A formula for membrane mediated point particle interactions on near spherical biomembranes

We consider a model of a biomembrane with attached proteins. The membrane is represented by a near spherical continuous surface and attached proteins are described as discrete rigid structures which attach to the membrane at a finite number of points. The resulting surface minimises a quadratic elas...

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Bibliographic Details
Published inInterfaces and free boundaries Vol. 24; no. 1; pp. 1 - 34
Main Authors Elliott, Charles M., Herbert, Philip J.
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.03.2022
Subjects
Mathematical models
Mathematical research
Membranes (Biology)
Proteins
Germany
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Summary:We consider a model of a biomembrane with attached proteins. The membrane is represented by a near spherical continuous surface and attached proteins are described as discrete rigid structures which attach to the membrane at a finite number of points. The resulting surface minimises a quadratic elastic energy (obtained by a perturbation of the Canham–Helfrich energy) subject to the point constraints which are imposed by the attachment of the proteins. We calculate the derivative of the energy with respect to protein configurations. The proteins are constrained to move tangentially by translation and by rotation in the axis normal to a reference point. Previous studies have typically restricted themselves to a nearly flat membrane and circular inclusions. A numerically accessible representation of this derivative is derived and employed in some numerical experiments.
ISSN:1463-9963
1463-9971
DOI:10.4171/ifb/464