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New contributions to elastic energy of lipid membranes: tilt-curvature coupling and curvature gradient terms | | Konstantin V. Pinigin
; Peter I. Kuzmin
; Sergey A. Akimov
; Timur R. Galimzyanov
; | | Date: |
18 Mar 2020 | | Abstract: | Lipid bilayer membranes are flexible thin laterally fluid films consisting of
two unimolecular layers of lipids. On spatial scales much larger than the
bilayer thickness, the membrane elasticity is well determined by its shape and
adequately described by the classical Helfrich Hamiltonian. However, various
local membrane heterogeneities can result in a lipids tilt relative to the
membrane surface normal. On the basis of the elasticity theory, M. Hamm and M.
M. Kozlov [M. Hamm and M. M. Kozlov, Eur. Phys. J. E 3, 323 (2000)] derived the
most general energy functional, taking into account the tilt and bending.
Recently, M. M. Terzi and M. Deserno [M. M. Terzi and M. Deserno, J. Chem.
Phys. 147, 084702 (2017)] showed that Hamm and Kozlov’s derivation is
incomplete because of the missing of the tilt-curvature coupling term. However,
the energy functional derived by Terzi and Deserno appeared to be unstable,
thereby being invalid for applications. Here, we derive a stable elastic energy
functional, showing that the squared gradient of the curvature was missed in
both of these papers. This change in the energy functional arises from a more
accurate consideration of the transverse shear deformation terms and their
influence on stability. We also consider the influence of the pre-stress on the
stability of the energy functional and show that the effective Gaussian
curvature should be neglected because of the stability requirements. We further
generalize the theory, including the stretching-compressing deformation modes,
and provide the geometrical interpretation of the terms that were previously
missed by Hamm and Kozlov. The physical consequences of the new terms are
analyzed in the case of a membrane-mediated interaction of two amphipathic
peptides located in the same monolayer. We also provide the expression for
director fluctuations, comparing it with that obtained by Terzi and Deserno. | | Source: | arXiv, 2003.8326 | | Services: | Forum | Review | PDF | Favorites | |
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