A feedback-loop extended stress fiber growth model with focal adhesion formation

Contractile cells play a prominent role in the adaptive nature of biological tissues. Contractility is mainly attributed to the growth of the tension dependent actomyosin bundles called stress fibers within the cytoskeleton. Stress fibers extend along the length of the cell and end at focal adhesions on the cell membrane. At the focal adhesion junctions on the cell membrane the integrin proteins are capable of sensing the environment, thereby making the cellular behavior dependent on the cell supporting substrate. It has been observed that the growth of stress fibers influences focal adhesions and vice-versa, resulting in a continuous cross-talk between different processes in the cell. Recent experiments have shown that cells subjected to uni-axial cyclic loading, depending on the substrate properties reorient themselves in a direction away from the loading direction, exhibiting strain avoidance.

Mathematical models are important to understand the dependence of the cellular behavior on the substrate properties along with feedback mechanisms and are further used in designing in-vitro experiments. The coupling of the models for stress fibers and focal adhesions results in a non-linear bio-chemo-mechanical problem. In this contribution, we present the positive influence of the growth of focal adhesions along with a mechanosensitive feedback loop on the stress fiber growth and further reveal the characteristics of the re-orientation process due to cyclic loading. We use a non-linear Hill-type model to capture the growth of the active stress involved in the evolution law for the stress fibers and a thermodynamical approach to model the focal adhesions. A highly stable and reliable monolithic solution scheme is used to solve the governing system of coupled equations. Finally, we validate our simulation results with experimental results in regard to different loading conditions.