Subterahertz Longitudinal Phonon Modes Propagating in a Lipid Bilayer Immersed in an Aqueous Medium

The properties of subterahertz longitudinal acoustic phonon modes in the hydrophobic region of a lipid bilayer immersed in a compressible viscous aqueous medium are investigated theoretically. An approximate expression is obtained for the Mandelstam–Brillouin components of the dynamic structure factor of a bilayer. The analysis is based on a generalized hydrodynamic model of the "two-dimensional lipid bilayer + three-dimensional fluid medium" system, as well as on known sharp estimates for the frequencies and lifetimes of long-wavelength longitudinal acoustic phonons in a free hydrated lipid bilayer and in water, obtained from inelastic X-ray scattering experiments and molecular dynamics simulations. It is shown that, for characteristic values of the parameters of the membrane system, subterahertz longitudinal phonon-like excitations in the hydrophobic part of the bilayer are underdamped. In this case, the contribution of the viscous flow of the aqueous medium to the damping of a longitudinal membrane mode is small compared with the contribution of the lipid bilayer. Quantitative estimates of the damping ratio agree well with the experimental results for the vibration mode of the enzyme lysozyme in aqueous solution [1]. It is also shown that a coupling between longitudinal phonon modes of the bilayer and relaxation processes in its fluid environment gives rise to an additional peak in the scattering spectrum, which corresponds to a non-propagating mode.