Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice
The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Institute of Physics
2016
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| _version_ | 1826262713009963008 |
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| author | Ellery, A Baker, R Simpson, M |
| author_facet | Ellery, A Baker, R Simpson, M |
| author_sort | Ellery, A |
| collection | OXFORD |
| description | The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations. |
| first_indexed | 2024-03-06T19:40:25Z |
| format | Journal article |
| id | oxford-uuid:2079d7c3-ca63-48a9-a61d-9f0bd5332f4b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:40:25Z |
| publishDate | 2016 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | oxford-uuid:2079d7c3-ca63-48a9-a61d-9f0bd5332f4b2022-03-26T11:27:49ZCommunication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded latticeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2079d7c3-ca63-48a9-a61d-9f0bd5332f4bEnglishSymplectic Elements at OxfordAmerican Institute of Physics2016Ellery, ABaker, RSimpson, MThe motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations. |
| spellingShingle | Ellery, A Baker, R Simpson, M Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice |
| title | Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice |
| title_full | Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice |
| title_fullStr | Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice |
| title_full_unstemmed | Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice |
| title_short | Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice |
| title_sort | communication distinguishing between short time non fickian diffusion and long time fickian diffusion for a random walk on a crowded lattice |
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