Mechanical Modelling of single and collective cells behavior

Recent experimental results have suggested important direct implications of viscoelasticity of human cells and cell cytoskeleton dynamics on some relevant collective and at single-cell behaviors such as migration, adhesion, and morphogenesis. Other experimental studies have been performed on individual cancer and healthy cells of different types, demonstrating that the former were about 70% softer than the latter. In this thesis with the aim of characterizing — and gaining insights into — the frequency response of single-cell systems to mechanical stimuli (typically LITUS), a generalized viscoelastic paradigm which combines classical and spring-pot based (fractional derivative) models is presented. Than the modelling has been enriched considering the non-linear effect of the prestress, induced in protein filaments during cell adhesion and in the cell membrane (with a simple multiscale scheme that incorporates finite elasticity and a 3-D circus tent-like model), on the overall cell stiffness and finally determining its influence on the in-frequency response of the cell. The theoretical results have shown that the differences in stiffness — at least in principle — allow us to mechanically discriminate between tumor and normal cells: the critical frequencies associated with oscillation magnitude peaks (from tens to hundreds of kilohertz) could be helpfully utilized for targeting or ad hoc altering the functions of cancer cells. An experimental validation of the theoretical results is an ongoing work and the preparation of the experimental setup is also presented. In this thesis some first models have been presented to replicate in-vivo collective behavior of cells. Coherent angular rotation of epithelial cells has been reproduced by a cell-centered based mechanical model in which units are polarized, motile, and interact with the neighboring cells via harmonic forces. Starting from this model a continuum non-linear viscoelastic model incorporating the dynamics of liquid crystals has been studied and some preliminary numerical simulations have been performed.