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Asymptotics of a Brownian ratchet for protein translocation

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  • Depperschmidt, Andrej
  • Pfaffelhuber, Peter

Abstract

Protein translocation in cells has been modelled by Brownian ratchets. In such models, the protein diffuses through a nanopore. On one side of the pore, ratcheting molecules bind to the protein and hinder it to diffuse out of the pore. We study a Brownian ratchet by means of a reflected Brownian motion (Xt)t>=0 with a changing reflection point (Rt)t>=0. The rate of change of Rt is [gamma](Xt-Rt) and the new reflection boundary is distributed uniformly between Rt- and Xt. The asymptotic speed of the ratchet scales with [gamma]1/3 and the asymptotic variance is independent of [gamma].

Suggested Citation

  • Depperschmidt, Andrej & Pfaffelhuber, Peter, 2010. "Asymptotics of a Brownian ratchet for protein translocation," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 901-925, June.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:6:p:901-925
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    References listed on IDEAS

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    1. Fitzsimmons, P. J. & Pitman, Jim, 1999. "Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 117-134, January.
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    Cited by:

    1. Pokalyuk, Cornelia & Mathew, Lisha A. & Metzler, Dirk & Pfaffelhuber, Peter, 2013. "Competing islands limit the rate of adaptation in structured populations," Theoretical Population Biology, Elsevier, vol. 90(C), pages 1-11.

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