Paramagnetic liquid- and solid-state NMR
Guido Pintacuda Centre de RMN à Très Hauts Champs de Lyon Université de Lyon (France)
GERM NMR School - Cargese (Corsica) 16-23 March 2013
The periodic table ... a lot of paramagnetic ions
Diamagnetic and paramagnetic NMR
ZnII
FeII
Diamagnetic and paramagnetic NMR
ZnII
FeII
Diamagnetic and paramagnetic NMR
ZnII
FeII
Diamagnetic and paramagnetic NMR
ZnII
FeII
I. Paramagnetic shift
Coupled nuclear spins I=1/2 |
H = ⌦01 Iˆ1z + ⌦01 Iˆ1z + 2⇡J Iˆ1z Iˆ2z |
i
| i
⌦01 | ↵i
|↵i
no field, no coupling
Zeeman splitting of spin I1
⌦02
|↵↵i
⇡J
⌦02
⇡J + 2
⌦02
| ↵i
|↵ i Zeeman splitting of spin I2
i
|↵ i ⇡J 2
⌦01 |↵↵i
J-coupling
⌦02
⌦01
⇡J
⌦01
⇡J + 2
⌦
⇡J 2
NMR and EPR signals EPR
= 1.76 x 1011 rad s-1 T -1
NMR
(rad s-1 T -1) 1H 2H 13C 15N 31P
2.67 x 108 4.11 x 107 6.72 x 107 -2.71 x 107 1.08 x 108
263 GHz of electron Larmor frequency 400 MHz of 1H Larmor frequency
Coupled nuclear and electron spins I=S=1/2
H=
0ˆ ⌦I Iz
|↵ i |↵i
| i no field, no coupling
Zeeman splitting of spin S
|↵ i
|↵↵i
|
i
|
i
⌦0I
A + 2
| ↵i Zeeman splitting of spin I
⌦0S ⌦0I
⌦0I
A 2
A + 2
| ↵i
A + 2
⌦0S
⌦0S ⌦
A 2 |↵↵i
A
EPR
A + 2
⌦0I
⌦0S
hyperfine coupling
A
+ AIˆz Sˆz
A 2
⌦0S
NMR
⌦0I
0 ˆ ⌦ S Sz
A 2
⌦
Nuclear and electron relaxation times methyl protons of ethylbenzene Amide protons in proteins of 10 kDa in CDCl3 carboxyl carbon (~0.5s) CH protons in triolein 2 (10s) of glycines (0.7s) CH2 protons in proteins (44s) water protons of 10 kDa (~0.3s) (3s) 81
27
9
3
1
0.3
0.1
T1 (s)
T1e NO˙ (1/2)
Mn2+ Cu2+ (5/2) Gd3+ (1/2) (7/2)
Fe3+ (5/2)
10-7
10-8
10-10
10-9
T1e (s)
Ru3+ Fe2+ (5/2) Fe3+ Ln3+ (2) (1/2) (1/2-15/2)
10-11
10-12
10-13
Bertini and Luchinat, Coord. Chem. Rev. (1996)
Coupled nuclear and electron spins I=S=1/2 |↵ i |↵i
| i no field, no coupling
Zeeman splitting of spin S
|↵ i
|↵↵i
|
|
i
⌦0I
A + 2
| ↵i Zeeman splitting of spin I
A
⌦0S ⌦0I
⌦0I
A 2
A + 2
| ↵i
A + 2
⌦0S
⌦0S ⌦
A 2 |↵↵i
A
EPR
A + 2
⌦0S
hyperfine coupling
NMR
⌦0I
A 2
⌦0S
i
⌦0I
A 2
⌦
Coupled nuclear and electron spins I=S=1/2 |↵ i |↵i
| i no field, no coupling
Zeeman splitting of spin S
|↵ i
|↵↵i
|
|
i
⌦0I
A + 2
| ↵i Zeeman splitting of spin I
⌦0S ⌦0I
⌦0I
A 2
A + 2
| ↵i
A + 2
⌦0S
⌦0S ⌦
A 2 |↵↵i
A
EPR
A + 2
⌦0S
hyperfine coupling
NMR
⌦0I
A 2
⌦0S
i
⌦0I
A 2
⌦
Curie spin hSz i µS =
ES,MS =
e hSz i
= B0 ⇢ X ES,MS MS exp kB T MS ⇢ hSz i = X ES,MS exp kB T hSz i =
MS
+1/2 1/2 3/2
hS, MS |Sz |S, MS i exp X MS
for
exp
⇢
MS +3/2
E
MS
X
g e µ B B 0 MS
⇢
ES,MS kB T
ES,MS kB T hSz i =
g e µB B0 S(S + 1) 3kT
B0
Fermi contact shift |↵ i |↵i
| i no field, no coupling
Zeeman splitting of spin S
|↵ i
|↵↵i
|
| ↵i Zeeman splitting of spin I
hyperfine coupling
NMR
⌦0I
A + 2
⌦0I
⌦0I
A 2
⌦0S
i
A 2
⌦
⌦0I
|
i
⌦0I
A + 2
⌦0S | ↵i
A 2 |↵↵i A + 2
Fermi contact shift |↵ i |↵i
| i no field, no coupling
Zeeman splitting of spin S
|↵ i
|↵↵i
|
| ↵i Zeeman splitting of spin I
hyperfine coupling
NMR
⌦0I
A + 2
⌦0I
⌦0I
A 2
⌦0S
i
A 2
⌦
⌦0I
|
i
⌦0I
A + 2
⌦0S | ↵i
A 2 |↵↵i A + 2
