Front Progagation in the Pearling Instability of Tubular Vesicles

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 0.7µm has a predicted initial sinusoidal perturbation in its diameter with wavelength 5.5µm, as observed. The perturbation propagates as a front with the qualitatively correct front velocity a bit less than 100µm/sec. 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. 9/95

The mechanism of shape instability for a vesicle in extensional flow

“…This instability is the buckling/wrinkling instability, as it creates short-wavelength ripples on the surface due to the creation of negative tensions. These stability margins agree with all previous studies, as we obtain the same bending factor Ω(k) (Goldstein et al 1996;Powers 2010;Boedec et al 2014). Our hydrodynamical factor Λ(k) agrees with…”

“…This analysis is not novel, as it has been performed many times in the literature (Goldstein et al 1996;Powers 2010), with the latest (and most accurate version) by Boedec, Jaeger & Leonetti (2014). We outline a simplified derivation of the dispersion relationship in § A.6, and plot the growth rates in figure 22(a,b).…”

“…Previous studies computed Λ(k) slightly incorrectly, as they forgot to take into account the spatially varying tension (i.e. σ (1) ) in their derivations (Goldstein et al 1996;Powers 2010).…”

Pearling, wrinkling, and buckling of vesicles in elongational flows

“…These shape transitions are a consequence of the external force inducing a tension on the vesicle's membrane. When this tension overcomes the membrane's bending resistance, the membrane becomes linearly unstable to long-wave, axisymmetric shape perturbations (Goldstein et al 1996;Powers 2010).…”

Stable and robust polymer nanotubes stretched from polymersomes

“…beads. Corrugation of tubular lipid vesicles have been explained as a Rayleigh-type instability arising during front propagation because of a sudden increase in membrane tension (24). Corrugated patterns observed in cylindrical polymer gels (25) have been attributed to stress associated with the spatial changes in the polymer density across the thickness of the polymer boundary, which limits the diffusion of water.…”