Dipolar Coupling and Solids NMR

BCMB/CHEM 8190

13C CP-MAS, 30 mg cellulose, 9 min13C solution, sat’d glucose, 8 min

Liquids v. SolidsOne can collect similar spectra

but some tricks are required

The Classical Dipole-Dipole Interaction:

E = (μ0/4π)(( μ1· μ2)/r3 – 3(μ1· r)( μ2·r)/r5)

r = i rx + j ry + k rz = i r sinθcosφ + j r sinθsinφ + k r cosθ

μ1

μ2

rB0

θ

x y

zθ

φ

r

Quantum Mechanical Dipolar Coupling

μ = (γh/2π)(i Ix + j Iy + k Iz) = (γh/2π)f(Iz, I+,-)

HD = (μ0γ1γ2h2)/(16π3r3)(A + B + C + D + E + F)

A,B,C .. Grouped by type of operator, 0,1,2 Quantum

A = - Iz1Iz2(3cos2θ - 1), B = (1/4)(I+1I-2 + I-1I+2) (3cos2θ - 1)

………..

E = -(3/4)(I+1I+2)sin2θexp(-2iφ), F = ……..

To First Order Only Iz1Iz2 Term is Important

A doublet would result – much like scalar couplingbut large: as much as -60,000 Hz for a 13C-1H pair.

Splittings are angle dependent – ranging from -60,000 to +30,000. In a solid all possibilities superimpose: The result is a powder pattern

Points at 90º on a sphere are most abundant

D

Other Anisotropies in NMR

H = HCSA + HD + HQ...

All share the following property:Solution: < 3 cos 2 θ '– 1 > = 0Solids: (3 cos 2 θ ' – 1) ≠ 0

CSA powder pattern

Techniques in Solids NMR

• Cross Polarization (CP)

• Magic Angle Spinning (MAS)

• High power decoupling

Cross Polarization Improves Sensitivity

Magnetization transfer via dipolar coupling.

Hartman-Hahn:γIBI = γSBS

Magic Angle Spinning• All interactions can be written in terms of Y2

0(θ) = (3cos2(θ)–1)/2

• Y20(θ) can be transformed to another frame using Wigner Rotation

elements: Y20(θ) = Σ2

m=-2 D2m0(θ’’,φ’’) Y2

m (θ’,φ’)

• D2m0(θ’’,φ’’) = (4π/5) Y2

m (θ’’,φ’’)

• With rapid averaging over φ’’, all terms except Y20(θ’’) go to zero

• Selecting θ’’ = 54.7°, all interactions, regardless of θ’ value, are zero• (3cos2(θ)–1) = (3cos2(θ’)–1) <3cos2(54.7°)–1> = 0

Dipolar couplingsCSA = 0Quadrupolar couplings

Z

X Y

θ’θ’’

θφ’’

Bo

θ

100 MHz Spectrometer with HFC Transmission-Line Probe

• 100 MHz Spectrometer

High power decoupling

Solution 13C-1H J = ~125 Hz

Solid 13C-1H J + D = ~125 kHz

Cellulose(10 minute spectra)

13C

What is this peak?

Spinning Sidebands are Frequently Seen

When rotation rate is not >> anisotropiesResonance position is modulated by rotationSidebands at the spinning frequency are produced

There are tricks that remove these: TOSS – Total Suppression of Spinning Sidebands180º pulses during rotor cycle dephases sideband magnetization but preserves center band magnetization

Peptide1,2-13C2-Gly

(9 minute spectra)

Biomolecular Applications

Spider Silk

Nephila edulis

Nature as Engineer• Strongest fiber• β-sheet• Poly-Ala = crystalline• Poly-Gly = amorphous

Spider Silk and SS-NMR

• Torsion angle pairs to resolve backbone structure

• Ala in two different environments

• Dynamics

Ψ

Φ

Rhodopsin• Absorbs light in visible

region• Binds retinal

http://www.blackwellscience.com/matthews/rhodopsin.html

Rhodopsin in simulated bilayerTheoretical and Computational Biophysics Group,Schulten LaboratoryUniv. Illinois Urbana-Champaign

Antibiotics & bacterial growth

Schaefer Laboratory, Washington University, St. Louis, MO

New Solids NMR Assignment Strategies Parallel Solution Methods

Aliphatic region of the 13C,13C CP MAS PDSD of Zn-MMP-12 (16.4 T,11.5 kHz MAS frequency, 15 ms mixing time). (Balayssac, Oschkinat, 2007)

Annual Reviews

2D solid-state NMR spectra of uniformly 15N,13C-labeled Aβ1-40amyloid fibrils. (a) 2D 13C-13C NMR spectrum, obtained in a 14.1-T magnetic field with 13.6-kHz magic-angle spinning, using a 2.94-ms finite-pulse radio-frequency-driven recoupling (fpRFDR) sequence for spin polarization transfer in the mixing period. (b) 2D 15N-13C spectrum, obtained with frequency-selective 15N-13C cross-polarization followed by fpRFDR in the mixing period.

SOLIDS NMR REFERENCES

Ashida, J., Ohgo, K., Komatsu, K., Kubota, A., and Asakura, T. (2003). Determination of the torsion angles of alanine and glycine residues of model compounds of spider silk using solid-state NMR methods. J. Biomol. NMR 25, 91-103.

Kim, S.J., Cegelski, L., Studelska, D.R., O'Connor, R.D., Mehta, A.K., and Schaefer, J. (2002). Rotational-echo double resonance characterization of vancomycin binding sites in Staphylococcus aureus. Biochemistry 41, 6967-6977.

Grobner, G., Burnett, I.J., Glaubitz, C., Choi, G., Mason, A.J., and Watts, A. (2000). Observations of light-induced structural changes of retinal within rhodopsin. Nature 405, 810-813.

Solid-state NMR of matrix metalloproteinase 12: An approach complementary to solution NMR (2007) Balayssac S, Bertini I, Falber K, Oschkinat, H, et al. CHEMBIOCHEM 8 486-489.

Solid-State NMR Studies of Amyloid Fibril Structure (2011) Tycko R. Ann. Rev. Phys. Chem. 62, 279-299.

Recent contributions from solid-state NMR to membrane protein structure and function, Judge, PJ and Watts, A, (2011) Cur. Opin. Chem. Biol. 15, 690-695.