(442h) Permeability, Osmosis, and Hydrodynamics of Planar Lipid Membranes

Biological lipid membranes make up the boundary of the cell and many of its internal organelles, including the nucleus, endoplasmic reticulum, and Golgi complex. Such membranes are often approximated to be impermeable to the surrounding, solute-containing fluid. However, biological membranes are subject to permeable and osmotic forces, whose effects are not well-understood. Here, the linear response of a planar lipid membrane to external perturbations is presented. Two cases are considered: (i) an impermeable bilayer surrounded by a fluid which cannot flow through the membrane, and (ii) a semipermeable bilayer surrounded by fluid and electrically neutral solutes—of which only the fluid can pass through the membrane. The impermeable system exhibits two dynamical modes: an inertial mode which quickly decays, and a membrane relaxation mode that persists to longer times. In the semipermeable case, the latter exists only when solutes rearrange more quickly than the membrane relaxes—corresponding to a finite range of wavenumbers. Disturbances outside this range are predicted to decay at the faster inertial rate. Moreover, as the membrane surface tension is increased, the aforementioned range shrinks, and above a critical tension only the inertial dynamics are allowed. When thermal fluctuations are incorporated, the fluctuation–dissipation theorem requires different forms of the thermal noise depending on whether or not membrane relaxation modes are permitted. The difference in behavior of impermeable and semipermeable systems are relevant when interpreting measurements in the many experimental investigations that regard lipid membranes as impermeable.