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Experiments suggest that the migration of some cells in the three-dimensional extracellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell made of two beads and an active spring moving along a rigid track. The active spring models the stress fibers with their myosin-driven contractility and a-actinin-driven extendability, while the friction coefficients of the two beads describe the catch and slip-bond behaviors of the integrins in focal adhesions. In the absence of active noise, net motion arises from an interplay between active contractility (and passive extendability) of the stress fibers and an asymmetry between the front and back of the cell due to catch-bond behavior of integrins at the front of the cell and slip-bond behavior of integrins at the back. We obtain reasonable cell speeds with independently estimated parameters. We also study the effects of hysteresis in the active spring, due to catch-bond behavior and the dynamics of cross linking, and the addition of active noise on the motion of the cell. Our model highlights the role of α-actinin in three-dimensional cell motility and does not require Arp2/3 actin filament nucleation for net motion. [ABSTRACT FROM AUTHOR]

We report detailed theoretical investigations of the micromechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments [V. Pelletier, N. Gal, P. Fournier, and M. L. Kilfoil, Phys. Rev. Lett. 102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of stiff rodlike inclusions. We show that the Poisson's ratio &ngr; of such a composite evolves with increasing rod density toward a particular value, or fixed point, independent of the material properties of the matrix, as long as it has a finite initial compressibility. This fixed point is &ngr; = 1/4 in three dimensions and &ngr; = 1 /3 in two dimensions. Our results suggest an important role for stiff filaments such as microtubules and stress fibers in cell mechanics. At the same time, our work has a wider elasticity context, with potential applications to composite elastic media with a wide separation of scales in stiffness of its constituents such as carbon nanotube-polymer composites, which have been shown to have highly tunable mechanics. [ABSTRACT FROM AUTHOR]

Cell migration in morphogenesis and cancer metastasis typically involves interplay between different cell types. We construct and study a minimal, one-dimensional model composed of two different motile cells with each cell represented as an active elastic dimer. The interaction between the two cells via cadherins is modeled as a spring that can rupture beyond a threshold force as it undergoes dynamic loading from the interacting motile cells. We obtain a phase diagram consisting of chase-and-run dynamics and clumping dynamics as a function of the stiffness of the interaction spring and the threshold force and, therefore, posit that active rupture, or rupture via active forces, is a mechanosensitive means to regulate dynamics between cells. Since the parameters in the model differentiate between N- and E-cadherins, we make predictions for the interactions between a placodelike cell and a neural crestlike cell in a microchannel as well as discuss how our results inform chase-and-run dynamics found in a group of placode cells interacting with a group of neural crest cells. In particular, an argument was made in the latter case that the feedback between cadherins and cell-substrate interaction via integrins was necessary to obtain the chase-and-run behavior. Based on our two-cell results, we argue that this feedback accentuates, but is not necessary for, the chase-and-run behavior. [ABSTRACT FROM AUTHOR]

We construct and analyze a model for a disordered linear spring network with anisotropy. The modeling is motivated by, for example, granular systems, nematic elastomers, and ultimately cytoskeletal networks exhibiting some underlying anisotropy. The model consists of a triangular lattice with two different bond occupation probabilities, px and py, for the linear springs. We develop an effective medium theory (EMT) to describe the network elasticity as a function of px and py. We find that the onset of rigidity in the EMT agrees with Maxwell constraint counting. We also find beyond linear behavior in the shear and bulk modulus as a function of occupation probability in the rigid phase for small strains, which differs from the isotropic case. We compare our EMT with numerical simulations to find rather good agreement. Finally, we discuss the implications of extending the reach of effective medium theory as well as draw connections with prior work on both anisotropic and isotropic spring networks. [ABSTRACT FROM AUTHOR]

We calculate both the micromechanical response and bulk elastic constants of composites of rods embedded in elastic media. We find two fixed points for Poisson's ratio with respect to rod density: there is an unstable fixed point for Poisson's ratio =1/2 (an incompressible system) and a stable fixed point for Poisson's ratio =1/4 (a compressible system). We also derive approximate expressions for the elastic constants for arbitrary rod density, which agree with exact results for both low and high density. These results may help to explain recent experiments [Phys. Rev. Lett. 102, 188303 (2009)10.1103/PhysRevLett.102.188303] that reported compressibility for composites of microtubules in filamentous actin networks.

