https://doi.org/10.1140/epje/s10189-022-00233-y
Regular Article - Soft Matter
Solitons in the Heimburg–Jackson model of sound propagation in lipid bilayers are enabled by dispersion of a stiff membrane
1
Laboratory of Physics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia
2
Department of Mechanics, Biomechanics and Mechatronics, Faculty of Mechanical Engineering, Czech Technical University in Prague, Technicka 4, 16607, Prague, Czech Republic
3
Faculty of Health Sciences, Laboratory of Clinical Biophysics, University of Ljubljana, Zdravstvena pot 5, 1000, Ljubljana, Slovenia
4
Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, Vrazov trg 2, 1000, Ljubljana, Slovenia
Received:
22
May
2022
Accepted:
1
September
2022
Published online:
20
September
2022
Experiments show that elastic constants of lipid bilayers vary greatly during the liquid-to-gel phase transition. This fact forms the cornerstone of the Heimburg–Jackson model of soliton propagation along membranes of axons, in which the action potential is accompanied by a traveling phase transition. However, the dispersion term, which is crucial for the existence of solitons, is added to the Heimburg–Jackson model ad hoc and set to fit experimental observations. In the present paper, we aim to consolidate this view with continuous membrane mechanics. Using literature data, we show that the compression modulus of a DPPC membrane is smaller by approximately an order of magnitude during phase transition. With a series expansion of the compression modulus, we write the action of a membrane and solve the corresponding wave equation analytically using an Exp-function method. We confirm that membrane solitons with speeds around 200 m/s are possible with amplitudes inversely proportional to their speed. We conclude that dispersion necessary for existence of solitons is directly related to a membrane’s bending properties, offering a possible explanation for h. Our findings are in general agreement with existing literature and give insight into a general mechanism of wave propagation in membranes close to transition.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022. corrected publication 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
