Abstract
In this paper we present a model describing the dynamics of biological membranes. The description presented here is based both on Fr\"olich's earlier conjectures and on the actual biophysical data concerning the structure, composition, and functions of biological membranes. A model Hamiltonian is proposed that involves the oscillations of both the lipid head groups and hydrocarbon chains of the membrane. The presence of dielectrically active material, mainly water, is also accounted for. It is subsequently demonstrated that, depending on the form of the coupling constant between head- and tail-group oscillations, two limiting regimes may occur. The Fr\"ohlich regime is manifested by Bose condensation in the space of dipole oscillation frequencies. This results in self-focusing in the frequency domain. On the other hand, the Davydov regime is associated with spatial localization of the polarized state and leads to soliton formation. Thermal dissipation of the membrane's energy and damping effects are also examined.
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