Paramagnetic Effects in NMR BCMB/CHEM 8190 April 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 = µB2g2 S(S+1) B0 / (3kT) Susceptibility contributions for averaging spins χm = µ0µB2g2 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 r

N (I)

e-(S) 2 2 ⎤ 3τC 6τC τC 2 ⎛ μ0 ⎞ γ2g2μB S(S +1) ⎡ R1M = ⎜ ⎟ + + ⎢ 6 2 2 2 2⎥ 2 2 15⎝ 4π⎠ r 1 ( ) 1 1 ( ) ω ω τ ω τ ω ω τ + − + + + ⎥ I S C I C I S C ⎦ ⎣⎢

2 2 3τC 6τC 6τC ⎤ τC 1 ⎛ μ0 ⎞ γ2g2μB S(S +1) ⎡ R2M = ⎜ ⎟ + + + ⎢4τC + 6 2 2 2 2 2 2⎥ 2 2 15⎝ 4π⎠ r 1+ (ωI − ωS ) τC 1+ ωI τC 1+ (ωI + ωS ) τC 1+ ωS τC ⎥⎦ ⎢⎣

Form of Equation Depends on τC τC-1 = τe-1 + τm-1 When electron spin relaxation is fast compared to ωI:

4 ⎛ μ0 ⎞ γ g μB S(S +1) R1M = R2M = ⎜ ⎟ T1e 6 3 ⎝ 4π⎠ r 2

Examples:

S(J)

2 2

τC(sec)

Mn2+ 5/2 10-8 Fe2+ (HS) Fe3+ (LS) 1/2 10-12 Co2+ (HS) Tb3+ 6 10-13 Gd3+ Nitroxide radical –

2

S(J)

τC (sec)

2 3/2 7/2 1/2

10-10 10-12 10-9 ~10-7

Relaxation Enhancement can also Identify Interaction Sites. Example: Galectin Interacting with LacNAc

Synthesis of a Spin-Labeled N-acetyllactosamine

O

OH

N O N

O

.

HO HO

O OH

O HO

OH O AcNH

HO HO

N O

.

THF, DCC

OH

OH O

Dhbt-OH N O

N

DMF, DIPEA CH3

CH3

NH O

O OH

O HO

CH3 N CH O 3

.

OH O AcNH

NH2

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

E165

R186

K227

A245

Curie Relaxation – Important at High Field Even rapidly relaxing lanthanides cause relaxation. Excess population of lower spin states becomes significant The effective moment is large and along the magnetic field Molecular tumbling modulates interaction with nuclei Only R2 is significant for macromolecule τC= 10-8 and ω= 5x109

R1M

1 ⎛ μ 0 ⎞ γ 2 B02 g 4μ B S 2 (S + 1) 2 = ⎜ ⎟ 5 ⎝ 4π ⎠ (3kT) 2 r 6

⎡ 3τC ⎤ ⎢ 2 2⎥ ⎣⎢1 + ωI τC ⎦⎥

R 2M

1 ⎛ μ 0 ⎞ γ 2 B02 g 4μ B S 2 (S + 1) 2 = ⎜ ⎟ 5 ⎝ 4π ⎠ (3kT) 2 r 6

⎡ 3τC ⎤ ⎢4τC + 2 2⎥ 1 + ωI τC ⎥⎦ ⎢⎣

2

2

4

4

R2 for Amide protons can be Measured by Intensity Loss in HSQC Spectra

1H(I)

τ 90-x

τ 180y

t2 180x

90y t1/2

15N(S)

90y

90-x t1/2 90-x

τ

180x

τ

decouple

180x

Proton magnetization is transverse for a total of 4τ in sequence This 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 λ

PRE

3τ 1 μ 1 B γ ( g μ ) J ( J + 1) (4τ + ) = ( ) 1+ ω τ 5 4π r ( 2k T ) o

2

2

2

o

H

4

J

2

2

B

r

6

r

2

B

2

2

H

r

• Paramagnetic relaxation enhancement can be approximated from intensity ratios. • tr calculated from Stoke’s law.

λ

PRE

1 I = ln( ) t I nl

wl

Nitin et al (2001), Protein Science, 10, 2393-2400 Battiste and Wagner (2000), Biochemistry, 39, 5355-5365

Paramagnetic enhancement of spin relaxation:

20-25 Å

15-20 Å

Ln3+

Distance mapping over 30Å Provides validation of assignments and limits class sizes

Lanthanide -Tagged Hum-Q-15691

Paramagnetic Systems Give Other Complementary Information Bertini, I., et al. (2002). Concepts in Magnetic Resonance 14: 259-286.

1 2 2 [Δ χ (3cos θ −1) − Δ χ sin θ cos2ϕ] PCS= ax rh 3 12πr 4 2 2 2 2 μ 1 B γ (g μ ) J (J +1) 1 3τ r PRE o 2 o H J B λ = ( ) 6 (4τ r + ) 2 2 2 5 4π r (2kBT) 1+ ω Hτr 1 μo 2 Boγ Hγ Νh(gJ μB ) J(J +1) (3cos ϑ −1) 3τ r CCR η = ( ) (4τ r + ) 3 3 2 2 rNHkBT r 1+ ω Hτr 30 4π 2 2

2

2

1 B2oγ Hγ ΝhS2 2 2 RDC= [Δ χ (3cos Θ−1) − Δ χ sin Θcos2Φ] 2 ax rh 3 120π rNHkBT

RDCs can be Collected Without Alignment Media: Lanthanide Tagged Proteins: χ3 Ln3+ χ1

χ2

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 RDCs These Provide Additional Orientation Data and Distance Constraints The 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

Characteristic Diagonal shifts