We develop an effective medium approach to the mechanics of disordered, semiflexible polymer networks and study the response of such networks to uniform and nonuniform strain. We identify distinct elastic regimes in which the contributions of either filament bending or stretching to the macroscopic modulus vanish. We also show that our effective medium theory predicts a crossover between affine and nonaffine strain, consistent with both prior numerical studies and scaling theory.

We study the formation and evolution of localized geometrical defects in an indented cylindrical elastic shell using a combination of experiment and numerical simulation. We find that as a symmetric localized indentation on a semicylindrical shell increases, there is a transition from a global mode of deformation to a localized one which leads to the condensation of curvature along a symmetric parabolic defect. This process introduces a soft mode in the system, converting a load-bearing structure into a hinged, kinematic mechanism. Further indentation leads to twinning wherein the parabolic defect bifurcates into two defects that move apart on either side of the line of symmetry. A qualitative theory captures the main features of the phenomena but leads to further questions about the mechanism of defect nucleation.

We numerically study the behavior of a collection of overdamped Brownian particles in a channel, in the presence of a flow field applied on similar but slower particles in a wide chamber in contact with the channel. For a suitable range of shear rates, we find that the flow field induces a unidirectional drift in the confined particles, and is stronger for narrower channels. The average drift velocity initially rises with increasing shear rate, then shows saturation for a while, thereafter starts decreasing, in qualitative agreement with recent theoretical studies [Phys. Rev. B 70, 205423 (2004)] based on Brownian drag and "loss of grip." Interestingly, if the sign of the interspecies interaction is reversed, the direction of the induced drift remains the same, but the flow rate at which loss of grip occurs is lower, and the level of fluctuations is higher.

With a view to understanding the "rheochaos" observed in recent experiments in a variety of orientable fluids, we study numerically the equations of motion of the spatiotemporal evolution of the traceless symmetric order parameter of a sheared nematogenic fluid. In particular we establish, by decisive numerical tests, that the irregular oscillatory behavior seen in a region of parameter space where the nematic is not stably flow-aligning is in fact spatiotemporal chaos. We outline the dynamical phase diagram of the model and study the route to the chaotic state. We find that spatiotemporal chaos in this system sets in via a regime of spatiotemporal intermittency, with a power-law distribution of the widths of laminar regions, as in H. Chaté and P. Manneville, Phys. Rev. Lett. 58, 112 (1987). Further, the evolution of the histogram of band sizes shows a growing length scale as one moves from the chaotic towards the flow-aligned phase. Finally we suggest possible experiments in which one can observe the intriguing behaviors discussed here.

Motivated by recent observations of rheochaos in sheared wormlike micelles, we study the coupled nonlinear partial differential equations for the hydrodynamic velocity and order-parameter fields in a sheared nematogenic fluid. In a suitable parameter range, we find irregular, dynamic shear banding and establish by decisive numerical tests that the chaos we observe in the model is spatiotemporal in nature.

The far-from-equilibrium dynamics of two crystalline two-dimensional monolayers driven past each other is studied using Brownian dynamics simulations. While at very high and low driving rates the layers slide past one another retaining their crystalline order, for intermediate range of drives the system alternates irregularly between the crystalline and fluidlike phases. A dynamical phase diagram in the space of interlayer coupling and drive is obtained. A qualitative understanding of this stochastic alternation between the liquidlike and crystalline phases is proposed in terms of a reduced model within which it can be understood as a stochastic resonance for the dynamics of collective order parameter variables. This remarkable example of stochastic resonance in a spatially extended system should be seen in experiments which we propose in the paper.