Dipolar Coupling and Solids NMR - University of ... Solid-state NMR of matrix metalloproteinase 12:...
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Dipolar Coupling and Solids NMR
13C CP-MAS, 30 mg cellulose, 9 min13C solution, sat’d glucose, 8 min
Liquids v. Solids One 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
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 coupling but 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
Other Anisotropies in NMR
H = HCSA + HD + HQ...
All share the following property: Solution: < 3 cos 2 θ '– 1 > = 0 Solids: (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 Y20(θ) = (3cos2(θ)–1)/2
• Y20(θ) can be transformed to another frame using Wigner Rotation elements: Y20(θ) = Σ2m=-2 D2m0(θ’’,φ’’) Y2m (θ’,φ’)
• D2m0(θ’’,φ’’) = (4π/5) Y2m (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) = 0
Dipolar couplings CSA = 0 Quadrupolar couplings
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)
What is this peak?
Spinning Sidebands are Frequently Seen
When rotation rate is not >> anisotropies Resonance position is modulated by rotation Sidebands at the spinning frequency are produced
There are tricks that remove these: TOSS – Total Suppression of Spinning Sidebands 180º pulses during rotor cycle dephases sideband magnetization but preserves center band magnetization
(9 minute spectra)
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
Rhodopsin • Absorbs light in visible
region • Binds retinal
Rhodopsin in simulated bilayer Theoretical and Computational Biophysics Group, Schulten Laboratory Univ. 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)
2D solid-state NMR spectra of uniformly 15N,13C-labeled Aβ1-40 amyloid 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.