274 research outputs found
Fiber networks amplify active stress
Large-scale force generation is essential for biological functions such as
cell motility, embryonic development, and muscle contraction. In these
processes, forces generated at the molecular level by motor proteins are
transmitted by disordered fiber networks, resulting in large-scale active
stresses. While these fiber networks are well characterized macroscopically,
this stress generation by microscopic active units is not well understood. Here
we theoretically study force transmission in these networks, and find that
local active forces are rectified towards isotropic contraction and strongly
amplified as fibers collectively buckle in the vicinity of the active units.
This stress amplification is reinforced by the networks' disordered nature, but
saturates for high densities of active units. Our predictions are
quantitatively consistent with experiments on reconstituted tissues and
actomyosin networks, and shed light on the role of the network microstructure
in shaping active stresses in cells and tissue.Comment: 8 pages, 4 figures. Supporting information: 5 pages, 5 figure
Effective medium approach for stiff polymer networks with flexible cross-links
Recent experiments have demonstrated that the nonlinear elasticity of in
vitro networks of the biopolymer actin is dramatically altered in the presence
of a flexible cross-linker such as the abundant cytoskeletal protein filamin.
The basic principles of such networks remain poorly understood. Here we
describe an effective medium theory of flexibly cross-linked stiff polymer
networks. We argue that the response of the cross-links can be fully attributed
to entropic stiffening, while softening due to domain unfolding can be ignored.
The network is modeled as a collection of randomly oriented rods connected by
flexible cross-links to an elastic continuum. This effective medium is treated
in a linear elastic limit as well as in a more general framework, in which the
medium self-consistently represents the nonlinear network behavior. This model
predicts that the nonlinear elastic response sets in at strains proportional to
cross-linker length and inversely proportional to filament length. Furthermore,
we find that the differential modulus scales linearly with the stress in the
stiffening regime. These results are in excellent agreement with bulk rheology
data.Comment: 12 pages, 8 figure
Inferring the dynamics of underdamped stochastic systems
Many complex systems, ranging from migrating cells to animal groups, exhibit
stochastic dynamics described by the underdamped Langevin equation. Inferring
such an equation of motion from experimental data can provide profound insight
into the physical laws governing the system. Here, we derive a principled
framework to infer the dynamics of underdamped stochastic systems from
realistic experimental trajectories, sampled at discrete times and subject to
measurement errors. This framework yields an operational method, Underdamped
Langevin Inference (ULI), which performs well on experimental trajectories of
single migrating cells and in complex high-dimensional systems, including
flocks with Viscek-like alignment interactions. Our method is robust to
experimental measurement errors, and includes a self-consistent estimate of the
inference error
Criticality and isostaticity in fiber networks
The rigidity of elastic networks depends sensitively on their internal
connectivity and the nature of the interactions between constituents. Particles
interacting via central forces undergo a zero-temperature rigidity-percolation
transition near the isostatic threshold, where the constraints and internal
degrees of freedom are equal in number. Fibrous networks, such as those that
form the cellular cytoskeleton, become rigid at a lower threshold due to
additional bending constraints. However, the degree to which bending governs
network mechanics remains a subject of considerable debate. We study disordered
fibrous networks with variable coordination number, both above and below the
central-force isostatic point. This point controls a broad crossover from
stretching- to bending-dominated elasticity. Strikingly, this crossover
exhibits an anomalous power-law dependence of the shear modulus on both
stretching and bending rigidities. At the central-force isostatic point---well
above the rigidity threshold---we find divergent strain fluctuations together
with a divergent correlation length , implying a breakdown of continuum
elasticity in this simple mechanical system on length scales less than .Comment: 6 pages, 5 figure
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