### Abstract

Original language | English |
---|---|

Pages (from-to) | 62-70 |

Number of pages | 9 |

Journal | Mathematical Biosciences |

Volume | 294 |

DOIs | |

Publication status | Published - 16 Oct 2017 |

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### Bibliographical note

© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/### Keywords

- Chemotaxis
- Cell clustering
- Mathematical model
- Diffusion equation
- Equations of motion

### Cite this

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*Mathematical Biosciences*, vol. 294, pp. 62-70. https://doi.org/10.1016/j.mbs.2017.10.008

**A simple mathematical model of cell clustering by chemotaxis.** / Harris, Paul.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A simple mathematical model of cell clustering by chemotaxis

AU - Harris, Paul

N1 - © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

PY - 2017/10/16

Y1 - 2017/10/16

N2 - Chemotaxis is the process by which cells and clusters of cells follow chemical signals in order to combine and form larger clusters. The spreading of the chemical signal from any given cell can be modelled using the linear diffusion equation, and the standard equations of motion can be used to determine how a cell, or cluster of cells, moves in response to the chemical signal. The resulting differential equations for the cell locations are integrated through time using the fourth-order Runge-Kutta method. The effect which changing the initial concentration magnitude, diffusion constant and velocity damping parameter has on the shape of the final clusters of cells is investigated and discussed.

AB - Chemotaxis is the process by which cells and clusters of cells follow chemical signals in order to combine and form larger clusters. The spreading of the chemical signal from any given cell can be modelled using the linear diffusion equation, and the standard equations of motion can be used to determine how a cell, or cluster of cells, moves in response to the chemical signal. The resulting differential equations for the cell locations are integrated through time using the fourth-order Runge-Kutta method. The effect which changing the initial concentration magnitude, diffusion constant and velocity damping parameter has on the shape of the final clusters of cells is investigated and discussed.

KW - Chemotaxis

KW - Cell clustering

KW - Mathematical model

KW - Diffusion equation

KW - Equations of motion

U2 - 10.1016/j.mbs.2017.10.008

DO - 10.1016/j.mbs.2017.10.008

M3 - Article

VL - 294

SP - 62

EP - 70

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

ER -