Abstract

Cells physical properties and functions like adhesion, migration and division are all regulated by an interplay between mechanical and biochemical processes occurring within and across the cell membrane. It is however known that mechanical forces spread through the cytoskeletal elements and reach equilibrium with characteristic times at least one order of magnitude smaller than the ones typically governing propagation of biochemical signals and biological phenomena like polymerization/depolymerization of protein microfilaments or even cell duplication and differentiation. This somehow allows to study as uncoupled many biochemo- mechanical events although they appear simultaneously and as concatenated. In this work, the complex machinery of the cell is hence deprived of its biochemical processes with the aim to bring out the crucial role that mechanics plays in regulating the cell as a whole as well as in terms of some interactions occurring at the interface with the extra-cellular matrix. In this sense, the single-cell is here described as a mechanical unit, endowed with an internal micro-architecture –the cytoskeleton– able to sense extra-cellular physical stimuli and to react to them through coordinated structural remodelling and stress redistribution that obey specific equilibrium principles. By coupling discrete and continuum theoretical models, cell mechanics is investigated from different perspectives, thus deriving the cell overall elastic response as the macroscopic projection of micro-structural kinematics involving subcellular constituents. Finally, some optimal arrangements of adherent cells in response to substrate-mediated elastic interactions with external loads are explored and compared with experimental evidences from the literature.