Nonequilibrium Fluctuations, Travelling Waves, and Instabilities in Active Membranes

The stability of a flexible fluid membrane containing a distribution of mobile, active proteins (e.g. proton pumps) is shown to depend on the structure and functional asymmetry of the proteins. A stable active membrane is in a nonequilibrium steady state with height fluctuations whose statistical properties are governed by the protein activity. Disturbances are predicted to travel as waves at sufficiently long wavelength, with speed set by the normal velocity of the pumps. The unstable case involves a spontaneous, pump-driven undulation of the membrane, with clumping of the proteins in regions of high activity.Comment: 4 two-column pages, two .eps figures included, revtex, uses eps

Polarity patterns of stress fibers

Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns.Comment: 5 pages, 3 figure

Generic phase diagram of active polar films

We study theoretically the phase diagram of compressible active polar gels such as the actin network of eukaryotic cells. Using generalized hydrodynamics equations, we perform a linear stability analysis of the uniform states in the case of an infinite bidimensional active gel to obtain the dynamic phase diagram of active polar films. We predict in particular modulated flowing phases, and a macroscopic phase separation at high activity. This qualitatively accounts for experimental observations of various active systems, such as acto-myosin gels, microtubules and kinesins in vitro solutions, or swimming bacterial colonies.Comment: 4 pages, 1 figur

Escape configuration lattice near the nematic-isotropic transition: Tilt analogue of blue phases

We predict the possible existence of a new phase of liquid crystals near the nematic-isotropic ($NI$) transition. This phase is an achiral, tilt-analogue of the blue phase and is composed of a lattice of {\em double-tilt}, escape-configuration cylinders. We discuss the structure and the stability of this phase and provide an estimate of the lattice parameter.Comment: 5 pages, 6 figures (major revision, typos corrected, references added

Mechanical Instabilities of Biological Tubes

We study theoretically the shapes of biological tubes affected by various pathologies. When epithelial cells grow at an uncontrolled rate, the negative tension produced by their division provokes a buckling instability. Several shapes are investigated : varicose, enlarged, sinusoidal or sausage-like, all of which are found in pathologies of tracheal, renal tubes or arteries. The final shape depends crucially on the mechanical parameters of the tissues : Young modulus, wall-to-lumen ratio, homeostatic pressure. We argue that since tissues must be in quasistatic mechanical equilibrium, abnormal shapes convey information as to what causes the pathology. We calculate a phase diagram of tubular instabilities which could be a helpful guide for investigating the underlying genetic regulation

Factors Responsible for the Stability and the Existence of a Clean Energy Gap of a Silicon Nanocluster

We present a critical theoretical study of electronic properties of silicon nanoclusters, in particular the roles played by symmetry, relaxation, and hydrogen passivation on the the stability, the gap states and the energy gap of the system using the order-N [O(N)] non-orthogonal tight-binding molecular dynamics and the local analysis of electronic structure.Comment: 26 pages including figure