γ S || ⊥ B0 3cos 2 θ −1 Iˆz 3
(
)
E/ ≤ 104-‐105 Hz
• Quadrupolar interaction spin/electric Sield I > 1/2
(
)
Hˆ IQ ≅ ω IQ 3 Iˆz2 − Iˆ.Iˆ ; ω IQ =
3eQI VzzI (θ ) 4 I (2I −1)
E/ ~ 2.105 Hz (2H) ; E/ ~ 3.106 Hz (14N)
• Unpaired electron 15
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
• Averaging of the secular interactions by the motions
ü Largest observable difference of resonance frequency (spectral width) ü Smallest observable difference of resonance frequency (resolution) ⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
⇤
B0 2⇡
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins. Carine van Heijenoort -‐ RMN et mouvements moléculaires
16
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
• Averaging of the secular interactions by the motions
ü Largest observable difference of resonance frequency (spectral width) ü Smallest observable difference of resonance frequency (resolution) ⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
⇤
B0 2⇡
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins. Carine van Heijenoort -‐ RMN et mouvements moléculaires
17
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
• Averaging of the secular interactions by the motions
ü Largest observable difference of resonance frequency (spectral width) ü Smallest observable difference of resonance frequency (resolution) ⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
⇤
B0 2⇡
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins.
Averaging of the chemical shift anisotropy (31P)
Burnell et al., Biochim. Biophys. Acta 603, 63 (1980) Carine van Heijenoort -‐ RMN et mouvements moléculaires
18
NMR timescales 2. «Spectral» or «chemical shift» timescale
Cargèse 2013
• Using motions to average interactions
ü Largest observable difference of resonance frequency (spectral width) Lipids + water
⌫(Hz) = ⌧spect
(ppm) ⇤ 10
6
⇤
B0 2⇡
1 = ⇡ ⌫(Hz)
ü Motions slower than Δν have no effect on the appearance of the spectra. ü Δν depends on the magnetic Sield strength B0, the type of the spins. ü Different nuclei or same nuclei in different environments ü Δν depends on the nature of the interactions between the spins. Carine van Heijenoort -‐ RMN et mouvements moléculaires
Magic angle Rotation ωr=5000Hz
ü Smallest observable difference of resonance frequency (resolution)
Static
Glycine powder
8
4
0
8
4
0
1H (kHz)
2
1
0
2
1
0
1H (kHz)
Davis, Auger & Hodges Biophysical Journal 69:1917-1932 (1995) Gross et al., J. Magn. Res. 106, 187-190 (1995) Carlotti, Aussenac & Dufourc Biochim. Biophys. Acta. 1564:156-164 (2002) 19
How motions are « visible » in NMR ?
Cargèse 2013
Functions
Folding ; order ↔ disorder Interactions Catalytic processes Regulation, signalization
Effect of motions on spins interaction
Types of motions
s
NMR parameters
ms
Internal motions
µs
ns
Macroscopic diffusion
ps
Molecular vibrations
Conformational exchange Molecular rotations Diffusion experiments
Dipolar Couplings averaging
Magnetization exchange Spin relaxation
Lineshape modiEications
averaging of non-‐secular interactions
Averaging of spectral components
T1, T2
1/Δω
1/ω0
Signal relaxation
frequencies differences
nutation frequencies
Carine van Heijenoort -‐ RMN et mouvements moléculaires
20
NMR timescales 3. Larmor timescale
Cargèse 2013
ü Resonance frequencies of the spin (i.e. difference of energy between the different observable states of the spin system)
|!0 | = | B0 | 1 ⌧Larmor = !0
ββ ωI
ωI+ωS
βα
ωI -ωS
αβ
ωI
ωS ü Motions in this timescale have no effect on the appearance of the spectra. ü Motions in this timescale are responsible for the efficiency of the relaxation processes.
ωS
αα B0=14,1T
|ωI|=2π.600MHz ; τL(I)=265ps |ωS|=2π.60MHz ; τL(S)=2,65ns
ü The relationship between «motions» and relaxation rate constants is indirect.
