Nonlinear elasticity of biopolymer gels under compression

Abstract eng:
Biopolymer gels, comprised of cross-linked semiflexible filaments, show nonlinear elasticity at small tensile strains (above some characteristic value) as well as softening for compressive strains. Here we predict an unusual elastic response to uniaxial compression. We focus on two competing mechanisms that contribute to the elasticity of biopolymer gels upon compression: (i) Stiffening, due to polymer densification by out-going water flow. (ii) Softening, due to polymer buckling under compression. We predict three generic types of behavior in different regions of the stress-strain curve: (1) Densification region at small strains, before the onset of polymer buckling, (2) Intermediate region where a fraction of the polymer segments are buckled which tends to counteract the densification effect, and (3) Buckled region where all the polymers are buckled and the modulus tends to very small values. Biopolymer hydrogels comprise crosslinked, semiflexible filaments (e.g., actin, collagen, and fibrin) [1]. They are important constituents of both the cellular cytoskeleton and extracellular matrix of tissues [2]. Unlike most synthetic gels, biopolymer gels often exhibit highly nonlinear elastic responses to applied tensile forces above some small strain or compressive forces at small strain [1, 3-6], e.g., fibrin gels stiffen at small shear strains above 10% [1, 3] and soften at compressive strain about 5% [5, 6]. The strain stiffening nonlinearity of biopolymer gels has been identified to be of great biological importance [1, 3] since it impacts force transmission by cells in such gels and many studies have aimed to understand its physical origin [1, 3]. However, relatively less attention has been paid to the elastic responses of biopolymer gels under compression [6, 7]. This nonlinear elastic response is also critical for the physiological function of animal cells and some tissues [1, 4, 7, 8]. For example, in recent work [4], we have shown that the nonlinear (asymmetric) responses of biopolymer gels to both tension and compression can together significantly increase the range of force transmission and are hence critical for the long-range cell-cell and cell-matrix communication. Moreover, recently it has been shown [7] that the understanding of the elastic responses of biopolymer gels to compression is a key feature of the self-contraction dynamics of cellular cytoskeleton at subcellular scale. In this paper, we investigate the elastic responses of biopolymer gels to uniaxial compression. We propose that the balance of two competing mechanisms contribute to the nonlinear elasticity of biopolymer gels upon compression (as schematic shown in Fig. 1): (i) Stiffening due to polymer densification by out-going water flow: Compression applied to biopolymer gels induces water to flow out of the gels and hence increase the density of polymer segments within the gel. This densification results in an increase in the elastic modulus of the gel which scales with the energy per unit volume per crosslink. (ii) Softening due to polymer buckling: Compression can also induce the buckling [1, 5, 6] of the polymer segments between cross-linkers. The buckled polymers lose resistance to the applied forces and this tends to decrease the elastic modulus of the gel.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket