Nonlinear and heterogeneous elasticity of multiply-crosslinked biopolymer networks

Abstract

We simulate randomly crosslinked networks of biopolymers, characterizing linear and nonlinear elasticity under different loading conditions (uniaxial extension, simple shear, and pure shear). Under uniaxial extension, and upon entering the nonlinear regime, the network switches from a dilatant to contractile response. Analogously, under isochoric conditions (pure shear), the normal stresses change their sign. Both effects are readily explained with a generic weakly nonlinear elasticity theory. The elastic moduli display an intermediate super-stiffening regime, where moduli increase much stronger with applied stress σ than predicted by the force-extension relation of a single wormlikechain (G wlc 3 2 σ ∼ ). We interpret this super-stiffening regime in terms of the reorientation of filaments with the maximum tensile direction of the deformation field. A simple model for the reorientation response gives an exponential stiffening, G e ∼ σ , in qualitative agreement with our data. The heterogeneous, anisotropic structure of the network is reflected in correspondingly heterogeneous and anisotropic elastic properties. We provide a coarse-graining scheme to quantify the local anisotropy, the fluctuations of the elastic moduli, and the local stresses as a function of coarse-graining length. Heterogeneities of the elastic moduli are strongly correlated with the local density and increase with applied strain.

Exact solution for the force-extension relation of a semiflexible polymer under compression

“…The equilibrium single-polymer behavior under tension or compression plays a crucial role as input for elastic properties of networks, and the regime of strong compression close to buckling may be useful to characterize the mechanical stability of such networks [7][8][9][10][11][12][13][14][15][16]. In particular, networks are often modeled as entangled solutions of single semiflexible polymers with entanglement points, where they cross or loop each other, branching points or cross-links [7][8][9][12][13][14][15][16]. Already in equilibrium, single polymers experience a stretching or compression force induced by the surrounding network, and consequently the mean distance between, for example, two cross-links differs from the contour length of the polymers.…”

Normal stress anisotropy and marginal stability in athermal elastic networks

“…The deviation from the LM relation in the bending-dominated regime appears to decrease with increasing system size as well. For a given network, the dominant force chains arise along the network's "shortest paths" [24] consisting of connected bonds oriented close to the principal extension axis at a given strain, which have some excess length for γ < γ c . The critical strain corresponds to the strain at which, in theκ = 0 limit, one or more of these shortest paths can no longer rearrange without the stretching of their constituent bonds.…”

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

“…In addition to the elastic properties of single polymers, the behavior of single polymers inside cells and the buckling behavior of entire networks composed of semiflexible polymers remains to be fully understood. We anticipate, that the single-polymer behavior in free space, as elaborated here, constitutes the reference for the more realistic case of polymers immersed in a densely crowded environment [67][68][69] and moreover, serves as input for the analysis of polymer networks [7][8][9][10][11][12][13][14][15][16][17]. In a simplified description, these polymeric networks can be regarded as entangled solutions of semiflexible polymers, which can cross or loop each other, exhibit branching points, or are tightly connected by cross-links.…”