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

Adherent eukaryotic cells are subjected to a broad 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, are still poorly understood. Here, we review the existing literature on computational models developed to investigate the chemo-mechanical behaviour of adherent eukaryotic cells. We analyse two main classes of models of single-cell mechanics, based either on the discrete or on the continuum approaches. We focus on the bio-chemo-mechanical model and modelling techniques accounting for the nuclear body. The modelling techniques are discussed highlighting their ability in predicting cytoskeletal contractility states and nuclear stress-strain states.