Classical description: magnetic susceptibility magnetization per unit volume for NA particles molar susceptibility
volume susceptibility average magnetic moment per particle
Classical description: magnetic susceptibility volume susceptibility
magnetization per unit volume
average magnetic moment per particle
for NA particles molar susceptibility
hµi =
µB ge hSz i M
=
hSz i =
2 2 S(S µ 0 NA µ B g e
g e µB B0 S(S + 1) 3kT
+ 1) 3kT
Classical description: magnetic susceptibility volume susceptibility
magnetization per unit volume
average magnetic moment per particle
for NA particles molar susceptibility
hµi =
µB ge hSz i M
=
hSz i =
2 2 S(S µ 0 NA µ B g e
g e µB B0 S(S + 1) 3kT
+ 1) 3kT
Paramagnetism and NMR Unpaired electron spins - Hyperfine Hamiltonian
N
Spin-delocalization on the nucleus
N
Long-range dipolar interaction
Fermi contact shift
frontier metal 3d orbitals
Fermi contact shift
frontier metal 3d orbitals
Fermi contact shift
ZnII
FeII
Fermi contact shift
ZnII
FeII
Fermi contact shift
ZnII
FeII
Fermi contact shift
H5/7
H10/14
H11/13
H2
H9
H6
Fermi contact shift
H5/7
H10/14
H11/13
H2
H9
H6
Fermi contact shift
iron-sulfur proteins
unpaired electron spin density on cysteine 1Hbeta nuclei is a function of the ligand orientation
Fe
H S
C
Bertini, Capozzi, Luchinat, Piccioli, Vila, J. Am. Chem. Soc., 1994
Fermi contact shift
Methyl protons in histidine cytochromes (Low spin Fe(III))
unpaired electron spin density on heme nuclei is a function of axial ligand orientation
I. Bertini, C. Luchinat, G. Parigi, F.A. Walker, JBIC 1999
Paramagnetism and NMR Unpaired electron spins - Hyperfine Hamiltonian
N
Spin-delocalization on the nucleus
N
Long-range dipolar interaction
Electron-nucleus dipolar coupling Magnetic susceptibility
the dipolar coupling with the average Curie spin results in an axial traceless shielding tensor DSA
r
Hyperfine dipolar shift
dipolar interaction
dipolar shift anisotropy 1
r3 ⇤iso ⇥= 2 r3
(a)
Anisotropic magnetic susceptibility If the electron orbital magnetic moment contribution is considered, the total magnetic moment and hence the magnetic susceptibility becomes anisotropic. In systems that are orbitally non-degenerate, the anisotropy can be adequately represented by an anisotropy of the g factor. A g tensor is thus introduced, with values gkk for any direction kk of the magnetic field, so that:
the induced moment, and thus the susceptibility, becomes a rank-2 tensor:
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless any more !
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless any more !
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless any more !
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless ay more !
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless ay more !
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless ay more !
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless ay more !
Electron-nucleus dipolar coupling pseudocontact shift
the paramagnetic dipolar shielding tensor is not traceless ay more !
