Constitutive modeling of the stress–strain behavior of F-actin filament networks

Palmer, Jeffrey S.; Boyce, Mary C.

doi:10.1016/j.actbio.2007.12.007

Cited by 135 publications

(157 citation statements)

References 53 publications

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“…The relationship between n and c actin with a given contour length L was derived earlier [14] (see also [13]) to be respectively. In Table 1 we summarize the values of the three concentrations used c ABP = 0.95, 0.475 and 0.238 μM, i.e.…”

Section: Application To a Specific Filament Free-energy Function W(λ)mentioning

confidence: 99%

“…For example, an algorithmic treatment for affine and non-affine networks, the micro-sphere model, was introduced by Miehe et al [10] and the affine network model was adopted for modeling the mechanics of collagen in arteries [11,12]. Applications of the filament-to-network approach to the elasticity of actin networks have also been proposed [13,14]. In particular, Unterberger et al [14] use a non-affinity parameter that is not intuitive, while a recently introduced model [15] facilitates the understanding of non-affinity but it turns out to be very expensive in terms of computational cost and is therefore not very practical.…”

Section: Introductionmentioning

confidence: 99%

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An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Holzapfel

Unterberger

Ogden

2014

Journal of the Mechanical Behavior of Biomedical Materials

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Abstract. Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of crosslinked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facili- * To whom correspondence should be addressed. Email address: holzapfel@tugraz.at tates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach.

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Section: Application To a Specific Filament Free-energy Function W(λ)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Holzapfel

Unterberger

Ogden

2014

Journal of the Mechanical Behavior of Biomedical Materials

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“…However, they assumed that the plasma and nuclear membranes are rigid and immobile, which is unrealistic. Later, more sophisticated models that focused on understanding the rheology of the actin network were presented [45,53,55,56]. The main concern of these studies was to connect these network models to the plasma and nuclear membranes.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, several models of the cytoskeleton have been constructed to investigate the hypothesis that this interconnected filamentous structure can act as a mechano-signal transmitter [44][45][46][47][48][49][50][51][52][53][54][55][56]. Shafrir & [46] proposed a two-dimensional model of the cytoskeleton as a random network of rigid rods representing the actin laments and linear Hookean springs representing the actin cross-linkers.…”

Section: Introductionmentioning

confidence: 99%

“…The activation of signalling pathways by shear forces arises at discrete locations in ECs by force amplification and forceinduced directional biasing of signal propagation [1][2][3][4][10][11][12][16][17][18][20][21][22][23]. Numerous sites have been implicated in transducing mechanical stresses, including the plasma membrane [1,2,5,21,22,24] and its associated glycocalyx [1,5,25 -36], focal adhesions (FAs) [4,7,16,17,37 -43], the nucleus [44,45], the cytoskeleton [4,7,18,19,24,33,38,39,[44][45][46][47][48][49][50][51][52][53][54][55][56], the cortical membrane [1,2,5] and the intercellular junctions …”

Section: Introductionmentioning

confidence: 99%

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Shear-induced force transmission in a multicomponent, multicell model of the endothelium

Dabagh

Jalali

Butler

et al. 2014

J. R. Soc. Interface.

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Haemodynamic forces applied at the apical surface of vascular endothelial cells (ECs) provide the mechanical signals at intracellular organelles and through the inter-connected cellular network. The objective of this study is to quantify the intracellular and intercellular stresses in a confluent vascular EC monolayer. A novel three-dimensional, multiscale and multicomponent model of focally adhered ECs is developed to account for the role of potential mechanosensors (glycocalyx layer, actin cortical layer, nucleus, cytoskeleton, focal adhesions (FAs) and adherens junctions (ADJs)) in mechanotransmission and EC deformation. The overriding issue addressed is the stress amplification in these regions, which may play a role in subcellular localization of mechanotransmission. The model predicts that the stresses are amplified 250-600-fold over apical values at ADJs and 175-200-fold at FAs for ECs exposed to a mean shear stress of 10 dyne cm 22 . Estimates of forces per molecule in the cell attachment points to the external cellular matrix and cell-cell adhesion points are of the order of 8 pN at FAs and as high as 3 pN at ADJs, suggesting that direct force-induced mechanotransmission by single molecules is possible in both. The maximum deformation of an EC in the monolayer is calculated as 400 nm in response to a mean shear stress of 1 Pa applied over the EC surface which is in accord with measurements. The model also predicts that the magnitude of the cell-cell junction inclination angle is independent of the cytoskeleton and glycocalyx. The inclination angle of the cell-cell junction is calculated to be 6.68 in an EC monolayer, which is somewhat below the measured value (9.98) reported previously for ECs subjected to 1.6 Pa shear stress for 30 min. The present model is able, for the first time, to cross the boundaries between different length scales in order to provide a global view of potential locations of mechanotransmission.

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Food Protein Nanoparticles: Formation, Properties and Applications

Loveday

Rao

Singh

2012

Food Materials Science and Engineering

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Constitutive modeling of the stress–strain behavior of F-actin filament networks

Cited by 135 publications

References 53 publications

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Shear-induced force transmission in a multicomponent, multicell model of the endothelium

Food Protein Nanoparticles: Formation, Properties and Applications

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