Bio-chemo-mechanical models for nuclear deformation in adherent eukaryotic cells

Adherent eukaryotic cells are subjected to abroad variety of extracellular and intracellular stimuli regulating their behaviour. These stimuli can be either purely chemical, for example soluble factors binding to the cell membrane, or mechano-chemical, for example integrin-based adhesion complexes stretching the cell cytoskeleton. Here, we focus on mechano-chemical stimuli such as extracellular forces (interstitial flow, pressurization) and intracellular forces (due to cell adhesion), which may combine generating stress–strain states in the cytoskeleton. These states are transferred to the nucleus to influence the transcription of specific genes, likely by changing the chromatin organization and by altering the permeability of the nuclear membrane. While there exists increasing experimental evidence of the mechanosensing role of the cell nucleus, both the underlying molecular mechanisms involved, and the nuclear structural behaviour in response to forces, arestill poorly understood. Here, we review the existing literatureon computational models developed to investigatethe chemo-mechanical behaviour of adherent eukaryoticcells. We analyse two main classes of models of single-cellmechanics, based either on the discrete or on the continuumapproaches. We focus on the bio-chemo-mechanicalmodel and modelling techniques accounting for the nuclearbody. The modelling techniques are discussed highlightingtheir ability in predicting cytoskeletal contractility states andnuclear stress–strain states.