DOI: 10.1051/jp2:1996210
J. Phys. II France 6 (1996) 767-796

Front Progagation in the Pearling Instability of Tubular Vesicles

Raymond E. Goldstein¹, Philip Nelson², Thomas Powers² and Udo Seifert<sup>3

1</sup>  Joseph Henry Laboratory of Physics, Princeton University, Princeton, NJ 08544, USA
²  Physics Department, University of Pennsylvania, University of Pennsylvania, Philadelphia, PA 19104, USA
³  Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Kantstrasse 55, 14513 Teltow-Seehof, Germany

(Received 3 October 1995, revised 12 December 1995, accepted 23 January 1996)

Abstract
Recently Bar-Ziv and Moses discovered a dynamical shape transformation induced in cylindrical lipid bilayer vesicles by the action of laser tweezers. We develop a hydrodynamic theory of fluid bilayers in interaction with the surrounding water and argue that the effect of the laser is to induce a sudden tension in the membrane. We refine our previous analysis to account for the fact that the shape transformation is not uniform but propagates outward from the laser trap. Applying the marginal stability criterion to this situation gives us an improved prediction for the selected initial wavelength and a new prediction for the propagation velocity, both in rough agreement with the experimental values. For example, a tubule of initial radius 0.7  m has a predicted initial sinusoidal perturbation in its diameter with wavelength 5.5  m, as observed. The perturbation propagates as a front with the qualitatively correct front velocity a bit less than 100  m/s. In particular we show why this velocity is initially constant, as observed and so much smaller than the natural scale set by the tension. We also predict that the front velocity should increase linearly with laser power. Finally we introduce an approximate hydrodynamic model applicable to the fully nonlinear regime. This model exhibits propagating fronts as well as fully-developed "pearled" vesicles similar to those seen in the experiments.

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