Pearling Instability Research Articles

Modeling morphological instabilities in lipid membranes with anchored amphiphilic polymers

Anchoring molecules, like amphiphilic polymers, are able to dynamically regulate membrane morphology. Such molecules insert their hydrophobic groups into the bilayer, generating a local membrane curvature. In order to minimize the elastic energy penalty, a dynamic shape instability may occur, as in the case of the curvature-driven pearling instability or the polymer-induced tubulation of lipid vesicles. We review recent works on modeling of such instabilities by means of a mesoscopic dynamic model of the phase-field kind, which take into account the bending energy of lipid bilayers.

Cell Division: Breaking Up Is Easy to Do

How did cells divide before protein machines evolved? A new study shows that bacteria can reproduce without the division machinery, supporting the idea that primordial cells could have divided using physical mechanisms alone.

Stability of liquid ridges on chemical micro- and nanostripes

We analyze the stability of sessile filaments (ridges) of nonvolatile liquids versus pearling in the case of externally driven flow along a chemical stripe within the framework of the thin-film approximation. The ridges can be stable with respect to pearling even if the contact line is not completely pinned. A generalized stability criterion for moving contact lines is provided. For large wavelengths and no driving force, within perturbation theory, an analytical expression of the growth rate of pearling instabilities is derived. A numerical analysis shows that a body force along the ridge further stabilizes the ridge by reducing the growth rate of unstable perturbations, even though there is no complete stabilization. Hence the stability criteria established in the absence of driven flow ensure overall stability.

Shape Deformation of Ternary Vesicles Coupled with Phase Separation

We report an experimental study on shape deformations of ternary vesicles undergoing phase separation under an osmotic pressure difference. The phase separation on various shape vesicles causes unique shape-deformation branches. In the domain coarsening stage, prolate, discocyte, and starfish vesicles show a shape convergence to discocytes, whereas a pearling instability is observed in tube vesicles. In late stages, the domains start to bud towards the inside or outside of the vesicle depending on the excess area. We discuss the deformation branches based on the membrane elasticity model.

Shape Deformation of Vesicle Coupled with Phase Separation

1. INTRODUCTIONHomogeneous lipid bilayer vesicles show a variety of shapes in water such as sphere, prolate, oblate,starfish, stomatocyte, tube and so on. These shape deformations may play important roles in thebiomembrane transport processes of the living cell membranes and well described by an area-differencefree energy (ADE) model [1], which consists of two terms, the Helfrich bending energy and the elasticenergy originating from area difference between inner and outer leaflets under constraints of fixed totalvolume and total surface area [2]. The important parameters to determine the shape of the vesicle are excessarea defined by a ratio of the total area to total volume, and the area difference. If we add salts outside of thevesicle, the excess area increases with elapse of time due to the osmotic pressure difference and the vesiclesshow a parade of deformation with repeating bifurcations. On the other hand, multi-component vesicles show a phase separation, which forms domain structure onthe vesicle [3]. In this case the domain boundary energy governs the total free energy and leads the domaincoarsening and the budding. Recently we found that the dynamical coupling between the shape deformationand the phase separation brings astonishing shape deformation pathways.2. RESULTS AND DISCUSSIONIn this study, we prepared the spherical ternary vesicles in homogeneous one phase region and thenadded salts outside of the vesicles. When the vesicles deformed to appropriate shapes, we decreased thetemperature to the coexisting two phase region where the shape deformation induced by the osmotic pressuredifference couples with the phase separation. In the domain coarsening stage, every polygonal (prolate,discocyte, and starfish) vesicle showed a shape convergence to discocytes with two large domains in bothflat sides. This shape convergence indicates that in the presence of two stiff domains the morphologyminimizing the ADE energy is a discocyte shape. Meanwhile, a tube vesicle deformed to a necklace structurecomposed of a chain of discocytes with two domains in both flat sides, like a pearling instability. For a shorttube having a small excess area, the domains showed coarsening and the vesicle finally transformed into adiscocyte, whereas for a long tube having a large excess area, the domain coarsening was kinetically trapped,which may be due to the bending penalty of the matrix. After the coarsening, domains started to bud towardinside or outside of the vesicle depending on the excess area. These unique shape-deformation branches canbe explained by the free energy analyses based on the ADE model for a multi-domain vesicle under thegeometrical constraints [4].REFERENCES1. U. Seifert, Adv. Phys. 46 (1997) 13.2. M. Yanagisawa, M. Imai, T. Masui, S. Komura and T. Ohta, Biophys. J. 92 (2007) 115.3. S. Veatch and S. Keller, Biochim. Biophys. Acta 1746 (2005) 172.4. M. Yanagisawa, M. Imai and T. Taniguchi, Phys. Rev. Lett. in press.

