  Recent biological experiments have shown that certain types of cells are able
to move in structured and confined environment even without the activation of
focal adhesion. Focusing on this particular phenomenon and based on previous
works, we derive a novel two-dimensional mechanical model, which relies on the
following physical ingredients: the asymmetrical renewal of the actin cortex
supporting the membrane, resulting in a backward flow of material; the
mechanical description of the nucleus membrane and the inner nuclear material;
the microtubule network guiding nucleus location; the contact interactions
between the cell and the external environment. The resulting fourth order
system of partial differential equations is then solved numerically to conduct
a study of the qualitative effects of the model parameters, mainly those
governing the mechanical properties of the nucleus and the geometry of the
confining structure. Coherently with biological observations, we find that
cells characterized by a stiff nucleus are unable to migrate in channels that
can be crossed by cells with a softer nucleus. Regarding the geometry, cell
velocity and ability to migrate are influenced by the width of the channel and
the wavelength of the external structure. Even though still preliminary, these
results can be potentially useful in determining the physical limit of cell
migration in confined environment and in designing scaffold for tissue
engineering.