Carine van Heijenoort -‐ RMN et mouvements moléculaires
21
NMR timescales 3. Larmor timescale
Cargèse 2013
ez
B0+Blocal(t) ü Resonance frequencies of the spin (i.e. difference of energy between the different observable states of the spin system)
|!0 | = | B0 | 1 ⌧Larmor = !0
ey ex
Blocal(t) 100μM)
conformational changes occur upon binding. Association rate constants can thus vary a lot and low afSinities can be associated with slow exchange regime. This is often the case for interactions involving peptides or intrinsically disordered proteins. Beware of multi-‐sites binding: strong afSinities can then be associated with fast exchange regime.
38
Characterization of dynamic processes in the spectral timescale conformational exchange
Cargèse 2013
Intermolecular processes
P
kon
+ L
U2AF65 conformation depends on Py tract strength
PL kof f
Pf Lf
Exchange regime & RNA binding affinity
Pb
ITC Kd
Lb
33 µM
kex = kon [P ] + kof f ωb
kex = kon [L] + kof f
Py tract “strength”
ωB
ωA
18 µM 16 µM 7.1 µM
ωf
[P ][L] kof f Kd = = [P L] kon
Carine van Heijenoort -‐ RMN et mouvements moléculaires
1.3 µM (Michael Sattler personal communication)
39
Characterization of dynamic processes in the spectral timescale Some methods to characterize conformational exchange k1
1/πΔν
ms “Slow” intermediate exchange
Coalescence
Cargèse 2013
µs
A ωA
“Fast” intermediate exchange
B
A
k
ωA
1
ωB
B
ωB
Ea
B ωA
A
longitudinal magnetization exchange
thermodynamic parameters Kd = k1 /k 1 = pB /pA G=
Lineshapes analysis weighted average values
δapp = pAδA +pBδB
ωB
RT ln K
kinetic parameters kex = 1/ ex = k1 + k 1 = k1 /pB = k kex (T ) = k0 exp ( Ea /kT )
1 /pA
R2apparent = R2 + Rex Δω ωA
Carine van Heijenoort -‐ RMN et mouvements moléculaires
ωB
40
Characterization of dynamic processes in the spectral timescale Some methods to characterize conformational exchange
Cargèse 2013
Lineshape perturbation
1/πΔν
ms
µs “Fast” intermediate exchange
Coalescence
“Slow” intermediate exchange
Changing the exchange regime by varying the temperature
R2+k
(Δω)
2
− 4k
1 ⎛ k ⎞ S ω = ⎜⎜1 + ⎟⎟L ω, R2 + k − D 2 ⎝ D⎠ 1 ⎛ k ⎞ + ⎜⎜1 − ⎟⎟L ω, R2 + k + D 2 ⎝ D⎠
()
2
D=
€
€
( (
2
k −
( ) Δω 2
⎛ E ⎞ k T = k 0 exp⎜⎜− a ⎟⎟ ⎝ RBT ⎠
()
Carine van Heijenoort -‐ RMN et mouvements moléculaires
) )
2
{13C} N,N’ diméthylformamide gaz, B0=4,7T
Ea=90,1kJ.mol-‐1 ; k0=1,16.104Hz Ross & True, J. Am. Chem. Soc. 106, 2451 (1984) 41
Characterization of dynamic processes in the spectral timescale Some methods to characterize conformational exchange
Cargèse 2013
Lineshape perturbation
g(⇥) = S
(1 + ⇤ /k)P + QR P 2 + R2
P = 4⇤ 2 [k Q= R=
1
(
2
/4
⇥2 +
2
/4) +
/4⇤]
2⇤⇥/k 2⇤⇥(1 + 2⇤ /k)
largeur de raie en absence d’´echange ;
⇤
EA kT = k298 exp RB
1 298
1 T
= ⇥A
⇥B
⇥⌅
-‐> Ea = 50,6kJ/mol
Fig. 2. Observed (a) and calculated (b) 188.3MHz 19F-n.m.r. spectra of 3',5'-difluoromethotrexate bound to L. casei dihydrofolate reductase. The sample contained slightly less than one molar equivalent of difluoromethotrexate, so that all the ligand is bound to the enzyme. The small sharp resonance marked X represents a small amount ( obs