Dynamic instabilities in biological membranes

AbstractA phase‐field model for dealing with the elastic bending energies is studied in the context of dynamic instabilities in membranes. We use it to study curvature‐driven pearling instability in vesicles induced by the anchorage of amphophilic polymers on the membrane. Within this model, we obtain the morphological changes reported in the experimental literature. The formation of a homogeneous pearled structure is achieved by consequent pearling of an initial cylindrical tube from the tip. For high enough concentration of anchors, we show theoretically that the homogeneous pearled shape is energetically less favorable than an inhomogeneous one, with a large sphere connected to an array of smaller spheres. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Model for Curvature-Driven Pearling Instability in Membranes

A phase-field model for dealing with dynamic instabilities in membranes is presented. We use it to study curvature-driven pearling instability in vesicles induced by the anchorage of amphiphilic polymers on the membrane. Within this model, we obtain the morphological changes reported in recent experiments. The formation of a homogeneous pearled structure is achieved by consequent pearling of an initial cylindrical tube from the tip. For high enough concentration of anchors, we show theoretically that the homogeneous pearled shape is energetically less favorable than an inhomogeneous one, with a large sphere connected to an array of smaller spheres.

Hollow Polyelectrolyte Multilayer Tubes: Mechanical Properties and Shape Changes

In this paper, novel hollow polyelectrolyte multilayer tubes from poly(diallyldimethylammonium chloride) (PDADMAC), poly(styrene sulfonate) (PSS), and poly(allylamine hydrochloride) (PAH) were prepared: Readily available glass fiber templates are coated with polyelectrolytes using the layer-by-layer technique, followed by subsequent fiber dissolution. Depending on the composition of the polymeric multilayer, stable hollow tubes or tubes showing a pearling instability are observed. This instability corresponds to the Rayleigh instability and is a consequence of an increased mobility of the polyelectrolyte chains within the multilayer. The well-defined stable tubes were characterized with fluorescence microscopy, confocal laser scanning microscopy, and atomic force microscopy (AFM). The tubes were found to be remarkably free of defects, which results in an impermeable tube wall for even low molecular weight molecules. The mechanical properties of the tubes were determined with AFM force spectroscopy in water, and because continuum mechanical models apply, the Young's modulus of the wall material was determined. Additionally, scaling relations for the dependency of tube stiffness on diameter and wall thickness were validated. Because both parameters can be experimentally controlled by our approach, the deformability of the tubes can be varied over a broad range and adjusted for the particular needs.

Preparation and mechanical characterization of artificial hollow tubes

In this paper, we present a novel route to prepare hollow tubes using the template assisted Layer-by-Layer technique. A readily available glass fibre template was coated with polyelectrolyte multilayers, followed by subsequent fibre dissolution. After the fibre dissolution we discovered stable hollow tubes or observed a pearling instability depending on the composition of the multilayer. Here we focus on hollow tubes: we precisely characterized the tubes with Fluorescence Microscopy, Confocal Laser Scanning Microscopy and AFM Topography Imaging. The tubes have an aspect ratio of around 10, with diameters from 5 μm up to 17 μm. The Layer-by-Layer technique allows us to control the tubes' wall thickness within a few nanometers; here the total wall thickness was 60 nm. Because the tubes can find a possible application in drug delivery, we tested the permeability of the multilayer membrane. The mechanical properties of the wall were investigated with AFM Force Spectroscopy and because continuum mechanical models apply to this system we derived a Young's modulus of the wall material.

Pearling instability of nanoscale fluid flow confined to a chemical channel

We investigate the flow of a nanoscale incompressible ridge of low-volatility liquid along a “chemical channel”: a long, straight, and completely wetting stripe embedded in a planar substrate, and sandwiched between two extended less wetting solid regions. Molecular dynamics simulations, a simple long-wavelength approximation, and a full stability analysis based on the Stokes equations are used, and give qualitatively consistent results. While thin liquid ridges are stable both statically and during flow, a (linear) pearling instability develops if the thickness of the ridge exceeds half of the width of the channel. In the flowing case, periodic bulges propagate along the channel and subsequently merge due to nonlinear effects. However, the ridge does not break up even when the flow is unstable, and the qualitative behavior is unchanged even when the fluid can spill over onto a partially wetting exterior solid region.

