@inproceedings{c2e9a8ed174249cfa3c767e8af89cdb3,
title = "Geometry of biological membranes and Willmore energy",
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.",
keywords = "Delaunay surface, Dirichlet energy, Helfrich energy, Willmore energy, beta barrels, beta sheets, biological membranes, constant mean curvature, minimal surface",
author = "Magdalena Toda and Bhagya Athukoralage",
year = "2013",
doi = "10.1063/1.4825638",
language = "English",
isbn = "9780735411845",
series = "AIP Conference Proceedings",
pages = "883--886",
booktitle = "11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013",
note = "11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 ; Conference date: 21-09-2013 Through 27-09-2013",
}