A non local model for cell migration in response to mechanical stimuli.

Cell migration is one of the most studied phenomena in biology since it plays a fundamental role in many physiological and pathological processes such as morphogenesis, wound healing and tumorigenesis. In recent years, researchers have performed experiments showing that cells can migrate in response to mechanical stimuli of the substrate they adhere to. Motion towards regions of the substrate with higher stiffness is called durotaxis, while motion guided by the stress or the deformation of the substrate itself is called tensotaxis.

The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments.

Recent biological experiments (Lämmermann et al. in Nature 453(7191):51-55, 2008; Reversat et al. in Nature 7813:582-585, 2020; Balzer et al.

Modelling Cell Orientation Under Stretch: The Effect of Substrate Elasticity.

When cells are seeded on a cyclically deformed substrate like silicon, they tend to reorient their major axis in two ways: either perpendicular to the main stretching direction, or forming an oblique angle with it. However, when the substrate is very soft such as a collagen gel, the oblique orientation is no longer observed, and the cells align either along the stretching direction, or perpendicularly to it. To explain this switch, we propose a simplified model of the cell, consisting of two elastic elements representing the stress fiber/focal adhesion complexes in the main and transverse directions.

Cell orientation under stretch: A review of experimental findings and mathematical modelling.

The key role of electro-chemical signals in cellular processes had been known for many years, but more recently the interplay with mechanics has been put in evidence and attracted substantial research interests. Indeed, the sensitivity of cells to mechanical stimuli coming from the microenvironment turns out to be relevant in many biological and physiological circumstances. In particular, experimental evidence demonstrated that cells on elastic planar substrates undergoing periodic stretches, mimicking native cyclic strains in the tissue where they reside, actively reorient their cytoskeletal stress fibres.

A Statistical Mechanics Approach to Describe Cell Reorientation Under Stretch.

Experiments show that when a monolayer of cells cultured on an elastic substratum is subject to a cyclic stretch, cells tend to reorient either perpendicularly or at an oblique angle with respect to the main stretching direction. Due to stochastic effects, however, the distribution of angles achieved by the cells is broader and, experimentally, histograms over the interval [Formula: see text] are usually reported. Here we will determine the evolution and the stationary state of probability density functions describing the statistical distribution of the orientations of the cells using Fokker-Planck equations derived from microscopic rules for describing the reorientation process of the cell.