ANALYSIS OF THE INFLUENCE OF SUBSTRATE PROPERTIES AND FOCAL ADHESION FORMATION ON THE STRESS FIBRE GROWTH AND REORIENTATION IN CONTRACTILE CELLS
Pradeep Keshavanarayana1, Rene De Borst2, Martin Ruess1
1University of Glasgow, UK;
2University of Sheffield, UK
Contractile cells play a prominent role in the adaptive nature of biological tissues. Contractility is mainly attributed to the growth of the tension dependent acto-myosin network called stress fibres within the cytoskeleton. Stress fibres extend along the length of the cell and end on the cell membrane at focal adhesions. Integrin proteins at the junctions of focal adhesions are capable of sensing the environment, thereby making the cellular behaviour dependent on the cell supporting substrate. The formation of the integrins, through a series of chemical reactions, influences the concentration of calcium ions in the cytoplasm. The growth of stress fibres is governed by the calcium thus present, and the contractile stresses. It has been observed that the growth of stress fibres influence 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 reorient itself in a direction away from the loading direction, exhibiting strain avoidance.
Mathematical models are necessary to understand the dependence of cellular behaviour on the substrate properties along with the feedback mechanisms and are further used in designing the in-vitro experiments. The coupling of the models for stress fibres and focal adhesions results in a non-linear bio-chemomechanical problem.
In this contribution, we present the positive influence of the growth of focal adhesions along with a mechanosensitive feedback loop on the reorientation process. We use a non-linear Hill-type model to capture the growth of active stress involved in the evolution law for the stress fibres and a thermodynamical approach to model the focal adhesions. A highly stable monolithic solution scheme with flexible time steps is used to solve the governing coupled system. Finally we compare our simulation results with experiments in regard to different substrate properties and loading conditions.