Small-on-large fractional derivative-based single-cell model incorporating cytoskeleton prestretch

Abstract

In the last years, experimental evidences have suggested important direct implications of vis-coelasticity of human cells and cell cytoskeleton dynamics on some relevant collective and at single cell behaviors such as migration, adhesion and morphogenesis. As a consequence, the me-chanical properties of single cells as well as how cells respond to mechanical stimuli have been –and currently are– at the center of a vivid debate in the scientific community. By making reference to important experimental findings from the literature which have shown that human metastatic tumor cells are about 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 means of a general-ized viscoelastic paradigm combining classical and fractional derivative-based models, it has been found that selected frequencies (from tens to hundreds kHz) are associated to resonance-like phe-nomena that are prevailing on thermal fluctuations and that could be hence, 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 here proposed to bottom-up enrich the spring-pot-based viscoelastic single-cell models, by incorporating finite elasticity and in this way determining, through sensitivity analyses, the role played by the stretched state of the cytoskeletal elements on the cell vibration.