On periodic curvature and standing wave motions in cell membranes

Cell membranes can form cubic arrangements and there is evidence for the occurrence of periodic curvature in simple membranes. The periodicity of the bilayer implies a standing wave character of vibrational motions. It is proposed that the periodic curvature reflects a dominating mode of standing wave oscillations, with the different cubic bilayer structures representing alternative standing wave conformations of the bilayer. The wave motions in lamellar liquid-crystalline phases, as well as in vesicles and membranes, which lack lateral periodicity, are known to exhibit statistically distributed undulations. The standing wave character of conformational fluctuations of periodically curved membranes, on the other hand, results in an organisation in time and space. Calculated models of standing wave conformations of membranes are demonstrated, and functional aspects of such biomembranes are discussed.