Nuclear spin relaxation of sodium cations in bacteriophage Pf1 solutions

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.