Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes
Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport...
| Main Authors: | , , , |
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| Format: | Journal article |
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Elsevier
2016
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| _version_ | 1797091868011397120 |
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| author | Ellery, A Baker, R McCue, S Simpson, M |
| author_facet | Ellery, A Baker, R McCue, S Simpson, M |
| author_sort | Ellery, A |
| collection | OXFORD |
| description | Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period. |
| first_indexed | 2024-03-07T03:38:29Z |
| format | Journal article |
| id | oxford-uuid:bd18b0a8-623c-473d-a83f-33a5e22fb1e6 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:38:29Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:bd18b0a8-623c-473d-a83f-33a5e22fb1e62022-03-27T05:29:12ZModeling transport through an environment crowded by a mixture of obstacles of different shapes and sizesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bd18b0a8-623c-473d-a83f-33a5e22fb1e6Symplectic Elements at OxfordElsevier2016Ellery, ABaker, RMcCue, SSimpson, MMany biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period. |
| spellingShingle | Ellery, A Baker, R McCue, S Simpson, M Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes |
| title | Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes |
| title_full | Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes |
| title_fullStr | Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes |
| title_full_unstemmed | Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes |
| title_short | Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes |
| title_sort | modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes |
| work_keys_str_mv | AT ellerya modelingtransportthroughanenvironmentcrowdedbyamixtureofobstaclesofdifferentshapesandsizes AT bakerr modelingtransportthroughanenvironmentcrowdedbyamixtureofobstaclesofdifferentshapesandsizes AT mccues modelingtransportthroughanenvironmentcrowdedbyamixtureofobstaclesofdifferentshapesandsizes AT simpsonm modelingtransportthroughanenvironmentcrowdedbyamixtureofobstaclesofdifferentshapesandsizes |