UNDULATIONS OF A STRAIGHT POLYMER-CHAIN EMBEDDED IN A MEMBRANE

We consider a sinusoidal undulation of a straight, linear polymer embe dded in a hat membrane exposed to a lateral tension. We determine the shape of the membrane and compute the elastic energy associated with t he undulation of the polymer. Analysing this energy at different wavel engths of the undulation, we find the criteria of stability of the str aight shape of the polymer, and show them to be controlled by the diff erence of moduli of Gaussian curvature, <<Delta(kappa)over bar>, of th e polymerized and unpolymerized membrane. We also discuss formal analo gies and differences between the behaviour of a polymer embedded into a membrane and a charged bilayer membrane immersed in a solution of el ectrolyte.