Electron-nucleus dipolar coupling pseudocontact shift
pc
1 = 12⇤r3
r
⌅ax (3 cos ⇥ 2
3 1) + ⌅rh sin2 ⇥ cos 2⇧ 2
⇥
Electron-nucleus dipolar coupling pseudocontact shift pc
1 = 12⇤r3
⌅ax (3 cos ⇥ 2
axial
r
3 1) + ⌅rh sin2 ⇥ cos 2⇧ 2
⇥
totally rhombic
Pseudocontact shifts Paramagnetic metals - d transition
Pseudocontact shifts Paramagnetic metals - f transition
Electron-nucleus dipolar coupling pseudocontact shift
Yb-DOTA
Electron-nucleus dipolar coupling pseudocontact shift
Yb-DOTA
Electron-nucleus dipolar coupling
Dy-ℇ
pseudocontact shift pc
1 = 12⇤r3
⌅ax (3 cos ⇥ 2
3 1) + ⌅rh sin2 ⇥ cos 2⇧ 2
⇥ r
15N-
ε
Dy3+
15N-
ε
Dy3+
15N-Leu
ε
Dy3+
PCS for structural refinement
Solution structure of M80A cytochrome c-CN
NOE only
NOE + 280 pcs values
Banci, Bertini, Bren, Cremonini, Gray, Luchinat, Turano JBIC 1, 117 (1996)
Hyperfine dipolar shift
dipolar interaction
dipolar shift anisotropy 1
r3 ⇤iso ⇥= 2 r3
(a)
Hyperfine dipolar coupling pseudocontact shift B0
Magic Angle Spinning (MAS)
54.7
(a) 1)
(b)
pc
=
1 12⇤r3
⌅ax (3 cos2 ⇥
1) +
3 ⌅rh sin2 ⇥ cos 2⇧ 2
⇥
Paramagnetic solids: large offsets and large shift anisotropies (SAs)
O i
Pr
N i
Cl Pr
O
N
Fe Fe
Cl i Pr
O
N
i
Pr
O O
Yb Yb
3- 3Na+
O O
N
O
O O
N
Tb Tb
rsion
400
200 0 S=2
O
N O O
O
J=5/2 200 0
-
200 D(1H)/ppm
O O
N
O O O
O
N O O
3- 3Cs+
-
200 D(1H)/ppm
O
O
J=15/2 600 400
800
100
100
100
80
80
80
200
0
-200
D(1H)/ppm
-400
-
PCS for structural refinement ZnII-SOD CoII-SOD
Co(II)
2 mg, 1-2 h
Knight, Felli, Gonnelli, Pierattelli, Bertini, Emsley, Herrmann and Pintacuda, J. Am. Chem. Soc. 2012, 134, 14730.
Ultra-fast MAS, 1H detection and pseudocontact shifts
257 non-trivial 1H-1H distances 260 dihedral angle restraints
without PCSs RMSD to mean 2.90 Å
with PCSs RMSD to mean 1.70 Å
445 CoII PCS (111 1H, 223 13C, 111 15N)
Knight, Felli, Gonnelli, Pierattelli, Bertini, Emsley, Herrmann and Pintacuda, J. Am. Chem. Soc. 2012, 134, 14730.
Ultra-fast MAS, 1H detection and pseudocontact shifts
257 non-trivial 1H-1H distances 260 dihedral angle restraints
without PCSs RMSD to mean 2.90 Å
a
Fitted PCS (ppm)
0
H CA CO 0 Observed PCS (ppm)
b
Fitted PCS (ppm)
0
445 CoII PCS (111 1H, 223 13C, 111 15N)
Knight, Felli, Gonnelli, Pierattelli, Bertini, Emsley, Herrmann and Pintacuda, J. Am. Chem. Soc. 2012, 134, 14730.
with PCSs RMSD to mean 1.70 Å
Ultra-fast MAS, 1H detection and pseudocontact shifts
257 non-trivial 1H-1H distances 260 dihedral angle restraints
without PCSs RMSD to mean 2.90 Å
a
Fitted PCS (ppm)
0
H CA CO 0 Observed PCS (ppm)
b
Fitted PCS (ppm)
0
445 CoII PCS (111 1H, 223 13C, 111 15N)
Knight, Felli, Gonnelli, Pierattelli, Bertini, Emsley, Herrmann and Pintacuda, J. Am. Chem. Soc. 2012, 134, 14730.
