paramagnetic effects in nmr - university of...
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Paramagnetic Effects in NMR –Outline and Useful References
• Relaxation by electron spins – distance mapping• Field induced orientation – RDC measurements• Pseudo-contact shifts – distance and angle data
• “Solution NMR of Paramagnetic Molecules” Bertini, Luchinat, Parigi, Elsevier, 2001
• “Useful review” Bertini, I., et al. (2002). Concepts in Magnetic Resonance 14: 259-286.
• “Lanthanide chelate tags” Ikegami, T., et al. (2004) J. Biomol. NMR 29:339-349.
• “Lanthanide peptide tags” Wohnert, J., et al. (2003) J. Am. Chem. Soc. 125:13338-13339.
Paramagnetic Centers Have Very High Magnetic Moments and Make Very Large
Susceptibility Contributions
For a single spin:µ = µBg (S(S+1))1/2 = γe(h/2π) (S(S+1))1/2
For spins undergoing rapid transitions:µeff = µB
2g2 S(S+1) B0 / (3kT)Susceptibility contributions for averaging spinsχm = µ0µB
2g2 S(S+1) / (6kT)Magnitudes about 2000 times that of protons
µB is the Bohr magneton (eh/(4πme))
There are Different Types of Paramagnetic Relaxation
Solomon Equations Give Electron-Nucleus Dipolar Relaxation
⎥⎥⎦
⎤
⎢⎢⎣
⎡
++
+++
++
−++
+⎟⎠⎞
⎜⎝⎛=
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+++
++
−++
⎟⎠⎞
⎜⎝⎛=
222222226
22220
2
2222226
22220
1
16
)(16
13
)(14)1(
4151
)(16
13
)(1)1(
4152
CS
C
CSI
C
CI
C
CSI
CC
BM
CSI
C
CI
C
CSI
CBM
rSSgR
rSSgR
τω
τ
τωω
τ
τω
τ
τωω
ττ
μγπμ
τωω
τ
τω
τ
τωω
τμγπμ
e-(S)
N (I)r
Form of Equation Depends on τC
τC-1 = τe
-1 + τm-1
When electron spin relaxation is fast compared to ωI:
eB
MM Tr
SSgRR 16
22220
21)1(
434 +
⎟⎠⎞
⎜⎝⎛==
μγπμ
Examples: S(J) τC(sec) S(J) τC (sec)
Mn2+ 5/2 10-8 Fe2+ (HS) 2 10-10
Fe3+ (LS) 1/2 10-12 Co2+ (HS) 3/2 10-12
Tb3+ 6 10-13 Gd3+ 7/2 10-9
Nitroxide radical – 1/2 ~10-7
Relaxation Enhancement can also Identify Interaction Sites.
Example: Galectin Interacting with LacNAc
NO.
OHONN
N
O
NO.
OO
Dhbt-OH
THF, DCC DMF, DIPEA
O
AcNHHOO
OH
O
OHHO
HO OH
NH2
O
AcNHHOO
OH
O
OHHO
HO OH
NHO N
CH3
CH3CH3
O.CH3
Synthesis of a Spin-Labeled N-acetyllactosamine
Curie Relaxation – Important at High Field
Even rapidly relaxing lanthanides cause relaxation.Excess population of lower spin states becomes significantThe effective moment is large and along the magnetic fieldMolecular tumbling modulates interaction with nucleiOnly R2 is significant for macromolecule τC= 10-8 and ω= 5x109
⎥⎥⎦
⎤
⎢⎢⎣
⎡
++
+⎟⎠⎞
⎜⎝⎛=
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+
+⎟⎠⎞
⎜⎝⎛=
2262
224420
220
2
2262
224420
220
1
13
4)3(
)1(45
1
13
)3()1(
451
CI
CC
BM
CI
CBM
rkTSSgB
R
rkTSSgB
R
τω
ττ
μγπμ
τω
τμγπμ
1H(I)
15N(S)90-x 180y 90y
90y
τ τ
t1/2 t1/2 τ τ decouple180x 90-x 180x
90-x 180x
t2
R2 for Amide protons can be Measured by Intensity Loss in HSQC Spectra
Proton magnetization is transverse for a total of 4τ in sequenceThis is about 10 ms – line with 30 Hz width looses 60% intensity
Relaxation while on nitrogen is 100 times less efficient
Dy3+-HN Distance Mapping from λPRE
• Paramagnetic relaxation enhancement can be approximated from intensity ratios.
• tr calculated from Stoke’s law.
)1
34()2(
)1()(Br1)
4(
51
222
2242
H
2
o
6
2
rH
rr
B
BJoPRE
TkJJg
τωττμγ
πμλ
++
+=
)ln(1
wl
nlPRE
II
t=λ
Nitin et al (2001), Protein Science, 10, 2393-2400Battiste and Wagner (2000), Biochemistry, 39, 5355-5365
15-20 Å
20-25 Å
Ln3+
Paramagnetic enhancement of spin relaxation:
Distance mappingover 30Å
Provides validation of assignmentsand limits class
sizesLanthanide -Tagged Hum-Q-15691
Paramagnetic Systems Give Other Complementary Information
Bertini, I., et al. (2002). Concepts in Magnetic Resonance 14: 259-286.
PCS=1
12πr3[Δχax(3cos2θ−1)−Δχrhsin2θcos2ϕ]
λPRE = 15
(μo
4π)2 1
r6Bo
2γH2 (gJμB)4J2(J+1)2
(2kBT)2(4τ r +
3τ r
1+ωH2 τr
2)
ηCCR = 1
30(μo
4π)2 Bo
2γH2 γΝh(gJμB)2J(J+1)
rNH3 kBT
(3cos2ϑ −1)
r3 (4τ r +3τ r
1+ωH2 τr
2)
RDC=1
120π 2
Bo2γHγΝhS2
rNH3 kBT
[Δχax(3cos2Θ−1)−Δχrhsin2Θcos2Φ]
RDCs can be Collected Without Alignment Media: Lanthanide Tagged Proteins:
Ln3+
χ1 χ2
χ3
Ikegami, T., et al. (2004) J. Biomol. NMR 29:339-349.Wohnert, J., et al. (2003) J. Am. Chem. Soc. 125:13338-13339.
Molecules in a Sufficiently High Magnetic Exhibit a Preferred Orientation
First Applications were to Diamagnetics
B0 W = (1/μ0)(-1/2)(B0•Χ•B0)
Bastiaan, Maclean, Van Zijl, Bothner-By, Ann. Rpts. NMR Spec., 19, 35-77 (1987)
Paramagnetics produce much larger effects:RDC = -(γγhB2)/(120π3r3kT) [½Δχ(3cos2θ-1) + ¾δχsin2θcosφ]
Note: B2 dependence
Pseudo-Contact Shifts Behave Like RDCsThese Provide Additional Orientation Data
and Distance ConstraintsThe pseudo-contact shift is due to the field from an induced dipole at the paramagnetic center. This field is given by:
B’ = u/r3 – 3r(u.r)/r5
We want just the field contribution in the direction of the applied field B0
v.B’ = v.u/r3 – 3v.r(u.r)/r5
= B0/(3r3 )(X11 + X22 + X33) + B0/r3 Σij Xij cosφi cosφj
The first term is the isotropic shift, the second is the anisotropic shift.The second term is the same form as the RDC term.
Sij = Xij (2B02/(15 u0 kT), Dmax = γ 15 u0 kT / (4π B0)