Modeling the dynamics of a tracer particle in an elastic active gel

Ben-Isaac, Eyal; Fodor, Étienne; Visco, Paolo; Wijland, Frédéric van; Gov, Nir S.

doi:10.1103/physreve.92.012716

Cited by 60 publications

(85 citation statements)

References 29 publications

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“…For a fluid at equilibrium, the temperatures from these two methods, MSD and p(v), are expected to be the same but not for systems that are out of equilibrium 5,41,43,44 , such as the bacterial suspensions investigated here. The good agreement in Fig.…”

Section: Effective Temperaturementioning

confidence: 96%

Particle diffusion in active fluids is non-monotonic in size

et al. 2016

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We experimentally investigate the effect of particle size on the motion of passive polystyrene spheres in suspensions of Escherichia coli. Using particles covering a range of sizes from 0.6 to 39 microns, we probe particle dynamics at both short and long time scales. In all cases, the particles exhibit super-diffusive ballistic behavior at short times before eventually transitioning to diffusive behavior. Surprisingly, we find a regime in which larger particles can diffuse faster than smaller particles: the particle long-time effective diffusivity exhibits a peak in particle size, which is a deviation from classical thermal diffusion. We also find that the active contribution to particle diffusion is controlled by a dimensionless parameter, the Péclet number. A minimal model qualitatively explains the existence of the effective diffusivity peak and its dependence on bacterial concentration. Our results have broad implications on characterizing active fluids using concepts drawn from classical thermodynamics.

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Section: Effective Temperaturementioning

confidence: 96%

Particle diffusion in active fluids is non-monotonic in size

et al. 2016

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“…This is just the equation of motion for a self-propelled particle tethered to a spring with active forcing that is strongest along the direction of the eigenvector [5]. The solution is then:

a_{ν} false(t false) = a_{ν} false(t = 0 false) e^{- k t} + ν_{0} {\int_{0}^{t} italicdt' e}^{- k false(t - t' false)} italiccos false(θ_{ν} - normalψ false),

where

k = μ ω_{ν}^{2}

.…”

Section: Expanding Cell Displacements In An Eigenbasis Associated mentioning

confidence: 99%

Motility-Driven Glass and Jamming Transitions in Biological Tissues

et al. 2016

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Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum Soft Glassy Rheology model precisely captures this transition in the limit of small persistence times, and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with Epithelial-to-Mesenchymal transition in these tissues.

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“…This result is particularly relevant, since experiments indicate that the thermal motion of tracer particles in bio-polymer gels is well described by a hopping model, with anomalous (sub-) diffusion, which therefore suggest that the distribution of traps is exponential [13].Active trap model. We consider a particle in a one dimensional trap described by a potential U (x) and kicked randomly by thermal and active forces [14]. The Langevin equation for the particle's velocity v (in a simplified one dimension reaction coordinate, with the mass set to one) isvwhere λ is the effective friction coefficient.…”

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confidence: 99%

Active Trap Model

Woillez¹,

Kafri²,

Gov³

2020

Phys. Rev. Lett.

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Motivated by the dynamics of particles embedded in active gels, both in-vitro and inside the cytoskeleton of living cells, we study an active generalization of the classical trap model. We demonstrate that activity leads to dramatic modifications in the diffusion compared to the thermal case: the mean square displacement becomes sub-diffusive, spreading as a power-law in time, when the trap depth distribution is a Gaussian and is slower than any power-law when it is drawn from an exponential distribution. The results are derived for a simple, exactly solvable, case of harmonic traps. We then argue that the results are robust for more realistic trap shapes when the activity is strong. PACS numbers:Introduction. In-vitro experiments have probed the non-thermal (active) fluctuations in an "active gel", which is most often realized as a network composed of cross-linked actin filaments and myosin-II molecular motors [1][2][3][4]. The fluctuations inside the active gel are measured using the tracking of tracer particles, and was used to demonstrate the non-equilibrium nature of these systems through the breaking of the Fluctuation-Dissipation theorem (FDT) [4]. In these active gels, myosin-II molecular motors generate relative motion between the actin filaments, through consumption of ATP, and thus drive the athermal random motion of the probe particles dispersed throughout the network. Similar motion of tracer particles was observed in living cells [5,6].In both the in-vitro gels, and in cells, over short times, the tracer particle seems to perform caged random motion, while trapped in the elastic network. On longer times it is observed that the actin network allows the tracer to perform "hopping" diffusion, as it makes large amplitude motions [2,[5][6][7][8], driven by the same active forces. This large scale motion was treated on a coarsegrained scale in [6] [37].Here we explore in more detail the process by which active forces can drive hopping diffusion in a heterogeneous medium. We use a trap model [9] where the particle is assumed to be trapped in a potential well of variable depth, representing the structural inhomogeneity present in the system. The particle is affected by random active forces, which eventually "kick" the particle from the well. This event can correspond to the release of the tracer particle from the confining network, or more generally to the triggering of some unspecified rearrangement of the constituents of the system. After each such event, the particle (system) is locked in a new confining organization, and a new activated escape process begins.The distribution of potential well depths determines the type of hopping diffusion performed by the particle. Indeed, it is well known that for a thermal system, a Gaussian distribution of potential depths gives rise to normal hopping diffusion, while an exponential distribution of potential depths can give rise to anomalous diffu-sion: x 2 ∝ t α , 0 < α < 1. (for a review see [10]). This result is a direct consequence of the Kramers escape rate whi...

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Modeling the dynamics of a tracer particle in an elastic active gel

Cited by 60 publications

References 29 publications

Particle diffusion in active fluids is non-monotonic in size

Particle diffusion in active fluids is non-monotonic in size

Motility-Driven Glass and Jamming Transitions in Biological Tissues

Active Trap Model

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