Paramagnetic Effects in NMR

BCMB/CHEM 8190April 20, 2005

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

Change in 15N HSQC spectrum (800 MHz)of Galectin-3 upon addition of LacNac-TEMPO

0 mM 10 mM

X-Ray crystal structure of Galectin-3 (Seetharamana et al. 1998)

E184

R186

E165

A245

K227

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

TROSY-HSQC correlations give RDC data.900 MHz Field-Induced Alignment

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)

Comparison of Lu3+ and Dy3+ Complexes of Tagged Q15691 gives Pseudo-Contact Shifts

CharacteristicDiagonal shifts