with PCSs RMSD to mean 1.70 Å
Why NMR of Paramagnetic Proteins? Many proteins binds paramagnetic metals (cytochrome c, ferritin, Cu-binding proteins, Mn-binding proteins…)
Paramagnetic metals can be introduced in metalloproteins by replacing diamagnetic metals
(Ca2+ binding proteins, Zn2+-binding proteins,…)
Paramagnetic metals can be introduced in any protein using suitably designed paramagnetic tags
(Schwalbe, Imperiali, Ubbink, Otting, Griesinger,…)
Paramagnetic labelling Introduction of a paramagnetic metal ion into a protein
Su and Otting, J. Biomol. NMR, 2010
Pseudocontact shifts Paramagnetic metals - f transition
Protein-protein interactions pseudocontact shift θ 15N-
ε
Dy3+
15N-
θ ε Dy3+
Protein-protein interactions pseudocontact shift θ 15N-
ε
Dy3+
15N-
θ ε Dy3+
Protein-protein interactions pseudocontact shift θ 15N-
ε
Dy3+
15N-
θ ε Dy3+
Protein-protein interactions pseudocontact shift θ 15N-
ε
Dy3+
15N-
θ ε Dy3+
Protein-protein interactions pseudocontact shift θ 15N-
ε
Dy3+
15N-
θ ε Dy3+
Protein-protein interactions pseudocontact shift
G. Pintacuda, M. A. Keniry, T. Huber, A.-Y. Park, N. E. Dixon and G. Otting J. Am. Chem. Soc., 2004, 126, 2963-2970. G. Pintacuda, M. A. Keniry, E. Owen, A.-Y. Park, N. E. Dixon and G. Otting J. Am. Chem. Soc., 2006, 128, 3696-3702. M. A. Keniry, A.-Y. Park, E. A. Owen, S. M. Hamdan, G. Pintacuda, G. Otting and N. E. Dixon J. Bacteriol., 2006, 188, 4464-4473.
II. Paramagnetic relaxation enhancement
Paramagnetic relaxation enhancement Solomon mechanism
N
N
Paramagnetic relaxation enhancement Solomon mechanism
N
N
Paramagnetic relaxation enhancement Solomon mechanism
N
N
spatial part interaction constant x Wigner matrices
spin part rank-2 irreducible spin tensor operators
Paramagnetic relaxation enhancement Solomon mechanism
N
N
spatial part interaction constant x Wigner matrices
spin part rank-2 irreducible spin tensor operators
correlation function
how much of the spatial part of the interaction tensor changes during .
Paramagnetic relaxation enhancement Solomon mechanism
N
correlation function
N
how much of the spatial part of the interaction tensor changes during .
Paramagnetic relaxation enhancement Solomon mechanism
Paramagnetic relaxation enhancement Solomon mechanism
spectral density function
how much of magnetic noise is available at the required frequencies
Paramagnetic relaxation enhancement Solomon mechanism
|↵ i |↵↵i |
i
| ↵i
Paramagnetic relaxation enhancement Solomon mechanism
R1 and R2 enhancements for different paramagnetic centers
Ru3+ Ln3+ Fe3+ (5/2) Fe2+ (1/2-15/2) (1/2) (2)
10-13
10-12
10-11
Fe3+ (5/2)
10-10
Mn2+ Cu2+ (1/2) Gd3+ (5/2) (7/2)
NO˙ (1/2)
10-9
10-7
10-8
Bertini and Luchinat, Coord. Chem. Rev. (1996)
R1 and R2 enhancements for different paramagnetic centers 107
S=1/2
105 103 101 10-1 13 12 11 10
Ru3+ Ln3+ Fe3+ (5/2) Fe2+ (1/2-15/2) (1/2) (2)
10-13
10-12
10-11
9
Fe3+ (5/2)
10-10
8
7
Mn2+ Cu2+ (1/2) Gd3+ (5/2) (7/2)
NO˙ (1/2)
10-9
10-7
10-8
Bertini and Luchinat, Coord. Chem. Rev. (1996)
Paramagnetic relaxation enhancement Bloembergen mechanism
contact coupling between nuclear and electron spins
|↵ i |↵↵i |
i
| ↵i
Reduced vs oxidized Cu-SOD Cu(II)/Cu(I) Zn(II)
Cu(I),Zn-SOD S=0
Cu(II),Zn-SOD S=1/2
Site-specific 15N T1s A
ϕ1
H
1
x CP y
y x
CP
N
15
Giraud et al. JACS 2005, 127, 18190
ϕ2 τrelax
slTPPM
x
t1
ϕ3
τsat
Cu(I)-SOD S=0
CP
Cu(II)-SOD S=1/2
ϕ4 CP WALTZ-16
x C
13
WALTZ-16
B
ϕ1
H
1
y
x CP
slTPPM
y N
15
CP
ϕ3
x
τspinlock
t1
τsat
CP
ϕ4 CP WALTZ-16
x C
13
C 1
ϕ5
136y (CuI)+116
WALTZ-16
(CuII)
ϕ4
relaxation rates - 2x2.5 days of experimental time!
