Emergent collective properties of many-motor systems in one dimension

TL;DR

This paper models the collective behavior of oppositely directed motor proteins on microtubules using quantum many-body techniques, revealing emergent phenomena like structure formation and mode transitions.

Contribution

It introduces a novel analogy between many-motor biological systems and quantum many-body models, applying advanced theoretical methods to analyze their collective dynamics.

Findings

Identification of structure formation in motor systems

Discovery of a transition from propagating to dissipative modes

Application of quantum techniques to biological motor dynamics

Abstract

Along a microtubule, certain active motors propel themselves in one direction whereas others propel themselves in the opposite direction. For example, the cargo transporting motor proteins dynein and kinesin propel themselves towards the so-called plus- and minus-ends of the microtubule, respectively, and in so doing are able to pass one another, but not without interacting. We address the emergent collective behavior of systems composed of many motors, some propelling towards the plus-end and others propelling towards the minus-end. To do this, we used an analogy between this strongly interacting, far-from-equilibrium, classical stochastic many-motor system and a certain quantum-mechanical many-body system evolving in imaginary time. We apply well-known methods from quantum many-body theory, including self-consistent mean-field theory and bosonization, to shed light on phenomena exhibited by the many-motor system such as structure formation and the dynamics of collective modes at low-frequencies and long-wavelengths. In particular, via the bosonized description we find analogs of chiral Luttinger liquids, as well as a qualitative transition in the nature of the low-frequency modes---from propagating to purely dissipative---controlled by density and interaction strength.