Redundancy and Cooperativity in the Mechanics of Compositely Crosslinked Filamentous Networks

Das, Moumita; Quint, David; Schwarz, J. M.

doi:10.1371/journal.pone.0035939

Cited by 53 publications

(107 citation statements)

References 52 publications

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“…The bond-bending scenario in the composite angleconstraining networks is analogous to the torsion in the crosslink in our filamentous networks connected with compliant crosslinks. However, unlike our sparse networks, the critical exponent obtained in the composite angle-constraining networks is 0.5, consistent with the mean-field predictions [33].…”

Section: Sparse Networksupporting

confidence: 89%

“…In the intermediate range of k τ network deformation couples to both torsion and stretching of cross-links, giving rise to the anomalous regime. A recent theoretical study on networks of soft filaments crosslinked with flexible angle-constraining crosslinks also reported a similar critical anomalous regime [33]. Due to the angleconstraining crosslinks, changing the relative orientation of the two bonds connected at the crosslink costs energy.…”

Section: Sparse Networkmentioning

confidence: 70%

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Elastic response of filamentous networks with compliant crosslinks

Sharma

Sheinman

Heidemann³

et al. 2013

Phys. Rev. E

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Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as worm-like chains. For relatively large extensions we allow for enthalpic stretching of crosslinks' backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments' length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of the recent experiments.PACS numbers: 787.16. Ka, 87.15. La, 82.35.Pq The mechanical response of animal cells is largely determined by a visco-elastic matrix known as the cytoskeleton, which is a network consisting of many different biopolymers together with various binding proteins that govern the organization and stability of these networks. One of the ways in which these networks differ from synthetic crosslinked polymer systems is the fact that many of the crosslinks are themselves highly compliant proteins, which can strongly affect the macroscopic network compliance. There have been many in vitro studies of reconstituted networks with rigid crosslinks [1][2][3][4][5][6][7][8][9][10][11][12]. By comparison, relatively few recent experimental or theoretical studies have focused on networks with compliant crosslinks [13][14][15][16][17][18][19].A model experimental system of filamentous networks with compliant crosslinks is that of F-actin networks with the highly compliant and physiological crosslink filamin. Experimental studies on such networks have demonstrated several striking elastic properties: These networks can have a linear modulus as low as 1 Pa, while able to withstand stresses as large as 100 Pa or more at strains of order 1 or less. They do so by stiffening dramatically by up to a factor of 1000 under applied shear stress. Moreover, in contrast to networks with noncompliant crosslinks, such networks can be subjected to relatively high strains 50% without rupturing [11,15]. Both the linear and nonlinear elastic properties of actinfilamin gels appear to be dramatically affected by the flexible nature of the crosslinks, resulting in novel behavior as compared to actin-networks with noncompliant crosslinks, and to synthetic polymer gels. Similar composites of rigid filaments and compliant crosslinks can be found in other systems, such as stiff DNA nanotubes * Author to whom correspondence should be addressed. Electronic mail: fcm@nat.vu.nl crosslinked by flexible DNA linkers [20], although much less is known about the nonlinear...

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Section: Sparse Networksupporting

confidence: 89%

Section: Sparse Networkmentioning

confidence: 70%

Elastic response of filamentous networks with compliant crosslinks

Sharma

Sheinman

Heidemann³

et al. 2013

Phys. Rev. E

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“…The role of network disorder and nonaffinity is also presumed to become more important in such under-connected networks. Indeed, the precise role of bending interactions in biological fiber networks has been subject of much debate (Buxton and Clarke, 2007;Chaudhuri et al, 2007;Gardel et al, 2004a;Head et al, 2003a,b;Heussinger and Frey, 2006a;Heussinger et al, 2007b;Huisman and Lubensky, 2011;Onck et al, 2005;Storm et al, 2005;Wilhelm and Frey, 2003) One fruitful approach to studying the role of network connectivity in 2D and 3D has been to use network architectures based on lattice structures (Broedersz et al, 2012;Das et al, 2007Das et al, , 2012Mao et al, 2013a,b;Sheinman et al, 2012a), and we discuss these studies in the next section.…”

Section: Marginal Stability and Critical Phenomena In Fiber Networkmentioning

confidence: 99%

Modeling semiflexible polymer networks

2014

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Here, we provide an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random coil. Many studies on semiflexible polymers and their assemblies have been motivated by their importance in biology. Indeed, crosslinked networks of semiflexible polymers form a major structural component of tissue and living cells. Reconstituted networks of such biopolymers have emerged as a new class of biological soft matter systems with remarkable material properties, which have spurred many of the theoretical developments discussed here. Starting from the mechanics and dynamics of individual semiflexible polymers, we review the physics of semiflexible bundles, entangled solutions and disordered cross-linked networks. Finally, we discuss recent developments on marginally stable fibrous networks, which exhibit critical behavior similar to other marginal systems such as jammed soft matter.

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“…We couple the two according to symmetry requirements and minimize the free energy with respect to their values. We have tried to calibrate the model by comparing with the simple lattice models described above (26,27). Our preliminary results are encouraging.…”

Section: Modeling Alignmentmentioning

confidence: 89%

“…It is interesting to see how the transition from nonaffine, bending dominated, to affine, stretching dominated, works out in a simple two-dimensional (2D) lattice model (26,27). Such models illustrate in an unambiguous way that linear elements can give rise to nonlinear stress-strain relations.…”

Section: Mechanics Of Collagenmentioning

confidence: 99%

Modeling Contact Guidance and Invasion by Cancer Cells

Sander

2014

Cancer Research

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The first step in the spread of cancer is invasion by malignant cells of the normal tissue surrounding a tumor. There is considerable evidence both in vitro and in vivo that mechanical interactions with the tissue, in particular with the biopolymer network that makes up the extracellular matrix (ECM), are important factors in invasion. The interactions take two forms: (i) contractile cells on the surface of the tumor act on the nearby ECM and remodel it; in some cases, they align the fibers of the biopolymers; (ii) the aligned fibers can enhance invasion via contact guidance, the tendency of motile cells to follow alignment. Here, we give evidence, mainly for in vitro systems, that both effects are important. We discuss how alignment occurs in biopolymers such as collagen-I (a major component of the ECM). We propose a modeling framework for computing alignment and propose phenomenologic models for contact guidance.

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Redundancy and Cooperativity in the Mechanics of Compositely Crosslinked Filamentous Networks

Cited by 53 publications

References 52 publications

Elastic response of filamentous networks with compliant crosslinks

Elastic response of filamentous networks with compliant crosslinks

Modeling semiflexible polymer networks

Modeling Contact Guidance and Invasion by Cancer Cells

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