Dipolar Coupling and Solids NMR

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

Techniques in Solids NMR

• Cross Polarization (CP)

• Magic Angle Spinning (MAS)

• High power decoupling

Cross Polarization

Magnetization transfer via dipolar coupling.

Hartman-Hahn:γIBI = γSBS

Magic Angle SpinningMagic Angle Rotation of Solids:

(3 cos 2 θ ' – 1) < 3 cos 2 θ – 1> = 0θ = 54.7°

Dipolar couplingsCSAQuadrupolar couplings

0 ~

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

Spinning Sidebands are Frequently Seen

When rotation rate is not >> anisotropiesResonance postion 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

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 (AGG)(10) using solid-state NMR methods. Journal of Biomolecular 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.

Smith, S.O., Aschheim, K., and Groesbeek, M. (1996). Magic angle spinning NMR spectroscopy of membrane proteins. Quarterly Reviews of Biophysics 29, 395-449.