  We propose a model for cell migration where epithelial cells are able to
detect trajectories of other cells and try to follow them. As cells move along
in 2D cell culture, they mark their paths by loosing tiny parts of cytoplasm.
Any cell moving on a surface where other cells have moved before faces a
network of cell trajectories, which it tries to restrict its motion onto. With
the Tsallis modification of classical thermodynamics one can solve the relevant
Fokker-Planck like equation and obtain experimentally testable distribution
functions. We compare the model to experimental data of normal mammary
epithelial cells and cells which have been genetically manipulated to change
their degree of cell-cell interaction.
