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A Quasi Random Walk to Model a Biological Transport Process

Author

Listed:
  • Peter Keller

    (University of Edinburgh)

  • Sylvie Rœlly

    (Universität Potsdam)

  • Angelo Valleriani

    (Abteilung Theorie & Bio-Systeme)

Abstract

Transport molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance and requires several biochemical transformations, which are modeled as internal states of the motor. While moving along the rope, the motor can also detach and the walk is interrupted. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.

Suggested Citation

  • Peter Keller & Sylvie Rœlly & Angelo Valleriani, 2015. "A Quasi Random Walk to Model a Biological Transport Process," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 125-137, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9372-5
    DOI: 10.1007/s11009-013-9372-5
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    References listed on IDEAS

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    1. Koen Visscher & Mark J. Schnitzer & Steven M. Block, 1999. "Single kinesin molecules studied with a molecular force clamp," Nature, Nature, vol. 400(6740), pages 184-189, July.
    2. van Doorn, Erik A. & Zeifman, Alexander I., 2005. "Birth-death processes with killing," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 33-42, April.
    3. N. J. Carter & R. A. Cross, 2005. "Mechanics of the kinesin step," Nature, Nature, vol. 435(7040), pages 308-312, May.
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