Fractional chemotaxis diffusion equations

T. A. M. Langlands and B. I. Henry
Phys. Rev. E 81, 051102 – Published 4 May 2010

Abstract

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

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  • Received 15 February 2010

DOI:https://doi.org/10.1103/PhysRevE.81.051102

©2010 American Physical Society

Authors & Affiliations

T. A. M. Langlands*

  • Department of Mathematics and Computing, University of Southern Queensland, Toowoomba, Queensland 4350, Australia

B. I. Henry

  • Department of Applied Mathematics, School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia

  • *t.langlands@usq.edu.au
  • b.henry@unsw.edu.au

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Vol. 81, Iss. 5 — May 2010

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