Multi-filament coordination rescues active transport from inertia-induced spinning arrest

Abstract

Active filaments driven by tangential forces can become trapped in a spinning state when attached to a heavy head, where activity and inertia drive persistent rotation rather than directed transport. Using three-dimensional Langevin dynamics of tangentially driven bead-spring chains anchored to a common heavy head, we demonstrate that increasing the filament number $\Nf$ systematically \emph{rescues} directed transport by sterically preventing the coiled conformations that underlie spinning. The rescue is established through three independent diagnostics: (i)~the mean-square displacement recovers monotonic growth (transport rescue), (ii)~the spatial tangent autocorrelation loses its negative dip signaling helical coiling (conformational rescue), and (iii)~the tangent time autocorrelation ceases crossing zero (orientational rescue). At high bending stiffness ($\kb = 1000$), coiling is fully eliminated at a critical filament number $\Nf^* \approx 3$. At moderate stiffness ($\kb = 100$), residual coiling persists ($\min C_s \approx -0.13$) yet transport is still rescued -- demonstrating that the destruction of spinning \emph{coherence}, not coiling elimination, is the essential mechanism. The multi-filament architecture achieves up to five orders of magnitude transport enhancement. Two physically distinct rescue pathways emerge: at high stiffness, steric constraints force filaments into a coordinated bundle sustaining directed propulsion; at low stiffness, steric interactions destroy orientational coherence, producing enhanced active diffusion. These results demonstrate a purely mechanical, density-independent route to overcome inertia-induced motility arrest, with implications for synthetic microswimmer design, motor-driven filament assays, and multi-filament organization in biological systems.

Figures (10)

• Figure 1: Schematic of the active filament model. (a) Single filament ($N_{\mathrm{f}}{=}1$): head bead (diameter $\alpha\sigma$) followed by $N$ body beads with tangential active forces directed toward the head. (b) Multi-filament arrangement ($N_{\mathrm{f}} > 1$): $N_{\mathrm{f}}$ chains anchored to a common head.
• Figure 2: Spinning arrest in a single filament ($N_{\mathrm{f}}{=}1$). (a) Beating conformation ($M_{\mathrm{h}}{=}10$): extended, undulating shape producing directed transport. (b) Spinning conformation ($M_{\mathrm{h}}{=}30$): filament coils tightly around the heavy head and rotates in place. Both at $\kappa_{\mathrm{b}}{=}1000$, $F_{\mathrm{act}}{=}40$.
• Figure 3: Phase diagram: $\Phi$ vs. $M_{\mathrm{h}}$ at $\kappa_{\mathrm{b}} = 100$ (blue) and $1000$ (orange) for $F_{\mathrm{act}} = 4,\,10,\,20,\,40$. Dashed line: $\Phi = 0.1$ threshold. Increasing activity shifts the spinning boundary to lower $M_{\mathrm{h}}$.
• Figure 4: Spinning signature in the TTAF for a single filament ($N_{\mathrm{f}}{=}1$, $M_{\mathrm{h}}{=}20$, $F_{\mathrm{act}}{=}20$). (a) $\kappa_{\mathrm{b}}{=}100$: oscillations decay by $\tau \approx 5000$. (b) $\kappa_{\mathrm{b}}{=}1000$: oscillations persist to $\tau \approx 15{,}000$. Stiffer chains spin faster and more persistently.
• Figure 5: Transport suppression in single filaments ($N_{\mathrm{f}}{=}1$): $\mathrm{MSD}_{\mathrm{ref}}$ vs. $M_{\mathrm{h}}$ at $\kappa_{\mathrm{b}} = 100$ and $1000$ for $F_{\mathrm{act}} = 4,\,10,\,20,\,40$. Three to four orders of magnitude drop from light to heavy heads.