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Updated: Jul 21, 2026

Chemotactic Response of Marine Micro-Organisms to Micro-Scale Nutrient Layers
Published on: May 28, 2007
Multiscale dynamics of biological cells with chemotactic interactions: from a discrete stochastic model to a
Mark Alber1, Nan Chen, Tilmann Glimm
1Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46656, USA. malber@nd.edu
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. We derive a continuous limit of a 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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