Geodesic
A formula for membrane mediated point particle interactions on near spherical biomembranes
Charles M. Elliott1 orcid ; Philip J. Herbert2
1University of Warwick, Coventry, UK
2Universität Koblenz-Landau, Germany
Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 1-34

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DOI

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.
DOI : 10.4171/ifb/464
Classification : 35-XX, 26-XX, 65-XX
Mots-clés : Membrane mediated interaction, Canham–Helfrich, surface PDE, point Dirichlet constraints, mixed finite elements, domain mapping

Charles M. Elliott  1   ; Philip J. Herbert  2

1 University of Warwick, Coventry, UK
2 Universität Koblenz-Landau, Germany 
Charles M. Elliott; Philip J. Herbert. A formula for membrane mediated point particle interactions on near spherical biomembranes. Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 1-34. doi: 10.4171/ifb/464
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