The cell cytoskeleton is made up of polar protein filaments that interact with each other via various proteins, either fixed or motile. The filamentous aspect of its structure gives it properties that resemble those of polymer solutions and liquid crystals. The cytoskeleton however is active: thanks to a direct energy consumption or its coupling to motor proteins, it produces local deformations and stresses that allow the cell to deform, move, exert forces, and divide. A major component of the cell cytoskeleton is actin: biopolymer filaments that can polymerize and depolymerize thanks to the hydrolyzis of ATP to create stresses or deformations.
When grown externally on a reconstituted liposome, a layer of crosslinked actin filaments that form a growing gel can deform the liposome and produce different shape instabilities1. We propose to study the phenomenon of stress buildup and deformations under the sole action of actin polymerization/depolymerization in this geometry and to look for dynamical instabilities of the spherical geometry. We shall rely on a previous expertise on the instability of cellular spheroids driven by inhomogeneous cell- renewal distributions2.
