Critical holes in undercooled wetting layers

The profile of a critical hole in an undercooled wetting layer is determined by the saddle-point equation of a standard interface Hamiltonian supported by convenient boundary conditions. It is shown that this saddle-point equation can be mapped onto an autonomous dynamical system in a three-dimensional phase space. The corresponding flux has a polynomial form and in general displays four fixed points, each with different stability properties. On the basis of this picture we derive the thermodynamic behaviour of critical holes in three different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.

Contraction Mechanisms in Composite Active Actin Networks

Simplified in vitro systems are ideally suited for studying the principle mechanisms of the contraction of cytoskeletal actin systems. To shed light on the dependence of the contraction mechanism on the nature of the crosslinking proteins, we study reconstituted in vitro active actin networks on different length scales ranging from the molecular organization to the macroscopic contraction. Distinct contraction mechanisms are observed in polar and apolar crosslinked active gels whereas composite active gels crosslinked in a polar and apolar fashion at the same time exhibit both mechanisms simultaneously. In polar active actin/fascin networks initially bundles are formed which are then rearranged. In contrast, apolar cortexillin-I crosslinked active gels are bundled only after reorganization of actin filaments by myosin-II motor filaments

Mechanics of bundled semiflexible polymer networks

While actin bundles are used by living cells for structural fortification, the microscopic origin of the elasticity of bundled networks is not understood. Here, we show that above a critical concentration of the actin binding protein fascin, a solution of actin filaments organizes into a pure network of bundles. While the elasticity of weakly crosslinked networks is dominated by the affine deformation of tubes, the network of bundles can be fully understood in terms of non-affine bending undulations.Comment: 5 pages, 3 figures, final version as publishe

Nucleation-induced transition to collective motion in active systems

While the existence of polar ordered states in active systems is well established, the dynamics of the self-assembly processes are still elusive. We study a lattice gas model of self-propelled elongated particles interacting through excluded volume and alignment interactions, which shows a phase transition from an isotropic to a polar ordered state. By analyzing the ordering process we find that the transition is driven by the formation of a critical nucleation cluster and a subsequent coarsening process. Moreover, the time to establish a polar ordered state shows a power-law divergence

Crystallography on Curved Surfaces

We study static and dynamical properties that distinguish two dimensional crystals constrained to lie on a curved substrate from their flat space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian curvature is presented in the context of a model surface amenable to full analytical treatment. We find that glide diffusion of isolated dislocations is suppressed by a binding potential of purely geometrical origin. Finally, the energetics and biased diffusion dynamics of point defects such as vacancies and interstitials is explained in terms of their geometric potential.Comment: 12 Pages, 8 Figure

Steric regulation of tandem calponin homology domain actin-binding affinity.

Tandem calponin homology (CH1-CH2) domains are common actin-binding domains in proteins that interact with and organize the actin cytoskeleton. Despite regions of high sequence similarity, CH1-CH2 domains can have remarkably different actin-binding properties, with disease-associated point mutants known to increase as well as decrease affinity for F-actin. To investigate features that affect CH1-CH2 affinity for F-actin in cells and in vitro, we perturbed the utrophin actin-binding domain by making point mutations at the CH1-CH2 interface, replacing the linker domain, and adding a polyethylene glycol (PEG) polymer to CH2. Consistent with a previous model describing CH2 as a steric negative regulator of actin binding, we find that utrophin CH1-CH2 affinity is both increased and decreased by modifications that change the effective "openness" of CH1 and CH2 in solution. We also identified interface mutations that caused a large increase in affinity without changing solution "openness," suggesting additional influences on affinity. Interestingly, we also observe nonuniform subcellular localization of utrophin CH1-CH2 that depends on the N-terminal flanking region but not on bulk affinity. These observations provide new insights into how small sequence changes, such as those found in diseases, can affect CH1-CH2 binding properties

Microrheology, stress fluctuations and active behavior of living cells

We report the first measurements of the intrinsic strain fluctuations of living cells using a recently-developed tracer correlation technique along with a theoretical framework for interpreting such data in heterogeneous media with non-thermal driving. The fluctuations' spatial and temporal correlations indicate that the cytoskeleton can be treated as a course-grained continuum with power-law rheology, driven by a spatially random stress tensor field. Combined with recent cell rheology results, our data imply that intracellular stress fluctuations have a nearly $1/\omega^2$ power spectrum, as expected for a continuum with a slowly evolving internal prestress.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let

Micro- and Macrorheological Properties of Isotropically Cross-linked Actin Networks

Cells make use of semi-flexible biopolymers such as actin or intermediate filaments to control their local viscoelastic response by dynamically adjusting the concentration and type of cross-linker molecules. The microstructure of the resulting networks mainly determines their mechanical properties. It remains an important challenge to relate structural transitions to both the molecular properties of the cross-linking molecules and the mechanical response of the network. This can be achieved best by well-defined in vitro model systems in combination with microscopic techniques. Here, we show that with increasing concentrations of the cross-linker HMM (heavy meromyosin) a transition in the mechanical network response occurs. At low cross-linker densities the network elasticity is dominated by the entanglement length of the polymer, while at high HMM densities the cross-linker distance determines the elastic behavior. Using microrheology the formation of heterogeneous networks is observed at low cross-linker concentrations. Micro- and macrorheology both report the same transition to a homogeneous cross-linked phase. This transition is set by a constant average cross-linker distance. Thus, the micro- and macromechanical properties of isotropically cross-linked in vitro actin networks are determined by only one intrinsic network parameter.Comment: 14 pages, 5 figure

Grain Boundary Scars and Spherical Crystallography

We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the minimum energy configurations of particles with arbitrary repulsive interactions on curved surfaces. Above a critical system size we find that crystals develop distinctive high-angle grain boundaries, or scars, not found in planar crystals. The number of excess defects in a scar is shown to grow linearly with the dimensionless system size. The observed slope is expected to be universal, independent of the microscopic potential.Comment: 4 pages, 3 eps figs (high quality images available from Mark Bowick