Queueing induced by bidirectional motor motion near the end of a microtubule

Peter Ashwin, Congping Lin, and Gero Steinberg
Phys. Rev. E 82, 051907 – Published 4 November 2010

Abstract

Recent live observations of motors in long-range microtubule (MT) dependent transport in the fungus Ustilago maydis have reported bidirectional motion of dynein and an accumulation of the motors at the polymerization-active (the plus-end) of the microtubule. Quantitative data derived from in vivo observation of dynein has enabled us to develop an accurate, quantitatively-valid asymmetric simple exclusion process (ASEP) model that describes the coordinated motion of anterograde and retrograde motors sharing a single oriented microtubule. We give approximate expressions for the size and distribution of the accumulation, and discuss queueing properties for motors entering this accumulation. We show for this ASEP model, that the mean accumulation can be modeled as an M/M/ queue that is Poisson distributed with mean Farr/pd, where Farr is the flux of motors that arrives at the tip and pd is the rate at which individual motors change direction from anterograde to retrograde motion. Deviations from this can in principle be used to gain information about other processes at work in the accumulation. Furthermore, our work is a significant step toward a mathematical description of the complex interactions of motors in cellular long-range transport of organelles.

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  • Received 13 August 2010

DOI:https://doi.org/10.1103/PhysRevE.82.051907

©2010 American Physical Society

Authors & Affiliations

Peter Ashwin1, Congping Lin1,2, and Gero Steinberg2

  • 1Mathematics Research Institute, University of Exeter, Exeter, Devon EX4 4QF, United Kingdom
  • 2School of Biosciences, University of Exeter, Exeter, Devon EX4 4QD, United Kingdom

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Issue

Vol. 82, Iss. 5 — November 2010

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