Eur. Phys. J. E 3, 323-335
Elastic energy of tilt and bending of fluid membranes
M. Hamm1 - M.M. Kozlov2
1 Department of Materials Science & Metallurgy, University of Cambridge, Cambridge CB2 3QZ, UK
2 Department of Physiology and Pharmacology - Sackler Faculty of Medicine,
Tel-Aviv University, Tel Aviv 69978, Israel
mh264@cus.cam.ac.uk
misha@devil.tau.ac.il
Received 10 February 2000 and Received in final form 19 June 2000
Abstract
Tilt of hydrocarbon chains of lipid molecules with respect to membrane
plane is commonly considered to characterize the internal structure of
a membrane in the crystalline state. However, membranes in the liquid
state can also exhibit tilt resulting from packing constraints imposed
on the lipid molecules in diverse biologically relevant structures
such as intermediates of membrane fusion, pores in lipid bilayers and
others. We analyze the energetics of tilt in liquid membranes and its coupling
with membrane bending. We consider three contributions to the elastic
energy: constant tilt, variation of tilt along the membrane surface
and membrane bending. The major assumption of the model is that the
core of a liquid membrane has the common properties of an elastic
continuum. We show that the variation of tilt and membrane bending are additive
and that their energy contributions are determined by the same elastic
coefficient: the Helfrich bending modulus, the modulus of Gaussian
curvature and the spontaneous curvature known from previous studies of
pure bending. The energy of a combined deformation of bending and
varying tilt is determined by an effective tensor accounting for the
two factors. In contrast, the deformation of constant tilt does not couple with
bending and its contribution to the elastic energy is determined by an
independent elastic constant. While accurate determination of this
constant requires additional measurements, we estimate its value using
a simplified approach. We discuss the relationships between the obtained elastic Hamiltonian
of a membrane and the previous models of membrane elasticity.
PACS
68.10.-m Fluid surfaces and fluid-fluid interfaces -
68.10.Et Interface elasticity, viscosity, and viscoelasticity -
87.16.Dg Membranes, bilayers, and vesicles
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag