Mechanics of lipid membranes subjected to boundary excitations and an elliptic substrate interactions

  • Kim, Chun IL
  • Received : 2015.12.21
  • Accepted : 2016.06.28
  • Published : 2016.07.25


We present relatively simple derivations of the Helfrich energy potential that has been widely adopted in the analysis of lipid membranes without detailed explanations. Through the energy variation methods (within the limit of Helfrich energy potential), we obtained series of analytical solutions in the case when the lipid membranes are excited through their edges. These affordable solutions can be readily applied in the related membrane experiments. In particular, it is shown that, in case of an elliptic cross section of a rigid substrate differing slightly from a circle and subjected to the incremental deformations, exact analytical expressions describing deformed configurations of lipid membranes can be obtained without the extensive use of Mathieu's function.


lipid membranes;bilayers;shape equation;substrate-membrane interaction;elliptical contact domain;analytic solution


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Supported by : Natural Sciences and Engineering Research Council of Canada