Journal of Mathematical Biology

, Volume 79, Issue 2, pp 571–594 | Cite as

Bidirectional sliding of two parallel microtubules generated by multiple identical motors

  • Jun Allard
  • Marie Doumic
  • Alex Mogilner
  • Dietmar OelzEmail author


It is often assumed in biophysical studies that when multiple identical molecular motors interact with two parallel microtubules, the microtubules will be crosslinked and locked together. The aim of this study is to examine this assumption mathematically. We model the forces and movements generated by motors with a time-continuous Markov process and find that, counter-intuitively, a tug-of-war results from opposing actions of identical motors bound to different microtubules. The model shows that many motors bound to the same microtubule generate a great force applied to a smaller number of motors bound to another microtubule, which increases detachment rate for the motors in minority, stabilizing the directional sliding. However, stochastic effects cause occasional changes of the sliding direction, which has a profound effect on the character of the long-term microtubule motility, making it effectively diffusion-like. Here, we estimate the time between the rare events of switching direction and use them to estimate the effective diffusion coefficient for the microtubule pair. Our main result is that parallel microtubules interacting with multiple identical motors are not locked together, but rather slide bidirectionally. We find explicit formulae for the time between directional switching for various motor numbers.


Tug-of-war Molecular motors Intra-cellular transport Reversal rate 

Mathematics Subject Classification

46N60 92C05 92C37 60J28 60J80 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California IrvineIrvineUSA
  2. 2.Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS 7598Sorbonne UniversitésParisFrance
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  4. 4.School of Mathematics and PhysicsThe University of QueenslandSt. LuciaAustralia

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