Dynamics of lipid bilayers from comparative analysis of ²H and ¹³C nuclear magnetic resonance relaxation data as a function of frequency and temperature

Analysis of the nuclear spin relaxation rates of lipid membranes provides a powerful means of studying the dynamics of these important biological representatives of soft matter. Here, temperature- and frequency-dependent ²H and ¹³C nuclear magnetic resonance (NMR) relaxation rates for vesicles and multilamellar dispersions of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) in the liquid-crystalline state have been fitted simultaneously to various dynamic models for different positions of the acyl chains. The data include ²H R_1z rates (Zeeman order of electric quadrupolar interaction) acquired at 12 external magnetic field strengths from 0.382 to 14.6 T, corresponding to a frequency range from ω_D/2π=2.50-95.3 MHz; and ²H R_1Q rates (quadrupolar order of electric quadrupolar interaction) at 15.3, 46.1, and 76.8 MHz. Moreover, ¹³C R_1z data (Zeeman order of magnetic dipolar interaction) for DMPC are included at six magnetic field strengths, ranging from 1.40 to 17.6 T, thereby enabling extension of the frequency range to effectively (ω_C+ω_H)/2π=938.7 MHz. Use of the generalized approach allows formulation of noncollective segmental and molecular diffusion models, as well as collective director fluctuation models, which were tested by fitting the ²H R_1Z data at different frequencies and temperatures (30 °C and 50 °C). The corresponding ¹³C relaxation rates were predicted theoretically and compared to experiment, thus allowing one to unify the ¹³C and ²H NMR data for bilayer lipids in the fluid state. A further new aspect is that the spectral densities of motion have been explicitly calculated from the ²H R_1Z and R_1Q data at 40 °C. We conclude that the relaxation in fluid membrane bilayers is governed predominantly by relatively slow motions, which modulate the residual coupling remaining from faster local motions (order fluctuations). Only the molecular diffusion model, including an additional slow motional process, and the membrane deformation model describing three-dimensional collective fluctuations fit the ²H NMR data and predict the ¹³C NMR data in the MHz range. Orientational correlation functions have been calculated, which emphasizes the importance of NMR relaxation as a unique tool for investigating the dynamics of lipid bilayers and biological membranes.