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Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

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Abstract

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in a percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times but anomalous diffusion at intermediate times. The effective exponents for square distance vs time usually are below one at these intermediate times, but they can also be larger than one for high barrier concentrations. Thus, we observe sub- and superdiffusion in a crowded environment.

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References

  1. Pederson, T.: Diffusional protein transport within the nucleus: a message in the medium. Nat. Cell Biol. 2, E73–E74 (2000)

    Article  Google Scholar 

  2. Guthold, M., Zhu, X., Rivetti, C., Yang, G., Thomson, N., Kasas, S., Hansma, H., Smith, B., Hansma, P., Bustamante, C.: Direct observation of one-dimensional diffusion and transcription by Escherichia coli RNA polymerase. Biophys. J. 77, 2284–2294 (1999)

    Google Scholar 

  3. Berry, H.: Monte Carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation. Biophys. J. 83, 1891–1901 (2002)

    Article  ADS  Google Scholar 

  4. Valdez-Taubas, J., Pelham, H.: Slow diffusion of proteins in the yeast plasma membrane allows polarity to be maintained by endocytic cycling. Curr. Biol. 13, 1636–1640 (2003)

    Article  Google Scholar 

  5. Weiss, M., Elsner, M., Kartberg, F., Nilsson, T.: Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells. Biophys. J. 87, 3518 (2004)

    Article  ADS  Google Scholar 

  6. Binder, K., Heermann, D.W.: Monte Carlo Simulation in Statistical Physics: An Introduction, 4th edn. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  7. Bouchaud, J.P., Georges, A.: Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195, 127 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  8. Frey, E., Kroy, K.: Brownian motion: a paradigm of soft matter and biological physics. Ann. Phys. (Leipzig) 14, 20 (2005)

    Article  MATH  ADS  Google Scholar 

  9. Lindenberg, K., Oshanin, G., Tachiya, M.: Chemical kinetics beyond the textbook: fluctuations, many- particle effects and anomalous dynamics. J. Phys. Condens. Mat. 19, 060301 (2007)

    Google Scholar 

  10. Saxton, M.J.: A biological interpretation of transient anomalous subdiffusion. Biophys. J. 92, 1178–1191 (2007)

    Article  ADS  Google Scholar 

  11. Ratynskaia, S., Rypdal, K., Knapek, C., Khrapak, S., Milovanov, A.V., Ivlev, A., Rasmussen, J.J., Morfill, G.E.: Superdiffusion and Viscoelastic Vortex Flows in a Two-Dimensional Complex Plasma. Phys. Rev. Lett. 96, 105010 (2006)

    Article  ADS  Google Scholar 

  12. Liu, B., Goree, J.: Superdiffusion in two-dimensional Yukawa liquids. Phys. Rev. E 75, 016405 (2007)

    Article  ADS  Google Scholar 

  13. Stauffer, D., Aharony, A.: Introduction to Percolation Theory. Taylor & Francis, London (1992)

    Google Scholar 

  14. Ruiz-Lorenzo, J.J., Yuste, S.B., Lindenberg, K.: Simulations for trapping reactions with subdiffusive traps and subdiffusive particles. J. Phys. Condens. Mat. 19, 065120 (2007)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, 50923, Köln, Germany

    Dietrich Stauffer & Christian Schulze

  2. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120, Heidelberg, Germany

    Dieter W. Heermann

Authors
  1. Dietrich Stauffer
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  2. Christian Schulze
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  3. Dieter W. Heermann
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Correspondence to Dieter W. Heermann.

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Stauffer, D., Schulze, C. & Heermann, D.W. Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment. J Biol Phys 33, 305–312 (2007). https://doi.org/10.1007/s10867-008-9075-2

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  • DOI: https://doi.org/10.1007/s10867-008-9075-2

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