Elastic response of filamentous networks with compliant crosslinks

Abstract

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...

Nonlinear and heterogeneous elasticity of multiply-crosslinked biopolymer networks

“…The stiffening then being due to the formation of percolating paths in the tensile direction of the shear deformation. Under large enough deformation the filament strands in these paths are brought to nearly full stretching, giving rise to a modulus that diverges with σ ∼ [6,7]. In contrast, here we find that the bending response itself initially dominates nonlinear behavior.…”

“…Nonlinear response is then a consequence of the complex elasticity of biological polymer networks as compared to synthetic polymer gels made from flexible polymers [5]. Different mechanisms have been proposed that mediate the strong increase of elastic modulus G with increasing strain γ or stress σ: first, the stretching response of a single semiflexible polymer, as described by the wormlike chain (WLC) model, is strongly nonlinear, and is expected to yield a nonlinear elastic modulus G 3 2 σ ∼ [6,7]. Alternatively, it has been argued that a crossover from a soft bending-dominated response to a stiffer stretching dominated response results in an increase of the modulus [8,9].…”

Response of biopolymer networks governed by the physical properties of cross-linking molecules

“…26–29 The only theoretical attempts considering this factor, to the best of our knowledge, were made by Sharma et al . 30 and most recently by Žagar and co-workers. 31 However, either the deformability of filaments was totally neglected 30 or different spring constants of the cross-linkers were assumed to be coupled with each other 31 ( i.e.…”

“…30 and most recently by Žagar and co-workers. 31 However, either the deformability of filaments was totally neglected 30 or different spring constants of the cross-linkers were assumed to be coupled with each other 31 ( i.e. they cannot vary independently) in those studies.…”

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

“…The elastic energy involves a summation over all fibers in the network and is a function of the strain γ and the reduced bending rigidityκ. Since the network stiffness or tangent modulus K = dσ/dγ involves the energy per unit volume, K is naturally proportional to the line density ρ defined as the total length of the fibers per unit volume [19,27,[30][31][32]. The modulus can therefore be expressed as…”