Affine and non-affine deformations quantified in cytoskeletal networks through three-dimensional form-finding model

Actin filaments and cross-linkers are main components of cytoskeletal networks in eukaryotic cells, and they support bending moments and axial forces respectively. A three-dimensional form-finding model is proposed in this work to investigate affine and non-affine deformations in cytoskeletal networks. In recent studies, modeling of cytoskeletal networks turns out to be a key piece in the cell mechanics puzzle. We used form-finding analysis to compute and analyze cytoskeletal models. A three-dimensional model is much more flexible and contains more elements than a two-dimensional model, and non-linear finite element analysis is difficult to converge. Thus, vector form intrinsic finite element analysis is employed here for valid results. The three-dimensional model reveals new behaviors beyond earlier two-dimensional models and better aligns with available data. Relative density of actin filaments and height of the form-finding model both play important roles in determining cytoskeletal stiffness, positively and negatively, respectively. Real cytoskeletal networks are quite mixed in terms of affine and non-affine deformations, which are quantified by internal strain energy in actin filaments and cross-linkers. Results are also influenced by actin filament relative density and height of the model. The three-dimensional form-finding model does provide much more room for intensive studies on cytoskeletal networks. In our future study, microtubules, fluidics, viscoelastic-plastic cross-linkers and even the whole cell model may be taken into account gradually to improve the cytoskeletal form-finding model.