Analysis and interpretation of stress fiber organization in cells subject to cyclic stretch.

Numerical simulations that incorporate a biochemomechanical model for the contractility of the cytoskeleton have been used to rationalize the following observations. Uniaxial cyclic stretching of cells causes stress fibers to align perpendicular to the stretch direction, with degree of alignment dependent on the stretch strain magnitude, as well as the frequency and the transverse contraction of the substrate. Conversely, equibiaxial cyclic stretching induces a uniform distribution of stress fiber orientations. Demonstrations that the model successfully predicts the alignments experimentally found are followed by a parameter study to investigate the influence of a range of key variables including the stretch magnitude, the intrinsic rate sensitivity of the stress fibers, the straining frequency, and the transverse contraction of the substrate. The primary predictions are as follows. The rate sensitivity has a strong influence on alignment, equivalent to that attained by a few percent of additional stretch. The fiber alignment increases with increasing cycling frequency. Transverse contraction of the substrate causes the stress fibers to organize into two symmetrical orientations with respect to the primary stretch direction.

The simulation of stress fibre and focal adhesion development in cells on patterned substrates.

The remodelling of the cytoskeleton and focal adhesion (FA) distributions for cells on substrates with micro-patterned ligand patches is investigated using a bio-chemo-mechanical model. We investigate the effect of ligand pattern shape on the cytoskeletal arrangements and FA distributions for cells having approximately the same area. The cytoskeleton model accounts for the dynamic rearrangement of the actin/myosin stress fibres. It entails the highly nonlinear interactions between signalling, the kinetics of tension-dependent stress-fibre formation/dissolution and stress-dependent contractility. This model is coupled with another model that governs FA formation and accounts for the mechano-sensitivity of the adhesions from thermodynamic considerations. This coupled modelling scheme is shown to capture a variety of key experimental observations including: (i) the formation of high concentrations of stress fibres and FAs at the periphery of circular and triangular, convex-shaped ligand patterns; (ii) the development of high FA concentrations along the edges of the V-, T-, Y- and U-shaped concave ligand patterns; and (iii) the formation of highly aligned stress fibres along the non-adhered edges of cells on the concave ligand patterns. When appropriately calibrated, the model also accurately predicts the radii of curvature of the non-adhered edges of cells on the concave-shaped ligand patterns.

A bio-chemo-mechanical model for cell contractility.

A general model for the contractility of cells is presented that accounts for the dynamic reorganization of the cytoskeleton. The model is motivated by three key biochemical processes: (i) an activation signal that triggers actin polymerization and myosin phosphorylation, (ii) the tension-dependent assembly of the actin and myosin into stress fibers, and (iii) the cross-bridge cycling between the actin and myosin filaments that generates the tension. Simple relations are proposed to model these coupled phenomena and a continuum model developed for simulating cell contractility. The model is capable of predicting key experimentally established characteristics including: (i) the decrease in the forces generated by the cell with increasing substrate compliance, (ii) the influence of cell shape and boundary conditions on the development of structural anisotropy, and (iii) the high concentration of the stress fibers at the focal adhesions. We present numerical examples of a square cell on four supports to demonstrate these capabilities.