Some properties of membranes in nematic solvents

The fluctuation spectrum of membranes in nematic solvents is altered by the boundary condition imposed on the bulk nematic director by the curved membrane. We discuss some properties of single and multi-membrane systems in nematic solvents, primarily based on the Berreman-de~Gennes model. We show that: membranes in nematic solvents are more rigid and less rough than in their isotropic counterparts; have a different Helfrich steric stabilization energy, proportional to $d^{-3}$, and hence a different compression modulus in the lamellar state; and can exhibit phase separation via unbinding during a quench into the nematic state. We also discuss the preparation and possible experimental effects of nematic-mediated surfactant membrane system

Bundling in brushes of directed and semiflexible polymers

We explore the effect of an attractive interaction between parallel-aligned polymers, which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength, which is set by the length scale of transverse fluctuations of the grafted polymers. We analyze the instability for two models of aligned polymers: directed polymers with a line tension and weakly bending chains with a bending stiffness.Comment: 7 pages, 5 figures, final version as published in PR

How cells feel: stochastic model for a molecular mechanosensor

Understanding mechanosensitivity, i.e. how cells sense the stiffness of their environment is very important, yet there is a fundamental difficulty in understanding its mechanism: to measure an elastic modulus one requires two points of application of force - a measuring and a reference point. The cell in contact with substrate has only one (adhesion) point to work with, and thus a new method of measurement needs to be invented. The aim of this theoretical work is to develop a self-consistent physical model for mechanosensitivity, a process by which a cell detects the mechanical stiffness of its environment (e.g. a substrate it is attached to via adhesion points) and generates an appropriate chemical signaling to remodel itself in response to this environment. The model uses the molecular mechanosensing complex of latent TGF-$\beta$ attached to the adhesion point as the biomarker. We show that the underlying Brownian motion in the substrate is the reference element in the measuring process. The model produces the closed expression for the rate of release of active TGF-$\beta$, which depends on the substrate stiffness and the pulling force coming from the cell in a subtle and non-trivial way. It is consistent with basic experimental data showing an increase in signal for stiffer substrates and higher pulling forces. In addition, we find that for each cell there is a range of stiffness where a homeostatic configuration of the cell can be achieved, outside of which the cell either relaxes its cytoskeletal forces and detaches from the very weak substrate, or generates an increasingly strong pulling force through stress fibers with a positive feedback loop on very stiff substrates. In this way, the theory offers the underlying mechanism for the myofibroblast conversion in wound healing and smooth muscle cell dysfunction in cardiac disease

Nonlinear elasticity of semiflexible filament networks.

We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model of network elasticity over several plausible candidates, and derive analytical expressions for the elastic energy at arbitrary strain, with the corresponding stress-strain relationship. The theory fits well to a wide range of experimental data on simple shear in different filament networks, quantitatively matching the differential shear modulus variation with stress, with only two adjustable parameters (which represent the filament stiffness and the pre-tension in the network, respectively). The general theory accurately describes the crossover between the positive and negative Poynting effect (normal stress on imposed shear) on increasing the stiffness of filaments forming the network. We discuss the network stability (the point of marginal rigidity) and the phenomenon of tensegrity, showing that filament pre-tension on crosslinking into the network determines the magnitude of linear modulus G0.This work has been funded by the TCM Critical Mass Grant from EPSRC (EP/J017639).This is the final version of the article. It first appeared from RSC at http://dx.doi.org/10.1039/C6SM01029F

Development of Nascent Focal Adhesions in Spreading Cells.

The eukaryotic cell develops organelles to sense and respond to the mechanical properties of its surroundings. These mechanosensing organelles aggregate into symmetry-breaking patterns to mediate cell motion and differentiation on substrate. The spreading of a cell plated onto a substrate is one of the simplest paradigms in which angular symmetry-breaking assemblies of mechanical sensors are seen to develop. We review evidence for the importance of the edge of the cell-extracellular matrix adhesion area in the aggregation of mechanosensors and develop a theoretical model for the clustering of mechanosensors into nascent focal adhesions on this contact ring. To study the spatial patterns arising on this topological feature, we use a one-dimensional lattice model with a nearest-neighbor interaction between individual integrin-mediated mechanosensors. We find the effective Ginzburg-Landau free energy for this model and determine the spectrum of spatial modes as the cell spreads and increases its contact area with the substrate. To test our model, we compare its predictions with measured distributions of paxillin in spreading fibroblasts.BBRSC DTP Cambridge (grant no. EP/M508007/