dorsal/arxiv
View SchemaContinuous macroscopic limit of a discrete stochastic model for interaction of living cells
| Authors | Mark Alber, Nan Chen, Pavel M. Lushnikov, Stuart A. Newman |
|---|---|
| Categories | |
| ArXiv ID | physics/0703026 |
| URL | https://arxiv.org/abs/physics/0703026 |
| DOI | 10.1103/PhysRevLett.99.168102 |
Abstract
In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume is derived, describing cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis. The continuous macroscopic model is obtained as a Fokker-Planck equation describing evolution of the cell probability density function. All coefficients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It is also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach is demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.
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"abstract": "In the development of multiscale biological models it is crucial to establish\na connection between discrete microscopic or mesoscopic stochastic models and\nmacroscopic continuous descriptions based on cellular density. In this paper a\ncontinuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded\nvolume is derived, describing cells moving in a medium and reacting to each\nother through both direct contact and long range chemotaxis. The continuous\nmacroscopic model is obtained as a Fokker-Planck equation describing evolution\nof the cell probability density function. All coefficients of the general\nmacroscopic model are derived from parameters of the CPM and a very good\nagreement is demonstrated between CPM Monte Carlo simulations and numerical\nsolution of the macroscopic model. It is also shown that in the absence of\ncontact cell-cell interactions, the obtained model reduces to the classical\nmacroscopic Keller-Segel model. General multiscale approach is demonstrated by\nsimulating spongy bone formation from loosely packed mesenchyme via the\nintramembranous route suggesting that self-organizing physical mechanisms can\naccount for this developmental process.",
"arxiv_id": "physics/0703026",
"authors": [
"Mark Alber",
"Nan Chen",
"Pavel M. Lushnikov",
"Stuart A. Newman"
],
"categories": [
"physics.bio-ph",
"q-bio.CB"
],
"doi": "10.1103/PhysRevLett.99.168102",
"title": "Continuous macroscopic limit of a discrete stochastic model for interaction of living cells",
"url": "https://arxiv.org/abs/physics/0703026"
},
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