Active Trap Model

Abstract

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...

Disordered collective motion in dense assemblies of persistent particles

“…This physical picture survives for modest values of the persistence times, as in Fig. 2(a), except that activated dynamics is now driven by a nonequilibrium colored noise, as recently studied in simpler active situations [44,45]. Therefore, glassy dynamics for weak persistence qualitatively resembles passive systems [11,18].…”

Fluctuation–Dissipation Relations in Active Matter Systems

“…We consider a well-known scheme to describe the behavior of self-propelled particles, the Active Ornstein-Uhlenbeck (AOUP) model [39][40][41][42][43][44][45][46] (also known as Gaussian Colored Noise (GCN)). The AOUP has been employed to reproduce the phenomenology of passive colloids immersed in a bath of active particles [47][48][49][50] but also-perhaps at a more approximate level-the dynamics of self-propelled particles themselves.…”

Time-dependent properties of interacting active matter: Dynamical behavior of one-dimensional systems of self-propelled particles

“…We study dense systems of N interacting self-propelled particles at density ρ 0 , employing the active Ornstein-Uhlenbeck particle (AOUP) model [50][51][52][53][54][55][56][57]. The AOUP is a versatile and popular model of active matter that can reproduce many aspects of the phenomenology of self-propelled particles, including the accumulation near rigid boundaries [58][59][60][61][62] or obstacles and the motility induced phase separation (MIPS) [63].…”