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A formula for membrane mediated point particle interactions on near spherical biomembranes
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Elliott, C. M. and Herbert, P. J. (2022) A formula for membrane mediated point particle interactions on near spherical biomembranes. Interfaces and Free Boundaries, 24 (1). pp. 1-34. doi:10.4171/IFB/464
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Official URL: https://doi.org/10.4171/IFB/464
Abstract
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.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QH Natural history |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Membranes (Biology) -- Mathematical models, Dirichlet problem -- Numerical solutions, Cell membranes | |||||||||
| Journal or Publication Title: | Interfaces and Free Boundaries | |||||||||
| Publisher: | European Mathematical Society Publishing House | |||||||||
| ISSN: | 1463-9963 | |||||||||
| Official Date: | 2022 | |||||||||
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| Volume: | 24 | |||||||||
| Number: | 1 | |||||||||
| Page Range: | pp. 1-34 | |||||||||
| DOI: | 10.4171/IFB/464 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| RIOXX Funder/Project Grant: |
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