Typical questions arising in that context are as follows:

- Assume a given network of bio-polymer fibers with known elastic response. Imagine embedded into this network a passive, spherical model cell of given elastic properties. What is the resulting effective 3D potential energy landscape ? Is it unique ? How can the viscosity or the active shape changes of the cell be included in a coarse-grained way ?

- Can the complex internal reorganizations of the cytoskeleton, the time-dependent point forces onto the extracellular matrix and the resulting matrix deformation be translated into an effective total force acting on the cell center ?

- What are the statistical properties of this effective migration force and what are the properties of the resulting random walk in the complex potential landscape (mean squared displacement, step with distribution) ?

- Can adaption of the cell to the local environment be incorporated into that model as a functional dependence of the statistical force parameters on the local shape of the potential landscape ? If yes, how must this adaptive modulation of force statistics be optimized in order to achieve efficient (fast and energy saving) migration ?

At present, we also follow a data-driven approach in order to understand cell migration: Living tumor cells are brought on the surface of a collagen gel with controlled mechanical properties. The invasion of the tumor cells into the collagen gel is then observed with a light microscope, resulting in trajectories of the individual cells, or more conveniently, distribution functions.

We now try to model the time-dependent invasion profiles as a stochastic process, described by Fokker-Planck equations with suitable diffusion and drift terms.

For first ideas and results, see the research blog.