The nuclear magnetic resonance ͑NMR͒ spectra of the Iϭ3/2 monovalent ions 23 Na, 35 Cl, 39 K, and 79 Br for NaCl and KBr dissolved into filamentous bacteriophage Pf1 solutions display line splittings and shifts consistent with an interaction between the nuclear spin and the electric field gradient produced by the Pf1 particles. The average electric field gradient and thus the spectral splitting for ions in the void space between magnetically aligned Pf1 particles is modeled using a numerical solution to the Poisson-Boltzmann equation. An NMR titration experiment in a 57 mg/mL Pf1 solution is used to determine the background Na ϩ ion concentration in solution as 32 mM which compares well with the 31.1 mM negative surface charge on Pf1.

The 23 Na nuclear magnetic resonance (NMR) spectra for NaCl dissolved in the nematic phase of dimyristoylphosphatidylcholine (DMPC)/dihexanoyl-phosphatidylcholine (DHPC) bicelle solutions at 34°C display line splittings consistent with the quadrupolar satellite transitions for the I ) 3 / 2 23 Na nucleus. At temperatures exceeding 40°C additional residual 23 Na satellite transition lines develop, suggesting that a new ordered phase similar to pure DMPC is present.

The nuclear magnetic resonance (NMR) spectra for the I=3/2 23Na cation dissolved into filamentous bacteriophage Pf1 solutions display line splittings and relaxation times consistent with an interaction between the 23Na nuclear quadrupole moment and the electric field gradient produced by the negatively charged Pf1 particles. The 23Na NMR line splittings and relaxation rates corresponding to magnetization recovery and single, double, and triple quantum coherence decays are measured in Pf1 solutions and compared to theoretical values. The deviation of the observed dc spectral density J0 from the equal first harmonic J(omega0) and second harmonic J(2omega0) values as J(omega0)=J(2omega0) not equal to J0 in these solutions suggests that ion migration in the electric field gradient of the Pf1 particles produces an anisotropic relaxation mechanism. Correlation functions and thus spectral densities for this process are calculated from solutions to the Fokker-Planck equation for radial motion in an electric potential and used to estimate measured relaxation rates. Appropriate electric potentials are generated from the solutions to the Poisson-Boltzmann equation for a charged Pf1 particle in aqueous phase, functions that lead to theoretical estimates of NMR line splittings consistent with experimental observations.

ABSTRACT:The measurement of residual dipolar and quadrupolar coupling constants in the liquid phase by using an electric field to destroy the isotropic nature of molecular tumbling is complicated by charge-induced turbulent motion. In many cases this motion is due to charge injection at electrode surfaces, an effect that leads to an apparent removal of electrically recovered anisotropic spectral splittings when measured from a spin-echo ( ) envelope modulation produced by a train of radio frequency rf pulses. To understand this averaging, the effect of quadrupolar couplings and enhanced molecular diffusion on free-induction, spin-echo, and Carr ᎐ Purcell signals is analytically determined in the special case of homogeneous rf pulses. Additional signal damping due to rf inhomogeneity and coupling constant heterogeneity is determined by numerically extending the kernel formalism introduced by Herzog and Hahn to understand spin diffusion in solids. Finally, the merit of the numerical approach is tested by comparison with analytical results for homogeneous rf pulses and experimental results for perdeuterated nitrobenzene involving inhomogeneous rf pulses and coupling heterogeneity. KEY WORDS: diffusion; rf inhomogeneity; multipulse; electric field; quadrupole; spin echo Ž . Nuclear magnetic resonance NMR spectroscopy has moved to the forefront of chemical structure determination techniques in solids, liquids, and Ž . gases 1 . As is well known, measurement of chemical shifts and scalar couplings as spectral peak positions and splittings yields information about primary and secondary structure. Three-dimensional tertiary and quaternary structural details can be obtained from changes in peak inten-Ž . Ž . sity via the nuclear Overhauser effect nOe 2 .Ž . As pioneered by Bothner-by et al. 3 , Prestegard Ž . Ž . et al. 4 , and Tjandra and Bax 5 , higher resolution molecular structures can be obtained in the liquid phase by measuring residual dipolar couplings. These couplings, manifested as NMR line splittings, display a less severe dependence on internuclear distance than do relaxation-based

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