Orientation-Dependent Dewetting of Patterned Thin Si Film on SiO2

AbstractThe agglomeration of a Silicon On Insulator (001) film during a thermal annealing at 900°C and 950°C under hydrogenated atmosphere has been characterized by Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM). At this temperature, the Si faceting along {110}, {111} and {113} planes is interpreted by a surface energy anisotropy. The anisotropy of the diffusion coefficient is also revealed by the formation of Si line along the <510>, <110> and <100> directions. A mechanism of the pearling instability of the <510> lines is proposed.

Surface charge relaxation and the pearling instability of charged surfactant tubes

The pearling instability of bilayer surfactant tubes was recently observed during the collapse of fluid monolayers of binary mixtures of Dimyristoylphosphocholine (DMPC): Palmitoyloleoylphosphoglycerol (POPG) and Dipalmitoylphosphocholine (DPPC):POPG surfactants. It can be explained by a Rayleigh-like instability under the action of the bilayer surface tension. The magnitude of surface tension is dictated by the electrostatic interaction between charged surfactants. Relaxation of charged molecules is proposed here as an additional mechanism driving the instability. We find the functional dependence of the electrostatic surface tension and relaxation energies on the screening length kappa(-1) explicitly. Relaxation lowers the cost of bending a tube into pearls making the cylindrical tube even more unstable. It is known that for the weak screening case in which the tube radius is smaller than the screening length of the solution, this effect is important. However, for the case of strong screening it is negligible. For the experiments mentioned, the situation is marginal. In this case, we show that the effect of relaxation remains small. It contributes about 20% to the total electrostatic energy.

Pearling instabilities in water-dispersed copolymer cylinders with charged brushes

We investigate the structural behavior of a poly(styrene)-block-poly(acrylic acid) diblock copolymer which forms hexagonally-packed PS cylinders (C-phase) in the melt state. The water dispersion of this structure provides hairy cylinders which comprise a PAA swollen cylindrical brush with a height h tunable via its degree of ionization and the ionic strength in the solution, and a water-free, PS cylindrical core of constant radius R(C). Such system constitutes an "out-of-equilibrium" frustrated model system: the selective swelling of the PAA brush results in a frustration of the interface curvature, which the ratio h/R(C) allows to quantify. Upon heating at a temperature higher than the glass transition temperature of the PS core, the glassiness of the core is relieved and the mechanical constraints arising from the selective swelling of the structure can be relaxed: the cylinders undergo a cylinder-to-sphere transition upon annealing at high temperature, when above a frustration threshold h/R(C) approximately 1.8. Thanks to a careful mapping of the transition diagram, an undulating cylindrical morphology (UC) is identified between unchanged cylinders ( h/R(C) approximately 1.8) and spheres ( h/R(C) < or = 2.0), which appears to result from a Rayleigh-like pearling instability of the copolymer cylinders.

Physics of cell elasticity, shape and adhesion

We review recent theoretical work that analyzes experimental measurements of the shape, fluctuations and adhesion properties of biological cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the shape and adhesion of elastic cells with fluid-filled vesicles. In red blood cells (RBC), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wavevector and frequency dependence of the fluctuation spectrum of RBC indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton–membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect topological defects induced in the cytoskeleton network by ATP. The shapes of cells that adhere to a substrate are strongly determined by the cytoskeletal elasticity that can be varied experimentally by drugs that depolymerize the cytoskeleton. This leads to a tension-driven retraction of the cell body and a pearling instability of the resulting ray-like protrusions. Recent experiments have shown that adhering cells exert polarized forces on substrates. The interactions of such “force dipoles” in either bulk gels or on surfaces can be used to predict the nature of self-assembly of cell aggregates and may be important in the formation of artificial tissues. Finally, we note that cell adhesion strongly depends on the forces exerted on the adhesion sites by the tension of the cytoskeleton. The size and shape of the adhesion regions are strongly modified as the tension is varied and we present an elastic model that relates this tension to deformations that induce the recruitment of new molecules to the adhesion region. In all these examples, cell shape and adhesion differ from vesicle shape and adhesion due to the presence of the elastic cytoskeleton and to the fact that active processes (ATP, molecular motors) within the cell modify cytoskeletal elasticity and tension.

