Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes

Ellery, Adam, Baker, Ruth, & Simpson, Matthew (2015) Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes. Physical Biology, 12(6), 066010.

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Abstract

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient),D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculateDdirectly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.

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ID Code: 91492
Item Type: Journal Article
Refereed: Yes
Keywords: diffusion, diffusion coefficient, crowded transport, hindered transport
DOI: 10.1088/1478-3975/12/6/066010
ISSN: 1478-3975
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Funding:
Copyright Owner: © 2015 IOP Publishing Ltd
Deposited On: 04 Jan 2016 05:11
Last Modified: 08 Nov 2016 14:15

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