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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2310.07938 |
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| _version_ | 1866917571319562240 |
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| author | Simpson, Matthew J Murphy, Keeley M McCue, Scott W Buenzli, Pascal R |
| author_facet | Simpson, Matthew J Murphy, Keeley M McCue, Scott W Buenzli, Pascal R |
| contents | Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion, however these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically-inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, that we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two--dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provides a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion Simpson, Matthew J Murphy, Keeley M McCue, Scott W Buenzli, Pascal R Cellular Automata and Lattice Gases Cell Behavior 92-10 Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion, however these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically-inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, that we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two--dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provides a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts |
| title | Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion |
| topic | Cellular Automata and Lattice Gases Cell Behavior 92-10 |
| url | https://arxiv.org/abs/2310.07938 |