Cell spreading provides one of the simplest configurations in which eukaryotic cells develop angular symmetry-breaking assemblies of mechanosensing and mechanotransducive organelles in preparation for cell differentiation and movement. By identifying the edge of the cell-ECM adhesion area as having an important role in mechanosensor complex aggregation, we consider the spatial patterns arising on this edge, within a 1D lattice model of the nearest-neighbour interaction between individual integrin-mediated mechanosensors. We obtain the Ginzburg-Landau free energy for this model and analyse the spectrum of spatial modes as the cell spreads and increases the contact area. We test the plausibility of our model by comparing its predictions for the azimuthal angular frequency of aggregation of mechanosensors into nascent focal adhesions (FAs) to observations of the paxillin distribution in spreading fibroblasts.STATEMENT OF SIGNIFICANCE. The topic of cell adhesion on substrates is very active, with numerous theoretical, experimental and computer simulation studies probing the mechanisms and signalling pathways of cell response to interacting with substrate. Integrin-based adhesion complexes are known to be the individual units of this process, and their dense aggregation into focal adhesions leads to cells developing asymmetry, polarity, and eventually -locomotion. Here we develop a theoretical model that suggests that physical interactions between individual adhesion complexes is the factor that defines the initial breaking of symmetry of the cell spreading on substrate, and predicts the characteristic wavelength of modulation above the critical size of adhesion area.

Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. The center of the basic unit of the muscle, the sarcomeric M-band, is perfectly placed to sense the different types of load to which the muscle is subjected. In particular, the kinase domain of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a quantitative mathematical model that describes the kinetics of TK-based mechanosensitive signaling and predicts trophic changes in response to exercise and rehabilitation regimes. First, we build the kinetic model for TK conformational changes under force: opening, phosphorylation, signaling, and autoinhibition. We find that TK opens as a metastable mechanosensitive switch, which naturally produces a much greater signal after high-load resistance exercise than an equally energetically costly endurance effort. Next, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber size. We suggest that the latter effect may occur via the steric inhibition of ribosome diffusion through the sieve-like myofilament lattice. The full model yields a steady-state solution (homeostasis) for muscle cross-sectional area and tension and, a quantitatively plausible hypertrophic response to training, as well as atrophy after an extended reduction in tension.

Cell spreading provides one of the simplest configurations in which eukaryotic cells develop angular symmetry-breaking assemblies of mechanosensing and mechanotransducive organelles in preparation for cell differentiation and movement. By identifying the edge of the cell-ECM adhesion area as having an important role in mechanosensor complex aggregation, we consider the spatial patterns arising on this edge, within a 1D lattice model of the nearest-neighbour interaction between individual integrin-mediated mechanosensors. We obtain the Ginzburg-Landau free energy for this model and analyse the spectrum of spatial modes as the cell spreads and increases the contact area. We test the plausibility of our model by comparing its predictions for the azimuthal angular frequency of aggregation of mechanosensors into nascent focal adhesions (FAs) to observations of the paxillin distribution in spreading fibroblasts.STATEMENT OF SIGNIFICANCE. The topic of cell adhesion on substrates is very active, with numerous theoretical, experimental and computer simulation studies probing the mechanisms and signalling pathways of cell response to interacting with substrate. Integrin-based adhesion complexes are known to be the individual units of this process, and their dense aggregation into focal adhesions leads to cells developing asymmetry, polarity, and eventually -locomotion. Here we develop a theoretical model that suggests that physical interactions between individual adhesion complexes is the factor that defines the initial breaking of symmetry of the cell spreading on substrate, and predicts the characteristic wavelength of modulation above the critical size of adhesion area.

Cadherins mediate cell-cell adhesion and help the cell determine its shape and function. Here we study collective cadherin organization and interactions within cell-cell contact areas, and find the cadherin density at which a ‘gas-liquid’ phase transition occurs, when cadherin monomers begin to aggregate into dense clusters. We use a 2D lattice model of a cell-cell contact area, and coarse-grain to the continuous number density of cadherin to map the model onto the Cahn-Hilliard coarsening theory. This predicts the density required for nucleation, the characteristic length scale of the process, and the number density of clusters. The analytical predictions of the model are in good agreement with experimental observations of cadherin clustering in epithelial tissues.