Eur. Phys. J. E (2011) 34: 67
https://doi.org/10.1140/epje/i2011-11067-x

Regular Article

Analytical expressions for the shape of axisymmetric membranes with multiple domains

¹ Department of Physics and Astronomy, University of Pennsylvania, 209 S 33rd street, 19104, Philadelphia, Pennsylvania, USA
² Department of Applied Physics and Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

^* e-mail: tidema@sas.upenn.edu

Received: 5 April 2011
Revised: 9 June 2011
Accepted: 21 June 2011
Published online: 14 July 2011

Abstract

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.