The National Institute of Diabetes & Digestive & Kidney Diseases

Dr. Tycko received the American Physical Society's Earle K. Plyler Prize for Molecular Spectroscopy in 2005, and is a Fellow of the American Physical Society and the American Association for the Advancement of Science. He received an NIH Director's Award in 2001, and was the Norman Hascoe Distinguished Lecturer (University of Connecticut, 2001), the Max T. Rogers Distinguished Lecturer (Michigan State University, 2003), and the R.W. Vaughan Lecturer (Rocky Mountain Conference on Analytical Chemistry, 2004). Dr. Tycko has served on the editorial boards of the Journal of Chemical Physics, the Journal of Magnetic Resonance, the Journal of Biomolecular NMR, and Molecular Physics. He chaired the Gordon Research Conference on Magnetic Resonance in 2001.

We are pursuing the development of solid state nuclear magnetic resonance (NMR) methods for structural studies of biopolymers and the application of these methods to problems in biophysical chemistry and structural biology. Solid state NMR methods can provide local structural information at atomic-level detail in systems that cannot be characterized by other structural methods, including x-ray diffraction and liquid state NMR. Examples of such systems include peptides and proteins that associate with biological membranes, amyloid fibrils and other noncrystalline aggregates, and frozen solutions of biopolymers with molecular weights in excess of 100 kD. The field of biomolecular solid state NMR is at a relatively early stage of development. As a result, our work tends to be highly exploratory and interdisciplinary, drawing heavily on experimental and theoretical techniques of the physical, as well as biological, sciences. Some ongoing projects include the following:

1. Development of general solid state NMR methods for structural characterization of peptides and proteins. Techniques developed in our group have been applied successfully in studies of HIV-related peptide/antibody complexes, amyloid fibrils associated with Alzheimer's disease, and other systems. Of particular interest recently are techniques for measuring specific interatomic distances and specific dihedral angles in samples that contain multiple uniformly 15N,13C-labeled residues. We are also interested in techniques for sensitivity enhancement in solid state NMR, including indirect detection methods, hyperpolarization methods, and low-temperature solid state NMR technology.

2. Structural studies of amyloid fibrils. Due to the involvement of amyloid fibrils in amyloid diseases and the recent realization that amyloid fibril formation is a common property of polypeptides with diverse amino acid sequences, these systems are of great current interest in both the biomedical and the biophysical research communities. We have shown that solid state NMR methods are uniquely capable of providing structural constraints on amyloid fibrils, which are inherently noncrystalline and insoluble. We have developed the first experimentally-based molecular structural models for fibrils formed by the beta-amyloid peptide associated with Alzheimer's disease. Current work is directed at refinement and extensions of these structural models, investigations of the structures of amyloid fibrils associated with type 2 diabetes and yeast prions, and structural characterization of amyloid fibrils that form in vivo.

3. Solid state NMR investigations of protein folding. Although the highly ordered, folded structures of thousands of proteins have been determined to high resolution by x-ray crystallography and liquid state NMR methods, relatively little is known about the structures and structural distributions of proteins in their unfolded states. The structural properties of unfolded and partially folded proteins are important as determinants of folding kinetics and thermodynamics, and as factors that affect protein aggregation in amyloid diseases. We are exploring the use of solid state NMR in conjunction with freeze-quenching as an approach to site-specific, quantitative characterization of unfolded and partially folded proteins. Initial results indicate that site-specific variations in conformational distributions and in folding equilibria are readily apparent in solid state NMR data.

4. Solid state NMR studies of membrane proteins. We are currently investigating the molecular structure of the HIV-1 Vpu protein, a relatively small transmembrane protein involved in the HIV-1 life cycle, with the goal of understanding how its structure and oligomerization state affect its biological function and its in vitro ion channel activity. We have also carried out studies of peptide/antibody complexes associated with AIDS, motivated in part by their utility as model systems for membrane-associated peptide/receptor complexes. As methods for producing micromole-scale quantities of membrane proteins improve, and as the sensitivity of solid state NMR measurements improves, studies of the structure, function, and interactions of membrane proteins by solid state NMR will accelerate.

