Fluctuations of the Casimir-like force between two membrane inclusions

Although Casimir forces are inseparable from their fluctuations, little is known about these fluctuations in soft matter systems. We use the membrane stress tensor to study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force is dominated by its fluctuations. Furthermore, when the distance d between the inclusions is decreased from infinity, the variance of the Casimir force decreases as -1/d^2. This distance dependence shares a common physical origin with the Casimir force itself.Comment: 5 pages, 3 figure

Knots in Charged Polymers

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.Comment: Revtex4, 9 pages, 9 eps figure

Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.Comment: 4 pages, 3 figure

Tightness of slip-linked polymer chains

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops which can exchange length between each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip-links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.Comment: 10 pages, 6 figures, REVTeX

Calcium-ion-controlled nanoparticle-induced tubulation in supported flat phospholipid vesicles

Biological nanotubes, often referred to as tunneling nanotubes, fulfill important functions within the cell, e.g. by supplying cell components, conducting signals and transporting virus particles and bacteria. Many functions are still insufficiently understood, which has placed these nanostructures in the focus of recent investigation. We report here on our observations of transient tubulation in nanoparticle-containing, supported flat giant unilamellar vesicles (FGUVs). The encapsulation of nanoparticles in FGUVs in conjunction with low (1-4 mM) Ca(2+) in the ambient buffer solution resulted in transient tube formation. Tubes extended from the FGUV up to a length of several hundred micrometres and exhibited, on some occasions, vesicle encapsulation. The findings represent an interesting confirmation of several reported theoretical and practical models of tube formation in biological or biomimetic systems

Fractal avalanche ruptures in biological membranes

Bilayer membranes envelope cells as well as organelles, and constitute the most ubiquitous biological material found in all branches of the phylogenetic tree. Cell membrane rupture is an important biological process, and substantial rupture rates are found in skeletal and cardiac muscle cells under a mechanical load(1). Rupture can also be induced by processes such as cell death(2), and active cell membrane repair mechanisms are essential to preserve cell integrity(3). Pore formation in cell membranes is also at the heart of many biomedical applications such as in drug, gene and short interfering RNA delivery(4). Membrane rupture dynamics has been studied in bilayer vesicles under tensile stress(5-8), which consistently produce circular pores(5,6). We observed very different rupture mechanics in bilayer membranes spreading on solid supports: in one instance fingering instabilities were seen resulting in floral-like pores and in another, the rupture proceeded in a series of rapid avalanches causing fractal membrane fragmentation. The intermittent character of rupture evolution and the broad distribution in avalanche sizes is consistent with crackling-noise dynamics(9). Such noisy dynamics appear in fracture of solid disordered materials(10), in dislocation avalanches in plastic deformations(11) and domain wall magnetization avalanches(12). We also observed similar fractal rupture mechanics in spreading cell membranes

Fractal avalanche ruptures in biological membranes

Bilayer membranes envelope cells as well as organelles, and constitute the most ubiquitous biological material found in all branches of the phylogenetic tree. Cell membrane rupture is an important biological process, and substantial rupture rates are found in skeletal and cardiac muscle cells under a mechanical load(1). Rupture can also be induced by processes such as cell death(2), and active cell membrane repair mechanisms are essential to preserve cell integrity(3). Pore formation in cell membranes is also at the heart of many biomedical applications such as in drug, gene and short interfering RNA delivery(4). Membrane rupture dynamics has been studied in bilayer vesicles under tensile stress(5-8), which consistently produce circular pores(5,6). We observed very different rupture mechanics in bilayer membranes spreading on solid supports: in one instance fingering instabilities were seen resulting in floral-like pores and in another, the rupture proceeded in a series of rapid avalanches causing fractal membrane fragmentation. The intermittent character of rupture evolution and the broad distribution in avalanche sizes is consistent with crackling-noise dynamics(9). Such noisy dynamics appear in fracture of solid disordered materials(10), in dislocation avalanches in plastic deformations(11) and domain wall magnetization avalanches(12). We also observed similar fractal rupture mechanics in spreading cell membranes