From a discrete to a continuous model of biological cell movement

To describe the biological cell movement a continuous model was constructed using a descrete Potts model. An expression for the diffusion coefficient of a collection on noninteraction cells which depends explicitly on the Potts model parameter was also developed. It was found that the coefficient varies when the Potts parameters for cell membrane cell membrane elasticity and cell-medium adhesion are varied. The relationship between the probability of occupancy of lattice points and the density profile in the continuous limit was also explained.