Small deformations of spherical biomembranes

Abstract

In this contribution to the proceedings of the 11th Mathematical Society of Japan (MSJ) Seasonal Institute (July 2018) we give an overview of some recent work on a mathematical model for small deformations of a spherical membrane. The idea is to consider perturbations to minimisers of a surface geometric energy. The model is obtained from consideration of second order approximations to a perturbed energy. In particular, the considered problems involve particle constraints and surface phase field energies.

Free energy computation of particles with membrane-mediated interactions via Langevin dynamics

“…There is a rich literature on coupling conditions typically prescribing contour and slope of the membrane either at particle boundaries [13,14,15] or in single points [16,17,18,19,20,21]. In a recently developed variational approach to hybrid models [22], see also [23,24], such coupling conditions take the role of constraints in energy minimization. While hybrid models are often formulated in the zerotemperature limit, effects of thermal fluctuations, mostly of the membrane, are about to attract more and more attention [25,26,27,28,29].…”