= ff
f
+ fb
b
Robs = ff Rf + fb Rb
R2,obs
= pEL R2,EL + pL R2,L +
pEL p2L (
EL
2 L)
kof f
43
Characterization of dynamic processes in the spectral timescale Some methods to characterize conformational exchange
ms “Slow” intermediate exchange
fb ff
=
1/πΔν Coalescence
Cargèse 2013
Temperature variation µs “Fast” intermediate exchange
Vbound Vbound +Vf ree
fP L fP fP L R2obs (L) = R2 (L) + kon [P ] = R2 (L) + kof f fL R2obs (P L) = R2 (P L) + kof f R2obs (P ) = R2 (P ) + kon [L] = R2 (P ) + kof f
Carine van Heijenoort -‐ RMN et mouvements moléculaires
‣ R2 decreases when T increases ‣ kex increases when T increases R2obs = R2,T exp(Ew /Rb T ) + kT exp( Ek /Rb T ) Fig. 5. The temperature dependence of the linewidth of the N1-proton resonance of trimethoprim in its complex with dihydrofolate reductase, presented as an Arrhenius plot [ln (pi x linewidth) vs 1/T]. The points are experimental data, the error bars indicating the estimated maximum uncertainty in linewidth (+ 2 Hz). The line was calculated using the following parameters: W0 (273K)=32Hz; Ea(W0)=13 kJ/mole; kex(313K)=160s-1; Ea(exchange)=75 kJ/mole, where W0 is the natural linewidth (in the absence of exchange) and Ea denotes activation energy. (from Bevan et al. (1985), Eur. Biophys. J. 11, 211.
Changing protein or ligand concentration.
44
Characterization of dynamic processes in the spectral timescale Some methods to characterize conformational exchange ms “Slow” intermediate exchange
1/πΔν Coalescence
Cargèse 2013
µs “Fast” intermediate exchange
Titration : disappearance/appearance of peaks
Protein
DNA
DNA + Protein ⇆ DNA-‐protein Carine van Heijenoort -‐ RMN et mouvements moléculaires
Cerdan et al., FEBS 408, 235 (1997)
45
Characterization of dynamic processes in the spectral timescale Some methods to characterize conformational exchange
Cargèse 2013
ms “Slow” intermediate exchange
MAz (t) MBz (t)
a (t) = AA aBA (t)
t1
Vb (⌧m ) = xb e
τm
⌧m
aAB (t) aBB (t)
Coalescence
1/πΔν
µs
DNA + Protein ⇆ DNA-‐protein [DNA]/[Prot]=2
“Fast” intermediate exchange
MAz (0) MBz (0)
t2
cosh(D⌧m ) sinh(D⌧m ) D Vf (⌧m ) = xf e ⌧m cosh(D⌧m ) + sinh(D⌧m ) D k Vcrosspeak (⌧m ) = xb xf e ⌧m sinh(D⌧m ) D q 1 1 2 + x x k2 = (R1b + R1f ); = (R1b R1f ); D = b f 2 2 Carine van Heijenoort -‐ RMN et mouvements moléculaires
➫
kex=14±2Hz τex=74±7ms
Cerdan et al., FEBS 408, 235 (1997)
46
Characterization of dynamic processes in the spectral timescale Some methods to characterize conformational exchange
Cargèse 2013
1/πΔν
“Slow” intermediate exchange
µs
2D longitudinal magnetization exchange experiment (EXSY)
“Fast” intermediate exchange
Coalescence
ms
Diagonal Peaks
1
Cross Peaks
MAz (t) MBz (t)
( /2)
=
aAA (t) aBA (t)
( /2) 1
2
1 0 1
2
2
MAz (0) MBz (0)
k
Vb (⌧m ) = xb e
4 ⌧m
k
m
>2
3
t2
m
3
Cross Peaks k m 2