5. Optical pumping and dynamic nuclear polarization solid state NMR. In certain materials, notably III-V semiconductors such as gallium arsenide and indium phosphide, irradiation with light at low temperatures produces enormous enhancements of nuclear spin polarizations and hence enormous enhancements of NMR signals. We are interested in understanding the physical mechanisms and exploring the generality of these optical pumping effects, with the goal of developing optical pumping methods that are useful in structural studies of organic and biological systems.  In other systems, such as frozen solutions containing paramagnetic species, nuclear spin polarizations can be enhanced by irradiation of electron spin resonances, an effect called dynamic nuclear polarization.  We are currently constructing novel equipment for dynamic nuclear polarization experiments at low temperatures and high magnetic fields.

1.   R. B. Wickner, F. Dyda, and R. Tycko, "Amyloid of Rnq1p, the basis of the [PIN+] prion, has a parallel in-register beta-sheet structure", Proc. Natl. Acad. Sci. U. S. A. 105 , 2403-2408 (2008).

2.  R. Tycko, "Theory of stochastic dipolar recoupling in solid state nuclear magnetic resonance", J. Phys. Chem. B 112, 6114-6121 (2008).

3.  K. R. Thurber and R. Tycko, "Biomolecular solid state NMR with magic-angle spinning at 25 K", J. Magn. Reson. 195, 179-186 (2008).

4.  A. K. Paravastu, R. D. Leapman, W. M. Yau, and R. Tycko, "Molecular structural basis for polymorphism in Alzheimer's beta-amyloid fibrils", Proc. Natl. Acad. Sci. U. S. A. 105, 18349-18354 (2008).

5.  R. Tycko, "Symmetry-based constant-time homonuclear dipolar recoupling in solid state NMR", J. Chem. Phys. 126 (2007).

6.  R. Tycko, "Stochastic dipolar recoupling in nuclear magnetic resonance of solids", Phys. Rev. Lett. 99 (2007).

7.  S. Luca, W. M. Yau, R. Leapman, and R. Tycko, "Peptide conformation and supramolecular organization in amylin fibrils: Constraints from solid state NMR", Biochemistry 46, 13505-13522 (2007).

8.  R. H. Havlin, F. J. Blanco, and R. Tycko, "Constraints on protein structure in HIV-1 Rev and Rev-RNA supramolecular assemblies from two-dimensional solid state nuclear magnetic resonance", Biochemistry 46, 3586-3593 (2007).

9.  U. Baxa, R. B. Wickner, A. C. Steven, D. E. Anderson, L. N. Marekov, W. M. Yau, and R. Tycko, "Characterization of beta-sheet structure in Ure2p(1-89) yeast prion fibrils by solid state nuclear magnetic resonance", Biochemistry 46, 13149-13162 (2007).

10.  R. Tycko, "Molecular structure of amyloid fibrils: Insights from solid state NMR", Q. Rev. Biophys. 39, 1-55 (2006).

11.  F. Shewmaker, R. B. Wickner, and R. Tycko, "Amyloid of the prion domain of Sup35p has an in-register parallel beta-sheet structure", Proc. Natl. Acad. Sci. U. S. A. 103, 19754-19759 (2006).

12.  S. Sharpe, W. M. Yau, and R. Tycko, "Structure and dynamics of the HIV-1 Vpu transmembrane domain revealed by solid state NMR with magic-angle spinning", Biochemistry 45, 918-933 (2006).

13.  A. T. Petkova, W. M. Yau, and R. Tycko, "Experimental constraints on quaternary structure in Alzheimer's beta-amyloid fibrils", Biochemistry 45, 498-512 (2006).

14.  A. K. Paravastu and R. Tycko, "Frequency-selective homonuclear dipolar recoupling in solid state NMR", J. Chem. Phys. 124 (2006).

15.  A. T. Petkova, R. D. Leapman, Z. H. Guo, W. M. Yau, M. P. Mattson, and R. Tycko, "Self-propagating, molecular-level polymorphism in Alzheimer's beta-amyloid fibrils", Science 307, 262-265 (2005).

16.  R. H. Havlin and R. Tycko, "Probing site-specific conformational distributions in protein folding with solid state NMR", Proc. Natl. Acad. Sci. U. S. A. 102, 3284-3289 (2005).

17.  J. C. C. Chan, N. A. Oyler, W. M. Yau, and R. Tycko, "Parallel beta-sheets and polar zippers in amyloid fibrils formed by residues 10-39 of the yeast prion protein Ure2p", Biochemistry 44, 10669-10680 (2005).

