Langlands, T. A. M. and Henry, B. I. (2010) Fractional chemotaxis diffusion equations. Physical Review E: Statistical Nonlinear and Soft Matter Physics, 81 (5). pp. 1-12. ISSN 1539-3755
|HTML Citation||EndNote||Dublin Core||Reference Manager|
Full text available as:
|PDF (Accepted Version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
Official URL: http://link.aps.org/doi/10.1103/PhysRevE.81.051102
Identification Number or DOI: doi: 10.1103/PhysRevE.81.051102
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.
Archive Staff Only: edit this record