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Abstract
In eukaryotic cells the actin-cytoskeletal network provides stiffness and the driving force that contributes to changes in cell shape and cell motility, but the elastic behavior of this network is not well understood. In this paper a two dimensional form-finding model is proposed to investigate the elasticity of the actin filament network. Utilizing an initially random array of actin filaments and actin-cross-linking proteins the form-finding model iterates until the random array is brought into a stable equilibrium configuration. With some care given to actin filament density and length, distance between host sites for cross-linkers, and overall domain size the resulting configurations from the form-finding model are found to be topologically similar to cytoskeletal networks in real cells. The resulting network may then be mechanically exercised to explore how the actin filaments deform and align under load and the sensitivity of the network’s stiffness to actin filament density, length, etc. Results of the model are consistent with the experimental literature, e.g. actin filaments tend to re-orient in the direction of stretching; and the filament relative density, filament length, and actin-cross-linking protein’s relative density, control the actin-network stiffness. The model provides a ready means of extension to more complicated domains and a three-dimensional form-finding model is under development as well as models studying the formation of actin bundles.
Highlights
IntroductionThe cytoskeleton forms the internal framework of eukaryotic cells and is responsible for a cell’s elasticity and plays an important role in cell shape and motility
Eukaryotic cells are the building blocks of higher organisms
Our objective is to demonstrate the possibility of designing more complex and topologically relevant actinnetwork models using an equilibrium form-finding method
Summary
The cytoskeleton forms the internal framework of eukaryotic cells and is responsible for a cell’s elasticity and plays an important role in cell shape and motility. The mechanical behavior of the cytoskeleton is determined by the interactions of three types of filaments: actin filaments, intermediate filaments, and microtubules [1]. Actin filaments provide cells with primary mechanical support and are engaged as a driving force in cell motility [2]. The stiffness of the cytoskeleton network governs passive and active mechanical performance of cells. Many biological functions are intimately associated to the mechanical response, and the cell’s stiffness may serve as a sensitive indicator for the development or health state of a cell [2]. Numerous efforts have been made to predict the elasticity of the cytoskeleton network by using computational models; including open-cell foam models [3], tensegrity models [4,5,6,7], cable network models [8], lattice-based models [9], coarse-grained models [10,11] and Brownian dynamics models [12,13]
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