[Paper Review] Filamentous Active Matter: Band Formation, Bending, Buckling, and Defects

G. A. Vliegenthart, Arvind Ravichandran+3 more|arXiv (Cornell University)|Feb 21, 2019

Micro and Nano Robotics53 references47 citations

TL;DR

This study uses component-based Langevin dynamics simulations to reveal how molecular motors drive self-organization in semi-flexible filaments, forming active polar nematic structures via polarity sorting and buckling instabilities. Key findings include universal scaling of active diffusion and domain size with motor activity, and the emergence of dynamic topological defects at domain boundaries driven by antiparallel motor forces, even without hydrodynamic interactions.

ABSTRACT

Motor proteins drive persistent motion and self-organisation of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modelling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organisation and dynamics from the two-filament level up to the mesoscopic domain level. Dynamic filament crosslinking and sliding, and excluded-volume interactions promote formation of bundles at small densities, and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.

Motivation & Objective

• . To understand the microscopic origins of self-organization in filament-motor systems.
• . To investigate how motor activity, filament flexibility, and crosslinking drive emergent structures like bands and defects.
• . To determine the role of antiparallel motors and activity in inducing buckling instabilities and domain formation.
• . To establish universal scaling laws for active diffusion and domain size in terms of motor force and system parameters.
• . To provide a minimal, component-based model bridging molecular-scale interactions to mesoscale dynamics in active matter.

Proposed method

• . Simulates two-dimensional suspensions of semi-flexible filaments and molecular motors using Langevin dynamics with periodic boundary conditions.
• . Models filaments as chains of beads connected by harmonic springs with bending rigidity to set persistence length.
• . Implements molecular motors as harmonic springs that walk unidirectionally along filaments with a step size equal to the bead spacing.
• . Uses a binding rate for motors that depends on local motor concentration and proximity, with detachment upon reaching filament ends or overextension.
• . Applies fluctuation-dissipation theorem to ensure thermal equilibrium in the overdamped regime, with time step and friction tuned for diffusive behavior.
• . Quantifies activity via the total force exerted by antiparallel motors, which correlates with system-scale dynamics and instability onset.

Experimental results

Research questions

• RQ1 . How do molecular motors induce polarity sorting and band formation in initially nematic filament suspensions?
• RQ2 . What determines the size and stability of polar domains in active filament-motor systems?
• RQ3 . How does motor activity, particularly through antiparallel crosslinking, lead to a buckling-type instability and defect formation?
• RQ4 . What is the scaling relationship between active diffusion, domain size, and motor-induced forces?
• RQ5 . To what extent can hydrodynamic interactions be excluded from driving defect dynamics in such systems?

Key findings

• . The system evolves from a disordered nematic state into an active polar nematic with coarsening polar bands, driven by motor-induced forces on antiparallel filaments.
• . A buckling-type instability emerges at high activity, disrupting ordered bands and leading to disordered, dynamic domains with persistent defect creation and annihilation.
• . The active diffusion coefficient and domain size scale universally with the motor-induced force, which depends on the number of antiparallel motors and their extension.
• . The fraction of antiparallel motors increases with decreasing filament persistence length and increasing motor velocity, promoting smaller domains and higher interface length.
• . Topological defects emerge at three-fold junctions of polar domains, with two distinct configurations distinguished by the orientation of polarities.
• . Defect dynamics are driven by extensile motion of ±1/2 defect pairs, which continuously form and annihilate, sustaining long-time-scale active diffusion.