J. Phys. II France
Volume 6, Numéro 12, December 1996
Page(s) 1743 - 1757
DOI: 10.1051/jp2:1996107
J. Phys. II France 6 (1996) 1743-1757

Undulations of a Straight Polymer Chain Embedded in a Membrane

M. Singh-Zocchi1, M.M. Kozlov2 and W. Helfrich1

1  Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
2  Deptartment of Physiology and Pharmacology, Sackler School of Med., Tel-Aviv University, Ramat-Aviv 69978, Israel

(Received 12 March 1996, revised 14 June 1996, accepted 6 September 1996)

We consider a sinusoidal undulation of a straight, linear polymer embedded in a flat membrane exposed to a lateral tension. We determine the shape of the membrane and compute the elastic energy associated with the undulation of the polymer. Analysing this energy at different wavelengths of the undulation, we find the criteria of stability of the straight shape of the polymer, and show them to be controlled by the difference of moduli of Gaussian curvature, $\Delta \bar{\kappa}$, of the polymerized and unpolymerized membrane. We also discuss formal analogies and differences between the behaviour of a polymer embedded into a membrane and a charged bilayer membrane immersed in a solution of electrolyte.

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