Preferred configurations of linear polymers embedded in planar membranes under lateral tension.

Abstract

We consider a linear polymer in a flat membrane exposed to a lateral tension ${\ensuremath{\gamma}}_{0}$. The polymer is assumed to produce a sharp bend in the membrane so that in its straight state it gives rise to a symmetric ridge of width \ensuremath{\lambda}= \ensuremath{\surd}\ensuremath{\kappa}/${\ensuremath{\gamma}}_{0}$ , \ensuremath{\kappa} being the bending rigidity of the membrane. We calculate the effective in-plane bending energy of the polymer that originates from the deformation of the membrane ridge. The parameter controlling the energy as a function of curvature of the polymer is \ensuremath{\Delta}\ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{}/\ensuremath{\kappa}, where \ensuremath{\Delta}\ensuremath{\kappa}\ifmmode\bar\else\textasciimacron\fi{} is the difference of the moduli of Gaussian curvature of unpolymerized and polymerized lipid. Depending on its value, the presence of the ridge increases the persistence length or destabilizes the straight configuration of the polymer. Destabilization occurs on both sides of a range of stability, leading in the case of circular configurations to craters with a depressed or elevated interior.