The Three-Dimensional Velocity Field of Kinesin-Driven Microtubules in Torroidal Channels

TL;DR

This study investigates the three-dimensional flow patterns of kinesin-driven microtubules in toroidal channels, revealing universal flow structures and the influence of channel geometry on flow regimes.

Contribution

It introduces a detailed analysis of flow regimes in microtubule systems within toroidal channels, highlighting universal flow structures after appropriate scaling.

Findings

Zero mean velocity in small aspect ratio torus

Faster coherent flows in higher aspect ratio tori

Universal flow structures after scaling by fluctuation strength

Abstract

We study two regimes of flow in multiple three-dimensional toroidal channels by tracking the fluorescent spherical particles in the kinesin-driven microtubule systems: ``chaotic'' flow and ``coherent'' flow. In the smallest aspect ratio torus, where the channel height $h$ is a quarter of the width $w$, the active system shows zero mean velocity, small-scale isotropy in fluctuation and no persistent flow structure. In other tori with higher aspect ratios $h/w$ close to 1, we find faster coherent flows along the azimuthal direction and increasing fluctuation strengths with growing confinement geometries. Regardless of flow regimes, the flow profiles at $r-z$ cross-section and $r-\theta$ plane are symmetric. The ``coherent'' profiles show two criteria: ``Poiseuille-like'' profiles, which have the peak velocities near the centers of channels; a ``peak-separated'' profile, which has four peak velocities near a certain distance to four confining surfaces. These flow profiles, after scaled by the local isotropic fluctuation strength, reveal universal three-dimensional flow structures among the ``Poiseuille-like'' criterion and the same level of scaled peak velocity at the ``peak-separated'' one. These results illustrate scalable flow structures in this kinesin-driven microtubule active system.