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A chemo-mechanical constitutive model for transiently cross-linked actin networks and a theoretical assessment of their viscoelastic behaviour
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).ORCID iD: 0000-0002-6388-0995
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
2013 (English)In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 12, no 2, 373-382 p.Article in journal (Refereed) Published
Abstract [en]

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 alpha-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 alpha-actinin.

Place, publisher, year, edition, pages
2013. Vol. 12, no 2, 373-382 p.
Keyword [en]
Viscoelasticity, alpha-actinin, Cross-link, Transient, Actin, Membrane
National Category
Biophysics
Identifiers
URN: urn:nbn:se:kth:diva-120524DOI: 10.1007/s10237-012-0406-7ISI: 000316283900014Scopus ID: 2-s2.0-84880729830OAI: oai:DiVA.org:kth-120524DiVA: diva2:615578
Note

QC 20130411

Available from: 2013-04-11 Created: 2013-04-11 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Mechanical response of cross-linked actin networks
Open this publication in new window or tab >>Mechanical response of cross-linked actin networks
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The ability to predict the mechanical properties of cells should be seen in the light of the close connection between abnormal cell states and a change in the cell response to stimuli. For example, it has been found that the stiffness of cancer cells is much lower than their healthy counterparts, influencing metastasis and cell migration. On the contrary, malaria cells have been found to exhibit a significant increase in stiffness.

The major structural entity of the cell is called the cytoskeleton, an interior network consisting of three types of protein filaments - actin filaments, intermediate filaments and microtubules. The remodelling ability of the cytoskeleton through polymerisation provides the cell with the ability to adapt its response to external forces accordingly. The properties of interfilament cross-links in terms of stiffness and ability to detach can be expected to influence the mechanical response. The work presented herein focuses on the mechanical response of cross-linked actin networks. The results indicate a strong dependence of the mechanical properties on cross-link dynamics and characteristics.

In Paper A, a constitutive model for the response of transiently cross-linked networks is developed using a continuum framework. The deformation is split into viscous (representing sliding of filaments) and elastic deformation. A strain energy function is proposed in the form of a neo-Hookean model, modified in terms of chemically activated cross-links. The disassociation rate constant is modified in terms of an exponential function taking into account the amount of strain energy available to break bonds. The constitutive model was compared with experimental relaxation tests and it was found that the initial region of fast stress relaxation can be attributed to breaking of bonds, and the subsequent slow relaxation to sliding of filaments.

In Paper B, a finite element framework was used to assess the influence of numerous geometrical and material parameters on the response of cross-linked actin networks. It was shown that considering the presence of a statistical dispersion in filament lengths has a significant effect on the mechanical properties of the network. Further, the compliance of the crosslinks was shown to influence the stress-strain curve and shift the region of strain hardening. The influence of boundary conditions and the effect of network parameters on experiments in terms of local and global effects were also addressed. Finally, a micromechanically motivated constitutive model in a continuum framework was presented, capturing some essential characteristic features of cross-linked actin networks.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. 23 p.
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 0549
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:kth:diva-131209 (URN)978-91-7501-875-1 (ISBN)
Presentation
2013-10-25, Seminarierummet, Hållfasthetslära, Teknikringen 8, KTH, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

QC 20131009

Available from: 2013-10-09 Created: 2013-10-09 Last updated: 2016-03-15Bibliographically approved
2. On the mechanics of actin and intermediate filament networks and their contribution to cellular mechanics
Open this publication in new window or tab >>On the mechanics of actin and intermediate filament networks and their contribution to cellular mechanics
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The mechanical behaviour of cells is essential in ensuring continued physiological function, and deficiencies therein can result in a variety of diseases. Also, altered mechanical response of cells can in certain cases be an indicator of a diseased state, and even actively promoting progression of pathology. In this thesis, methods to model cell and cytoskeletal mechanics are developed and analysed.

In Paper A, a constitutive model for the response of transiently cross-linked actin networks is developed using a continuum framework. A strain energy function is proposed and modified in terms of chemically activated cross-links.

In Paper B, a finite element framework was used to assess the influence of numerous geometrical and material parameters on the response of cross-linked actin networks, quantifying the influence of microstructural properties and cross-link compliance. Also, a micromechanically motivated constitutive model for cross-linked networks in a continuum framework was proposed.

In Paper C, the discrete model is extended to include the stochastic nature of cross-links. The strain rate dependence observed in experiments is suggested to depend partly on this.

In Paper D, the continuum model for cross-linked networks is extended to encompass more composite networks. Favourable comparisons to experiments indicate the interplay between phenomenological evolution laws to predict effects in biopolymer networks.

In Paper E, experimental and computational techniques are used to assess influence of the actin cytoskeleton on the mechanical response of fibroblast cells. The influence of cell shape is assessed, and experimental and computational aspects of cell mechanics are discussed.

In Paper F, the filament-based cytoskeletal model is extended with an active response to predict active force generation.  Importantly, experimentally observed stiffening of cells with applied stress is predicted.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. 68 p.
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 0583
Keyword
actin, cell, mechanical, constitutive, intermediate, continuum, constitutive
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:kth:diva-175748 (URN)978-91-7595-752-4 (ISBN)
Public defence
2016-01-29, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, A0437201
Note

QC 20151209

Available from: 2015-12-09 Created: 2015-10-20 Last updated: 2015-12-09Bibliographically approved

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