A chemo-mechanical constitutive model for transiently cross-linked actin networks and a theoretical assessment of their viscoelastic behaviour

Abstract

Biological materials can undergo large deformations and also show viscoelastic behaviour. One such material is the network of actin filaments found in biological cells, giving the cell much of its mechanical stiffness. A theory for predicting the relaxation behaviour of actin networks cross-linked with the cross-linker α-actinin is proposed. The constitutive model is based on a continuum approach involving a neo-Hookean material model, modified in terms of concentration of chemically activated cross-links. The chemical model builds on work done by Spiros (Doctoral thesis, University of British Columbia, Vancouver, Canada, 1998) and has been modified to respond to mechanical stress experienced by the network. The deformation is split into a viscous and elastic part, and a thermodynamically motivated rate equation is assigned for the evolution of viscous deformation. The model predictions were evaluated for stress relaxation tests at different levels of strain and found to be in good agreement with experimental results for actin networks cross-linked with α-actinin.

Implementing cell contractility in filament‐based cytoskeletal models

“…In particular, and relevant to the case of contractility, several experimental investigations have detected calcium-permeable channels sensitive to mechanical stimuli [Arora et al, 1994;Ko et al, 2001], voltage [Chen et al, 1988] and growth factors [Puro and Mano, 1991]. Coupling the contractile motor activity to deformation state can be achieved in numerous ways, for example by introduction of an Arrhenius factor [Fallqvist and Kroon, 2012] in the rate equations. It can also be introduced as a direct dependence on a measure of deformation, e.g.…”

“…The cytoskeleton consists of polymerised actin, intermediate and microtubule filament networks. Actin has been the recipient of most attention, modelled as semiflexible polymer [Mackintosh et al, 1995;Storm et al, 2005;van Dillen et al, 2008], simple lattice [Kamm and Mofrad, 2006], finite element [Head et al, 2003;Onck et al, 2005;Huisman et al, 2007;Abhilash et al, 2012Abhilash et al, , 2014Fallqvist et al, 2014] and continuum [Palmer and Boyce, 2008;Fallqvist and Kroon, 2012;Fallqvist et al, 2014] models. Intermediate filaments, while known to contribute to cellular stiffness [Wang and Stamenovic, 2000;Guo et al, 2013], have received less attention, as have microtubules.…”

A Parametric Investigation on the Neo-Hookean Material Constant

“…The neo-Hookean material model has also been successfully applied to include concentration of chemically activated cross-links for biological materials with large deformation and viscoelastic behaviour [19]. The neo-Hookean model was also found to perfectly fit small and finite deformation of thin polymer layers, elastomers as well as the human orbital fat and its encapsulating connective tissue [20,21,22].…”

“…It is evident from the aforementioned literature, that no parametric study was ever conducted to obtain the material constant, C 1 of the neo-Hookean constitutive equation as per Eq.1. [17] Pulmonary Artery Tissue 5 kPa Uniaxial Tests Henak et al [18] Human Hip 5.32 MPa Compression Fallqvist and Kroon [19] Transiently Cross-Linked Actin Networks 300 kPa Chemo-Mechanical Constitutive Model Chen and Diebels [20] Thin Polymer Layers 0.6513 to 1 MPa Tension Chen and Weiland [21] Orbital Fat And Connective Tissue 0.8 to 1.7 kPa (n=5) 2.1 to 3.5 kPa (n=11)…”

Cross-link debonding in actin networks - influence on mechanical properties

“…To predict the mechanical response of these actin networks a homogenised continuum-based approach, in which the network is assumed to behave as a continuous solid, can be utilised. We have previously proposed such a phenomenological chemo-mechanical constitutive model, in which the strain energy function of the material is assumed to be proportional to the concentration of cross-linked filaments (Fallqvist and Kroon, 2012).…”