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Subdiffusive Transport in Heterogeneous Patchy Environments

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Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues

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Abstract

Transport across heterogeneous, patchy environments is a ubiquitous phenomenon spanning fields of study including ecological movement, intracellular transport and regions of specialised function in a cell. These regions or patches may be highly heterogeneous in their properties, and often exhibit anomalous behaviour (resulting from e.g. crowding or viscoelastic effects) which necessitates the inclusion of non-Markovian dynamics in their study. However, many such processes are also subject to an internal self-regulating or tempering process due to concurrent competing functions being carried out. In this work we develop a model for anomalous transport across a heterogeneous, patchy environment subject to tempering. We show that in the long-time an equilibrium may be reached with constant effective transport rates between the patches. This result is qualitatively different from untempered systems where subdiffusion results in the long-time accumulation of all particles in the patch with lowest anomalous exponent, 0 < μ < 1.

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Acknowledgements

The authors would like to thank N. Korabel and T. Waigh for fruitful discussions. This work is supported by EPSRC grant EP/N018060/1.

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Authors and Affiliations

  1. School of Mathematics, The University of Manchester, Manchester, UK

    Sergei Fedotov & Helena Stage

Authors
  1. Sergei Fedotov
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  2. Helena Stage
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Correspondence to Helena Stage .

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Editors and Affiliations

  1. Universidad Autónoma de la Ciudad de México (UACM), Mexico City, Mexico

    Luis Olivares-Quiroz

  2. Human Systems Biology Laboratory, Instituto Nacional de Medicina Genómica (INMEGEN), México City, Mexico

    Osbaldo Resendis-Antonio

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Fedotov, S., Stage, H. (2018). Subdiffusive Transport in Heterogeneous Patchy Environments. In: Olivares-Quiroz, L., Resendis-Antonio, O. (eds) Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues. Springer, Cham. https://doi.org/10.1007/978-3-319-73975-5_3

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