Stochastic phenomena in single cell migration: theory, experiments, and simulations

Cell migration plays important roles in the development of multicellular organisms and processes as immune response and in cancer metastasis. We present here a review on cell migration modelling of single cells on a flat substrate. Re-analyses of experimental data evinced a behavior that deviates from the canonical Langevin model of a particle immersed on a viscous fluid that presents a Brownian persistent motion. The proposition of a semi-empirical model yields a diffusive behavior in short-time intervals and fits the experimental data, but challenges velocity definition and the corresponding measurement protocol. The solution is presented on the form of an anisotropic model for cell migration, that considers an additional, internal variable, that accounts for the spatial symmetry break of a migrating cell. The theoretical results yield the proposition of natural units for the problem that allows the collapse of theoretical and experimental curves onto a single parameter family of curves. We also discuss a simulation model for three dimensional cells migrating on a flat substrate. The simulation results are quantitatively validated using the theoretical results. The simulation model is now ready to be used in investigating cell migration in more complex environments, that imply non-linear interactions and require numerical solutions.

Keywords
Cell migration; Modified Fürth equation; Ornstein-Uhlenbeck processes; CompuCel3D