Site-specific
C
ϕ5
H
1
13CO
slTPPM
x
y 15
CP
C
13
D
ϕ1
H
1
x CP y
N
15
ϕ6
y
x
T1s at ultra-fast MAS ϕ4
y CP
N
Lewandowski et al. JACS 2010, 132, 8252
CP
τrelax
CP
t1
ϕ3
Cu(I)-SOD S=0
CP
Cu(II)-SOD S=1/2
y
τsat CP WALTZ-16
x
x CP
WALTZ-16
y slTPPM
ϕ3
x
t1
τsat
CP
ϕ4 CP WALTZ-16
x C
13
WALTZ-16
136 (CuI)+116 (CuII) relaxation rates - 2x3.5 days of experimental time!
Oxidized vs reduced Cu-SOD Paramagnetic relaxation enhancements Jaroniec et al. JACS 2008, JACS 2009
PRE
R1
=k
(
e N ~)
2
S(S + 1)
6 reN
⇥e 1 + (⇤N ⇥e )2
Paramagnetic relaxation enhancements Long-range structural constraints
without PREs
RMSD to mean 2.9 Å
with PREs
RMSD to mean 1.6 Å
Knight, Pell, Bertini, Felli, Gonnelli, Pierattelli, Herrmann, Emsley and Pintacuda, Proc. Natl. Acad. Sci. USA 2012, 109, 28,11095-11100.
Paramagnetic relaxation enhancement Curie mechanism
dipolar coupling between nuclear and average Curie spin r
|↵ i |↵↵i |
i
| ↵i
Paramagnetic relaxation enhancement Curie mechanism
R1 and R2 enhancements for different paramagnetic centers 107
S=1/2
105 103 101 10-1 13 12 11 10
Ru3+ Ln3+ Fe3+ (5/2) Fe2+ (1/2-15/2) (1/2) (2)
10-13
10-12
10-11
Fe3+ (5/2)
10-10
9
8
7
Mn2+ Cu2+ (1/2) Gd3+ (5/2) (7/2)
NO˙ (1/2)
10-9
10-7
10-8
Bertini and Luchinat, Coord. Chem. Rev. (1996)
Paramagnetic relaxation enhancement Curie mechanism
R1 and R2 enhancements for different paramagnetic centers 105
Dy3+
Cu2+
NO˙
103 101 10-1 10-3 = 5·10-13 13
12
11
= 3·10-9
J=15/2 10
9
8
7
13
Ru3+ Ln3+ Fe3+ (5/2) Fe2+ (1/2-15/2) (1/2) (2)
10-13
10-12
10-11
12
11
10
Fe3+ (5/2)
10-10
~ 10-7
S=1/2 9
8
7
13
12
11
S=1/2 10
9
Mn2+ Cu2+ (1/2) Gd3+ (5/2) (7/2)
NO˙ (1/2)
10-9
10-7
10-8
8
7
Bertini and Luchinat, Coord. Chem. Rev. (1996)
Paramagnetism and NMR Fast and slow-relaxing paramagnetic metals - d transition
Paramagnetism and NMR Fast and slow-relaxing paramagnetic metals - f transition
Slow and fast relaxing metal ions Cu(II)/Cu(I)
Zn(II)
Slow and fast relaxing metal ions Co(II)
Ultra-fast MAS, 1H detection and paramagnetic effects
Knight, Felli, Pierattelli, Emsley and Pintacuda, Acc. Chem. Res.. 2013, in press.
Ultra-fast MAS, 1H detection and paramagnetic effects
with PREs
with PCSs
Knight, Felli, Pierattelli, Emsley and Pintacuda, Acc. Chem. Res.. 2013, in press.
with PCSs and PREs
Gwendal Kervern (Nancy) Michael J. Knight Alessandro Marchetti Anne Lesage Andrew J. Pell Emeline Barbet-Massin Lyndon Emsley Stefan Jehle Michele Felletti Torsten Herrmann Hugh W. Dannatt Chiara Ferrara Moreno Lelli Amy L. Webber Raphaele J. Clement
FP7-PEOPLE-2012-ITN
pNMR Pushing the Envelope of Nuclear Magnetic Resonance Spectroscopy for Paramagnetic Systems. A Combined Experimental and Theoretical Approach
www.pnmr.eu