18.  R. Tycko, "Sensitivity enhancement in two-dimensional solid state NMR spectroscopy by transverse mixing", ChemPhysChem 5, 863-868 (2004).

19.  S. Sharpe, N. Kessler, J. A. Anglister, W. M. Yau, and R. Tycko, "Solid state NMR yields structural constraints on the V3 loop from HIV-1 gp120 bound to the 447-52d antibody Fv fragment", J. Am. Chem. Soc. 126, 4979-4990 (2004).

20.  A. T. Petkova and R. Tycko, "Rotational resonance in uniformly C-13-labeled solids: Effects on high-resolution magic-angle spinning NMR spectra and applications in structural studies of biomolecular systems", J. Magn. Reson. 168, 137-146 (2004).

21.  A. T. Petkova, G. Buntkowsky, F. Dyda, R. D. Leapman, W. M. Yau, and R. Tycko, "Solid state NMR reveals a pH-dependent antiparallel beta-sheet registry in fibrils formed by a beta-amyloid peptide", J. Mol. Biol. 335, 247-260 (2004).

22.  N. A. Oyler and R. Tycko, "Absolute structural constraints on amyloid fibrils from solid state NMR spectroscopy of partially oriented samples", J. Am. Chem. Soc. 126, 4478-4479 (2004).

23.  D. J. Gordon, J. J. Balbach, R. Tycko, and S. C. Meredith, "Increasing the amphiphilicity of an amyloidogenic peptide changes the beta-sheet structure in the fibrils from antiparallel to parallel", Biophys. J. 86, 428-434 (2004).

24.  J. C. C. Chan and R. Tycko, "Broadband rotational resonance in solid state NMR spectroscopy", J. Chem. Phys. 120, 8349-8352 (2004).

25.  R. Tycko and Y. Ishii, "Constraints on supramolecular structure in amyloid fibrils from two-dimensional solid state NMR spectroscopy with uniform isotopic labeling", J. Am. Chem. Soc. 125, 6606-6607 (2003).

26.  J. C. C. Chan and R. Tycko, "Recoupling of chemical shift anisotropies in solid state NMR under high-speed magic-angle spinning and in uniformly C-13-labeled systems", J. Chem. Phys. 118, 8378-8389 (2003).

27.  J. C. C. Chan and R. Tycko, "Solid state NMR spectroscopy method for determination of the backbone torsion angle psi in peptides with isolated uniformly labeled residues", J. Am. Chem. Soc. 125, 11828-11829 (2003).

28.  A. T. Petkova and R. Tycko, "Sensitivity enhancement in structural measurements by solid state NMR through pulsed spin locking", J. Magn. Reson. 155, 293-299 (2002).

29.  A. T. Petkova, Y. Ishii, J. J. Balbach, O. N. Antzutkin, R. D. Leapman, F. Delaglio, and R. Tycko, "A structural model for Alzheimer's beta-amyloid fibrils based on experimental constraints from solid state NMR", Proc. Natl. Acad. Sci. U. S. A. 99, 16742-16747 (2002).

30.  N. A. Oyler and R. Tycko, "Multiple quantum C-13 NMR spectroscopy in solids under high-speed magic-angle spinning", J. Phys. Chem. B 106, 8382-8389 (2002).

31.  J. J. Balbach, A. T. Petkova, N. A. Oyler, O. N. Antzutkin, D. J. Gordon, S. C. Meredith, and R. Tycko, "Supramolecular structure in full-length Alzheimer's beta-amyloid fibrils: Evidence for a parallel beta-sheet organization from solid state nuclear magnetic resonance", Biophys. J. 83, 1205-1216 (2002).

32.  O. N. Antzutkin, R. D. Leapman, J. J. Balbach, and R. Tycko, "Supramolecular structural constraints on Alzheimer's beta-amyloid fibrils from electron microscopy and solid state nuclear magnetic resonance", Biochemistry 41, 15436-15450 (2002).

33.  C. A. Michal and R. Tycko, "Time-reversal of the evolution of a dipole-coupled, many-spin system under continuous resonant irradiation", J. Chem. Phys. 114, 409-415 (2001).

34.  Y. Ishii, J. P. Yesinowski, and R. Tycko, "Sensitivity enhancement in solid state C-13 NMR of synthetic polymers and biopolymers by H-1 NMR detection with high-speed magic angle spinning", J. Am. Chem. Soc. 123, 2921-2922 (2001).

