Membrane curvature of a biological cell is actively involved in various fundamental cell biological functions. It has been discovered that membrane curvature and binding of peripheral membrane proteins follow a symbiotic relationship. The exact mechanism behind this interplay of protein binding and membrane curvature has not yet been properly understood. To improve understanding of the mechanism, we study curvature sorting of proteins in a model system consisting of a tether pulled from a giant unilamellar vesicle using mechanical-thermodynamic models. The concentration of proteins bound to the membrane changes significantly due to curvature. This has also been observed in experiments by other researchers. We also find that there is a phase transition based on protein concentration and we discuss the coexistence of phases and stability of solutions. Furthermore, when sorting is favorable, the increase in protein concentration stabilizes the tether in the sense that less pulling force is required to maintain the tether. A similar mechanism may be in place, when motor proteins pull tethers from donor membranes.

Adsorption of proteins on membrane surfaces plays an important role in cell biological processes. In this work, we develop a two-dimensional fluid model for proteins. The protein molecules have been modeled as two-dimensional convex and soft particles. The Lennard-Jones potential for circular particles and Kihara (12,6) potential for elliptical particles with hard core have been used to model pairwise intermolecular interactions. The equation of state of the fluid model has been derived using Weeks-Chandler-Andersen decomposition and it involves three parameters, an attraction, a repulsion, and a size parameter, which depend on the shape and core size of the molecules. For validation of the model, a two-dimensional molecular dynamics simulation has been performed. Finally, the model has been applied to study the adsorption of proteins on a flat membrane. In comparison with the existing model of hard and convex particles for protein adsorption, our model predicts a higher packing fraction for the adsorption equilibria. Although the present work is based on Lennard-Jones-type interaction, it can be extended for other specific soft interactions between convex molecules. Thus the model has general applicability for any other two-dimensional adsorption systems of molecules with soft interaction.

We carry out a linear elastic analysis to study wavy structure generation on lipid membrane by peripheral membrane proteins. We model the lipid membrane as linearly elastic and anisotropic material. The hydrophobic insertion by proteins into the lipid membrane has been idealized as penetration of rigid rod-like inclusions into the membrane and the electrostatic interaction between protein and membrane has been modeled by a distributed surface traction acting on the membrane surface. With the proposed model we study curvature generation by several binding domains of peripheral membrane proteins containing BAR domains and amphipathic alpha-helices. It is observed that electrostatic interaction is essential for curvature generation by the BAR domains.

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CoVID-19 virus SARS-CoV-2 follows the endocytosis process to enter inside a cell to infect it. It is important to study the endocytosis of SARS-CoV-2 in cell membrane to prevent the pandemic of CoVID-19. In this paper we develop a finite element based computational model for endocytosis of SARS-CoV-2 in cell membrane and determine curvature generation on it during the process. The virus SARS-CoV-2 is modeled as a rigid spherical particle and cell membrane as an anisotropic elastic material, while its fluidic nature due to lipid exchange with infinite reservoir is preserved using suitable conditions. With the help of a contact pair created between the virus particle and cell membrane, endocytosis process is computationally studied and the curvature of membrane is evaluated as the time progresses during the endocytosis process. At the tip of the virus particle and half-radius distance from it, the membrane follows the curvature of virus very quickly. However, it takes more time for the membrane point located at a distance equal to the radius of the virus particle. This is compensated by the cytoplasmic peripheral proteins binding onto the inside surface of the cell membrane. The role of cytoplasmic peripheral BAR proteins is investigated by using a linear curvature-coupling model with protein concentrations. It is observed that F-BAR protein is more sensitive to the curvature of virus particle in comparison to the other BAR proteins. The sensitiveness deteriorates as the curvature is increased.