Dispersion relation of lipid membrane shape fluctuations by neutron spin-echo spectrometry

We have studied the mesoscopic shape fluctuations in aligned multilamellar stacks of DMPC bilayers using the neutron spin-echo technique. The corresponding in plane dispersion relation $\tau^{-1}$(q$_{||}$) at different temperatures in the gel (ripple, P$_{\beta'}$) and the fluid (L$_{\alpha}$) phase of this model system has been determined. Two relaxation processes, one at about 10ns and a second, slower process at about 100ns can be quantified. The dispersion relation in the fluid phase is fitted to a smectic hydrodynamic theory, with a correction for finite q$_z$ resolution. We extract values for, the bilayer bending rigidity $\kappa$, the compressional modulus of the stacks $B$, and the effective sliding viscosity $\eta_3$. The softening of a mode which can be associated with the formation of the ripple structure is observed close to the main phase transition.