Coiling instabilities of multilamellar tubes.

Myelin figures are densely packed stacks of coaxial cylindrical bilayers that are unstable to the formation of coils or double helices. These myelin figures appear to have no intrinsic chirality. We show that such cylindrical membrane stacks can develop an instability when they acquire a spontaneous curvature or when the equilibrium distance between membranes is decreased. This instability breaks the chiral symmetry of the stack and may result in coiling. A unilamellar cylindrical vesicle, on the other hand, will develop an axisymmetric instability, possibly related to the pearling instability.

Template-directed self-assembly of buried nanowires and the pearling instability

The fabrication of more and more miniaturized electronic and photonic devices relies on new, ingenious methods for the fabrication of spatially controlled nanostructures. Examples are electronic devices based on semiconducting nanowires and photonic devices based on chains of metallic nanoclusters that guide the light by coupled surface plasmons. In this contribution, a template-directed ion beam synthesis (IBS) of nanowires and regular nanocluster chains will be presented. As templates, V-grooves etched in (001)Si and subsequently oxidized are used. High-fluence Ge + implantation is carried out into the SiO 2 layer at 70 keV. Thereby, the implanted Ge enriches itself in the V-groove bottom to a critical amount, which may result in nanowire formation by nucleation, growth and coalescence during subsequent thermal treatment. TEM investigations indicate the formation of a nanowire buried in the SiO 2 at the V-groove bottom. Kinetic lattice Monte Carlo simulations (KLMC) of the nanowire formation process were performed in order to understand the phase separation mechanism and results are compared to TEM images. Furthermore, it is shown that even ideal nanowires show an instability and form during long-lasting annealing equal-spaced and equal-sized nanoclusters (“nanocluster chains”) by self-organization.

Pearling instabilities of membrane tubes with anchored polymers.

We have studied the pearling instability induced on hollow tubular lipid vesicles by hydrophilic polymers with hydrophobic side groups along the backbone. The results show that the polymer concentration is coupled to local membrane curvature. The relaxation of a pearled tube is characterized by two different well-separated time scales, indicating two physical mechanisms. We present a model, which explains the observed phenomena and predicts polymer segregation according to local membrane curvature at late stages.

Pearling in cells: A clue to understanding cell shape

Gradual disruption of the actin cytoskeleton induces a series of structural shape changes in cells leading to a transformation of cylindrical cell extensions into a periodic chain of "pearls." Quantitative measurements of the pearling instability give a square-root behavior for the wavelength as a function of drug concentration. We present a theory that explains these observations in terms of the interplay between rigidity of the submembranous actin shell and tension that is induced by boundary conditions set by adhesion points. The theory allows estimation of the rigidity and thickness of this supporting shell. The same theoretical considerations explain the shape of nonadherent edges in the general case of untreated cells.

Spontaneous curvature-induced pearling instability

We investigate the instability of a tubular fluid membranes made of a water soluble surfactant. The tubules are obtained at high salinities. The instability is due to the introduction within the vesicle multilayer of an alkane. We measure the wavelength of this instability versus the unperturbed radius of the tubules. To interpretthis dependance we use a model that includes not only the surface tension in the elastic energy but the spontaneous curvature as well. The spontaneous curvature is induced by the presenceof the oil in the bilayer of the membrane and give a selection of a non-zero wavelength.

Dynamic Excitations in Membranes Induced by Optical Tweezers

We present the phenomenology of transformations in lipid bilayers that are excited by laser tweezers. A variety of dynamic instabilities and shape transformations are observed, including the pearling instability, expulsion of vesicles, and more exotic ones, such as the formation of passages. Our physical picture of the laser-membrane interaction is based on the generation of tension in the bilayer and loss of surface area. Although tension is the origin of the pearling instability, it does not suffice to explain expulsion of vesicles, where we observe opening of giant pores and creeping motion of bilayers. We present a quantitative theoretical framework to understand most of the observed phenomenology. The main hypothesis is that lipid is pulled into the optical trap by the familiar dielectric effect, is disrupted, and finally is repackaged into an optically unresolvable suspension of colloidal particles. This suspension, in turn, can produce osmotic pressure and depletion forces, driving the observed transformations.