Material and structural instabilities are ubiquitous at the various length scales in continua experiencing deformation. This is particularly evident in soft media, like biological tissues, starting from the cell’s level. At this scale, physical properties and functions like adhesion, migration and division are regulated by the interplay between mechanical and biochemical processes occurring within and across the cell membrane. 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 the propagation of biochemical signals and biological phenomena. The latter can then be treated as uncoupled from mechanics, although they appear simultaneously, thereby bringing out the crucial role that mechanical instabilities have in regulating the cell behavior.
The single-cell can be treated 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 remodeling and stress redistribution. Although several homogenization approaches have been set up in the last several decades, standard Continuum Mechanics cannot be directly applied to this context, as it is known to be inadequate whenever micro-heterogeneities, defects, and reconfiguration of the microstructure arise. This can be done through Structured Deformations, suitable for predicting the effective dynamics of bodies experiencing sub-macroscopic disarrangements, such as configurational changes, switching, slips, separations, etc. This is the case for (i) actin filaments and (ii) the cytoskeleton, as specified in the sequel.
- Actin filaments experience disarrangements at the level of their molecular architectures. Biochemically induced sliding disarrangements between actin segments and myosin heads are known to affect the mechanics of actomyosin filaments embedded in the cytoskeleton apparatus through tensile instabilities, predicted by our approach.
- The cytoskeleton, formed by actin microfilaments, intermediate filaments and microtubule continuously changing their spatial organization and prestresses through polymerization/depolymerization processes, steers migration, adhesion and cell division by obeying a tensegrity construct, resembling actin filaments (cables) and microtubules (struts). Evidence of buckled microtubules and highly stretched filaments suggested us to account for such effects within the 30-element tensegrity cell paradigm. For the first time in the literature this allows for predicting extreme and counter-intuitive behaviors exploited by cells, such as instability-guided configurational switching.