A coarse-Grained Monte Carlo Model of Cytoskeletal Actin Filament Alignment under Cyclic Stretch

Abstract

The cytoskeleton is a dynamic system linked to the cell'S environment through sites of potential mechanical interaction such as focal adhesions, integrins, cellular junctions, and the extracellular matrix. The physiologic mechanical stimulation experienced by cells such as endothelium is comprised of multiple mechanical modes (e.g., stretching and shear), thus presenting a challenge to characterize their influence on cell structure. Furthermore, physiologically, both endothelial cells and fibroblasts align themselves perpendicular to the direction of cyclic stress. Here, we simulate this behavior using a minimalistic coarse-grained Monte Carlo model of the actin filament network undergoing uniaxial cyclic stretch. A filament network is prescribed within a two-dimensional circular space through filaments connecting nodes. Perimeter nodes represent focal adhesion complexes and interior nodes represent actin binding proteins. Filaments representing actin filaments are randomly generated between nodes. During a stretch cycle, the perimeter nodes are stretched and a Gauss-Seidel relaxation iteration is applied to adjust the position of the interior nodes until the system reaches equilibrium. This equilibrium is defined to occur when the cumulative stress on the nodes from filaments falls below a prescribed tolerance. This repositioning results in a gradual alignment of the filaments in the direction perpendicular to stretch with increasing cycle count. In addition, we corroborate our model with experimental data showing gradual alignment of NIH 3T3 fibroblasts perpendicular to 1 Hz cyclic stretch. With this work, we test the hypothesis that a first-principles mechanical model of filament assembly in a confined space is by itself capable of yielding the remodeling behavior observed experimentally. We believe that this work is of interest to a wide variety of fields including physics, biology, mechanics, and computer science.