Constitutive modeling of the stress-strain behavior of F-actin filament networks

The central role of the cytoskeleton in both healthy and diseased cellular functions makes it a compelling subject for detailed three-dimensional (3D) micromechanical modeling. Microstructural features of the cytoskeleton govern the cell's mechanical behavior in many of the regulating cellular functions including cell division, adhesion, spreading, migration, contraction, and other mechanotransductive effects which influence biochemical processes. Actin microfilaments (AF) combine to form one of the predominant cytoskeletal networks important to these biological processes. Here, the AF cytoskeletal microstructure and stress-strain behavior is modeled via a microstructurally-informed continuum mechanics approach. The force-extension behavior of the individual filaments is captured using the MacKintosh derivation of the worm-like chain (WLC) constitutive relationship for short chains where a new and direct analytical expression for the filament force as a function of filament extension is developed in this paper. The filament force-extension behavior is then used in conjunction with the Arruda-Boyce eight-chain network model to capture the 3D multiaxial stress-strain behavior of the network. The resulting 3D cytoskeletal network constitutive model provides the ability to track microstructural stretch and orientation states during 3D macroscopic stretching conditions. The non-affine nature of the network model effectively accommodates the imposed macroscopic shear strain through filament rotation and a relatively small amount of filament stretch. These characteristics enable the network model, using physically realistic material properties, to capture the initial stiffness of the AF network as well as the nonlinear strain stiffening observed at large stresses. The network model predictions compare favorably with published microrheological data of in vitro AF networks.