A new approach to model cross-linked actin networks: multi-scale continuum formulation and computational analysis

Area of Science:

• Biophysics
• Cell Mechanics
• Materials Science

Background:

• Cellular mechanical properties are primarily determined by the cytoskeleton.
• The actin cortex, a densely cross-linked protein network beneath the lipid bilayer, significantly contributes to cellular mechanics.
• Understanding the actin cortex's mechanical behavior is crucial for cell biology and biophysics.

Purpose of the Study:

• To develop a continuum mechanical formulation for modeling the mechanical properties of in vitro actin networks.
• To describe the behavior of individual actin filaments and their spatial arrangement within the network.
• To validate the model against experimental data from reconstituted actin networks.

Main Methods:

• A continuum mechanical formulation was developed, neglecting viscous effects and considering the network as elastic.
• The nonlinear force-stretch relationship of filamentous actin was modeled using an extensible worm-like chain model (β-model).
• A non-affine micro-sphere network was employed to extend 2D properties to 3D, accounting for spatially distributed filaments. The model was implemented in a finite element program.

Main Results:

• The β-model accurately describes the nonlinear force-stretch relationship of individual actin filaments.
• The continuum mechanical model, incorporating micro-structural properties, accurately predicts the strain-energy density of reconstituted actin networks.
• The model yields Cauchy stress and elasticity tensors, validated through rheological experiments.

Conclusions:

• The developed continuum mechanical model effectively captures the elastic properties of actin networks based on their micro-structure.
• The model provides a framework for understanding and predicting the mechanical behavior of the actin cortex.
• This work offers a valuable tool for simulating cellular mechanical responses in various biological contexts.