Transverse nuclear spin relaxation measurements employing Carr−Purcell (CP) pulse sequences can provide
detailed information on the slow-motional dynamics in biomembranes. In this paper, a comprehensive relaxation
model is developed for the analysis of such experiments performed on unilamellar quasi-spherical vesicles.
The basis of the model is the stochastic Liouville equation in which two different relaxation processes are
considered (i.e., vesicle shape fluctuations and molecular translational diffusion). It is shown that for vesicle
radii R
0 ≥ 200 nm, translational diffusion of the lipid molecules along the vesicle shell is too slow to contribute
significantly to transverse spin relaxation in the kHz range, whereas vesicle shape fluctuations constitute the
dominant transverse relaxation process. The theory is employed in model calculations for pulse frequency-dependent transverse 31P nuclear spin relaxation rates,
(ω), from CP sequences. The analysis reveals that
(ω), induced by vesicle fluctuations, depends linearly on ω-1 over a wide frequency range in the kHz
regime. Notably, within this linear dispersion regime, the bending elastic modulus κ is the only relevant
parameter because the magnitude of
(ω) does not depend on the size of the vesicle R
0, the effective
lateral tension σ, or the viscosity of the surrounding fluid η. On the other hand, R
0, σ, η, and κ determine the
frequency at which
(ω) levels off to a constant “plateau” value independent of ω. Thus, analysis of the
(ω) dispersion profiles is a direct way to determine the bending elastic modulus and other viscoelastic
parameters of membrane vesicles.