IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v17y2015i1d10.1007_s11009-013-9372-5.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-013-9372-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-013-9372-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. van Doorn, Erik A. & Zeifman, Alexander I., 2005. "Birth-death processes with killing," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 33-42, April.
    2. 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.
    3. N. J. Carter & R. A. Cross, 2005. "Mechanics of the kinesin step," Nature, Nature, vol. 435(7040), pages 308-312, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chou, Y.C. & Hsiao, Yi-Feng & To, Kiwing, 2015. "Dynamic model of the force driving kinesin to move along microtubule—Simulation with a model system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 66-73.
    2. James F. Cass & Hermes Bloomfield-Gadêlha, 2023. "The reaction-diffusion basis of animated patterns in eukaryotic flagella," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    3. van Doorn, Erik A., 2012. "Conditions for the existence of quasi-stationary distributions for birth–death processes with killing," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2400-2410.
    4. Lipowsky, Reinhard & Klumpp, Stefan, 2005. "‘Life is motion’: multiscale motility of molecular motors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(1), pages 53-112.
    5. Lv, Wangyong & Wang, Huiqi & Lin, Lifeng & Wang, Fei & Zhong, Suchuan, 2015. "Transport properties of elastically coupled fractional Brownian motors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 149-161.
    6. Bibi Najma & Minu Varghese & Lev Tsidilkovski & Linnea Lemma & Aparna Baskaran & Guillaume Duclos, 2022. "Competing instabilities reveal how to rationally design and control active crosslinked gels," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    7. A. Kuznetsov, 2012. "Modelling transport of layered double hydroxide nanoparticles in axons and dendrites of cortical neurons," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 15(12), pages 1263-1271.
    8. Woochul Nam & Bogdan I Epureanu, 2016. "Effects of Obstacles on the Dynamics of Kinesins, Including Velocity and Run Length, Predicted by a Model of Two Dimensional Motion," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-18, January.
    9. Lipowsky, Reinhard & Chai, Yan & Klumpp, Stefan & Liepelt, Steffen & Müller, Melanie J.I., 2006. "Molecular motor traffic: From biological nanomachines to macroscopic transport," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(1), pages 34-51.
    10. Zhang, Yunxin, 2009. "A general two-cycle network model of molecular motors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3465-3474.
    11. I.A. Kuznetsov & A.V. Kuznetsov, 2015. "Modelling organelle transport after traumatic axonal injury," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(6), pages 583-591, April.
    12. Hao Wu & Yiyu Chen & Wenlong Xu & Chen Xin & Tao Wu & Wei Feng & Hao Yu & Chao Chen & Shaojun Jiang & Yachao Zhang & Xiaojie Wang & Minghui Duan & Cong Zhang & Shunli Liu & Dawei Wang & Yanlei Hu & Ji, 2023. "High-performance Marangoni hydrogel rotors with asymmetric porosity and drag reduction profile," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    13. A.V. Kuznetsov, 2014. "Sorting of cargos between axons and dendrites: modelling of differences in cargo transport in these two types of neurites," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 17(7), pages 792-799, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-013-9372-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.