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

Abstract

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.

Modeling and simulation of biopolymer networks: Classification of the cytoskeleton models according to multiple scales

“…An elastic model is sufficient to describe small deformations following Hook' s law, whereas a nonlinear elastic model, such as the Gaussian model, is required for larger deformations [29]. However, the elastic models are only suitable for modeling cell material properties and cell dynamic behaviors at limited time scales (near equilibrium) due to their oversimplification [29,31]. The time-dependent stress-strain behaviors can be described by the viscoelastic models that utilize typical viscoelastic constitutive equations, such as typical or modified Maxwell models [31,32].…”

“…However, the elastic models are only suitable for modeling cell material properties and cell dynamic behaviors at limited time scales (near equilibrium) due to their oversimplification [29,31]. The time-dependent stress-strain behaviors can be described by the viscoelastic models that utilize typical viscoelastic constitutive equations, such as typical or modified Maxwell models [31,32]. Viscoelastic models have been able to predict the cellular mechanics for blood cells, which are under continuous shear and high mechanical perturbations, as well as for adherent cells such as epithelial and endothelial cells [39].…”

“…[29]. Nava and co-workers [31] and Moeendarbary and Harris [32] have unified various models ranging from cell mechanics (>10 µm) to cytoskeleton behaviors (~1 µm). The former, which is mostly related to mechanics of adherent cells, proposed a model classification that included only continuum-based models and structure-based models (they used the terms of continuum model and microstructural model).…”

A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering

“…Firstly, according to the concept of ''force isotropy'' on the cell introduced in [45,46], cells that occupy the bio-synthesizing compartment (v compartment) experience an isotropic adherence condition and consequently tend to assume a spherical shape (see Fig. 5, left) whereas cells that live in the proliferating compartment (n compartment) are subjected to an anisotropic adhesion state and tend to elongate (see Fig.…”

“…Cartilage tissue growth in engineered constructs had been already studied in a series of papers by Klisch and coauthors [30][31][32]. In this work, we enrich the description of the biophysical phenomena by introducing the conceptual framework developed in [43,45,46]. In these works, the isotropic/anistropic state of the cytoskeletal tension is shown to be responsible for triggering signalling transduction cascades which regulate functional cell behaviors related to proliferation and/or ECM secretion.…”