Deformation of an elastic membrane interacting electrostatically with a rigid curved domain: implications to biosystems
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O R I G I NA L
Paritosh Mahata · Laxminarsimharao Vennamneni
Deformation of an elastic membrane interacting electrostatically with a rigid curved domain: implications to biosystems
Received: 4 February 2020 / Accepted: 12 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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–Hückel 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. Keywords Deformation · Elastic membrane · Electrostatic interaction · Protein binding
1 Introduction Elastic membrane deformations driven by electrostatic forces are common in many engineering and biological systems. For example, in cell-biological systems, peripheral proteins bend the cell membrane due to electrostatic interactions between them [1,2]. This is an important phenomenon for several cell-biological processes like endocytosis and exocytosis. Malfunctioning of these processes produces diseases like cancer and Parkinson’s [3]. To analyze the binding mechanism between the protein and cell membrane, the out-of-plane deformation of cell membrane is analyzed while treating it as an elastic membrane [4–6]. In addition to this, the membrane deformation, driven by electrostatic forces, plays an important role in many industrial applications like in electrophotography, powder technology, semiconductor and pharmaceutical industries [7–10]. In electrophotography, the charged sheet of the toner particles deformed due to electrostatic interaction with a conductive surface and adhere onto it for the images [8]. For high-quality electrophotographic printing, the electrostatic P. Mahata (B) Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi 835215, India E-mail: [email protected] L. Vennamneni Department of Mechanical Engineering, SR University, Warangal Urban, Telangana 506371, India L. Vennamneni Engineering Mechanics Unit, Jawaharla
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