dorsal/arxiv
View SchemaMultiscale dynamics of biological cells with chemotactic interactions: from a discrete stochastic model to a continuous description
| Authors | Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov |
|---|---|
| Categories | |
| ArXiv ID | physics/0601216 |
| URL | https://arxiv.org/abs/physics/0601216 |
| DOI | 10.1103/PhysRevE.73.051901 |
Abstract
The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. In this paper, we derive continuous limit of discrete one dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.
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"abstract": "The Cellular Potts Model (CPM) has been used for simulating various\nbiological phenomena such as differential adhesion, fruiting body formation of\nthe slime mold Dictyostelium discoideum, angiogenesis, cancer invasion,\nchondrogenesis in embryonic vertebrate limbs, and many others. In this paper,\nwe derive continuous limit of discrete one dimensional CPM with the chemotactic\ninteractions between cells in the form of a Fokker-Planck equation for the\nevolution of the cell probability density function. This equation is then\nreduced to the classical macroscopic Keller-Segel model. In particular, all\ncoefficients of the Keller-Segel model are obtained from parameters of the CPM.\nTheoretical results are verified numerically by comparing Monte Carlo\nsimulations for the CPM with numerics for the Keller-Segel model.",
"arxiv_id": "physics/0601216",
"authors": [
"Mark Alber",
"Nan Chen",
"Tilmann Glimm",
"Pavel M. Lushnikov"
],
"categories": [
"physics.bio-ph",
"physics.data-an"
],
"doi": "10.1103/PhysRevE.73.051901",
"title": "Multiscale dynamics of biological cells with chemotactic interactions: from a discrete stochastic model to a continuous description",
"url": "https://arxiv.org/abs/physics/0601216"
},
"schema_id": "dorsal/arxiv",
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"execution_id": "fc6d4a03-0d33-4da5-9156-cdccb207017e",
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"type": "Model",
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