Dynamics of Rayleigh-like Instability Induced by Laser Tweezers in Tubular Vesicles of Self-Assembled Membranes

Abstract

We present a theoretical study of the Rayleigh-like, pearling, instability recently observed in tubular vesicles of bilayer membranes under the action of optical tweezers. The tweezers are argued to pull the membrane into their operation zone, thereby inducing a tension in it. Consequently, the membrane can respond in a Rayleigh-like instability, in which its area decreases. Our approach is based on a linear stability analysis of the deformations. However, because of the non-linear coupling existing between the suction process and the growth of the unstable modes, the instability develops different characteristics. At long times, the growth of the instability is controlled by the suction rate of the tweezers, assumed constant in time. The wavelength λ* of the most unstable mode is time-dependent: at short times it decreases as ∼ t -1/2 ; at long times it is either constant, of the order of the tube radius R, or increases as ∼ t 1/4 . The amplitude of the most unstable mode increases (at long times) as ∼ t 1/2 . We delineate the different regimes under which these behaviours are predicted, and discuss their possible implications on experiment. We also briefly discuss the possibility for other non-linear effects, such as an induced spontaneous curvature in the membrane, which may be responsible for the appearance of very narrow tubes in the late stages.