Active polymers translocate faster in confinement

TL;DR

The paper investigates how confinement width and filament stiffness interact with activity to govern translocation of flexible active filaments. By combining California blackworm experiments with Brownian-dynamics simulations of tangentially propelled polymers, it identifies a single control parameter $W_tilde^2/ell_p_tilde$ that organizes escape dynamics, MSD behavior, and reorientation events. It delineates Odijk-like axis-aligned and de Gennes-like reorientation-dominated regimes and offers a practical confinement-stiffness boundary and a translocation-success criterion for design of flexible robotic filaments navigating confined spaces. The work provides a unified framework for active translocation in confinement and has implications for soft robotics, microrobotics, and nanoscale transport in tortuous environments.

Abstract

Living organisms employ diverse strategies to navigate confined environments. Inspired by translocation observations on California blackworms (\textit{Lumbriculus variegatus}), we combine biological experiments and active-polymer simulations to examine how confinement and stiffness govern translocation. Active filaments translocate fastest when the channel width is comparable to their diameter, with escape time determined by propulsion speed, filament length, and channel geometry. In wider channels, activity and flexibility induce reorientation-dominated conformational changes that prolong escape. A single dimensionless ratio linking confinement to stiffness captures the transition from axis-aligned escape with short wall deflections for stiffer filaments, to reorientation-controlled motion with blob-like shapes for flexible filaments. These results provide a unified physical framework for active translocation in confinement and suggest design principles for flexible robotic filaments in complex environments.

Figures (8)

• Figure 1: Translocation and escape time of active filaments in confined channels: (a-b) Experiments: at scaled width ($\widetilde{W}=2$), a blackworm escapes within $t_{esc}=56\pm16$ seconds; in a wider channel ($\widetilde{W}=8$), it traverses only half the channel over the same interval. (d-e) Simulation snapshots for active polymer translocation ${\widetilde{\ell_p}=0.07}$: at $\widetilde{W}=1.4$, strong confinement aligns the filament and speeds escape; in wider channels $\widetilde{W}=3.0$, frequent reorientations and lateral exploration slow transport. (c,f) Escape time measurements from both biological experiments and AP simulations showing that the escape time scales with the effective channel width, $t_{esc}= \widetilde{W}^\alpha+C$: worms (solid line) $\alpha=1.8$; AP simulations $\alpha=[2.8-3.4]$ with $C \sim t_{th}$ for $\widetilde{\ell_p}\le 0.5$. In AP simulations, at higher stiffness, $t_{esc}$ becomes nearly width-independent and approaches $t_{th}$.
• Figure 1: Schematic of experimental setup. (a) Quasi-2D setup used for worm translocation experiments: two circular chambers connected by an open-ended, narrow channel (dimensions annotated in schematic). (b) Imaging setup: a top-mounted camera records motion of the worm between chambers under fixed illumination. (c) Image of California blackworm (Lumbriculus variegatus) inside the channel.
• Figure 2: A single parameter ($\widetilde{W}^2/\widetilde{\ell}_p$) controls active translocation. (a) Mean-squared displacement (MSD) of the center of mass versus time for varying $\widetilde{W}$ and $\widetilde{\ell_p}$. Decreasing $\widetilde{W}$ increases MSD, indicating enhanced transport in simulations and experiments (inset). (b) Transverse or radial rMSD, shown for various confinement widths for $\widetilde{\ell_p}=0.07$, grows then saturates; the saturation level (shown in inset, $\textrm{rMSD}_\textrm{sat}$) increases with $\widetilde{W}$ and is largely stiffness-independent, showing that radial exploration is not rate-limiting. (c) The average axial reorientation count $\langle N_{\mathrm{RE}}\rangle$, obtained from sign changes of the end-to-end vector $\mathbf{R}_E$, collapses onto a single curve when plotted against $\widetilde{W}^2/\widetilde{\ell}_p$, identifying a single control parameter that links lateral space to stiffness and rationalizes the escape slowdown in wide channels; experiments show similar trends (inset).
• Figure 2: Active Polymer (AP) model. (a) Tangentially-propelled filament: each monomer propels with an active force ${f_p}$ directed along the local tangent. (b) The active filament moves within an open-ended cylindrical channel of width $W$ and length $L_c$. (c) Escape time measurement: $t_{esc}$ is measured from $\tau_0$ (head entry, first monomer) to $\tau_2$ (tail exit, last monomer), including the residence interval $\tau_1$ during which the filament undergoes propulsion-driven motion, reorientations, and conformational fluctuations.
• Figure 3: A simple confinement–stiffness boundary predicts escape success. Translocation success probability $P_s$ versus scaled width $\widetilde{W}$ and stiffness $\widetilde{\ell}_p$. Each symbol represents $200$ independent runs, and its area scales with $P_s$. The dashed line ($P_s = 0.85$) gives an empirical boundary, $\widetilde{W} = 4.83\widetilde{\ell}_p + 1.6$, separating high-success, axis-aligned, Odijk-like transport from low-success, reorientation-dominated, de Gennes-like motion for $\widetilde{W} >2$. Strong confinement ($\widetilde{W} \le 2$) yields $P_s\approx1$. Representative conformations illustrate both regimes.