35.  Y. Ishii, M. A. Markus, and R. Tycko, "Controlling residual dipolar couplings in high-resolution NMR of proteins by strain induced alignment in a gel", J. Biomol. NMR 21, 141-151 (2001).

36.  Y. Ishii, J. J. Balbach, and R. Tycko, "Measurement of dipole-coupled lineshapes in a many-spin system by constant-time two-dimensional solid state NMR with high-speed magic-angle spinning", Chem. Phys. 266, 231-236 (2001).

37.  F. J. Blanco and R. Tycko, "Determination of polypeptide backbone dihedral angles in solid state NMR by double quantum C-13 chemical shift anisotropy measurements", J. Magn. Reson. 149, 131-138 (2001).

38.  F. J. Blanco, S. Hess, L. K. Pannell, N. W. Rizzo, and R. Tycko, "Solid state NMR data support a helix-loop-helix structural model for the N-terminal half of HIV-1 Rev in fibrillar form", J. Mol. Biol. 313, 845-859 (2001).

39.  R. Tycko, F. J. Blanco, and Y. Ishii, "Alignment of biopolymers in strained gels: A new way to create detectable dipole-dipole couplings in high-resolution biomolecular NMR", J. Am. Chem. Soc. 122, 9340-9341 (2000).

40.  Y. Ishii and R. Tycko, "Sensitivity enhancement in solid state N-15 NMR by indirect detection with high-speed magic angle spinning", J. Magn. Reson. 142, 199-204 (2000).

41.  Y. Ishii and R. Tycko, "Multidimensional heteronuclear correlation spectroscopy of a uniformly N-15- and C-13-labeled peptide crystal: Toward spectral resolution, assignment, and structure determination of oriented molecules in solid state NMR", J. Am. Chem. Soc. 122, 1443-1455 (2000).

42.  J. J. Balbach, J. Yang, D. P. Weliky, P. J. Steinbach, V. Tugarinov, J. Anglister, and R. Tycko, "Probing hydrogen bonds in the antibody-bound HIV-1 gp120 v3 loop by solid state NMR REDOR measurements", J. Biomol. NMR 16, 313-327 (2000).

43.  J. J. Balbach, Y. Ishii, O. N. Antzutkin, R. D. Leapman, N. W. Rizzo, F. Dyda, J. Reed, and R. Tycko, "Amyloid fibril formation by Abeta(16-22), a seven-residue fragment of the Alzheimer's beta-amyloid peptide, and structural characterization by solid state NMR", Biochemistry 39, 13748-13759 (2000).

44.  O. N. Antzutkin, J. J. Balbach, R. D. Leapman, N. W. Rizzo, J. Reed, and R. Tycko, "Multiple quantum solid state NMR indicates a parallel, not antiparallel, organization of beta-sheets in Alzheimer's beta-amyloid fibrils", Proc. Natl. Acad. Sci. U. S. A. 97, 13045-13050 (2000).

45.  D. P. Weliky, A. E. Bennett, A. Zvi, J. Anglister, P. J. Steinbach, and R. Tycko, "Solid state NMR evidence for an antibody-dependent conformation of the V3 loop of HIV-1 gp120", Nat. Struct. Biol. 6, 141-145 (1999).

46.  R. Tycko and A. E. Berger, "Dual processing of two-dimensional exchange data in magic angle spinning NMR of solids", J. Magn. Reson. 141, 141-147 (1999).

47.  R. Tycko, "Selection rules for multiple quantum NMR excitation in solids: Derivation from time-reversal symmetry and comparison with simulations and C-13 NMR experiments", J. Magn. Reson. 139, 302-307 (1999).

48.  C. A. Michal and R. Tycko, "Stray-field NMR imaging and wavelength dependence of optically pumped nuclear spin polarization in InP", Phys. Rev. B 60, 8672-8679 (1999).

49.  O. N. Antzutkin and R. Tycko, "High-order multiple quantum excitation in C-13 nuclear magnetic resonance spectroscopy of organic solids", J. Chem. Phys. 110, 2749-2752 (1999).

50.  R. Tycko, "Optical pumping in indium phosphide: P-31 NMR measurements and potential for signal enhancement in biological solid state NMR", Solid State Nucl. Magn. Reson. 11, 1-9 (1998).

