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Bulletin of Mathematical Biology

, Volume 73, Issue 8, pp 1932–1951 | Cite as

Stochastic Analysis of the Motion of DNA Nanomechanical Bipeds

  • Iddo Ben-Ari
  • Khalid Boushaba
  • Anastasios MatzavinosEmail author
  • Alexander Roitershtein
Original Article

Abstract

In this paper, we formulate and analyze a Markov process modeling the motion of DNA nanomechanical walking devices. We consider a molecular biped restricted to a well-defined one-dimensional track and study its asymptotic behavior. Our analysis allows for the biped legs to be of different molecular composition, and thus to contribute differently to the dynamics. Our main result is a functional central limit theorem for the biped with an explicit formula for the effective diffusivity coefficient in terms of the parameters of the model. A law of large numbers, a recurrence/transience characterization and large deviations estimates are also obtained. Our approach is applicable to a variety of other biological motors such as myosin and motor proteins on polymer filaments.

Keywords

DNA nanodevices Molecular spiders Controlled random walks Markov additive processes Law of large numbers Recurrence-transience criteria Large deviations Central limit theorem Regeneration structure 

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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • Iddo Ben-Ari
    • 1
  • Khalid Boushaba
    • 2
  • Anastasios Matzavinos
    • 2
    Email author
  • Alexander Roitershtein
    • 2
  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA
  2. 2.Department of MathematicsIowa State UniversityAmesUSA

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