  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.