51.  C. A. Michal and R. Tycko, "Nuclear spin polarization transfer with a single radio-frequency field in optically pumped indium phosphide", Phys. Rev. Lett. 81, 3988-3991 (1998).

52.  H. W. Long and R. Tycko, "Biopolymer conformational distributions from solid state NMR: Alpha-helix and 3(10)-helix contents of a helical peptide", J. Am. Chem. Soc. 120, 7039-7048 (1998).

53.  A. E. Bennett, D. P. Weliky, and R. Tycko, "Quantitative conformational measurements in solid state NMR by constant-time homonuclear dipolar recoupling", J. Am. Chem. Soc. 120, 4897-4898 (1998).

54.  D. P. Weliky and R. Tycko, "Determination of peptide conformations by two-dimensional magic angle spinning NMR exchange spectroscopy with rotor synchronization", J. Am. Chem. Soc. 118, 8487-8488 (1996).

55.  R. Tycko, D. P. Weliky, and A. E. Berger, "Investigation of molecular structure in solids by two-dimensional NMR exchange spectroscopy with magic angle spinning", J. Chem. Phys. 105, 7915-7930 (1996).

56.  R. Tycko and J. A. Reimer, "Optical pumping in solid state nuclear magnetic resonance", J. Phys. Chem. 100, 13240-13250 (1996).

57.  R. Tycko, "Prospects for resonance assignments in multidimensional solid state NMR spectra of uniformly labeled proteins", J. Biomol. NMR 8, 239-251 (1996).

58.  R. Tycko, S. E. Barrett, G. Dabbagh, L. N. Pfeiffer, and K. W. West, "Electronic states in gallium arsenide quantum wells probed by optically pumped NMR", Science 268, 1460-1463 (1995).

59.  S. E. Barrett, G. Dabbagh, L. N. Pfeiffer, K. W. West, and R. Tycko, "Optically pumped NMR evidence for finite-size skyrmions in GaAs quantum wells near Landau-level filling nu=1", Phys. Rev. Lett. 74, 5112-5115 (1995).

60.  R. Tycko, "Normal angle spinning dipolar spectroscopy for structural studies by solid state nuclear magnetic resonance", J. Am. Chem. Soc. 116, 2217-2218 (1994).

61.  G. Dabbagh, D. P. Weliky, and R. Tycko, "Determination of monomer conformations in noncrystalline solid polymers by two-dimensional NMR exchange spectroscopy", Macromolecules 27, 6183-6191 (1994).

62.  S. E. Barrett, R. Tycko, L. N. Pfeiffer, and K. W. West, "Directly detected nuclear magnetic resonance of optically pumped GaAs quantum wells", Phys. Rev. Lett. 72, 1368-1371 (1994).

63.  D. P. Weliky, G. Dabbagh, and R. Tycko, "Correlation of chemical bond directions and functional group orientations in solids by two-dimensional NMR", J. Magn. Reson. Ser. A 104, 10-16 (1993).

64.  R. Tycko and S. O. Smith, "Symmetry principles in the design of pulse sequences for structural measurements in magic angle spinning nuclear magnetic resonance", J. Chem. Phys. 98, 932-943 (1993).

65.  R. Tycko, G. Dabbagh, G. B. M. Vaughan, P. A. Heiney, R. M. Strongin, M. A. Cichy, and A. B. Smith, "Molecular orientational dynamics in solid C-70: Investigation by one-dimensional and two-dimensional magic angle spinning nuclear magnetic resonance", J. Chem. Phys. 99, 7554-7564 (1993).

66.  R. Tycko, G. Dabbagh, D. W. Murphy, Q. Zhu, and J. E. Fischer, "Electronic properties and phase transitions of RbC60 and CsC60:  Investigation by NMR spectroscopy", Phys. Rev. B 48, 9097-9105 (1993).

67.  R. Tycko, G. Dabbagh, M. J. Rosseinsky, D. W. Murphy, A. P. Ramirez, and R. M. Fleming, "Electronic properties of normal and superconducting alkali fullerides probed by C-13 nuclear magnetic resonance", Phys. Rev. Lett. 68, 1912-1915 (1992).

