Anomalous diffusion on dynamical networks: A model for interacting epithelial cell migration

Stefan Thurner, Nikolaus Wick, Rudolf Hanel, Roland Sedivy, and Lukas Huber a Klinik für HNO, Universität Wien; Austria, b Institut für Mathematik, NuHAG, Universität Wien; Austria, c Klinisches Institut für Pathologie, Universität Wien; Austria, d Institute for Molecular Pathology, Vienna; Austria, e Institut für Biomedizinische Technik und Physik, Universität Wien; Austria, f Institut für Anatomie und Histologie, Universität Innsbruck; Austria Abstract 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.