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- Unterberger, M. J., et al.
(author)
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A new approach to model cross-linked actin networks : Multi-scale continuum formulation and computational analysis
- 2013
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In: Journal of The Mechanical Behavior of Biomedical Materials. - : Elsevier BV. - 1751-6161 .- 1878-0180. ; 22, s. 95-114
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Journal article (peer-reviewed)abstract
- The mechanical properties of a cell are defined mainly by the cytoskeleton. One contributor within this three-dimensional structure is the actin cortex which is located underneath the lipid bilayer. It forms a nearly isotropic and densely cross-linked protein network. We present a continuum mechanical formulation for describing the mechanical properties of in vitro model systems based on their micro-structure, i.e. the behavior of a single filament and its spatial arrangement. The network is considered elastic, viscous effects being neglected. Filamentous actin is a biopolymer with a highly nonlinear force-stretch relationship. This can be well described by a worm-like chain model that includes extensibility of the filament, which we call the . β-model. A comparison with experimental data shows good agreement with values for the physically interpretable parameters. To make these properties applicable to three dimensions we used a non-affine micro-sphere network, which accounts for filaments, equally distributed in space. The assembled model results in a strain-energy density which is a function of the deformation gradient, and it is validated with experimental data from rheological experiments of in vitro reconstituted actin networks. The Cauchy stress and elasticity tensors are obtained within the continuum mechanics framework and implemented into a finite element program to solve boundary-value problems.
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- Unterberger, Michael J., et al.
(author)
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Viscoelasticity of cross-linked actin networks : Experimental tests, mechanical modeling and finite-element analysis
- 2013
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In: Acta Biomaterialia. - : Elsevier BV. - 1742-7061 .- 1878-7568. ; 9:7, s. 7343-7353
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Journal article (peer-reviewed)abstract
- Filamentous actin is one of the main constituents of the eukaryotic cytoskeleton. The actin cortex, a densely cross-linked network, resides underneath the lipid bilayer. In the present work we propose a continuum mechanical formulation for describing the viscoelastic properties of in vitro actin networks, which serve as model systems for the cortex, by including the microstructure, i.e. the behavior of a single filament and its spatial arrangement. The modeling of the viscoelastic response in terms of physically interpretable parameters is conducted using a multiscale approach consisting of two steps: modeling of the single filament response of F-actin by a worm-like chain model including the extensibility of the filament, and assembling the three-dimensional biopolymer network by using the microsphere model which accounts for filaments equally distributed in space. The viscoelastic effects of the network are taken into account using a generalized Maxwell model. The Cauchy stress and elasticity tensors are obtained within a continuum mechanics framework and implemented into a finite-element program. The model is validated on the network level using large strain experiments on reconstituted actin gels. Comparisons of the proposed model with rheological experiments recover reasonable values for the material parameters. Finite-element simulations of the indentation of a sphere on a network slab and the aspiration of a droplet in a micropipette allow for further insights of the viscoelastic behavior of actin networks.
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