Cell motility as persistent random motion: How to turn time-lapse recorded trajectories into simple dynamical models in continuous time

The "body-language" of cells on the move in a given environment speaks about the cells and their environment. To read this language, we must first characterize it. Models and their parameters do that, qualitatively and quantitatively. I sketch how a systematic analysis of experimental trajectories yields cell-type-specific motility models in the form of stochastic differential equations.

With a model at hand, the next problem is how to fit the model's description of continuous motion to the discrete time-series of positions that make up experimental trajectories. The challenge is discreteness and experimental errors on positions. This is a general problem, encountered also in, e.g., the study of Brownian motion of individual particles with well-known theories. I describe some pitfalls and techniques that avoid them.