Geometry of biological membranes and Willmore energy

Magdalena Toda, Bhagya Athukoralage

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

This article represents a differential geometric approach to the study of elastic membranes in microbiology. We provide a model for the energy of secondary structures in proteins, which is a Willmore-type energy that is similar to the Helfrich energy from the model of lipid bilayers. We propose a new model for beta barrels, as solutions of what we call the Willmore-Helfrich type equation. We hereby reject older models of beta barrels (like a best-fit by one-sheeted hyperboloids, or twisted hyperboloids) and we accept, as a particular and singular case, the catenoidal (minimal) model for beta barrels. We provide theoretical and experimental arguments in favor of a new model for beta barrels as Delaunay surfaces, based on the Willmore-Helfrich type energy.

Original languageEnglish
Title of host publication11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
Pages883-886
Number of pages4
DOIs
StatePublished - 2013
Event11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 - Rhodes, Greece
Duration: Sep 21 2013Sep 27 2013

Publication series

NameAIP Conference Proceedings
Volume1558
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
CountryGreece
CityRhodes
Period09/21/1309/27/13

Keywords

  • Delaunay surface
  • Dirichlet energy
  • Helfrich energy
  • Willmore energy
  • beta barrels
  • beta sheets
  • biological membranes
  • constant mean curvature
  • minimal surface

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