Networks of filamentous proteins play a crucial role in cell mechanics. These cytoskeletal networks, together with various cross-linking and other associated proteins largely determine the (visco)elastic response of cells. In this Letter we study a model system of cross-linked, stiff filaments in order to explore the connection between the microstructure under strain and the macroscopic response of cytoskeletal networks. We find two distinct regimes as a function primarily of cross-link density and filament rigidity: one characterized by affine deformation and one by nonaffine deformation. We characterize the crossover between these two.

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0+/-0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.

Quantitatively measuring the mechanical properties of soft matter over a wide range of length and time scales, especially if a sample is as complex as typical biological materials, remains challenging. Living cells present a further complication because forces are generated within these nonequilibrium materials that can change material properties. We have here developed high-bandwidth techniques for active one-and two-particle microrheology to tackle these issues. By combining active micromanipulation of probe particles with an optical trap with high-resolution tracking of thermal motions of the very same particles by laser interferometry, we can both measure the mechanical properties of and, at the same time, identify nonequilibrium forces in soft materials. In both simple liquids and equilibrium cytoskeletal actin networks, active microrheology (AMR) proves to be less noise sensitive than and offers extended bandwidth (0.1-100 kHz) compared to passive microrheology (PMR), which merely tracks thermal motions. We confirm high-frequency power-law dynamics in equilibrium actin networks with two-particle AMR and also discuss low-frequency local mechanical response near probe particles which shows up in one-particle AMR. The combination of AMR and PMR allowed us to quantify nonthermal force fluctuations in actin networks driven by myosin motor proteins. Our approach offers a new direct way to investigate the nonequilibrium dynamics of living materials.

Semiflexible polymers such as filamentous actin (F-actin) play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.

Dynamic networks designed to model the cell cytoskeleton can be reconstituted from filamentous actin, the motor protein myosin and a permanent cross-linker. They are driven out of equilibrium when the molecular motors are active. This gives rise to athermal fluctuations that can be recorded by tracking probe particles that are dispersed in the network. We have here probed athermal fluctuations in such "active gels" using video microrheology. We have measured the full 10 distribution of probe displacements, also known as the van Hove correlation function. The dominant influence of thermal or athermal fluctuations can be detected by varying the lag time over which the displacements are measured. We argue that the exponential tails of the distribution derive from single motors close to the probes, and we extract an estimate of the velocity of motor heads along the actin filaments. The distribution exhibits a central Gaussian region which we 15 assume derives from the action of many independent motor proteins far from the probe particles when athermal fluctuations dominate. Recording the whole distribution rather than just the typically measured second moment of probe fluctuations (mean-squared displacement) thus allowed us to differentiate between the effect of individual motors and the collective action of many motors.

Humans have co-evolved with micro-organisms and have a symbiotic or mutualistic relationship with their resident microbiome. As at other body surfaces, the mouth has a diverse microbiota that grows on oral surfaces as structurally and functionally organised biofilms. The oral microbiota is natural and provides important benefits to the host, including immunological priming, down-regulation of excessive pro-inflammatory responses, regulation of gastrointestinal and cardiovascular systems, and colonisation by exogenous microbes. On occasions, this symbiotic relationship breaks down, and previously minor components of the microbiota outcompete beneficial bacteria, thereby increasing the risk of disease. Antimicrobial agents have been formulated into many oral care products to augment mechanical plaque control. A delicate balance is needed, however, to control the oral microbiota at levels compatible with health, without killing beneficial bacteria and losing the key benefits delivered by these resident microbes. These antimicrobial agents may achieve this by virtue of their recommended twice daily topical use, which results in pharmacokinetic profiles indicating that they are retained in the mouth for relatively long periods at sublethal levels. At these concentrations they are still able to inhibit bacterial traits implicated in disease (e.g. sugar transport/acid production; protease activity) and retard growth without eliminating beneficial species. In silico modelling studies have been performed which support the concept that either reducing the frequency of acid challenge and/or the terminal pH, or by merely slowing bacterial growth, results in maintaining a community of beneficial bacteria under conditions that might otherwise lead to disease (control without killing).

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress is driven at a constant shear rate ␥ and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R( 1 ) and a linear decay at rate 2 . Here 1,2 (t) ϭ 1,2 Ϫ1 ͐ 0 t (tЈ)exp͓Ϫ(tϪtЈ)/ 1,2 ͔dtЈ are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when 2 Ͼ 1 and 0ϾRЈ()ϾϪ so that monotonicity is restored only through the strongly retarded term ͑which might model a slow evolution of the material structure under stress͒. Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case 1 →0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows. Rheochaos can be defined as the occurrence of macroscopic chaos ͓1͔ in a viscoelastic material at a negligible Reynolds number. With the neglect of inertia that this implies, the nonlinearity must come not from the advection of momentum ͑as in the Navier-Stokes turbulence͒ but from the constitutive behavior of the material, which may include strong memory effects. Likewise, for the chaos to be macroscopically observable ͑for example in time series data on the stress measured at a fixed strain rate, or vice versa, in a bulk sample͒ a mechanism must be present that goes beyond the microscale chaos known to be present in, e.g., colloidal Stokes flow ͓2͔.Strong candidates for rheochaos include micellar materials ͓3͔, dense lamellar phases ͓4͔, and also dense suspensions where erratic stress response at fixed strain rate ͑or vice versa͒ is widespread but poorly documented ͑see, e.g., Ref.͓5͔͒. It is not yet clear whether spatial as well as temporal inhomogeneity is present for all instances of rheochaos, and if so to what extent. This could range from a shear-banded flow in which the interface between the bands of the fast and slow flowing materials is unsteady in time ͑as suspected in micelles ͓3,6͔͒ through to fully developed ''elastic turbulence'' as recently reported in polymer solutions near the overlap threshold ͓7͔. Spatial inhomogeneities are also known to occur in shear-thickening colloid solutions ͓5,8͔. However, the closely related phenomenon of director chaos in sheared nematics has been studied theoretically and does not seem to require spatial inhomogeneity ͓9͔. In the present state of understanding, a theoretical search for temporal rheochaos in spatially homogenous models remains justified.Recent work by the authors has studied the onset of temporal instability in spatially homogeneous mesoscopic models of the shear-thickening type ͓10͔. One interesting prediction was that such instability could arise in a system where the steady state flow curve (␥ ) is monotonic ͓10͔. This contrasts with the conventional instability to spatial inhomogeneity in the form of shear bands: this is always associated with regions of negative slope on the flow curv...

Cells actively probe mechanical properties of their environment by exerting internally generated forces. The response they encounter profoundly affects their behavior. Here we measure in a simple geometry the forces a cell exerts suspended by two optical traps. Our assay quantifies both the overall force and the fraction of that force transmitted to the environment. Mimicking environments of varying stiffness by adjusting the strength of the traps, we found that the force transmission is highly dependent on external compliance. This suggests a calibration mechanism for cellular mechanosensing.