  The response of cells during spreading and motility is dictated by several
multi-physics events, which are triggered by extracellular cues and occur at
different time-scales. For this sake, it is not completely appropriate to
provide a cell with classical notions of the mechanics of materials, as for
"rheology" or "mechanical response". Rather, a cell is an alive system with
constituents that show a reproducible response, as for the {\em{contractility}}
for single stress fibers or for the mechanical response of a biopolymer actin
network, but that reorganize in response to external cues in a
non-exactly-predictable and reproducible way. Aware of such complexity, in this
note we aim at formulating a multi-physics framework for modeling cells
spreading and motility, accounting for the relocation of proteins on advecting
lipid membranes.

Soft Condensed Matter