Abstract
We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (\(v>0\)) and the shrinking (\(v<0\)) regimes of the dynamics.
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Acknowledgements
This work was started when the second author (AME) visited the UK within the IAESTE exchange programme. He thanks Durham University for hospitality.
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Hryniv, O., Martínez Esteban, A. Stochastic Model of Microtubule Dynamics. J Stat Phys 169, 203–222 (2017). https://doi.org/10.1007/s10955-017-1855-2
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DOI: https://doi.org/10.1007/s10955-017-1855-2
Keywords
- Microtubules
- Phase transition
- Birth-and-death process
- Renewal decomposition
- Stochastic domination
- Coupling