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Journal of Statistical Physics

, Volume 157, Issue 6, pp 1062–1096 | Cite as

Discrete Kinetic Models for Molecular Motors: Asymptotic Velocity and Gaussian Fluctuations

  • Alessandra Faggionato
  • Vittoria Silvestri
Article

Abstract

We consider random walks on quasi one dimensional lattices, as introduced in Faggionato and Silvestri (Random Walks on Quasi One Dimensional Lattices: Large Deviations and Fluctuation Theorems, 2014). This mathematical setting covers a large class of discrete kinetic models for non-cooperative molecular motors on periodic tracks. We derive general formulas for the asymptotic velocity and diffusion coefficient, and we show how to reduce their computation to suitable linear systems of the same degree of a single fundamental cell, with possible linear chain removals. We apply the above results to special families of kinetic models, also catching some errors in the biophysics literature.

Keywords

Markov chain Law of large numbers Invariance principle Molecular motors 

Notes

Acknowledgments

The authors thank Prof. A.B. Kolomeisky for useful discussions. V. Silvestri thanks the Department of Mathematics in University “La Sapienza” for the hospitality and acknowledges the support of the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma ‘La Sapienza’RomeItaly
  2. 2.Cambridge Centre for AnalysisCambridgeUK

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