An affine micro-sphere-based constitutive model, accounting for junctional sliding, can capture F-actin network mechanics

Actin filaments are a major component of the cytoskeleton and play a crucial role in cell mechanotransduction. F-actin networks can be reconstituted in vitro and their mechanical behaviour has been studied experimentally. Constitutive models that assume an idealised network structure, in combination with a non-affine network deformation, have been successful in capturing the elastic response of the network. In this study, an affine network deformation is assumed, in which we propose an alternative 3D finite strain constitutive model. The model makes use of a micro-sphere to calculate the strain energy density of the network, which is represented as a continuous distribution of filament orientations in space. By incorporating a simplified sliding mechanism at the filament-to-filament junctions, premature filament locking, inherent to affine network deformation, could be avoided. The model could successfully fit experimental shear data for a specific cross-linked F-actin network, demonstrating the potential of the novel model.