68.  R. Tycko, G. Dabbagh, S. R. Kurtz, and J. P. Goral, "Quantitative study of atomic ordering in Ga0.5In0.5P thin films by P-31 nuclear magnetic resonance", Phys. Rev. B 45, 13452-13458 (1992).

69.  R. Tycko and G. Dabbagh, "A simple theory of C-13 nuclear spin diffusion in organic solids", Isr. J. Chem. 32, 179-184 (1992).

70.  S. E. Barrett and R. Tycko, "Molecular orientational dynamics in K3C60 probed by two-dimensional nuclear magnetic resonance", Phys. Rev. Lett. 69, 3754-3757 (1992).

71.  R. Tycko, R. C. Haddon, G. Dabbagh, S. H. Glarum, D. C. Douglass, and A. M. Mujsce, "Solid state magnetic resonance spectroscopy of fullerenes", J. Phys. Chem. 95, 518-520 (1991).

72.  R. Tycko, G. Dabbagh, M. J. Rosseinsky, D. W. Murphy, R. M. Fleming, A. P. Ramirez, and J. C. Tully, "C 13 NMR-spectroscopy of KxC60: Phase separation, molecular dynamics, and metallic properties", Science 253, 884-886 (1991).

73.  R. Tycko, G. Dabbagh, R. M. Fleming, R. C. Haddon, A. V. Makhija, and S. M. Zahurak, "Molecular dynamics and the phase transition in solid C60", Phys. Rev. Lett. 67, 1886-1889 (1991).

74.  R. Tycko and G. Dabbagh, "Nuclear magnetic resonance crystallography: Molecular orientational ordering in three forms of solid methanol", J. Am. Chem. Soc. 113, 3592-3593 (1991).

75.  R. Tycko and G. Dabbagh, "Double quantum filtering in magic angle spinning NMR spectroscopy: An approach to spectral simplification and molecular structure determination", J. Am. Chem. Soc. 113, 9444-9448 (1991).

76.  R. C. Haddon, L. F. Schneemeyer, J. V. Waszczak, S. H. Glarum, R. Tycko, G. Dabbagh, A. R. Kortan, A. J. Muller, A. M. Mujsce, M. J. Rosseinsky, S. M. Zahurak, A. V. Makhija, F. A. Thiel, K. Raghavachari, E. Cockayne, and V. Elser, "Experimental and theoretical determination of the magnetic susceptibility of C60 and C70", Nature 350, 46-47 (1991).

77.  R. C. Haddon, A. F. Hebard, M. J. Rosseinsky, D. W. Murphy, S. J. Duclos, K. B. Lyons, B. Miller, J. M. Rosamilia, R. M. Fleming, A. R. Kortan, S. H. Glarum, A. V. Makhija, A. J. Muller, R. H. Eick, S. M. Zahurak, R. Tycko, G. Dabbagh, and F. A. Thiel, "Conducting films of C60 and C70 by alkali metal doping", Nature 350, 320-322 (1991).

78.  R. Tycko, G. Dabbagh, J. C. Duchamp, and K. W. Zilm, "C-13 zero field NMR in high field", J. Magn. Reson. 89, 205-209 (1990).

79.  R. Tycko and G. Dabbagh, "Measurement of nuclear magnetic dipole-dipole couplings in magic angle spinning NMR", Chem. Phys. Lett. 173, 461-465 (1990).

80.  R. Tycko, "Zero field nuclear magnetic resonance in high field", J. Chem. Phys. 92, 5776-5793 (1990).

81.  W. W. Warren, R. E. Walstedt, G. F. Brennert, R. J. Cava, R. Tycko, R. F. Bell, and G. Dabbagh, "Cu spin dynamics and superconducting precursor effects in planes above Tc in YBa2Cu3O6.7", Phys. Rev. Lett. 62, 1193-1196 (1989).

82.  R. Tycko, G. Dabbagh, and P. A. Mirau, "Determination of chemical shift anisotropy lineshapes in a two-dimensional magic angle spinning NMR experiment", J. Magn. Reson. 85, 265-274 (1989).

83.  T. Sleator and R. Tycko, "Observation of individual organic molecules at a crystal surface with use of a scanning tunneling microscope", Phys. Rev. Lett. 60, 1418-1421 (1988).

84.  R. Tycko, "Adiabatic rotational splittings and Berry's phase in nuclear quadrupole resonance", Phys. Rev. Lett. 58, 2281-2284 (1987).