Low-Frequency Sound Propagation in Lipid Membranes

In the recent years, we have shown that cylindrical biological membranes such as nerve axons under physiological conditions are able to support stable electromechanical pulses called solitons. These pulses sharemany similarities with the nervous impulse, for example, thepropagationvelocityaswell as themeasured reversibleheatproductionandchanges in thickness and length that cannot be explained with traditional nerve models. A necessary condition for solitary pulse propagation is the simultaneous existence of nonlinearity and dispersion, that is, the dependence of the speed of sound on density and frequency. A prerequisite for the nonlinearity is the presence of a chain-melting transition close to physiological temperatures. The transition causes a density dependence of the elastic constants which can easily be determined by an experiment. The frequency dependence is more difficult to determine. The typical timescale of a nerve pulse is 1 ms, corresponding to a characteristic frequency in the range up to 1 kHz. Dispersion in the sub-kilohertz regime is difficult to measure due to the very long wave lengths involved. In this contribution, weaddress theoretically thedispersionof thespeedof sound in lipidmembranesand relate it to experimentally accessible relaxation times by using linear response theory. This ultimately leads to an extension of the differential equation for soliton propagation. Advances in Planar Lipid Bilayers and Liposomes, Volume 16 # 2012 Elsevier Inc. ISSN 1554-4516 All rights reserved. http://dx.doi.org/10.1016/B978-0-12-396534-9.00002-7 51 ABBREVIATIONS DPPC dipalmitoyl phosphatidylcholine DSC differential scanning calorimetry