Segregation dynamics in active-passive mixtures of semiflexible filaments

TL;DR

The paper addresses how active self-propelled semiflexible filaments segregate from a passive background in nonequilibrium mixtures. Using Langevin dynamics of a 2D active Wormlike-Chain model, it maps segregation as a function of activity quantified by $Pe$ and stiffness parameters $\xi^{a}/L$ and $\xi^{p}/L$. It finds a non-monotonic dependence on $Pe$ with strong segregation at intermediate values due to flocking, followed by remixing at high $Pe$ caused by collision-induced softening, captured by a scaling relation $\kappa_{\text{eff}}=\frac{\kappa}{1+ g|\mathbf{f}_a|^2}$. Passive-filament properties further modulate segregation, offering design principles for tunable active materials and providing mechanistic insight into cellular organization such as actin–microtubule networks.

Abstract

We study the segregation of motile semiflexible filaments from a background of similar but non-motile filaments. Our Langevin dynamics simulations reveal a wide range of emergent structures governed by filament flexibility and activity, i.e., self-propulsion strength. The system segregates at low activities, while at high activities it undergoes remixing which is a characteristic feature of semi-flexible active filaments. We show that collision-induced softening of single filaments is the dominant mode for this remixing. We provide a scaling argument for the lowering of the active polymer stiffness and show that it agrees well with the lowering of the segregation order parameter. We expect that our studies will shed light on the spatial organization of biofilaments within the cell, on the plasma-membrane, and beyond, and help in the design of novel biomaterials whose structure can be tuned via the properties of the active or the passive filaments.

Figures (4)

• Figure 1: Schematic representation of our polymer model (both active and passive) showing all relevant forces involved. Harmonic bonds join together each bead constituting a filament. The conservative forces are shown as gradients of appropriate potentials while the non-conservative active force acts along bond unit vectors which leads to an effective tangent force along a bead.
• Figure 2: Dependence of segregation on activity and active filament stiffness.(a) Plot showing the variation of the segregation order parameter as a function of the active filament stiffness. (b) Simulation snapshots of the polymer mixtures at steady state for increasing active filament stiffness. Stiffer active filaments lead to better segregation. For these snapshots Pe is set to 125. (c) Plot showing the variation of the segregation order parameter as a function of activity. Active stiffness $\xi^a$ is set to 4. (d) Simulation snapshots of the polymer mixtures at steady state for increasing activity. For all runs passive stiffness was kept fixed at $\xi^\text{p} : 4$
• Figure 3: Collision driven filament bending explains the loss in segregation (a) Plot comparing the decrease in persistence lengths of isolated active filaments (solid lines) and active filaments in mixtures (individual dots). The persistence length decrease for active filaments in mixtures is significantly more as compared to isolated filaments.(b) Plot showing the scaled persistence length as a function of activity. The curves for different active stiffnesses collapse onto a single curve and can be explained by a simple scaling argument based on collisions. The single fit parameter (g) is 0.11. (c) Plot showing the change in the segregation order parameter as a function of activity for different active stiffness values ($\xi^a /L \in \{2,4,12\}$). The effective stiffness (in maroon) is overlayed on top of the plot.
• Figure 4: Effects of the passive filament stiffness on the Segregation dynamics (a) Plot showing the segregation order parameter as a function of the end-to-end length leads to the collapse of the data on a single line which suggests that the “effective size” of the passive filaments plays an important role in the segregation dynamics. (b) Plot showing the percent increase in the segregation order parameter on increasing $\xi^p /L$ from 0.04 ($\Sigma_{0.04}$) to 4 ($\Sigma_{4}$) as a function of activity for two active stiffness values ($\xi^a /L :\{1.78,3.56\}$). The percent increase in segregation is only significant for a certain window of activity (Pe 10 - 100).