Stochastic modelling of collective motor protein transport through a crossing of microtubules

TL;DR

This paper models collective motor protein transport at microtubule crossings using a stochastic TASEP framework, revealing complex behaviors and phase diagrams that differ from simple branching models, with implications for experimental interpretation.

Contribution

It introduces a detailed stochastic model for microtubule crossings that captures complex transport behaviors not seen in simpler models.

Findings

Transport flow exhibits non-single-valued current-density relations.

Transport properties differ upstream and downstream of the crossing.

The model's predictions align with potential experimental observations.

Abstract

The cytoskeleton in eukaryotic cells plays several crucial roles. In terms of intracellular transport, motor proteins use the cytoskeletal filaments as a backbone along which they can actively transport biological cargos such as vesicles carrying biochemical reactants. Crossings between such filaments constitute a key element, as they may serve to alter the destination of such payload. Although motor proteins are known to display a rich behaviour at such crossings, the latter have so far only been modelled as simple branching points. Here we explore a model for a crossing between two microtubules which retains the individual tracks consisting of protofilaments, and we construct a schematic representation of the transport paths. We study collective transport exemplified by the Totally Asymmetric Simple Exclusion Process (TASEP), and provide a full analysis of the transport features and the associated phase diagram, by a generic mean-field approach which we confirm through particle-based stochastic simulations. In particular we show that transport through such a compound crossing cannot be approximated from a coarse-grained structure with a simple branching point. Instead, it gives rise to entirely new and counterintuitive features: the fundamental current-density relation for traffic flow is no longer a single-valued function, and it furthermore differs according to whether it is observed upstream or downstream from the crossing. We argue that these novel features may be directly relevant for interpreting experimental measurements.