Soap film spanning electrically repulsive elastic protein links

Abstract

We study the equilibrium problem of a mechanical system consisting of two Kirchhoff rods linked in an arbitrary way and also forming knots, constrained not to touch themselves by means of electrical repulsion and tied by a soap film, as a model to describe the interaction between an electrically charged protein and a biomembrane. We prove the existence of a solution with minimum total energy, which may be quite irregular, by using techniques of the Calculus of Variations.