# Bidirectional motion of filaments: Role of motor proteins and passive cross linkers

## TL;DR

This study models the interplay between motor proteins and passive cross linkers in microtubule overlaps, revealing dynamic phase transitions and oscillatory behaviors relevant to cell division stability.

## Contribution

The paper introduces a novel model analyzing how active motor proteins and passive cross linkers jointly influence microtubule overlap dynamics, including phase transitions and oscillations.

## Key findings

- Dynamic phase transitions with changing activity levels.
- Emergence of stable limit cycle oscillations via Hopf bifurcation.
- Overlap stability depends on whether microtubules are movable or fixed.

## Abstract

In eukaryotic cells, motor proteins (MP) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules (MT) form whose stability and dynamics under the influence of MPs has been studied extensively. Although passive cross linkers (PCL) were known to provide structural stability to filamentous network, consequences of the interplay between ATP dependent active forces of MPs and passive entropic forces of PCLs on MT overlap remains largely unexplored. Here, we formulate and characterize a model to study this, using linear stability analysis and numerical integration. In presence of PCLs, we find dynamic phase transitions with changing activity exhibiting regimes of stable partial overlap with or without oscillations, instability towards complete overlap, and stable limit cycle oscillations that emerge via a supercritical Hopf bifurcation characterized by an oscillation frequency determined by the MP and PCL parameters. We show that the overlap dynamics and stability depend crucially on whether both the MTs of overlapping pair are movable or one is immobilized, having potential implications for in vivo and in vitro studies.