Instabilities and Spatiotemporal Dynamics of Active Elastic Filaments

Abstract

Biological filaments driven by molecular motors tend to experience tangential propulsive forces also known as active follower forces. When such a filament encounters an obstacle, it deforms, which reorients its follower forces and alters its entire motion. If the filament pushes a cargo, the friction on the cargo can be enough to deform the filament, thus affecting the transport properties of the cargo. Motivated by cytoskeletal filament motility assays, we study the dynamic buckling instabilities of a two-dimensional slender elastic filament driven through a dissipative medium by tangential propulsive forces in the presence of obstacles or cargo. We observe two distinct instabilities. When the filament's head is pinned or experiences significant translational but little rotational drag from its cargo, it buckles into a steadily rotating coiled state. When it is clamped or experiences both significant translational and rotational drag from its cargo, it buckles into a periodically beating, overall translating state. Using minimal analytically tractable models, linear stability theory, and fully non-linear computations, we study the onset of each buckling instability, characterize each buckled state, and map out the phase diagram of the system. Finally, we use particle-based Brownian dynamics simulations to show our main results are robust to moderate noise and steric repulsion. Overall, our results provide a unified framework to understand the dynamics of tangentially propelled filaments and filament-cargo assemblies.

Aging and rejuvenation of active matter under topological constraints

“…These latter processes are generally understood in terms of an energy-landscape picture, whereby aging and rejuvenation correspond to relaxation toward deeper and shallower energy minima, respectively [32]. However, owing to the non-Hamiltonian nature of particle activity, the potential (or free) energy is generally not a useful metric for active matter, and hence it remains unclear if and how aging and rejuvenation might be manifested in an active glass.A different avenue of research concerns the effects of geometric [33][34][35][36][37][38] and topological [39][40][41][42][43][44][45] constraints on active matter. For passive soft matter systems, it is well established that confining a system to a curved surface can both frustrate and promote long-range orientational order [46][47][48], induce complex topological-defect structures [49][50][51][52], and affect a system's glass-forming properties [53].…”

Elastohydrodynamical instabilities of active filaments, arrays and carpets analyzed using slender body theory

“…The frequency of the oscillations increases as the hydrodynamic drag is decreased. It is illustrative to compare the values obtained here with previous analyses of the instability of a clamped filament subject to compressional follower forces using closed form analytical equations [29] and discrete Brownian Dynamics simulations [39]. These previous studies differ from the present study in two main aspects.…”

“…with c 3 = 0.5 and c 4 = 2.5. Equations (28) and (29) show that the net resistance to motion in each case is the sum of the resistances by the sphere and the filament. Once again, R 2 ( , A) may be regarded as the resistivity of the filament for its transverse motion.…”

“…The tension here combines the active and hydrodynamic traction forces and is the magnitude of the effective force introduced in equation (11) in §II. Combining force and torque balances on a differential element of the deforming filament along with geometric constraints, and simplifying the equations for the case at hand (details in [29]), we find the deformed shape to be governed by the coupled non-linear equations βT + (θ θ ) − 1 γ θ (−θ + βT θ ) = 0 (51) −θ + (βT θ ) + γ θ (βT + θ θ − β) = β ξ ⊥ 8πµ θ (52) where we have denoted ∂θ/∂t byθ and derivatives with respect to arc-length s by primes. Equations (51) and (52) feature three dimensionless parameters γ ≡ ξ ⊥ /ξ and β ≡ f 3 /B and the aspext ratio parameter through the exact form of ξ ⊥ .…”

“…where R 1 ( , A), R 2 ( , A) and R 1 ( , A) are obtained from equations (28), (29) and (30). The eigenvalue problem corresponding to equations (56)-(62) was solved using a standard second order scheme finite differences scheme with 51 grid points chosen in the discretization of the spatial coordinate s. Care was taken to ensure that the boundary conditions were implemented consistently (see the discussion in ESM [29]). For each set (I or II), substituting Θ = Θ(s) exp (pt) yields the resulting matrix equation whose eigenspectrum was checked.…”