Deformation of an elastic membrane interacting electrostatically with a rigid curved domain: implications to biosystems

Abstract

Deformation of thin elastic sheet due to electrostatic forces play important role in engineering and biological systems. In this work, we analyze the deformation of thin elastic sheet, while interacting with a rigid curved domain in the presence of dielectric fluid. Mechanical deformation of the sheet is coupled with the electrostatic interaction in its equilibrium configuration. We consider small deformation of the sheet, which obeys Hooke’s law. The electrostatic forces acting between the sheet and curved domain are calculated by using Debye–Huckel equation. It is observed that the sheet deformation is proportional to the electrostatic forces acting on it. Increase in inverse Debye length (which signifies the strength of electrostatic field) of the dielectric fluid decreases the sheet deformation. With the help of present model, binding mechanism between peripheral BAR proteins and cell membrane is studied by treating cell membrane as an elastic membrane and BAR protein as a rigid curved domain. For small curvature of BAR protein, the present model captures very well the scaffolding mechanism of protein binding. This model can also be used to analyze problems in electrophotography, powder technology, semiconductor and pharmaceutical industries.