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The Cellular Potts Model (CPM) has been used for simulating variousbiological phenomena such as differential adhesion, fruiting body formation ofthe 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 chemotacticinteractions between cells in the form of a Fokker-Planck equation for theevolution of the cell probability density function. This equation is thenreduced to the classical macroscopic Keller-Segel model. In particular, allcoefficients of the Keller-Segel model are obtained from parameters of the CPM.Theoretical results are verified numerically by comparing Monte Carlosimulations for the CPM with numerics for the Keller-Segel model.Comment: 15 pages, 7 figure

Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description