Small-on-Large Fractional Derivative–Based Single-Cell Model Incorporating Cytoskeleton Prestretch

In recent years, experimental evidences have suggested important direct implications of viscoelasticity of human cells and cell cytoskeleton dynamics on some relevant collective and single-cell behaviors such as migration, adhesion, and morphogenesis. Consequently, the mechanical properties of single cells and how cells respond to mechanical stimuli have been at the center of a vivid debate in the scientific community. By referencing important experimental findings from the literature that have shown that human metastatic tumor cells are approximately 70% softer than benign cells, independently from the cell lines examined, the present authors have very recently theoretically demonstrated that these differences in stiffness might be exploited to mechanically discriminate healthy and cancer cells, for example, through low-intensity therapeutic ultrasound. In particular, by using a generalized viscoelastic paradigm combining classical and fractional derivative-based models, it has been found that selected frequencies (from tens to hundreds of kilohertz) are associated with resonancelike phenomena that are prevailing on thermal fluctuations and hence could be, at least in principle, helpfully utilized for both targeting and selectively attacking tumor cells. With the aim of investigating the effect of the prestress (for instance, induced in protein filaments during cell adhesion) on the overall cell stiffness and, in turn, on its in-frequency response, a simple multiscale scheme is proposed in this paper to bottom-up enrich the spring-pot-based viscoelastic single-cell models by incorporating finite elasticity and thereby determining through sensitivity analyses the role played by the stretched state of the cytoskeletal elements on the cell vibration.