Controlling cell-matrix traction forces by extracellular geometry

We present a minimal continuum model of strongly adhering cells as active contractile isotropic media and use the model to study the effect of the geometry of the adhesion patch in controlling the spatial distribution of traction and cellular stresses. Activity is introduced as a contractile, hence negative, spatially homogeneous contribution to the pressure. The model shows that patterning of adhesion regions can be used to control traction stress distribution and yields several results consistent with experimental observations. Specifically, the cell spread area is found to increase with substrate stiffness and an analytic expression for the dependence is obtained for circular cells. The correlation between the magnitude of traction stresses and cell boundary curvature is also demonstrated and analyzed.Comment: 12 pages, 4 figure

Hydrodynamic and rheology of active polar filaments

The cytoskeleton provides eukaryotic cells with mechanical support and helps them perform their biological functions. It is a network of semiflexible polar protein filaments and many accessory proteins that bind to these filaments, regulate their assembly, link them to organelles and continuously remodel the network. Here we review recent theoretical work that aims to describe the cytoskeleton as a polar continuum driven out of equilibrium by internal chemical reactions. This work uses methods from soft condensed matter physics and has led to the formulation of a general framework for the description of the structure and rheology of active suspension of polar filaments and molecular motors.Comment: 30 pages, 5 figures. To appear in "Cell Motility", Peter Lenz, ed. (Springer, New York, 2007

Organization and instabilities of entangled active polar filaments

We study the dynamics of an entangled, isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and entanglement. At low filament density the system develops a density instability, while at high filament density entanglement effects drive the instability of orientational fluctuations.Comment: 4pages, 2 eps figure, revtex

Nonreciprocity as a generic route to traveling states

We examine a non-reciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross diffusivities, provides a generic mechanism for the emergence of traveling patterns in purely diffusive systems with conservative dynamics. In the absence of non-reciprocity, the binary fluid mixture undergoes a phase transition from a homogeneous mixed state to a demixed state with spatially separated regions rich in one of the two components. Above a critical value of the parameter tuning non-reciprocity, the static demixed pattern acquires a finite velocity, resulting in a state that breaks both spatial and time translational symmetry, as well as the reflection parity of the static pattern. We elucidate the generic nature of the transition to traveling patterns using a minimal model that can be studied analytically. Our work has direct relevance to nonequilibrium assembly in mixtures of chemically interacting colloids that are known to exhibit non-reciprocal effective interactions, as well as to mixtures of active and passive agents where traveling states of the type predicted here have been observed in simulations. It also provides insight on transitions to traveling and oscillatory states seen in a broad range of nonreciprocal systems with non-conservative dynamics, from reaction-diffusion and prey-predators models to multispecies mixtures of microorganisms with antagonistic interactions.Comment: 8 pages, 3 figure

Active Jamming: Self-propelled soft particles at high density

We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells. The phase diagram exhibits a liquid phase with giant number fluctuations at low packing fraction and high self-propulsion speed and a jammed phase at high packing fraction and low self-propulsion speed. The dynamics of the jammed phase is controlled by the low frequency modes of the jammed packing.Comment: 4 pages, 4 figure